SCHOOL OF MECHANICAL
DEPARTMENT OF MECHANICAL ENGINEERING
LESSON NOTES
U6MEA30 ENGINEERING METROLOGY AND MEASUREMENTS
VELTECH Dr.RR & Dr.SR TECHNICAL UNIVERSITY
1
SYLLABUS
U6MEA30 ENGINEERING METROLOGY AND MEASUREMENTS
LTPC
3003
OBJECTIVE:
 To understand the basic principles of measurements
 To learn the various linear and angular measuring equipments, their principle of
operation and applications
 To learn about various methods of measuring Mechanical parameters
UNIT I CONCEPT OF MEASUREMENT
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General concept – Generalised measurement system-Units and standards-measuring instruments- sensitivity,
readability, range of accuracy, precision-static and dynamic response-repeatability-systematic and random
errors-correction, calibration, interchangeability.
UNIT II LINEAR AND ANGULAR MEASUREMENT
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Definition of metrology-Linear measuring instruments: Vernier, micrometer, interval measurement, Slip
gauges and classification, interferometery, optical flats, limit gauges- Comparators: Mechanical, pneumatic
and electrical types, applications.
Angular measurements: -Sine bar, optical bevel protractor, angle Decker – Taper measurements.
UNIT III FORM MEASUREMENT
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Measurement of screw threads-Thread gauges, floating carriage micrometer-measurement of gears-tooth
thickness-constant chord and base tangent method-Gleason gear testing machine – radius measurementssurface finish, straightness, flatness and roundness measurements.
UNIT IV LASER AND ADVANCES IN METROLOGY
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Precision instruments based on laser-Principles- laser interferometer-application in linear, angular
measurements and machine tool metrology, Coordinate measuring machine (CMM) - Constructional
features – types, applications – digital devices- computer aided inspection.
UNIT V MEASUREMENT OF POWER, FLOW AND TEMPERATURE RELATED PROPERTIES
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Force, torque, power:-mechanical, pneumatic, hydraulic and electrical type-Flow measurement:
Venturi, orifice, Rota meter, and Pitot tube –Temperature: bimetallic strip, pressure
thermometers, thermocouples, electrical resistance thermister.
TOTAL: 45 periods
TEXT BOOKS
1. Jain. R. K., Engineering Metrology, Khanna Publishers, New Delhi, 1987
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2. Gupta. R. C., Statistical Quality Control, Khanna Publishers, New Delhi, 1994
REFERENCE BOOKS
1. Alan S. Morris, “The Essence of Measurement”, Prentice Hall of India, 1997
2. Jayal A.K, “Instrumentation and Mechanical Measurements”, Galgotia Publications 2000
3. Beckwith T.G, and N. Lewis Buck, “Mechanical Measurements”, Addison Wesley, 1991
4. Donald D Eckman, “Industrial Instrumentation”, Wiley Eastern, 1985.
5. Measurement System: Application and Design by Doebelin E.O McGraw Hill Publishing Company.
6. Experimental Methods for Engineers by Holman JP McGraw Hill Publication Company.
7. Mechanical Measurement and Control by Kumar DS; Metropolitan Book Co Pvt. Ltd., New Delhi.
8. Automatic Control systems by Kuo BC; Prentice Hall.
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UNIT – I
CONCEPT OF MEASUREMENT
Calibration.
Calibration is the process of establishing the relationship between a measuring device and the
units of measure. This is done by comparing a devise or the output of an instrument to a standard
having known measurement characteristics. For example the length of a stick can be calibrated by
comparing it to a standard that has a known length. Once the relationship of the stick to the
standard is known the stick can be used to measure the length of other things.
Sensitivity of a measuring instrument.
Sensitivity =
Instrument
Reading
Change in the output signal
Change in the input signal
dy
dx
Measured quantity
Readability.
In the sciences, readability is a measure of an instrument's ability to display incremental
changes in its output value. For example, a balance with a readability of 1 mg will not display any
difference between objects with masses from 0.6 mg to 1.4 mg, because possible display values are
0 mg, 1 mg, 2 mg etc. Likewise, a balance with a readability of 0.1 mg will not display any
difference between objects with masses from 0.06 mg to 0.14 mg.
True size and Actual size.
True size  Theoretical size of a dimension which is free from errors.
Actual size  size obtained through measurement with permissible error.
Hysterisis.
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A system with hysteresis can be summarised as a system that may be in any number of
states, independent of the inputs to the system. To be exact, a system with hysteresis exhibits pathdependence, or "rate-independent memory”.
Range.
Range is the difference between the highest and lowest value.
Span.
Span is the distance or interval between two points.
Example : In a measurement of temperature higher value is 200 C and lower value is 150 C means
span = 200 – 150 = 50 C.
resolution.
Resolution is the quantitative measure of the ability of an optical instrument to produce
separable images of different points on an object; usually, the smallest angular or linear separation
of two object points for which they may be resolved according to the Rayleigh criterion.
Verification.
It is the process of testing the instrument for determining the errors.
Scale interval.
It is the difference between two successive scale marks in units.
Dead Zone.
Dead zone is the range through which a stimulus can be varied without producing a change in the
response of the measuring instrument.
Threshold.
Threshold is the smallest detectable sensation of an instrument.
Discrimination.
Discrimination is the ability of an instrument to differentiate between various physical parameters
or ability to measure even the minute changes in readings.
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Back lash.
Back lash is the play or loose motion in an instrument due to the clearance existing between
mechanically contacting parts. It is similar to hysterisis but more commonly applied to mechanical
systems. It often occurs between interacting mechanical parts as a result of looseness.
response time.
Response time (technology), the time a generic system or functional unit takes to react to a given
input
Repeatability.
Repeatability is the variation in measurements taken by a single person or instrument on the
same item and under the same conditions. A measurement may be said to be repeatable when this
variation is smaller than some agreed limit.
Bias.
Bias is a term used to describe a tendency or preference towards a particular perspective,
ideology or result. All information and points of view have some form of bias. A person is
generally said to be biased if a reasonable observer would conclude that the person is markedly
influenced by inner biases, rendering it unlikely for them to be able to be objective.
magnification.
Magnification is the process of enlarging something only in appearance, not in physical size.
Magnification is also a number describing by which factor an object was magnified.
Drift.
Drift is a slow change. In metrology and measurements it refers to delay in response of an
instrument for changes in input signals.
reproducibility.
Reproducibility is one of the main principles of the scientific method, and refers to the ability of a
test or experiment to be accurately reproduced, or replicated, by someone else working
independently.
uncertainty.
Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to
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exactly describe existing state or future outcome, more than one possible outcome. It applies to
predictions of future events, to physical measurements already made, or to the unknown.
Trace ability.
Traceability refers to the completeness of the information about every step in a process chain.
Fiducial value.
The prescribed value of a quantity to which the reference is made.
Parallax.
Parallax, more accurately motion parallax, is the change of angular position of two observations
of a single object relative to each other as seen by an observer, caused by the motion of the
observer.
accuracy and uncertainty with example.
Accuracy – Closeness to the true value.
Example: Measuring accuracy is ± 0.02mm for diameter of part is 25mm.
Here the measurement true value lie between 24.98 to 25.02 mm.
Uncertainty about the true value ± 0.02mm.
Difference between precision and accuracy.
Accuracy  The maximum amount by which the result differ from true value.
Precision  Degree of repetitiveness. If an instrument is not precise it will give different results
for the same dimension for the repeated readings.
Differentiate between sensitivity and range with suitable example.
Example : A Instrument have a scale reading of 0.01mm to 100 mm.
Here, the sensitivity of the instrument is 0.01mm i.e the minimum value by the scale by which the
instrument can read. The range is 0.01 to 1000mm i.e the minimum to maximum value by which
the instrument can read.
From the figure the instrument is ______.
X
X
X
X
XX
X
Average
True
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Precise but not accurate
system error and correction.
Error : The deviation between the results of measured value to the actual value.
Correction : The numerical value which should be added to the measured value to get the correct
result.
Measured.
Measured is physically quantity or property like length, diameter, and angle to be measured.
Deterministic Metrology.
Them metrology in which part measurement is replaced by process measurement. The new
techniques such as 3D error compensation by CNC systems are applied.
over damped and under damped system.
Over Damped : The final indication of measurement is approached exponentially from one side.
Under damped : The pointer approach the position corresponding to final reading and makes a
number of oscillations around it.
Under Damped
Indication
Over Damped
accuracy in terms of repeatability and systematic error.
Accuracy = (Reponsibility) 2  (Systematic error) 2
four methods of measurement.
1.
2.
Direct Method
Indirect Method
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3.
4.
Comparison Method
Coincidence Method.
classification of measuring instruments.
1.
2.
3.
4.
Angle measuring instruments
Length measuring instruments
Instruments for surface finish
Instruments for deviations.
metrology.
Metrology s as the Science of pure measurement. But in engineering purposes, it in restricted to
measurements of length and angles and other qualities which are expressed in linear or angular
terms.
Dynamic metrology .
It refers to a group of techniques for measuring small variation of a continuous nature. These
technique has proved very valuable and a record of continuous measurement over a surface.
basic need for Measurement
The basic need for Measurement in the engineering industry in to determine whether a
component has been manufactured to the requirements of a specification.
dimensional properties need to be considered when checking or measuring a component
Length, Flatness, parallelism, surface, roughness, angle, profile, relative position. Roundness
and concentricity, accuracy of form.
difference between indicative type measuring instrument and Non-indicative type measuring
instrument
The indicative type measuring instrument indicate the size of the measured value.
The Non-indicate type of instrument does not indicate the measured size. Ex. "Go" and "Not - go"
gauge.
factors affecting the accuracy of measurement
1. Temperature difference
2. Support position
3. Reading and parallel effects
4. Accuracy of equipment
5. Application of force
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6. Sine and Cosine error
7. Different inspectors
Abbe's principle (or) state alignment principle.
Abbe's principle of alignment states that the line of axis of measurement should coincide
with the line of scale or other dimensional reference.
optical principles employed in metrology
1) Reflection
2) Refraction 3) Interference
sources of controllable error
1.
2.
3.
4.
Calibration error
Ambient condition
Stylus pressure
Avoidable error.
sources of random error
Specific causes for such error can not be determined. But likely sources are
1.
2.
3.
4.
Small variations in the position of setting standards and workpiece.
Slight displace of lever joints in the measuring device
Transient fluctuation in the friction in measuring instrument
Operator error in reading scale.
accuracy of Measurement is affected by poor contact between the work piece and measuring
probe
The poor contact between the work piece and instrument will cause for error. Although
everything feels all right yet the error in bound to occur. Gauge with wide areas of contact should
not be used on part with irregular or curved surfaces.
A test indicator is used to check concentricity of a soft but its stylus is set so that in movement
makes an angle of 30' with the normal to the shaft, if the total indicator reading 0.02 mm what is
the true eccentricity
This is the case of cosine error although the stylus movement in small, the alignment error
in large and this cosine error is appreciable.
Total reading = 0.02 cos30'
= 0.017 mm
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there fore Eccentricity = 1/2 ( True value )
= 0.0085 mm
" Precision "
Precision refers in variability when used to make repeated measurements under carefully
controlled conditions.
Reproducibility.
The term reproducibility of a method of measurement refers to the consistency of its
pattern of variation.
Accuracy.
The term accuracy refers to the agreement of the results of a measurement with the true
value of the measure quantity.
difference between indicating and recording instrument
In indicative type measure instrument the value of the measured quantity in visually
indicative but not recorded. In case of recording instruments the values of the measured quantity
are recorded on a chart, digital computer or data logger.
accuracy and sensitivity of a measuring instrument.
Accuracy is the closeness with which the measuring instrument can measure the "true
value" of a quantity under stated conditions of use. ie its ability to "tell the truth".
Sensitivity in the relationship between a change in output reading for a given change of
input. Sensitivity in often known as scale factor or instrument magnification.
readability
Readability in d as the ease with which readings may be taken an instrument. Readability
difficulties may often arise due to parallax errors.
methods of measurements.
In precision measurement various methods are followed depends upon the accuracy required.
1.
2.
3.
4.
Direct method of measurement
Indirect method of measurement
Fundamental method of measurement
Comparison method of measurement
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5. Substitution method of measurement
6. Transposition method of measurement
7. Coincidence method of measurement
8. Transposition method of measurement
9. Deflection method of measurement
10. Interpolation method of measurement
11. Extrapolation method of measurement
12. Complementary method of measurement
13. Composite method of measurement
14. Element method of measurement
15. Contact and contact less method of measurement
measuring Instruments.
According to the functions:
1. Length measuring instrument
2. Angle measuring instrument
3. Instrument for checking deviation from geometrical forms
4. Instrument for determining the quality of surface finish.
According to the accuracy.
1. Most accurate instruments
2. Less accurate instrument
Example - light interference instrument
Example - Pool room Microscope, Comparators, Optimeter
3. Still less accurate instrument
Example - Dial indicator, vernier caliper.
Damping.
Damping is any effect, that tends to reduce the amplitude of oscillations of an oscillatory system.
Geometric dimensioning and tolerancing
Geometric dimensioning and tolerancing (GD&T) is a symbolic language used on engineering
drawings and computer generated three-dimensional solid models for explicitly describing
nominal geometry and its allowable variation.
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sources of error
During measurement several types of error may arise as indicated and these error can be broadly
classified into two categories.
a) Controllable Errors:
These are controllable in both their magnitude and sense. These can be determined and
reduced, if attempts are made to analyse them. These are also known as systematic errors. These
can be due to:
1.Calibration Errors :
The actual length of standards such as slip gauges and engraved scales will vary from nominal
value by small amount. Sometimes the instrument inertia and hysteresis effects do not let the
instrument translate with complete fidelity. Often signal transmission errors such as a drop in
voltage along the wires between the transducer and the electric meter occur. For high order
accuracy these variations have positive significance and to minimize such variations calibration
curves much be used.
2. Ambient Conditions :
Variations in the ambient conditions from internationally agreed standard value of 20 oC,
barometric pressure 760mm of mercury and 10mm of mercury vapour pressure, can give rise to
errors in the measured size of the component. Temperature is by far the most significant of these
ambient conditions and due correction is needed to obtain error free results.
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1.Stylus Pressure :
Error induced due to stylus pressure are also appreciable. Whenever any component in
measured under a definite stylus pressure both the deformation of the workpiece surface and
deflection of the workpiece shape will occur.
Avoidable Errors :
These error include the errors due to Parallel and the effect of misalignment of the workpiece
centers. Instrument location errors such as placing a thermometer is sunlight when attempting to
measure air temperature also being to this category.
b) Random Errors :
These occur randomly and the specific causes of such errors cannot be determined, but
likely sources of this type of error are small variations in the position of setting standards and
workpiece, slight displacement of lever joints in the measuring joints in the measuring instrument,
transient flaction in the friction in the measuring instrument and operator errors in reading scale
and pointer type displays or in reading engraved scale positions.
From the above, it is clear that systematic errors are those which are repeated consistently
with repetition of the experiment, where as random errors are those which are accidental and
whose magnitude and sign cannot be predicted from a knowledge of the measuring system and
condition of measurement.
classification of measurements
In the precision measurements, various methods of measurement are followed depending
upon the accuracy required and the amount of permissible error.
The various methods of measurement are classified as follow :Direct
method of measurement
Indirect method of measurement
Absolute method of measurement
Comparative method of measurement
Contact method of measurement
Contact less method of measurement
The direct method of measurement is one in which the measurement value in determined
directly where as in the indirect method of measurement the dimension in determined by
measuring the values functionally related to the required value. The direct method of
measurement is simple and most widely employed in production.
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In many cases, for example, as when checking the pitch diameter of treads, the direct
method may lead to large errors in measurement. In this case, it is more expedient to make
indirect measurement.
An absolute method of measurement in one in which the zero division of the measuring
tool or instrument corresponding zero value of the measured dimension. eg. Steel rule, vernier
Caliper, micrometer, Screw gauge). By absolute method the full value of the dimension is
determined.
In the comparative method, only the deviation of the measured dimension from a master
gauge are determined (eg. Dial comparator).
In contact methods of measurement, the measuring tip of the instrument actually touches
the surface to be measured, eg. By dial comparator, screw gauges etc. In such cases arrangements
for constant contact pressure should be provided in order to prevent errors due to excess contact
pressure.
In Contact less method of measurement, no contact is required. Such instruments include
tool maker's micrometer and projection comparator.
According to the functions, the measuring instruments classified as.
Length measuring instruments
Angle measuring instruments
Instrument for checking deviation from geometrical forms
Instrument for determining the quality of surface finish.
According to the accuracy of measurement, the measuring instrument are classified as follows.
Most accurate instrument eg : light – interference instruments.

Second
group consists of less accurate instruments. Such as tool room Microscopes, comparator
optimeter etc.

Third
group consists of , still less accurate instruments eg: dial indicators, vernier caliper and
rules with vernier skills.
Measuring instrument are also classified in accordance with then metrological proper ties,
such as range of instrument, scale graduation value, scale spacing, sensitivity and reading
accuracy.
Range of Measurement :
It indicates the size values between which measurements may be made on the given
instrument.
Scale Spacing :
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It is the distance between the axis of two adjacent graduations on the scale.
Scale division Value :
It the measured value corresponding to one division of the instrument scale, eg. For
Vernier Caliper the scale division value 0.1mm.
Sensitivity (amplification or gearing ratio ):
It is the ratio of the scale spacing to the space division value. It would also be expressed as
the ratio of the product of all the larger lever arms and the product of all the smaller lever arms.
Sensitivity Threshold :
It is d as the minimum measured value which may cause any movement whatsoever of the
indicating hand..
Reading Accuracy :
It is the accuracy that may be attained in using a measuring instrument.
Reading Error :
It is d as the difference between the reading of the instrument and the actual value of the
dimension being measured.
Mention a few important precautions for use of instruments towards achieving accuracy in
measurement are as follows :
The measurement must be made at right angles to the surfaces of the component.
The
component must be supported so that it does not collapse under the measuring pressure or
under its own weight.

The
work piece must be cleaned before being measured, and coated with oil or a corruption
inhibitor after inspection.

Measuring
instrument must be handled with care so that they are not damaged or strained. They
must be kept in their cases when not in use and kept clean and lightly oiled on the bright
surfaces. They should be regularly checked to ensure that they have not lost their mutual
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accuracy.

It must be emphasized that it is not good practice to rely on the accuracy of the instruments
and on the readings taken – readings should be double checked and the instruments should be
periodically checked against the appropriate standards. Measuring instruments are produced to
a high degree of accuracy, form the engineer's common rule to the most complex optical
instrument, and they should be treated accordingly. Instruments are easily damaged, and very
often the damage is not noticeable. Always handle instrument with great care, and report
immediately any accidental damage. Protect highly polished surfaces from corrosion by
handling them as little as possible and by covering them with petroleum jelly when not in use.
Sources of errors in precision measurement .
Failure to consider the following factors may introduce errors in measurement :
Alignment
Principle
Location of the measured part
Temperature
Parallax.
Alignment Principle (Abbe's Principle) :
Abbe's principle of alignment states that " the axis or line of measurement of the measured
part should consider with the measuring scale or axis or measurement of measuring instrument ".
The effect of simple scale alignment error is shown in fig.
L
L
Q
JCL
if Q = angle of scale misalignment
L = apparent length
Loose = true length
if e = induced error
then,
e = L-L cose
= L(1-CoseC)
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An alignment error of 2o over iN introduces an error of approximately 0.6mm.
Error in introduced to dial indicator readings if the plunger axis does not coincide with the
axis or line of measurement.
Q
If e = Induced error
L = change in indicator reading,
reading.
L case = Surface displacement
\ e = L (1-Cose)
Line or axis of measure Dial gauge axis.
To ensure correct displacement readings on the dial indicator the plunger must, of course
be normal to the surface in both mutually perpendicular planes.
A second source of error will illustrated by the vernier Caliper and similar instruments or
circumstance is associated with measuring pressure or "feel". The measuring pressure in applied
by the adjusting screw which is adjacent and parallel to the scale. A bending moment in
introduced equal to the product of the force applied by the adjusting screw and the perpendicular
distance between the screw centre line and the line of measurement as in Fig.
Variation of force applied at the screw are augmented at the line of measurement and a hot
unusual form of damage to Vernier Caliper is permanent distortion to the measuring jaws
presumably from this source as in fig.
Location :
when using a sensitive comparator, the measured part in located on a table which forms the
datum for comparison with the standard. The comparator reading in thus an indication of the
displacement of the upper surface of the measured part from the datum. Faults at the location
surface of the part damage, geometrical variations from part to part or the presence of foreign
matter are also transmitted to the indicator. This provides false information regarding the true
length of the part by introducing both sine and cosine error.
Where location conditions may not be ideal, ex:- inter stage measurement during
production, sensors, operating on each side of the component can be used which eliminate the
more serious sine type error. A two probe system measures length rather than surface
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displacement and highly sensitive electronic comparators of this type are used for slip gauge
measurement.
Temperature :The standard reference temp. at which line and end standards are said to be at their true
length is 20o and for highest accuracy in measurement this temp. Should be maintained. When
this is not possible and the length at reference temp. must be known, a correction is made to allow
for the difference between ambient and reference temp. The correction value required to –
0.001375mm, when steel object exactly 25mm long at 20oC and Co-efficient of linear expansion
11Mm c/m in measured at 25oC, Which is rather larger than the increment step the M88/2 stip
gauge set.
However, for less stringent measurement requirements it is not essential that correction to
reference temperature is made provided that the following precautions and conditions are
observed.
a) The temp. at which measurement is made is not changing significantly.
b) The gauge and work being compared are at the same temp and the temp is the same as
ambient temp.
c) The gauge and work have the same Co-efficient of linear expansion.
Conditions a) and b) can be met if gauge and work allowed sufficient time to reach equal temp
with surrounding after being arranged in the measuring positions.
If the measurement can be carried out on the surface of a large mass, eg: Surface plate, then
temp. equalization will be family vapid as heat will be conducted away form the work and gauge
but will not contribute any significant temp. change to the plate.
A component having a co-efficient of linear expansion significantly different from the gauge may
be said to correct to size only at a given temp.
Parallax Effect :
On most dials the indicating finger or pointer lies in a plane parallel to the scale but
displaced a small distance away to allow free movement of the pointer. It is then essential to
observe the pointer along a line normal to the scale otherwise a reading error will occur. This
effect is shown in fig. Where a dial is shown observed from three positions where the pointer is
set at zero on the scale, observed from position 1) ie, from the left, the pointer appears to indicate
some value, to the right off zero, and from position 2) Some value slightly to the left of zero, while
only at position. 3) With the pointer Coincide with zero on the scale. Rules and micrometer
thimbles are beveled to reduce this effect and on dials the indicates may be arranged to lie in the
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same plane as the scale, thus completely eliminating parallax, or a silvered reflector may be
incorporated on the scale so that the line between the of eye and pointer is normal to the scale only
when the pointer obscures in own image in the reflector.
classification of methods of measurements.
Classifications of Methods of Measurements
In precision measurements various methods of measurement are followed depending upon
the accuracy required and the amount of permissible error.
There are numerous ways in which a quantity can be measured. Any method of
measurements should be d in such a detail and followed by such a standard practice that there is
little scope for uncertainty. The nature of the procedure in some of the most common
measurements is described below. Actual measurements may employ one or more combinations
of the following.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Direct method of measurement: In this method the value of a quantity of obtained
directly by comparing the unknown with the standard. It involves no mathematical
calculations to arrive at the results, for example, measurement of length by a graduated
scale. The method is not very accurate because it depends on human insensitiveness in
making judgement.
Indirect method of measurement: In this method several parameters (to which the
quantity to be measured is linked with) are measured directly and then the value is
determined by mathematical relationship. For example, measurement of density by
measuring mass and geometrical dimensions.
Fundamental method of measurement: Also known as the absolute method of
measurement, it is based on the measurement of the base quantities used to the
quantity. For example, measuring a quantity directly in accordance with the definition
of that quantity, or measuring a quantity indirectly by direct measurement of the
quantities linked with the definition of the quantity to be measured.
Comparison method of measurement: This method involves comparison with either a
known value of the same quantity or another quantity which is function of the quantity
to be measured.
Substitution method of measurement: In this method, the quantity to be measured is
measured by direct comparison on an indicating device by replacing the measuring
quantity with some other known quantity which produce same effect on the indicating
device. For example, determination of mass by Borda method.
Transposition method of measurement: This is a method of measurement by direct
comparison in which the value of the quantity to be measured is first balanced by a
initial known value A of the same quantity; next the value of the quantity to be
measured is put in the place of that known value and is balanced again by a second
known value B. When the balance indicating device gives the same indication in both
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(vii)
(viii)
(ix)
(x)
(xi)
(xii)
(xiii)
(xiv)
(xv)
(xvi)
cases, the value of the quantity to be measured is AB . For example, determination of
a mass by means of a balance and known weights, using the Gauss double weighing
method.
Differential or comparison method of measurement: This method involves measuring
the difference between the given quantity and a known master of near about the same
value. For example, determination of diameter with master cylinder on a comparator.
Coincidence method of measurement: In this differential method of measurement the
very small difference between the given quantity and the reference is determined is
determined by the observation of the coincidence of scale marks. For example,
measurement on vernier caliper.
Null method of measurement: In this method the quantity to be measured is compared
with a known source and the difference between these two is made zero.
Deflection method of measurement: In this method, the value of the quantity is directly
indicated by deflection of a pointer on a calibrated scale.
Interpolation method of measurement: In this method, the given quantity is compared
with two or more known value of near about same value ensuring at least one smaller
and one bigger than the quantity to be measured and the readings interpolated.
Extrapolation method of measurement: In this method, the given quantity is compared
with two or more known smaller values and extrapolating the reading.
Complimentary method of measurement: This is the method of measurement by
comparison in which the value of the quantity to be measured is combined with a
known value of the same quantity so adjusted that the sum of these two values is equal
to predetermined comparison value. For example, determination of the volume of a
solid by liquid displacement.
Composite method of measurement: In involves the comparison of the actual contour of
a component to be checked with its contours in maximum and minimum tolerable
limits. This method provides for the checking of the cumulative errors of the
interconnected elements of the component which are controlled through a combined
tolerance. This method is most reliable to ensure inter-changeability and is usually
effected through the use of composite “Go” gauges, for example, checking of the thread
of a nut with a screw plug “GO” gauge.
Element method: In this method, the several related dimensions are gauged
individually, i.e., each component element is checked separately. For example, in the
case of thread, the pitch diameter, pitch, and flank angle are checked separately and
then the virtual pitch diameter is calculated. It may be noted that value of virtual pitch
diameter depends on the deviations of the above thread elements. The functioning of
thread depends on virtual pitch diameter lying within the specified tolerable limits.
In case of composite method, all the three elements need not be checked separately and
is thus useful for checking the product parts. Element method is used for checking tools
and for detecting the causes of rejects in the product.
Contact and contact less methods of measurements: In contact methods of
measurements, the measuring tip of the instrument actually touches the surface to be
measured. In such cases, arrangements for constant contact pressure should be
21
provided in order to prevent errors due to excess contact pressure. In contactless
method of measurements, no contact is required. Such instruments include tool –
maker’s microscope and projection comparator, etc.
For every method of measurement a detailed definition of the equipment to be used, a
sequential list of operations to be performed, the surrounding environmental conditions and
descriptions of all factors influencing accuracy of measurement at the required level must be
prepared and followed.
Metrological characteristics of Measuring Instruments.
Metrological characteristics of Measuring Instruments:
Measuring instruments are usually specified by their metrological properties, such as range
of measurement, scale graduation value, scale spacing, sensitivity and reading accuracy.
Range of Measurement: It indicates the size values between which measurements may be
made on the given instrument.
Scale range: It is the difference between the values of the measured quantities corresponding
to the terminal scale marks.
Instrument range: It is the capacity or total range of values which an instrument is capable of
measuring. For example, a micrometer screw gauge with capacity of 25 to 50mm has instrument
range of 25 to 50mm but scale range is 25mm.
Scale Spacing: It is the distance between the axes of two adjacent graduations on the scale.
Most instruments have a constant value of scale spacing throughout the scale. Such scales are said
to be linear.
In case of non – linear scales, the scale spacing value is variable within the limits of the
scale.
Scale Division Value: It is the measured value of the measured quantity corresponding to one
division of the instrument, e.g. for ordinary scale, the scale division value is 1mm. As a rule, the
scale division should not be smaller in value than the permissible indication error of an
instrument.
Sensitivity (Amplication or gearing ratio): It is the ratio of the scale spacing to the division
value. It could also be expressed as the ratio of the product of all the larger lever arms and the
product of all the smaller lever arms. It is the property of a measuring instrument to respond to
changes in the measurement quantity.
22
Sensitivity Threshold: It is d as the minimum measured value which may cause any
movement whatsoever of the indicating hand. It is also called the discrimination or resolving
power of an instrument and is the minimum change in the quantity being measured which
produces a perceptible movement of the index.
Reading Accuracy: It is the accuracy that may be attained in using a measuring instrument.
Reading Error: It is d as the difference between the reading of the instrument and the actual
value of the dimension being measured.
Accuracy of observation: It is accuracy attainable in reading the scale of an instrument. It
depends on the quality of the scale marks, the width or the pointer / index, the space between the
pointer and the scale, the illumination of the scale, and the skill of the inspector. The width of
scale mark is usually kept one – tenth of the scale spacing for accurate reading of indications.
Parallax: It is apparent change in the position of the index relative to the scale marks, when
the scale is observed in a direction other than perpendicular to its plane.
Repeatability: It is the variation of indications in repeated measurements of the same
dimension. The variations may be due to clearances, friction and distortions in the instrument’s
mechanism. Repeatability represents the reproducibility of the readings of an instrument when a
series of measurements in carried out under fixed conditions of use.
Measuring force: It is the force produced by an instrument and acting upon the measured
surface in the direction of measurement. It is usually developed by springs whose deformation
and pressure change with the displacement of the instrument’s measuring spindle.
Systematic error and random error.
For statistical study and the study of accumulation of errors, errors are categorized as
controllable errors and random errors.
(a) Systematic or controllable errors:
Systematic error is just a euphemism for experimental mistakes. These are controllable in
both their magnitude and sense. These can be determined and reduced, if attempts are made to
analyse them. However, they can not be revealed by repeated observations. These errors either
have a constant value or a value changing according to a definite law. These can be due to:
1. Calibration Errors: The actual length of standards such as slip gauges and engraved scales
will vary from nominal value by small amount. Sometimes the instrument inertia,
hysteresis effects do not let the instrument translate with complete fidelity. Often signal
transmission errors such as drop in voltage along the wires between the transducer and the
23
2.
3.
4.
5.
6.
electric meter occur. For high order accuracy these variations have positive significance and
to minimize such variations calibration curves must be used.
Ambient Conditions: Variations in the ambient conditions from internationally agreed
standard value of 20C, barometric pressure 760 mm of mercury, and 10mm of mercury
vapour pressure, can give rise to errors in the measured size of the component.
Temperature is by far the most significant of these ambient conditions and due correction is
needed to obtain error free results.
Styles Pressure: Error induced due to styles pressure is also appreciable. Whenever any
component is measured under a definite stylus pressure both the deformation of the
workpiece surface and deflection of the workpiece shape will occur.
Avoidable Errors: These errors include the errors due to parallax and the effect of
misalignment of the workpiece centre. Instrument location errors such as placing a
thermometer in sunlight when attempting to measure air temperature also belong to this
category.
Experimental arrangement being different from that assumed in theory.
Incorrect theory i.e., the presence of effects not taken into account.
(b) Random Errors:
These occur randomly and the specific cases of such errors cannot be determined, but likely
sources of this type of errors are small variations in the position of setting standard and
workpiece, slight displacement of lever joints in the measuring joints in measuring instrument,
transient fluctuation in the friction in the measuring instrument, and operator errors in reading
scale and pointer type displays or in reading engraved scale positions.
Characteristics of random errors:
The various characteristics of random errors are:
 These are due to large number of unpredictable and fluctuating causes that can not be
controlled by the experimenter. Hence they are sometimes positive and sometimes negative
and of variable magnitude. Accordingly they get revealed by repeated observations.
 These are caused by friction and play in the instrument’s linkages, estimation of reading by
judging fractional part of a scale division, by errors in position the measured object, etc.
 These are variable in magnitude and sign and are introduced by the very process of
observation itself.
 The frequency of the occurrence of random errors depends on the occurrence probability for
different values of random errors.
 Random errors show up as various indication values within the specified limits of error in a
series of measurements of a given dimension.
 The probability of occurrence is equal for positive and negative errors of the same absolute
value since random errors follow normal frequency distribution.
 Random errors of larger absolute value are rather than those of smaller values.
24
 The arithmetic mean of random errors in a given series of measurements approaches zero as
the number of measurements increases.
 For each method of measurement, random errors do not exceed a certain definite value.
Errors exceeding this value are regarded as gross errors (errors which greatly distort the
results and need to be ignored).
 The most reliable value of the size being sought in a series of measurements is the arithmetic
mean of the results obtained.
 The main characteristic of random errors, which is used to determine the maximum
measuring error, is the standard deviation.
 The maximum error for a given method of measurement is determined as three times the
standard deviation.
 The maximum error determines the spread of possible random error values
 The standard deviation and the maximum error determine the accuracy of a single
measurement in given series.
From the above, it is clear that systematic errors are those which are repeated consistently with
repetition of the experiment, whereas Random Errors are those which are accidental and whose
magnitude and sign cannot be predicted from knowledge of measuring system and conditions of
measurement.
accuracy and precision and
distinction between precision and accuracy.
The agreement of the measured value with the true value of the measured quantity is called
accuracy. If the measurement of a dimensions of a part approximates very closely to the true
value of that dimension, it is said to be accurate. Thus the term accuracy denotes the closeness of
the measured value with the true value. The difference between the measured value and the true
value is the error of measurement. The lesser the error, more is the accuracy.
Precision and Accuracy
Precision, The terms precision and accuracy are used in connection with the performance of
the instrument. Precision is the repeatability of the measuring process. It refers to the group of
measurements for the same characteristics taken under identical conditions. It indicates to what
extent the identically performed measurements agree with each other. If the instrument is not
precise it will give different (widely varying) results for the same dimension when measured
again and again. The set of observations will scatter about the mean. The scatter of these
measurements is designated as , the standard deviation. It is used as an index of precision. The
less the scattering more precise is the instrument. Thus, lower, the value of , the more precise is
the instrument.
Accuracy: Accuracy is the degree to which the measured value of the quality characteristic
agrees with the true value. The difference between the true value and the measured value is
known as error of measurement.
25
Distinction between Precision and Accuracy
Accuracy is very often confused with precision though much different. The distinction
between the precision and accuracy will become clear by the following example. Several
measurements are made on a component by different types of instruments (A, B and C
respectively) and the results are plotted. In any set of measurements, the individual
measurements are scattered about the mean, and the precision signifies how well the various
measurements performed by same instrument on the same quality characteristics agree with each
other.
The difference between the mean of set of readings of the same quality characteristic and
the true value is called as error. Less the error more accurate is the instrument.
Figure shows that the instrument A is precise since the results of number of measurements
are close to the average value. However, there is a large difference (error) between the true value
and the average value hence it is not accurate.
The readings taken by the instruments are scattered much from the average value and
hence it is not precise but accurate as there is a small difference between the average value and
true value.
Figure shows that the instrument is accurate as well as precise.
26
Factors affecting the accuracy of the measuring system.
The basic components of an accuracy evaluation are the five elements of a measuring
system such as:
1. Factors affecting the calibration standards
2. Factors affecting the workpiece
3. Factors affecting the inherent characteristics of the instrument
4. Factors affecting the person, who carries out the measurements, and
5. Factors affecting the environment.
1. Factors affecting the standard. It may be affected by:
a. Coefficient of thermal expansion,
b. Calibration interval,
c. Stability with time,
d. Elastic properties,
e. Geometric compatibility
2. Factors affecting the Workpiece, these are:
a. Cleanliness, surface finish, waviness, scratch, surface defects etc.,
b. Hidden geometry,
c. Elastic properties,
d. Adequate datum on the workpiece
e. Arrangement of supporting workpiece
f. Thermal equalization etc.
3. Factors affecting the inherent characteristics of Instrument
a. Adequate amplification for accuracy objective,
b. Scale error,
c. Effect of friction, backlash, hysteresis, zero drift error,
d. Deformation in handling or use, when heavy workpieces are measured
e. Calibration errors,
f. Mechanical parts (slides, guide ways or moving elements)
g. Repeatability and readability
h. Contact geometry for both workpiece and standard
4. Factors affecting person:
a. Training, skill
b. Sense of precision appreciation,
c. Ability to select measuring instruments and standards
d. Sensible appreciation of measuring cost,
e. Attitude towards personal accuracy achievements
f. Planning measurement techniques for minimum cost, consistent with precision
requirements etc
5. Factors affecting Environment:
27
a.
b.
c.
d.
e.
Temperature, humidity etc.,
Clean surrounding and minimum vibration enhance precision,
Adequate illumination
Temperature equalization between standard, workpiece, and instrument,
Thermal expansion effects due to heat radiation from lights, heating elements,
sunlight and people,
f. Manual handling may also introduce thermal expansion.
Higher accuracy can be achieved only if, all the sources of error due to the above five elements in
the measuring system are analysed and steps taken to eliminate them.
The above analysis of five basic metrology elements can be composed into the acronym.
SWIPE, for convenient reference
Where, S – STANDARD
W
I
P
E
- WORKPIECE
- INSTRUMENT
- PERSON
- ENVIRONMENT
Sensitivity ,Readability , Calibration , Repeatability
Sensitivity
Sensitivity may be d as the rate of displacement of the indicating device of a
instrument, with respect to the measured quantity. In other words, sensitivity of an instrument is
the ratio of the scale spacing to the scale division value. For example, if on a dial indicator, the
scale spacing is 1.0 mm and the scale division value is 0.01 mm, then sensitivity is 100. It is also
called as amplification factor or gearing ratio.
If we now consider sensitivity over the full range o instrument reading with respect to
dy
measured quantities as shown in Fig., the sensitivity at any value of y 
where dx and dy are
dx
increments of x and y, taken over the full instrument scale, the sensitivity is the slope of the curve
at any value of y.
28
The sensitivity may be constant or variable along the scale. In the first case we get linear
transmission and in the second non-linear transmission and in the second non-linear transmission.
Sensitivity refers to the ability of measuring device to detect small difference in a quantity
being measured. High sensitivity instruments may lead to drifts due to thermal or other effects,
and indications of lower sensitivity.
Readability
Readability refers to the ease with which the readings of a measuring instrument can be
read. It is the susceptibility of a measuring device to have its indications converted into
meaningful number. Fine and widely spaced graduation lines ordinarily improve the readability.
If the graduation lines are very finely spaced, the scale will be more readable by using the
microscope, however, with the naked eye the readability will be poor.
To make micrometers more readable they are provided with vernier scale. It can also be
improved by using magnifying devices.
Calibration:
The calibration of any measuring instrument is necessary to measure the quantity in terms
of standard unit. It is the process of framing the scale of the instrument by applying some
standardized signals. Calibration is a premeasurement process, generally carried out by
manufactures.
It is carried out by making adjustments such that the read out device produces zero output
for zero measured input. Similarly, it should display an output equivalent to the known
measured input near the full scale input value.
The accuracy of the instrument depends upon the calibration. Constant uses of instruments
affect heir accuracy. If the accuracy is to be maintained, the instruments must be checked and
recalibrated if necessary. The schedule of such calibration depends upon the severity of use,
environmental conditions, accuracy of measurement required etc. as far as possible calibration
should be performed under environmental conditions which are vary close to the conditions
under which actual measurements are carried out. If the output of a measuring system is linear
and repeatable, it can be easily calibrated.
Repeatability,
It is the ability of the measuring instrument to repeat the same results for the measurements
for the same quantity, when the measurement are carried out
29
-
by the same observer
With the same instrument
Under the same conditions.
Without any change in location.
line standard and end standard measurements and their characteristics.
Line and End Measurements
A length may be measured as the distance between two lines or as he distance between two
parallel faces. So, the instruments for direct measurement of linear dimensions fall into two
categories
1. Line standards
2. End standards
Line standards. When the length is measured as the distance between centres of two
engraved lines, it is called line standard. Both material standards yard and metre are line
standards. The most common example of line measurement is the rule with divisions shown as
lines marked on it.
Characteristics of Line Standard
1. Scales can be accurately engraved but the engraved lines them selves possess thickness
and it is not possible to take measurements with high accuracy.
2. A scale is a quick and easy to use over a wide range.
3. The scale markings are not subjected to wear. However, he leading ends are subjected
to wear and this may lead to undersize measurements.
4. A scale does not posses a “built in “ datum. Therefore it is not possible to align the scale
with the axis of measurement.
5. Scales are subjected to parallax error.
6. Also, the assistance of magnifying glass or microscope is required if sufficient accuracy
is to be achieved.
End standards: When length is expressed as the distance between two flat parallel faces, it is
known as ends standard. Examples: Measurement by slip gauges, end bars, ends of micrometer
anvils, vernier calipers etc. the end faces are hardened, lapped flat and parallel to a very high
degree of accuracy.
Characteristics of End Standards:
30
1. These standards are highly accurate and used for measurement of close tolerance in
precision engineering as well as in standard laboratories, tool rooms, inspection
departments etc.
2. They require more time for measurements and measure only one dimension at a time.
3. They are subjected to wear on their measuring faces.
4. Group of slips can be “wrung” together to build up a given size; faulty wringing and
careless use may lead to inaccurate results.
5. End standards have built in datum since their measuring faces are flat and parallel and
can positively locked on datum surface.
6. They are not subjected to parallax effect as their use depends on feel.
The accuracy of both these standards is affected by temperature change and both are
1
originally calibrated at 20 C. It is also necessary to take utmost case in their manufacture to
2
ensure that the change of shape with time, secular change is reduced to negligible.
line and end standard measurements:
Comparison between line standards and End Standards:
Sr.
No.
Characteristics
1.
Principle
2.
Accuracy
3.
Ease and time of
and easy.
4.
Effect of wear
5.
Alignment
Line standard
Length is expressed as the
distance between two lines
Limited to is 0.2 mm for high
accuracy, scales have to be used
in conjunction with magnifying
glass or microscope.
Measurement is quick and easy.
Scale markings are not subject to
wear. However, significant wear
may occur on leading ends. Thus
it may be difficult to assume zero
of scale as datum.
Cannot be easily aligned with the
axis of measurement.
31
End standard
Length is expressed as the distance between two flat
parallel faces
Highly accurate for measurement of close tolerances
up to  0.001 mm.
Use of end standard requires skill and is time
consuming.
These are subjected to wear on their measuring
surfaces.
Can be easily aligned with the axis of measurement.
6.
Manufacture and
cost
7.
Parallax effect
8.
Examples
Simple to manufacture at low
cost.
They are subjected to parallax
error.
Scale (yard, metre etc.,)
Manufacturing process is complex and cost is high
They are not subjected to parallax error.
Slip gauges, end bars, V. caliper, micrometers etc.
Geometric dimensioning and tolerancing
Geometric dimensioning and tolerancing (GD&T) is used to the nominal geometry of parts and
assemblies, to the allowable variation in form and possibly size of individual features, and to the
allowable variation between features. Dimensioning and tolerancing and geometric dimensioning
and tolerancing specifications are used as follows:


Dimensioning specifications the nominal, as-modeled or as-intended geometry. One
example is a Basic Dimension.
Tolerancing specifications the allowable variation for the form and possibly the size of
individual features, and the allowable variation in orientation and location between
features. Two examples are Linear Dimensions and Feature Control Frames using a datum
reference.
There are several standards available worldwide that describe the symbols and the rules used in
GD&T. One such standard is American Society of Mechanical Engineers (ASME) Y14.5M-1994.
This article is based on that standard, but other standards, such as those from the International
Organization for Standardization (ISO), may vary slightly. The Y14.5M standard has the
advantage of providing a fairly complete set of standards for GD&T in one document. The ISO
standards, in comparison, typically only address a single topic at a time. There are separate
standards that provide the details for each of the major symbols and topics below (e.g. position,
flatness, profile, etc)
Dimensioning and tolerancing philosophy
According to the ASME Y14.5M-1994 standard, the purpose of geometric dimensioning and
tolerancing (GD&T) is to describe the engineering intent of parts and assemblies. This is not a
completely correct explanation of the purpose of GD&T or dimensioning and tolerancing in
general.
The purpose of GD&T is more accurately d as describing the geometric requirements for part and
assembly geometry. Proper application of GD&T will ensure that the allowable part and assembly
geometry d on the drawing leads to parts that have the desired form and fit (within limits) and
function as intended.
There are some fundamental rules that need to be applied (these can be found on page 4 of the
1994 edition of the standard):
32













All dimensions must have a tolerance. Every feature on every manufactured part is subject
to variation, therefore, the limits of allowable variation must be specified. Plus and minus
tolerances may be applied directly to dimensions or applied from a general tolerance block
or general note. For basic dimensions, geometric tolerances are indirectly applied in a
related Feature Control Frame. The only exceptions are for dimensions marked as
minimum, maximum, stock or reference.
Dimensioning and tolerancing shall completely the nominal geometry and allowable
variation. Measurement and scaling of the drawing is not allowed except in certain cases.
Engineering drawings the requirements of finished (complete) parts. Every dimension and
tolerance required to the finished part shall be shown on the drawing. If additional
dimensions would be helpful, but are not required, they may be marked as reference.
Dimensions should be applied to features and arranged in such a way as to represent the
function of the features.
Descriptions of manufacturing methods should be avoided. The geometry should be
described without explicitly defining the method of manufacture.
If certain sizes are required during manufacturing but are not required in the final
geometry (due to shrinkage or other causes) they should be marked as non-mandatory.
All dimensioning and tolerancing should be arranged for maximum readability and should
be applied to visible lines in true profiles.
When geometry is normally controlled by gage sizes or by code (e.g. stock materials), the
dimension(s) shall be included with the gage or code number in parentheses following or
below the dimension.
Angles of 90° are assumed when lines (including center lines) are shown at right angles, but
no angular dimension is explicitly shown. (This also applies to other orthogonal angles of
0°, 180°, 270°, etc.)
Dimensions and tolerances are valid at 20 °C unless stated otherwise.
Unless explicitly stated, all dimensions and tolerances are valid when the item is in a free
state.
Dimensions and tolerances apply to the full length, width, and depth of a feature.
Dimensions and tolerances only apply at the level of the drawing where they are specified.
It is not mandatory that they apply at other drawing levels, unless the specifications are
repeated on the higher level drawing(s).
Geometric tolerancing reference chart
Type of
tolerance
Geometric
characteristics
Form
Straightness
Form
Flatness
Form
Circularity
Can be
Can be Can be
Can be
Can
applied
Datum Can use Can use affected affected
applied
affect
Symbol
to a
reference
by a
by a
to a
virtual
feature
used modifier modifier bonus
shift
feature
condition
of size
tolerance tolerance
33
Form
Cylindricity
Profile
Profile of a line
Profile
Profile of a
surface
Orientation Perpendicularity
Orientation
Angularity
Orientation
Parallelism
Location
Symmetry
Location
Positional
tolerance
Location
Concentricity
Runout
Circular runout
Runout
Total runout
Tolerance Frame with Symbol identifications
Indication of datum
34
GD&T data exchange
Exchange of geometric dimensioning and tolerancing (GD&T) information between CAD systems
is available on different levels of fidelity for different purposes:




In the early days of CAD exchange only lines, texts and symbols were written into the
exchange file. A receiving system could only display them on the screen or print them out,
but only a human could interpret them.
GD&T presentation: On a next higher level the presentation information is enhanced by
grouping them together into callouts for a particular purpose, e.g. a datum feature callout and
a datum reference frame. And there is also the information which of the curves in the
exchange file are leader, projection or dimension curves and which are used to form the
shape of a product.
GD&T representation: Unlike GD&T presentation, the GD&T representation does not deal
with how the information is presented to the user but only deal with which element of a
shape of a product has which GD&T characteristic. A system supporting GD&T
representation may display the GD&T information in some tree and other dialogs and
allow the user to directly select and highlight the corresponding feature on the shape of the
product, 2D and 3D.
Ideally both GD&T presentation and representation are available in the exchange file and
are associated with each other. Then a receiving system can allow a user to select a GD&T
callout and get the corresponding feature highlighted on the shape of the product.
An enhancement of GD&T representation is defining a formal language for GD&T (similar like a
programming language) which also has build in rules and restrictions for the proper GD&T usage.
This is still a research area.
35
UNIT – II
LINEAR AND ANGULAR MEASUREMENT
PART – A
purpose of Hook rules.
Hook rules are used to make accurate measurements from a shoulder step, or edge of
workpiece. They may be used to measure franges, circular pieces and for setting inside caliper to
a dimension.
short length rule.
Short length rules are useful in measuring small openings and hard to reach locations
where ordinary rules cannot be used.
how accurate measurement can be made if the end of the rule in worn.
In case of worn rules, measurement can be made by placing the 1cm graduation in line on
the edge of the work, taking the reading and subtracting them from final reading.
rule used as a straight edge
The edge of a steel rule are ground flat. The edge of a rule in placed on the work surface
which in then held up to the light. In accuracies as small as 0.02 mm may easily be seen by this
method.
two types of outside caliper.
1. Spring joint caliper
36
2. Firm joint caliper
dangerous to measure work while revolving ,outside caliper should be held position when
measuring work
An attempt to measure the work while it is revolving would result in an accident and any
measurement taken will not be accurate.
Caliper should be held tightly between the thumbs and forefinger in order to get the most
accurate measurement. The caliper must be held at right angles.
purposes of inside caliper
Inside Calipers are used to measure the diameter of holes, or width of keyways and slots.
two uses of a surface plate.
1. As a datum reference plane for marking out or inspection.
2. To check the flatness of another surface.
the materials used for surface plate and uses of that material comparing with Cast Iron.
1)
1)
2)
3)
4)
Cast Iron 2) Granite
3) Glass
4)Non-metallic substance
Granite and Glass plates of same depth are more rigid than Cast Iron plates.
Damage to this surfaces Causes indentation and does not throw up a projecting burn.
Corrosion in virtually absent.
It is easier to slide metallic articles such as weight gauges and squares, on their surfaces.
Cast Iron in a preferred material for surface plates and tables
1.
2.
3.
4.
It is a self-lubricating, and the equipment slides on its working surface with a pleasant feel.
It is easy to provide complex shape of stiffening ribs.
It is stable and rigid metal and relatively in-expensive
It is easily machined and scrapped to an accurate plane surface.
V-Blocks are generally bought in pairs
V-Blocks are manufactured in pairs so that long components can be supported parallel to
the datum surface and for this reason they must always be bought and kept as a pain.
the accuracy of a Vernier Caliper
Vernier Caliper are normally available in measuring accuracy of 0.02mm.
37
advantage of a vernier depth gauge as compared to micrometer depth gauge
The vernier depth gauge has longer scale than a micrometer depth gauge and does scale
than a micrometer depth gauge and does not require the length bars for measuring deep depths.
purpose of the dial test indicator in this application of the varnier height gauge and need for a
datum surface
The dial gauge in used to remove errors due to feel and to maintain constant pressure
during measurement the datum is required because the reading of vernier height gauge starts
from the base.
two usual methods of testing the accuracy of a micrometer.
The first method to check is the zero line on the thimble coin cider with the centre (index)
line on the sleeve. If it does coincide, the micrometer in correct.
In the second method a standard or a gauge blocks is measured with the micrometer. The
reading of the micrometer must be the same the standard or a gauge block.
two types of dial indicator
1. Those with a linear moving plunger called plunger type.
2. Those with an angular moving stylus called level type.
"magnification" of a dial indicator
The magnification of a dial indicator in the ratio of the movement of the pointer to the
movement of the dial indicator item.
As an example, suppose the end of the pointer traverses a circle of diameter 21mm and a
full pointer resolution of say 0-100 is in units of 0.01mm
Magnification = 21/100 x 0.01
= 66 to 1
important feature of slip gauges which makes them of considerable importance in engineering
measurement.
The important factor in the geometric accuracy of opposing gauging surfaces. The accuracy
of flatness enables slip gauges to be wrong to each other to make up a specified length. They can
also be wrong to surfaces whose accuracy is of the same orders as the slip gauges. The thickness
of the wringing films can be discounted in comparison with the overall size of the slip gauge pile.
The accuracy is not only that of flatness, but includes parallelism and length. Combinations of slip
gauge produce end standards whose length, flatness and parallelism are of a higher order of
38
accuracy.
Where will you support on end bar of 200mm length
The supports should be 0.557l apart and equidistant from ends as shown in fig .If
l=200mm,the support distance should be 0.577 x 200 =115.4mm .The distance of each support from
respective end is
(200 -115.4 )/2=42.3mm
Comparator.
Comparator is an instrument which enables a comparison to be made between the item being
measured and a length standard.
surface gauge.
It is also known as height transfer gage which is used to check the accuracy or parallelism of
surfaces, and to transfer measurement in layout work by scribing them on a vertical surface.
surface plate.
it is an accurately machined flat casting or lapped granite block upon which the part to be check
and the surface checking instruments are placed for obtaining some measure of the accuracy of a
surface or the condition of finish.
tools maker's flat.
It is a small plate which is lapped to a greater degree of accuracy and is used for inspection
of small parts with precision gauge blocks.
optical flats.
Optical flats are flat lenses usually made from natural quality with very accurately polished
surfaces having light transmitting quality. These are used in connection with interferometer
measurements (science of measuring with light waves ) for testing of plane surfaces.
profilometer.
It is an instrument used for measuring surface roughness. It measures the number of
roughness peaks in unit traverse length above a reselected length by passing a fine tracing point
over the surface.
characteristic advantages of mechanical indicators
39
1. Ling measuring range: Mechanical indicators operating on the rack and pinion system have
measuring ranges extending over several turns.
2. Small overall size: This property is of great help where space is confined or where several
indicators have to be mounted at close distances to each other.
3. Positive contact and controlled measuring force.
4. Rugged construction: Ideally suited for operating machines where substantial vibrations are
present. These are also less sensitive to inadvertently caused over travel.
5. Economical: Initial cost is low. can be easily maintained and repaired implant at reasonable
cost.
overall magnification or sensitivity of the system.
It is the ratio of scale movement for a given change of dimension and it is the product of
sensitivities of measuring head, pneumatic sensitivity and indicator sensitivity.
advantages of differential type pneumatics comparators
The advantage of differential type pneumatics comparator over ordinary pneumatic
comparators are:i) The small variation in supply pressure are compensated for by the differential pressure
measurement.
ii) The differential pressure can be zeroed, using the adjusting valve, corresponding to given
mean size.
iii) Full range of scale of measuring device can be used.
different types of comparator.
1. Mechanical
5. Pneumatic
9. Auto gauging.
2. Mechanical- optical
6. Fluid displacement
3. Electrical and Electronic
7. Electro-Mechanical
4. Optical
8. Multi check
" Damping of an instrument”
The damping may be an inherent factor in the operation of a measuring instrument or it
may deliberately be introduced as a feature in its design. An instrument is said to be damped
when there is a progressive reduction in the amplitude or complete suppression of successive
oscillations of the index after an abrupt change in the value of the measured quantity.
How the damping effect is achieved on the " Johansson mikrokator"
In Johansson microkator the damping in provided by immersing a portion of the twisted
band in a drop of oil in a split bush adjacent to the pointer and also perforating the strip as shown
in fig.
40
" Magnification " as applied to a mechanical comparator
There are four methods of magnification used in compactor,
1. Mechanical Magnification
a)lever & radius arm
b)inclined plane (or) wedge
c)gear train
2. Optical Magnification
a)optical reflection by optical lever
b)optical projection for enlarging the images
3. Electrical Magnification
a)inductance bridge circuit
b)capacitance bridge circuit
4. Prematic Magnification
a)back pressure system
Usual range of a magnification of mechanical comparator
The usual range of magnification in mechanical comparator does not exceed x500, because of
play and size f gears and levels
The magnification to be changed to suit the work
The mechanical comparator Johansson Mikrokator in so designed as to allow easy change
in magnification. The magnification can be changed by increasing or reducing the length of
cantilever spring.
An increased length reduces the force available to unwind the strip they reducing
magnification.
Specialty of a toolmaker's microscope as compared to an ordinary laboratory microscope
A toolmakers microscope shows the object and movements in this natural aspect and
direction instead of reversed as in the ordinary laboratory microscope.
Angle dekkor is less sensitive than an autocollimator
While an autocollimator incorporators a microscopy, the same is normally fitted in an angle
dekkor and reflected image in viewed through an eyepiece only.
41
Sine bar with angle gauges
Fine bar is most often used in conjunction with slip gauges. It is not used with angle gauges.
The accuracy of a sine bar depends on following charactors.
The accuracy of a fine bar depends upon the following six factors.
1.
2.
3.
4.
5.
6.
Equality of size of rollers.
Centre distance of rollers.
Parallelism of rollers axes to each other.
Parallelism of roller axes to upper surface of bar.
Flatness of upper surface.
Equality of distance from roller centers to upper surface.
The three sources of error in angular rotation.
1. Eccentricity of rotation when considered separately is of sinusoidal form.
2. Error in the indexing mechanism, backlash, wear and etc.
3. Error in the plane of rotation is wobble.
The classification of Angular measurement.
1.
2.
Measurement of angular features on components or gauges.
Measurement of the angular rotation of a divided circle.
The advantages of photo electric autocollimator
1.
2.
3.
These replace the judgments of the human eye with appropriate photoelectric systems.
Setting accuracy in increased and constant for all operators.
Remote reading (digital or analog) are possible.
Important rules for putting dimensions on drawings in respect of Tolerance
1.
2.
3.
The dimension should be shown at place where it can be measured directly.
Considering the interchangeability of part all important dimensions with reference to the
locating surface should be clearly marked.
Contradictory additive dimensions which affect the actual location and interchangeability.
Nominal size and tolerance
A nominal size in ascribed to a part for general identification purpose. Thus a shaft may
have a nominal size of 60mm, but for practical reasons this size cannot be manufactured without
great cost. Hence, certain tolerance or machining allowance must be added to it depending upon
42
the intended application for which this part is to be used.
Taylor’s principle for the design of "Limit gauge".
The Taylor's principle for limit gauges can be divided into the following two statements.
1.
2.
"Go" gauges should inspect all the features of a component at a time and should be able to
control the maximum metal limit, or in other words the maximum metal limit of as many
related dimensions as possible should be incorporated in the "Go" gauge.
"Not - Go" gauge should check only one element at a time for the minimum metal limit.
Ways of measuring the angle of Taper.
1.
2.
3.
4.
5.
6.
Vernier bevel Protractor
Tool room microscope
Sine bar and dial gauge
Auto Collimator
Taper measuring machine
Roller, Slip gauge, and micrometer.
The objective of measurement of thread elements mention some important thread elements of
linear measurement
The purpose of thread measurement in to ensure that the thread element are within the
tolerance limits in order to satisfy the conditions of required fit.
The important thread elements which have linear measurement are,
1. Effective diameter
2. Major diameter
3. Miner diameter
4. Pith
"best wire" size
The best wire (diameter of the wire) is one such that its points of contact with the thread are
on the pitch line or effective diameter.
The desirable qualities of good rule
1.
2.
Made from hardened and tempered spring steel.
Engine divided, that in, graduations should be precision engraved for accuracy and clarity.
43
3.
4.
Ground on the edges so that it can be used as straight-edge when scribing lines or testing a
surface for flatness.
Satin chrome (or) matt finish so as to reduce glare and make it easier to read, also to prevent
Corrosion
End measuring and line measuring instruments.
End measuring Instrument - Slip gauge block, length bar
Line measuring Instrument - Engineer's Rule, Vernier Caliper, Micrometer.
Smallest graduation which can be clearly seen on a metric rule on an in circle
The smallest graduation on a metric rule : 0.5mm. While on an inch rule it in 1/64 inch.
Types of steel rules used in machine shop work.
1.
2.
3.
4.
Spring - tempered
Flexible type
Narrow type
Hook type.
Accurate measurement can be made of the end of the rule in worn.
Measurement can be made by Piecing the 1cm graduation in line on the edge of the work
taking the reading and subtracting1cm from the final reading.
Two types of outside Calipers.
1. Spring joint Caliper.
2. Firm joint Caliper.
Principle of Vernier Caliper.
The Vernier contains scale of length 9mm divided into 10 parts. The vernier scale is read in
conjunction with the main scale, which in marked in divisions of 1mm, the vernier scale is marked
in divisions of 9/10mm (i.e. 0.9mm). That it is possible the read the scale to (1.0 - 0.9) mm or
0.1mm. The accuracy of reading of the vernier scale, a typical size being 12mm divided into 25
graduation. The main scale graduation may also be changed from 1.0mm to 0.5mm. The smallest
measurement which may then be conveniently read in.
(0.5 - 12/25)mm = (0.5 - 0.48)mm = 0.02mm.
The main use of a vernier height gauge
44
The main use of a vernier height gauge in to measure (or) mark out components that
require a high degree of dimensional accuracy.
PART – B
Slip gauges
(i)
Explain wringing of slip gauges.
(ii)
Explain the classification of slip gauges.
Slip Gauges
Slip gauges or gauge blocks are universally accepted end standard of length in industry. These
were introduced by Johnson, a Sweedish engineer, and are also called as Johnson Gauges.
Slip gauges are rectangular blocks of high grade steel with exceptionally close tolerances. These
blocks are suitably hardened though out to ensure maximum resistance to wear. They are then
stabilized by heating and cooling successively in stages so that hardening stresses are removed.
After being hardened they are carefully finished by high grade lapping to a high degree of
finish, flatness and accuracy. For successful use of slip gauges their working face are made truly
flat and parallel. A slip gauge are also made from tungsten carbide which is extremely hard and
wear resistance.
The cross- sections of these gauges are 9mm 30mm for sizes up to 10mm and 9mm35mm for
larger sizes. Any two slips when perfectly clean may be wrung together. The dimensions are
45
permanently marked on one of the measuring faces of gauge blocks.
Gauges blocks are used for:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Direct precise measurement, where the accuracy of the work piece demands it.
For checking accuracy of venire calipers, micro metes, and such other measuring
instruments.
Setting up a comparator to specific dimension.
For measuring angle of work piece and also for angular setting in conjunction with a
sine bar.
The distances of plugs, spigots, etc. on fixture are often best measured with the slip
gauges or end bars for large dimensions.
To check gap between parallel locations such as in gap gauges or between two mating
parts.
There are many measurements which can be made with slip gauges either alone or in
conjunction with other simple apparatus such as straight edges, rollers, balls sine bars etc.
Wringing of Slip Gauges
The success of precision measurement by slip gauges on the phenomenon of wringing. The slip
gauges are wrung together by hand through a combined sliding and twisting motion. The gap
between two wrung slips is only of the order of 0.00635 microns (0.63510-3mm) which is
negligible.
Procedure for Wringing
(i)
(ii)
(iii)
Before using, the slip gauges are cleaned by using a lint free cloth, a chamois leather or a
cleansing tissue.
One slip gauge is then oscillated slightly over the other gauge with a light pressure.
One gauge is then placed at 900 to other by using light pressure and then it is rotated
until the blocks one brought in one line.
In this way is air is expelled out from between the gauge faces causing the gauge blocks to
adhere. The adhesion is caused partly by molecular attraction and partly by atmospheric pressure.
When two gauges are wrung in this manner is exactly the sum of their individual dimensions. The
wrung gauge can be handled as a unit without the need for clamping all the pieces together.
46
Indian Standard on Slip Gauges
According to IS: 2984-1966, the size of the slip gauges is d as the distance l between two plane
measuring faces, are being constituted by the surface of an auxiliary body with which one of the
slip gauge faces is wrung and the other by the exposed face to the slip gauge faces is wrung and
the other by the exposed face to the slip gauge. Generally the slip gauges are made from high
grade steel with coefficient of thermal expansion (11.5+1.5) 10-6 per degree Celsius between 10C to
300C. The slip gauges are hardened more than 800 HV to make them wear resistant. IS:2984 ‘ slip
gauges’ gives recommendations covering the manufacture of gauge blocks upto 90mm in length in
five grades of accuracy.
Grade II. Grade II gauge blocks are workshop grade for rough checks. They are used for
preliminary setting up of components where production tolerances are relatively wide; for
positioning milling cutters and checking mechanical widths.
Grade I. Grade I gauge blocks are used fro more precise work such as setting up since bars,
checking gap gauges and setting dial test indicators to zero.
Grade 0. These are inspection grade gauge blocks, used in tool room and inspection department
for high accuracy work.
Grade OO. These gauges are placed in the standard room and used for highest precision work.
Such as checking Grade I and Grade II slip gauges.
Calibration Grade. This is a special grade, with the actual size of the slips calibrated on a special
chart supplied with a set. The chart must be referred while making up dimension.
The following two sets of slip gauges are in general use:
Normal set (M-45)
Range (mm),
Step (mm)
1.01 to 1.009
1.01 to 1.09
1.1 to 1.9
1 to 9
10 to 90
Pieces
0.001
0.01
0.1
1
10
9
9
9
9
9
Total 45 Pieces
Special set (M-87)
Range (mm)
1.001 to 1.009
Step (mm)
0.001
47
Pieces
9
1.01 to 1.09
0.5 to 0.5
10 to 90
1.005
0.01
0.5
10
-
49
19
9
1
Total 87 Pieces
The other sets available in metric units are: M112,M105,M50,M33 and M27. The sets M112 and
M33 are as follows.
Set M112
Range (mm)
1.001 to 1.00
1.01 to 1.49
0.5 to 24.50
25 to 100
1.005
Step (mm)
0.001
0.01
0.05
25
-
Pieces
9
49
49
4
1
Total 112 Pieces
Set M33/2(2mm based set
Range (mm)
2.005
2.01 to 2.09
2.10 to 2.90
1 to 9
10.30
60
100
Step (mm)
0.01
0.1
1
10
-
Pieces
1
9
9
9
3
1
1
Total 33 Pieces
Limit gauges and the different types of limit gauges
Limit Gauges: Limit gauges are very widely used in industries. As there are two permissible
limits of the dimension of a part, high and low, two gauges are needed to check each dimension of
the part, one corresponding the low limit of size and other to the high limit of size of that
dimension. These are known as GO and NO-GO gauges.
The differences between the sizes of these two gauges is equal to the tolerance on the work
piece. GO gauges check the Maximum Metal Limit (MML) and NO-GO gauge checks the
minimum metal limit (LML). In the case of hole, maximum metal limit is when the hole is as small
as possible, that is, it is the low limit of size. In case of hole, therefore, GO gauge corresponds to
the low limit of size, while NO- GO gauge corresponds to high limit of size. For a shaft, the
maximum metal limit is when the shaft is on the high limit of size. Thus, in case of a shift GO
gauge corresponds to the high limit of size and NO-GO gauge corresponds to the low limit size.
48
While checking, each of these two gauges is offered in turn to the work. A part is considered to
be good, if the GO gauge passes through or over the work and NO-GO gauge fails to pass under
the action of the part ;is within the specified tolerance. If both the gauges fail to pass, it indicates
that hole is under size or shaft is over size. If both the gauges pass, it means that the hole is over
size or the shaft is under size.
Limit Plug Gauges
Gauges used for checking the holes are called “Plug gauges”. The ‘GO’ plug gauge is the size of
the low limit of the hole while ‘NO-GO’ plug gauge is the size of the high limit of hole.
Types of Plug Gauges
1. Solid type. For sizes up to 10mm. (Refer Fig. 9.17)
2. Renewable type (Taper inserted type). For sizes over 10mm and up to 30mm. (Refer Fig.
9.18)
3. Fastened type:
49
(a) Double – ended: For sizes over 30mm and up to 63mm
(b) Single-ended: For sizes over 63mm and up to 100mm (Refer Fig. 9.20).
4. Flat type. For
100mm and up
(Refer
Fig.
sizes
to
9.22).
50
over
250mm.
Fig. 9.24
5. Progressive type. For relatively short through hole. It has both the ends on one side of the
gauge as shown in Fig. 9.21.
6. Pilot Plug gauge. To avoid jamming of the plug gauge inside of the hole pilot groove type
gauge (Fig. 9.25) may be used. In pilot plug gauge there is first a small chamber, then a
narrow ring or pilot-its diameter being equal to that of the body of the gauge, the pilot is of
the nature of an ellipse in respect to the hole. It touches at two points across the major axis
which is the diameter of the plug on entering the hole. If the pilot enters the hole it is
sufficiently large for the rest of the gauge to enter. The chamber behind the pilot lifts the
gauge into link, making jamming impossible. The advantages of such a gauge are that the
operator can work even with less care and there is saving in time.
Pilot Plug Gauge
7. Combined dual purpose limit gauge. Combined plug gauge combines both the GO and
NO-GO dimensions in a single member. Thus a single gauge may be used to check both the
upper and lower limits. It consist of a spherical end A of the diameter equal to the lower
limit. A spherical projection B of the outer edge of the spherical member (Refer Fig. 9.26) is
arranged so that the spherical surface B and the diametrically opposite part on the spherical
surface is equal to the maximum limit.
For checking the hole by combined limit gauge, for ‘GO’ limit the gauge is inserted into the hole
with the handle parallel to the axis of the hole. For checking the hole the ‘NO- GO’ limit, the gauge
is tilted so that the spherical projection B is normal to the hole. The gauge in this position should
not enter the hole.
51
The plug gauges are marked with the following on their handles for their identification:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Nominal size,
Class of tolerance
The word Go on the Go side
The words NOGO (or Not- Go) on the Not-Go side
The actual value of the tolerance
Manufacturer’s trade mark.
A red colour band near the Not-Go end to distinguish in from the Go-end.
Snap, Gap or Ring Gauges
Snap gauges, Gap gauges or Ring gauges are used for checking the shafts or male components.
Snap gauges can be used for both cylindrical as well as non-cylindrical work or compared to ring
gauges which are conventionally used only for cylindrical work. To Go snap gauge is the size
corresponding to the high limit of the shaft, while the ‘NO GO’ gauge corresponds to the low
limit. Double – ended snap gauges can be conveniently used for checking sizes from 3 mm to
100mm and single- ended progressive type snap gauges are suitable for sizes from 100mm to
250mm. The gauging surfaces of the snap gauges are hardened up to 750 HV and are suitably
stabilized, ground, and
lapped. Ring gauges are
available in two designs,
‘GO’ and ‘NO-GO’. These
are designated by ‘GO’
and ‘NO-GO’ as may be
applicable, the nominal
size, the tolerance of the
work piece to be gauged,
and the number of the
standard allowed.
52
Adjustable Type Gap Gauges
In case of fixed gap gauges, no change can be made in the size, range, whereas in adjustable
gauges the gauging anvils are adjustable endwise in the horse-shoe frame. Thus, a small change
within
about
0.002mm can be
made in the size
range. For example,
suppose gauge is
used to check a
50mm for shaft. If
for some reason the
tolerance is changed
to, say, a tolerance
grade of f8 or f6, the
same gauge can be
used
after
adjustment. Also the
anvils
of
such
gauges can be reset
with the help of slip
gauges, by means of
independent
and
finely
threaded
screws provided at
the back end. After
resetting they can be
finally locked in
position by means of
clamping
screw.
Fixed gauges are less
expensive initially,
but they do not
permit adjustment to
compensate for wear
and can also be used
over a small range of
different setting.
53
Fig9.29
Fig9.30
Fig.9.31
Fig.9.32
Taylor’s Principle of Gauge Design.
54
It state that (1) GO gauges should be designed to check the maximum material limit, while the
NO-GO gauges should be designed to check the minimum material limit.
Now, the plug gauges are used to check the hole, therefore the size of the GO plug gauge
should correspond to the low limit of hole, while that of NO-GO plug gauge corresponds to the
high limit of hole.
Similarly, the ‘GO Snap gauge’ on the other hand corresponds to the high limit of shaft, while
‘NO-GO Snap’ gauge corresponds to the low limit of shaft.
The difference in size between the GO and NOGO plug gauges, as well as the difference in size
between GO and NO-GO Snap gauges is approximately equal to the tolerance of the tested hole or
shaft in case of standard gauges.
(2) ‘GO’ gauges should check all the related dimensions (roundness, size, location etc).
Simultaneously whereas ‘NO-GO’ gauge should check only one element of the dimension at a
time.
According to this rule, GO plus gauge should have a full circular section and be of full length of
the hole it has to check. This ensures that any lack of straightness, or roundness of the hole will
prevent the entry of full length GO-plug gauge. If this condition is not fulfilled, the inspection of
the part with the gauge may give wrong give wrong results.
For example, suppose the bush to be inspected has a curved axis and a short ‘GO’ plug gauge is
used to check it. The short plug gauge will pass through all the curves of the bent bushing. This
will lead to a wrong result that the work pieces (hole) are within the prescribed limits. Actually,
such a bushing with a curved hole will not mute properly with its mating part and thus defective.
A GO plug gauge with adequate length will not pass through a curved bushing and the error will
be detected. A long plug gauge will thus check the cylindrical surface not in one direction, but in a
number of sections simultaneously. The length of the ‘GO’ plug gauge should not be less than 1.5
times the diameter of the hole to be checked.
55
Fig. 9.34
Now suppose the hole to be checked has an oval shape While checking it with the cylindrical
‘NOT GO’ gauge the hole under inspection will over lap (hatched portion) the plug and thus will
not enter the hole. This will again lead to wrong conclusion that the part is within the prescribed
limits. It will be therefore more appropriate to make the ‘NOT GO’ gauge in the form of a pin as
shown in Fig. 9.35.
The uses, characteristics and classification of a comparator.
(i) Uses of Comparator
The various ways in which comparators can be used are:
1. Laboratory Standards: Comparators are used
as laboratory standards from which working or inspection gauges are sent and co-related.
2. Working Gauges: They are also used as
working gauges to prevent work spoilage and to maintain required tolerance at all important
stages of manufacture.
3. Final Inspection Gauges: Comparators may be used as final inspection gauges where
selective assembly, of production parts is necessary.
4. Receiving Inspection Gauges: As receiving
inspection gauges comparators are used for checking parts received from outside sources.
5. For checking newly purchased gauges: The use of comparators enables the checking of the
parts (components in mass production at a very fast rate)
(ii) Essential characteristics of a good comparator
56
1. Robust design and construction: The design and construction of the comparator should be
robust so that it can withstand the effects of ordinary uses without affecting its measuring
accuracy.
2. Linear characteristics of scale: Recording or measuring scale should be linear and uniform
(straight line characteristic) and its indications should be clear.
3. High magnification: The magnification of the comparator should be such that a smallest
deviation in size of components can be easily detected.
4. Quick in results: The indicating system should be such that the readings are obtained in
least possible time.
5. Versatility: Instruments should be designed that it can be used for wide range of
measurements.
6. Minimum wear of contact point. The measuring plunger should have hardened steel
contact or diamond to minimize wear effects. Further the contact pressure should be low
and uniform.
7. Free from oscillations: The pointer should come rapidly to rest and should be free from
oscillations.
8. Free from back lash: System should be free from back lash and unnecessary friction and it
should have minimum inertia.
9. Quick insertion of workpiece: Means should be provided for lifting the plunger for quick
insertion of work.
10. Adjustable Table: The table of the instrument should, preferably, be adjustable in a vertical
sense.
11. Compensation from temperature effects: The indicator should be provided with maximum
compensation for temperature effects.
12. Means to prevent damage: Suitable means should be provided for preventing damage of
the instrument in the event of the plunger moving through a greater distance than that
corresponding to the range of its measuring scale.
(iii) Classification
A wide variety of comparators are commercially available at present. They are classified
according to the method used for amplifying and recording the variations measured into the
following types.
1. Mechanical comparators
2. Optical comparators
3. Mechanical-Optical comparators
4. Electrical and Electronics comparators
5. Pneumatic comparators
6. Fluid displacement comparators
7. Projection comparators.
8. Multi check comparators
9. Automatic Gauging Machines
10. Electro-Mech. Comparators.
57
In addition to above, comparators of particularly high sensitivity and magnification, used in
standard rooms for calibration of gauge include.
1. The Brookes Level comparator
2. The Eden-Rolt’millionth’ comparator.
The work principle of Johansson Mikrokator
The Johansson Mikrokator
This instrument was first devised by m/s C.F. Johansson and hence the name. It uses a
twisted strip to convert small linear movement of a plunger into a large circular movement of a
pointer. It is therefore, also called as twisted strip comparator. It uses the simplest method for
obtaining the mechanical magnification designed by H.Abramson which is known as ‘Abramson,
movement’.
A twisted thin metal strip carries at the centre of its length a very light pointer made of thin
glass. One end of the strip is fixed to the adjustable cantilever strip and the other end is anchored
to the spring elbow, one arm of which is carried on measuring plunger. The spring elbow acts as a
bell crank lever. The construction of such a comparator is shown in Fig.5.2.
Fig.5.2.Johansson Mikrokator
F.g.5.3 Twisted strip of Mikrokator
A slight upward movement of plunger will make the bell crank lever to rotate.
Due to this a tension will be applied to the twisted strip in the direction of the arrow. This
causes the strip to untwist resulting in the movement of the point. The spring will ensure that the
plunger returns when the contact pressure between the bottom tip of the plunger and the
workpiece is not there, that is, when the workpiece is removed from underneath the plunger.
The length of the cantilever can be varied to adjust the magnification. In order to prevent
58
excessive stress on the central portion, the strip is perforated along the centre line by per
formation as shown in Fig.5.3. The magnification of the instrument is approximately equal to the
dQ
ratio of rate of change of pointer movement to rate of change in length of the strip, i.e.,
. It can
dL
dQ
L
 2 ,
be shown that the magnification of the instrument
dL  n
Where, Q = twist of mid point of strip with respect to
the end
L = length of twisted strip measured along its
neutral axis
 = width of twisted strip and,
n = number of turns
It is thus obvious that in order to increase the magnification of the instrument a very thin
rectangular strip must be used.
Working of a Reed Type mechanical comparator
Reed Type Mechanical Comparator
In reed type mechanical comparator, the gauging head is usually a sensitive, high quality,
dial indicator. The dial indicator is mounted on a base supported by a sturdy column. Fig.5.4
shows a read type mechanical comparator.
The read mechanism is frictionless device for magnifying small motions of the spindle. It
consists of a fixed block. A which is rigidly fastened to the gauge head case, and floating block B,
which carries the gauging spindle and is connected horizontally to the fixed block by read C.
A vertical reeds are
extends a pointer. A linear motion
block vertically causing the
to slide past the vertical reed on
vertical reeds are joined at the
movement causes both reeds
indicated by D. Beyond this joint
of the spindle moves the free
vertical reed on the floating block
the fixed block. However, as the
upper end, instead of slipping, the
swing through an arc.
The scale may be calibrated
indicate any deviation from an
amplification is usually less than
optical lens system. It is available
to 1000.
by means of gauge block to
initial setting. The mechanical
100 but it is multiplied by the
in amplification ranging from 500
The working of a sigma mechanical comparator
Sigma comparator
59
This is a mechanical comparator providing magnification in the range of 300 to 5000. It
consists of a plunger mounted on two flat steel strings
Fig.5.5 Sigma of comparator
This is a mechanical comparator providing manificaton in the range of 300 to 5000. it consists of
a plunger mounted on two flat steel string (diaphragms) this provides a frictionless linear
movement for the plunger. The plunger carries a knife edge, which bears upon the face of the
mounting block of a cross-strip hinge. The cross strip hinge is formed by pieces of flat steel springs
arranged at right angle and is a very efficient pivot for smaller angular movements. The moving
block carries a might metal Y-forked arms. A thin phosphor bronze ribbon is fastened to the ends
of the forked arms and wrapped around a small drum, mounted on a spindle carrying the pointer.
Any vertical displacement of the measuring plunger and hence that of the knife edge makes
the moving block of the cross strip liver to pivot. This causes the rotation of the Y-arms. The
metallic band attached to the arms makes the driving drum and hence the pointer to rotate.
The ratio of the effective length (L) of the arm and the distance (a) of the knife edge from
the pivot gives the first stage magnification and the ratio of the pointer length (l) and radius ( r ) of
the driving drum gives second stage magnification of the instrument. Total magnification of the
L l
instrument is thus    . The magnification of the instrument can be varied by changing the
a r
distance (a) of Knife edge of tightening or slackening of the adjusting screws: The range of
instruments available provides magnifications of x 300 to X 5000, the most sensitive models
allowing scale estimation of the order of 0,0001 mm to be made.
Some important features (advantages) of the sigma comparator are:
60
1. Safety: As the knife edge moves away from the moving member of the hinge and is
followed by it, therefore, if too robust movement of plunger is made due to shock load, that
will not be transmitted through the movement.
2. Dead beat Readings: By mounting a nonferrous disc on the pointer spindle and making it
move in field of a permanent magnet, dead beat reading can be obtained.
3. Parallax: The error due to Parallax is avoided by having a reflective strip on the scale.
4. Constant pressures: The constant measuring pressure over the range of the instrument is
obtained by the use of magnet plunger. On the frame
5. Fine adjustments are possible
Disadvantages: 1. Due to motion of the parts there is a wear in the moving parts. 2. It is not
sensible as optical comparator due to friction of the moving parts.
Fig.5.6 cross strip liver used in sigma comparator.
Advantages and disadvantages of mechanical comparators.
Advantages of Mechanical comparators
1. Cheaper, Mechanical comparators are less costly as compared to other amplifying devices.
2. No need of external agency. These instruments do not require any external agency such as
electricity or air and as such the variations in outside supply do not affect the accuracy.
3. Linear Scale. Usually the mechanical comparators have linear scale.
4. Robust and compact: These instruments are robust and compact in design and easy to
handle.
5. Portable: For ordinary workshop conditions, these instruments are very suitable and being
portable can be issued from the stores.
Disadvantages of Mechanical Comparators
1. Less accuracy (a) Due to more moving parts, the friction is more which reduces the
accuracy.
2. Sensitive to vibrations: The mechanisms in mechanical comparators have more inertia and
this may cause them to be sensitive to vibrations.
3. Faults magnified: Any wear backlash or dimensional faults in the mechanical devices used
will also be magnified.
61
4. Limited range: The range of the instrument is limited as the pointer moves over a fixed
scale.
5. Parallax error: Error due to Parallax are more likely with these instruments as the pointer
moves over a fixed scale.
The working principle of an electrical comparator
Electrical Comparators:
Principle: These comparators depend on their operation on an A.C. Whetstone bridge circuit
incorporating a galvanometer. In these comparators, the movement of the measuring contact is
converted into an electrical signal. This electrical signal is recorded by an instrument which can be
calibrated in terms of plunger movement.
Fig.5.11 Principle of electrical comparator
The principle of an electrical comparator is shown in Fig.5.11. An armature supported on
thin steel strips is suspended between two coils A and B. When the distance of the armature
surface from the two coils is equal, the Whetstone bridge is balanced and no current flows through
its galvanometer. Sight movement of the measuring plunger unbalances the bridge resulting in the
flow of current through the galvanometer. The scale of the galvanometer is calibrated to give the
movement of the plunger. Electrical comparators have minimum moving parts and therefore give
a high degree of reliability. Magnification of the order of X30,000 are possible with these
comparators.
Visual Gauging Heads
The purpose of the visual gauging heads is to give visual inspection using small coloured
signal lamps, of the acceptability of an engineering component with regard to the dimension
under test. Clearly an electrical principle is involved, which may be simply described, as follows,
with reference to Fig.5.12. Vertical displacement of an interchangeable plunger causes movement
of the rod C either to the left or right, as shown in the figure A and B are electrical contacts,
62
capable of precise adjustment in the direction of the arrows, a micrometer device is available.
In the position shown, that is to say with the rod in mid position between the contacts A
and B, the dimension under test is within the limits. If the dimension is oversize, the rod C moves
to the right and makes contact with B. Immediately the top red lamp is illuminated. Likewise if the
dimension is undersize the rod moves to left, making contact with A and illuminating the yellow
lamp.
It may, however, be noted that the actual magnifying device is not shown in the figure;
levers and thin steel strips, together with knife-edge seatings, are employed.
With various detachable plungers, there is practically no limit to the application of this
instrument. Fig.5.12 illustrates the visual gauging of a single dimension, but the same principle
can be applied in measuring the several dimensions simultaneously.
Fig.5.12. Visual gauging head
The Advantages and disadvantages of electrical comparators.
Advantages of electrical comparators:
1. Few number of moving parts: The electric and electronic comparators have few number of
moving parts, and there is less friction and wear.
2. High magnification: It has a wide range of magnification.
3. Not sensitive to vibrations: The mechanism carrying the pointer is very light and not
sensitive to vibrations.
4. Easy to set up and operate.
63
5. Less error due to sliding friction: operation of the instrument on AC supply reduces sliding
friction errors.
6. The instrument is small and compact.
7. The indicating instrument need not be placed close to the measuring unit.
(ii) Disadvantages:
1.
2.
3.
4.
5.
Fluctuation in the voltage or frequency of the electric supply may affect the results.
Heating of coils in the measuring unit may cause zero drift and alter the calibration.
When measuring unit is remote from the indicating unit, reliability is lower.
Cost is generally more than mechanical comparator.
If only a fixed scale is used with a moving pointer than with high magnification a very
small range is obtained.
The working of Solex pneumatic gauge with a neat sketch.
Solex pneumatic Gauges
This instrument was commercially introduced by solex Air Gauges Ltd. It is generally
designed for internal measurement, but with suitable measuring head it can be used for external
gauging also.
Fig.5.15 Solex Pneumatic Gauge
It uses a water manometer for the indication of back pressure. It consist of a vertical metal
cylinder filled with water upto a certain level and a dip tube immersed into it upto a depth
corresponding to the air pressure required. A calibrated manometer tube is connected between the
cylinder and control artifice as shown in Fig.5.15.
If the pressure of the air supplied is higher than the desired pressure, some air will bubble
out from the bottom of the dip tube and air moving to the control volume will be at the desired
constant pressure. The constant pressure air then passes through the control orifice and escape
from the measuring jets when there is no restriction to the escape of air, the level of water in the
manometer tube will coincide with that in the cylinder. But, if there is a restriction to the escape of
air through the jets, a back pressure will be induced in the circuit and level of water in the
manometer tube will fall. The restriction to the escape of air depends upon the variations in the
dimensions to be measured.
64
Thus the variation in the dimension to be measured are converted into corresponding
pressure variations, which can be read from the calibrated scale provided with the manometer.
To find concentricity (roundness of any job at any section).the workpiece may be
revolved around measuring gauge. If no change in reading is there, then it is perfectly round hole.
Similarly the diameter can be noted down at several places along the length of bore and thus
tapering of hole is determined. This is method is therefore, best suited for measuring roundness
and taper ness of cylinder bases and gun barrel bores.
The working if Differential comparator
Differential Comparator
It is the balanced circuit type of air gauge. Fig.5.16 shows a differential comparator.
Compressed air from a suitable source, after passing through air-drier and filter is regulated for
constant pressure by a pressure regulator. The air flows into two channels each of which has
control orifice O1 and O2. From the control artifice O1, air flows to the measuring head where it
meets further restriction of workpiece or the master setting. The restriction of the workpiece builds
up back pressure. At the same time, other half of the air is flowing through the other control
orifice O2 to the reference jet on. By closing or opening the valve of reference jet O m, the pressure in
the space between O2 and Om is regulated codjusted to match the back pressure from the
measuring jets, which is sensed by the pressure indicating device fitted across the two channels as
shown. At this adjustment of the reference jet, the preference indicator would indicate equal
pressure in the two channels and hence read zero on the scale. The zero setting (adjusting of
reference jet Om) is
done with master
workpiece whose
dimension is exact
nominal size.
Fig. 5.16 Differential circuit.
Now, the variation of the dimension at the measuring head will cause change of back
pressure in channel A. This pressure will be different from the mean pressure which has been
already set in the channel B (by reference jet. Now the difference of pressure of the two channels
will be indicated device which can be directly calibrated in terms of variation of dimension from
the mean dimensions. The instrument is thus based on the measurement of differential pressure
65
and is called as differential comparator.
Advantages and disadvantages of pneumatic comparators.
Advantages of pneumatic Comparators
1. It is possible to obtain high degree of magnification (30,000 : 1) or more coupled with good
stability and readability.
2. The gauging member does not come in contract with the part to be measured and hence
practically no wear takes place on gauging member.
3. It has few number of moving parts and in some cases none. Thus the accuracy obtainable is
more due to absence of friction and less inertia.
4. Measuring pressure is very small and the jet of air helps in cleaning the dust, if any, from
the part to be measures.
5. The indicating instrument can be remote from the measuring unit.
6. It is very suitable for measuring diameter of holes whose the diameter is small compared
with the length.
7. It is probably the best method to determine the loyalty and taperness of circular holes.
Disadvantages:
1.
2.
3.
4.
5.
Limited range of measurement is available with these comparators.
It gives low speed of response compared with electrical magnification system.
It requires elaborate auxiliary equipment such as accurate pressure regulator.
The scale is generally not uniform.
When indicating device is the glass tube, then high magnification is necessary in order to
avoid the meniscus errors.
6. The apparatus is not easily portable.
7. Different gauging heads are required for different dimensions.
Explain the uses of Sine bar
1. Locating any work to a given angle: To set the given angle, the surface plate is assumed to be
perfectly flat, so that the surface can be treated as horizontal. One roller of the sine bar is placed on
the surface plate and a combination of slip gauges is inserted under the second roller. Let, h be the
height of slip gauge combination and the sine is to be set at an angle .
Then sin  = h/l, where l is the distance between the centre of the rollers. Thus knowing , h
can be found out and any work could be set at this angle, as the top face of the sine bar is inclined
at angle  to the surface plate. For better results, both the rollers could also be placed on slip
gauges of height h1 and h2 respectively,
sin  
h2  h1
l
66
Fig.6.9
2. Checking or measuring unknown angle:
(a) When component is of small size. For measuring unknown angle it is necessary to first find the
angle approximately with the help of a bevel protractor. The sine bar is then set up at that nominal
(approximate) angle on a surface plate by suitable combination of slip gauges. The component to
be checked is placed over the surface of the sine bar (if necessary the component may be clamped
with the angle plate). The dial gauge is then set at one end of the work and moved along the upper
surface of the component. If there is a variation in parallelism of the upper surface of the
component and the surface plate, it is indicated by the dial gauge. The combination of the slip
gauges is so adjusted that the upper surface of the component is truly parallel with the surface
plate.
Fig.6.10
h
The angle of the component is then calculated by the relation   sin 1  
 L
The perfect adjustment of slip gauge combination requires too much time, so the variation
in the parallelism of the upper surface of the component and the surface plate indicated by the dial
gauge is converted into corresponding angular variation. If ‘dx’ is the variation in parallelism over
h
a distance ‘x’ the corresponding variation in angle   sin 1  
 L
b. When the component is of large size/heavy. In such cases, the component is placed over a
surface plate. The sine bar is placed over the component as shown in Fig.6.11. The height over the
rollers can then be measured by a vernier height gauge; using a dial test gauge mounted on the
anvil of height gauge to ensure constant measuring pressure.
67
The anvil of height gauge is adjusted with probe of dial test gauge showing same reading
for the topmost position of rollers of sine bar. The height gauge is thus used to obtain two
readings for either of the rollers of sine bar. If ‘h’ is the difference in the heights and T distance
h
between the roller centres of the sine bar, then   sin 1   .
 L
Another method of determining angle of large size part is shown Fig.6.12. The component
is placed over a surface plate and the sine bar is set up at approximate angle on the component so
that its surface is nearly parallel to the surface plate. A dial gauge is moved along the top surface
of the sine bar to note the variation in parallelism. If ‘h’ is height of the combination of the slip
gauge and ‘dh’ the variation in parallelism over distance ‘L’ then,
h
  sin 1  
 L
Fig.6.12
The limitations and source of errors in sine bar.
Imitations of Sine Bars
Sine bar is fairly reliable for angles less than 15o, and becomes increasingly inaccurate as the
angle increases. It is impractical to use sine bars for angle above 45o.
(ii) It is physically clumsy to hold in position.
(iii) Slight errors of the sine bar cause larger angular errors.
(iv) A difference of deformation occurs at the point of roller contact with the surface plate and to
the gauge blocks.
(v) The size of parts which can be inspected by since bar is limited.
(i)
Sources of Error in Sine Bars
The difference sources of errors in angular measurement by a sine bar are:
68
1.
2.
3.
4.
5.
6.
Error in distance between roller centres.
Error in slip gauge combination used for angle setting.
Error in parallelism between gauging surface and plane of roller axes.
Error in equality of size of rollers and cylindrical accuracy in the form of the rollers.
Error is parallelism of roller axes with each other.
Error in flatness of the upper surface of the bar.
The modifications of sine bar.
Sine Centre: Due to difficulty of mounting conical work easily on a conventional sine bar, sine
centres are used. Two blocks as shown in Fig.6.13 are mounted on the top of sine bar. These blocks
accommodate centres and can be clamped at any position on the sine bar. The centres can also be
adjusted depending on the length of the conical work-piece, to be held between centres. Sine
centres are extremely useful for the testing of conical work, since the centres ensure correct
alignment of the work-piece. The procedure for its setting is the same as that for sine bar.
Fig.6.13
Sine Table: The sine table is the most convenient and accurate design for heavy work-piece. The
equipment consist of a self-contained sine bar, hinged at one roller and mounted on its datum
surface. The table is quite rigid one and the weight of unit and work-piece is given fuller and safer
support. The table may be safety swing to any angle from 0 to 90 0 by pivoting it about it hinged
end. Due to the work being held axially between centres, the angle of inclination will be half the
included angle of the work. The use of since centres and sine table provides a convenient method
of measuring the angle of a taper plug gauge.
69
The working principle of angle Dekkor
Angle Dekkor.
This is a type of auto-collimator. It consists of microscope, objective (collimating) lens and
two scales engraved on a glass screen which is placed in the focal plane of the objective lens. One
of the scales, called datum scale, is horizontal and fixed. It is engraved across the centre of the
screen and is always visible in the microscope eye-piece. Another scale is an illuminated vertical
scale fixed across the centre of the screen and the reflected image of the illuminated scale is
received at right angles to this fixed scale, and the two scales, in the position intersect each other.
Thus the reading on illuminated scale measures angular deviations from one axis at 90 o to the
optical axis, and the reading on the fixed datum scale measures the deviation about an axis
mutually perpendicular to the other two.
Figure. Angle dekkor
70
Thus, the changes in angular position of the reflector in two planes are indicated by
changes in the point of intersection of the two scales. Readings from scale are read direct to 1’
without the use of a micrometer.
The uses of angle dekkor in combination with angle gauges.
(i) Measuring angle of a component:It may be made clear that angle dekkor is capable of measuring small variations in angular
setting, i.e. determining angular tilt. In operation the measuring principle is that of measurement
by comparison; the angle dekkor is set to give a fixed reading form a known angle (i.e. using
known angular standards to obtain a zero reading). (Refer Figure)
Thus first the angle gauge combination is set up to the nearest known angle of the
component and the angle dekkor is set, (using special attachment and link), such that zero reading
is obtained on the illuminated scale. The angle-gauge build up is then removed and replaced by
the component under test, a straight-edge being used to ensure that there is no change in lateral
positions. The new position of the reflected scale with respect to the fixed scale gives the angular
tilt of the component from the set angle (Refer Figure).
Figure. Measuring
(ii) To obtain precise
operations.
angle of a component.
angular
setting
for
71
machining
We will consider an example of milling a slot at a precise angle to a previously machined
datum face. A parallel bar is used as a datum face, the component being securely clamped when in
close contact with it parallel bar is positioned on the table of milling machine with the aid of angle
dekkor. The setting-up technique is illustrated in Figure. Wit the aid of this surface as reference,
the angle dekkor is set up such that zero reading is obtained; in other words, the axis of the optical
beam is truly at 90o to the table feed. Then build up the combination of angle gauges to the exact
value , i.e. the inclination of the slot to the milled on the component. The angle gauges along with
the parallel bar are placed on the table and adjusted in position such that the angle dekkor shows
zero reading when viewing the flat surface of the angle gauge combination. It means that the
angular inclination between the datum face of the parallel bar and the feed direction of the table is
now o. The parallel bar is firmly clamped in this position, a check being made to ensure that no
movement has taken place during clamping; a few gentle taps will soon allows a zero reading on
the angle dekkor to be regained. Finally, now the workpiece can be clamped on milling machine
table, in closed contact with this pre-set parallel bar.
(iii) Checking the sloping angle of a V-block:The set up for checking the sloping angle of V-block is illustrated in Figure. The principle
consists of comparing the reading obtained from the polished slip gauge in close contact with the
work-surface, and a zero reading obtained from the angle-gauge build-up.
Figure
(iv) To measure
taper gauge:-
the angle of cone or
A simple set-up for this purpose is shown in Figure. The instrument is first set for the
nominal angle of cone on a combination of angle gauges or on a sine bar set to the nominal angle.
The cone is then placed in position with its base resting on the surface plate. A slip gauge or other
parallel reflector is held against the conical surface as no reflection can be obtained fro ma curved
surface. Any deviation from the set angle will be noted by the angle dekkor in its eye-piece and
indicated by the shifting of image of illuminated scale, whose reading while setting with angle
gauge is noted down before hand.
The working principle and uses of vernier bevel protractor.
72
Vernier Bevel Protractor:Vernier bevel protractor is the simplest angle measuring instrument. It consists of
1.
2.
3.
4.
5.
Main body
Base plate stock
Adjustable blade
Circular plate containing Vernier scale
Acute angle attachment
Figure shows a Vernier bevel protractor with acute angle attachment. The body of the
Vernier Bevel protractor is designed in such a way that its back is flat and there are no projections
beyond its back. The flatness of the body is tested by checking the squareness of blade with
respect to base plate when the blade is set at 90o.
Figure. Vernier Bevel Protractor
The base plate is attached to the main body, and an adjustable blade is attached to a circular
plate containing Vernier scale. The main scale graduated in degrees is provided on the main body.
The adjustable blade is capable of rotating freely about the centre of the main scale engraved on
the body of the instrument can be locked in any position. An acute angle attachment is provided
at the top as shown in the figure for measuring acute angles. The base of the base of the base plate
is made flat so that it could be laid flat upon the work and any type of angle measured.
The blade can be moved along throughout its length and can also be reversed. It is about
150 or 300 m long, 13 mm wide and 2 mm thick. Its ends are beveled at angles of 45 o and 60o. The
acute angle attachment can be readily fitted into the body and clamped in any position.
The bevel protractors are tested for flatness, squareness, parallelism, straightness, etc.
73
Figure. The principle of the vernier protractor
As shown in Figure the main scale is graduated in degrees of arc. The Vernier scale has 12
divisions each side of the centre zero. These are marked 0-60 minutes of arc, so that each division
equals 1/12 of 60, that is 5 minutes of arc. These 12 divisions occupy the same space as 23 degrees
1
11
on the main scale. Therefore, each division of the Vernier is equal to :
of 23o or 1 .
12
12
Since two divisions on the main scale equals 2 degrees of arc, the difference between two
divisions on the main scale equals 2 degrees of arc, the difference between two divisions on the
11
1 o
main scale and one division on the vernier scale is 2o - 1
=
or 5 minutes of arc.
12 12
Uses of the Vernier Bevel Protractor
Figure shows the various uses of bevel protractors.
Figure (a) Use of bevel protractor for checking inside beveled face of a ground surface.
74
Figure(b)Use of bevel protractor for checking ‘V’ block
(c) Use of Vernier protractor for measuring acute angle
The various methods of taper measurements.
Taper Measurement
Use of Precisions Balls and Rollers:Precision balls and rollers are used to determine both linear and angular dimensions in
conjunction with gauge blocks. These are made of good quality steel and are hardened and
tapered. The length for the roller is equal to the diameter. The balls and rollers are available in
sizes ranging from 1 to 25 mm diameter. The use of precision balls and rollers for determining
both linear and angular dimensions is explained with the held of following examples:
1. Angle of the right – tapered piece can be measured by using two rollers of different sizes, slip
gauges and a dial indicator. The two rollers whose diameters are known and slip gauges are
placed on a surface plate as shown in Figure. The rollers (discs) may be clamped in position
against an angle plate by c- clamps. The work is then placed on top of rollers and clamped against
the angle plate by C-clamp. If the angle of the piece is all right, then the top edge will be parallel to
surface plate and the
dial indicator will
show no variation
when traversed
along its surface.
Figure
75
With reference to Figure from triangle O1 A O2
d 2 d1

O1 A
tan /2 =
 2 2
AO2 1  d1  d 2
2 2
i.e.,
tan /2 =
d 2  d1
2l  d1  d 2
…(i)
Where l = length of slip gauge pile and d1 and d2 are diameters of rollers.
From equation (i) the slip gauge length
d 2  d1
d d 
2
L=
 1 2 
tan  / 2  2 
…(ii)
Thus, initially the length of the slip gauges is calculated by the above equation and the
rollers are placed just in contact with the slip gauges.
Checking the angle of taper using rollers, micrometer and slip gauges.
Figure
Figure
shows the method of
checking the angle of a taper plug gauge using rollers, micrometer and slip gauges. Taper plug is
placed on a surface plate. First two rollers of equal diameters are placed toughing on the opposite
sides of the lower surface of the plug on the slip gauge combinations of equal heights (H 1). The
distance (M1) between the ends of the roller is measured with a micrometer. Then the rollers are
placed on slip gauge combinations of height (H2) touching on the opposite sides of the top portion
of the plug. The distance (M2) between the ends of the roller in this new position is again
measured by means of micrometer. The half the taper angle of the plug is then calculated as
follows:
If d = diameter of roller, then
76
 M 2  d   M 1  d  
 2    2  

 


tan
 
2 
d 

 H 2  d / 2    H1  2  



thus,
M 2  M1
tan  /2=
2  H 2  H1 
To check the angle of a taper hole.
Figure shows the arrangement for checking the internal taper of a taper ring gauge using
two precision balls of different sizes. The taper ring gauge is placed on a surface plate and a small
ball of radius ‘r1’ is inserted in the ole close to the small end of the taper.
Two piles of slip gauges of equal heights are then placed on the surface plate on either sides
of tapered ring gauge. A depth micrometer is then used to determine the distance from the top
face of the gauge blocks to the surface of the precision ball. Then, a bigger ball of radius r 2 is
placed in the hole near the big end of taper, and the distance from the top face of the gauge blocks
to the surface of the bigger precision ball is determined with the depth micrometer. From Figure.
Figure
O2O1S = /2
Where
 =
sin  / 2 
angle of tapered hole
02 S
0102

r2  r2
centre distance of balls (01  02 )

r2  r1
r2  r1

h2  r2  h1  r1 h2  h1  r2  r1
77
Measuring of included angle of an internal dovetail
Dovetail slides are widely used in machine tool construction. The sloping sides of dovetail
slide act as guide and prevent the lifting of the female mating part during sliding operation.
This angle can be measured by using two rollers of equal size, slip gauges and a
micrometer. The two rollers of equal diameters are placed, one each at the two corners and
distance l1 is measured across the rollers with a micrometer. Then the rollers are placed on two
sets of equal size slip gauge blocks and the distance l2 is measured. It should be noted that the
rollers do not extend above the top surface of dovetail. Let the height of slip gauges be h, then
l l
tan   2 1 .
2
h
Measuring External Dovetail Slide
Figure shows an external dovetail slide with angle of dovetail . To check the width of
opening  as shown in figure, two rollers of equal diameter d are placed one each in the two
corners. Then the length l is obtained by trail and error with the help of slip gauges or end bars if l
I greater than 250 mm. Then the width ‘’ can be calculated by the relation:
 = l + d + d cot /2
Figure
19. Explain why it is not
measuring angles more than 45o.
preferred to use sine bar for
The accuracy of the angle set by a sine bar depends upon the errors in its important
dimensions such as error in distance between roller centres, errors in combination of slip gauges
used for setting, error in parallelism between the gauging surface and plane of roller axes, etc.
The slip gauge combination (h) required to set an angle () is given by,
h = L sin 
The effect of error in spacing of roller centres (dL) or error in combination of slip gauges
(dh), on angular setting accuracy can be obtained by partial differentiation of the above equation.
Now,
h = L sin 
78
Therefore,
i.e.,
i.e.,
i.e.,
i.e.,
i.e.,
But
Therefore,
dh
dL
 sin  .
 L cos 
d
d
dh = sin . dL + L cos . d
dh – sin  dL = L cos . d
dh
sin dL
d 

L cos  L cos 
dh
dL
d 
 .tan 
L cos L
dL 
 dh
 tan  


 L cos  L 
L sin  = h
 dh dL 
d  tan    
L 
 h
Figure. Angular setting errors in a sine bar
From the above equation we can see that the effect of error in roller spacing or slip gauge
combination is a function of tangent of angle ‘’. As the angle ‘’ increases, the error (d) in the
angular measurement increase and above 45o valve it is more significant, because above 45o the
value of tan  is greater than unity and increases progressively in the spacing of rollers a
nominally 250 mm sine bar on the angular setting. It is seen that below 45o the effect is small.
However, above 45o the effect becomes progressively more significant. Thus, in general, it is
preferable not to use the sine bar for measuring angles larger than 45o if high accuracy is required:
Uhe use of sine bar for measurement of taper plug gauge.
79
Figure illustrates the use of sine bar for measurement of angle of a taper plug gauge.
The sine bar is set up on a surface plate to the nominal angle of the taper plug gauge and
clamped to an angle plate. Taper plug gauge is placed on the sine bar and prevented from
slogging down by a stop plate. The axis of the taper plug gauge is aligned with the bar axis. A dial
gauge, supported in a stand is set at one end of the plug gauge and moved to the other end, and
the difference in the readings is noted.
Let ‘dx’ be the difference in the readings of the dial gauge over a distance ‘x’. Let ‘h’ be the
height of the combination of the slip gauges used and ‘L’, distance between the roller centres.
h
Then, nominal angle  = sin-1   and variation in the angle,
 L
 dx 
d  sin 1  
 x 
Therefore, actual angle of the taper plug gauge,
h
 dx 
=   d = sin    s in 1  
 x 
 L
The angle of taper and minimum diameter of an internal taper from the following readings:
Diameter of bigger ball – 10.25 mm
Diameter of smaller ball – 6.07 mm
Height of top of bigger ball from datum–30.13mm
Height of top of smaller ball from datum = 10.08 mm.
Figure
80
Now, d1 = 10.25 mm, d2 = 6.07 mm, h1 = 30.13 mm and h2 = 10.08 mm
sin  / 2 
O1 A
O1 A

O1O2 BD  O1 B  O2 D
d1 d 2

d1  d 2
2
2


d 
d  2h1  d1  2h2  d 2
h1  1   h2  2 
2 
2
d1  d 2
Therefore sin /2 =
2  h1  h2    d1  d 2 
Sin /2 =
4.18
35.92
and /2 = 6.6826o,  = 13.3652o
To calculate minimum diameter (d) of internal taper:
From triangle O2DE
d2
d /2
O1 E
sin  / 2 
 2
d
O2 D
h2  2
2
d d
 2
2h2  d 2
Now,
12 = 6.6826
Therefore, sin 6.6826 =
and
6.07  d
2  10.08  6.07
d = 4.43 mm
Thus, Angle of taper = 13.3652o
and minimum diameter of taper = 4.43 mm.
81
UNIT – III
FORM MEASUREMENT
The elements to be taken into account while measuring the Screw threads to determine the
accuracy
Major diameter, Minor diameter, Effective diameter, pitch, thread form
Following in relation to screw threads.
1. Periodic Errors :
Periodic errors are those which vary at regular intervals.
2. Druken thread :
If the periodic error occur every revolution, then the thread is known as Drunkeh Thread.
Standards do not specify tolerance on pitch
The error in pitch have the effective of virtually increasing the effective diameter of an
external thread and decreasing that of an internal thread, and the simplest way of controlling
them in to fix a limit for main equivalent in terms of the effective diameter.
The effect of the lead angle on a three wire measurement for an effective diameter of a screw
thread.
If the lead angle in lack as in case of worms, quick transversing lead screw etc. the ordinary
rule or formula for checking the effective diameter by the three wire method is inaccurate and the
effect of the lead angle on the position of the wires should e taken into account. This effect
depends not only upon the size of the lead angle, but to some extent upon the size of the lead
angle, but to some extent upon the degree of accuracy required In checking the effective diameter.
The error in measurement in about 0.0125mm when the lead angle is 41/2" for 60 single thread.
For lead angle, above 41/2 degree the compensation for rake and compression must be
taken in to account.
Reason for using three wire.
a) Generally three wires are used to measure a screw thread with a hand micrometer and
only two wires when using a floating carriage machine for same purpose.
The use of three wires for measurement, when using a hand micrometers in essential,
because two wires on one side help in aligning the micrometer square to the thread and the third
placed on the other side is essential for taking the readings
82
In a floating carriage machine the alignment is inherent and thus the purpose in served with two
wires only.
b) A screw is never placed on centers to measure its major diameter whereas for measuring
the effective or minor diameters it in placed on the centers
While measuring the major diameter, the micrometer "Sine error" which are likely to be
introduced if the thread on the centers and the micrometer are misaligned. Therefore for
measuring major diameter, the screw thread should not be placed on the centers. In the
measurement of effective diameter and minor diameter, VECS are used and with the help of wires
or three only a negligible error can be introduced by such misalignment.
The pitch of a screw thread.
The pitch of a thread is d as the distance between corresponding points on the adjacent
thread forms, measured parallel to the thread axis. In the same plane and on the same side of the
axis.
Course thread .
When the lead relative to the diameter is large, the thread is known as course thread.
The two corrections applied in the measurement of effective diameter by the method of wires
1. Rake correction
2. Compression correction
Rake Correction.
The rake correction becomes necessary because in the determination of the formula for
effective diameter by three wire method, a plane axial section of the thread had been considered
and it in assured that the wire touches each flank of the thread in this plane. This occupation in
true for angular grooves with zero helical angle, but not for screw thread which have a helix; and
it the later case wire lies parallel to the helix at the radius of the point of contact. The points of
contact on opposite flanks will lies on opposite gides of the mean axial plane. As a result of this,
the wire lies slightly farther from the thread axis than what has been assured and a correction has
to be applied to the effective diameter as measured and calculate. This correction is different for
difference effective diameter being measured.
A general formula for calculating rake correction is,
C
Cos x / 2
22
Cot x/2 =
l2 A 2 (l  A sin x/2+A 2Sin2 x)
d
83
C=
X/2 =
d=
A=
Rake Correction
Half the included angle the thread
Diameter of wire
Constant = d/T+d
T = Diameter under the wire.
This correction is always subtracted from the measured diameter.
Compression correction.
As the micrometer exerts some force on the wire while measuring the effective diameter of
the thread, some degree of compression takes place and as a result the diameter observed in less.
This correction in, therefore, added to the value of diameter obtained. This correction is more
pronounced on fine thread and those whose inclined angle is small, example B, A threads. For
measuring forces up to about 350gm, the correction in with in 0.0025mm for thread diameter
down to about 3.5mm and only 0.04mm at 1mm diameter. For larger threads, for the some
measuring force, the compression correction in less and can be ignored.
E2 / 3
Compression correction = 0.01 1/ 3 mm
E
E = Measuring force in Newton’s.
The classification of Thread gauges.
Thread gauges are mainly classified in to two groups.
1. Working gauge (or) Inspection gauge
2. Setting gauge (or) checking gauge
1. Working gauge :
It is used to check the product as it is being manufactured and the inspection gauge. Which
are used to determine the acceptance or rejection of the product.
2. Setting gauge :
Which are generally plug gauges with the help of which adjustable thread ring gauges,
thread snap gauges and other thread comparator are set for checking size of master or basic
gauge.
The various forms of thread gauges
1. Plug screw gauges
2. Ring screw gauges
3. Caliper gauge
84
4. Screw thread gauge
The various method of specifying the pitch of a gear
Three different methods for specifying the pitch of a gear are
1. base pitch 2. circular pitch 3. Diameter pitch.
In all the above, only base pitch is directly measured and the other two are computed (or)
calculated.
Base pitch = circular pitch x Cosine of pressure angle.
The base pitch of a spur gear is so important
Base pitch is of importance in the case of interchangeable gears as all gears generated from
the same basic rack have the same base pitch.
The case of involutes gears the Chordal thickness, merits and demerits
Chordal Thickness :
It is the Chordal tooth thickness at the base circle. It is denoted by "M".
 90 
M = mT sin 

 T 
Merits and Demerits :
The chordal thickness element is simple to understand, easy to measure and is correct for
tooth forms other than involutes. For these reason it is not delay used, but as can be seen from the
mathematical formula it depend upon the number of teeth in the gear.
Involutes gears the base pitch, its merit and demerits
The base pitch "Pn" a gear in the circular pitch of the teeth measured on the base circle.
-----------------The base pitch is an important gear tooth parameter, but can not easily be gauged as can the
chordal thickness or the constant Chord elements. However, it can be measured.
The tooth thickness in the case of a simple spur gear.
The tooth thickness is d as the length of the are of the pitch circle between opposite facts of
the same tooth.
85
Some special features of a gear tooth Vernier Caliper.
A gear tooth vernier has a length measuring Caliper and also has a vernier depth gauge to
fix the depth at which the length in to be measured.
Accuracy of gear tooth vernier in the vanity of 0.05mm.
A gear tooth vernier actually measure the d tooth thickness.
The gear tooth Vernier measures the Chordal thickness which is not a tooth thickness as per
definition It "M" is the Chordal thickness, then the thickness or actual tooth thickness (M') in
computed by
A gear tooth Vernier may be set to one of two possible pains of dimensions for measuring tooth
thickness. Which of the settings has the widest application and why
A gear tooth Vernier may be set to measure the tooth thickness in two ways.
1. To measure tooth chordal thickness at pitch line.
2. To measure the Chordal thickness as constant chord. Out of the above two ways, the following
reasons
a) The depth form the tip of the tooth (ie "n") at which the measurement in taken is independent
of the number of teeth in the gear. Also the measured dimensions, ie constant chart (m) in
independent of the number of teeth
b) No separate setting are required for the gears of one set but having different number of teeth.
c) The vernier setting can be easily educated.
Gear tooth thickness
The gear tooth thickness is d as the are length of the pitch circle of one tooth.
The chordal thickness of a gear tooth can be found by a gear Caliper provided with sliding
vernier at 90 degree. Adjustment can be made to the jaws that are integrate with the vernier slides
so that the thickness of a gear tooth can be gauged at any pre-determined distance below the tip of
the tools. It is usual to measure Chordal thickness between those points of a tooth that lie on the
pitch circles and redial distance from those points to the tip of the teeth. If this dimension is "M",
then the arc length M' is given by
Expected order of accuracy in a gear tooth Vernier
The expected order of accuracy in a gear tooth vernier is in the vicinity of 0.05mm.
The various methods for determining the gear tooth thickness
86
Various methods available for a gear tooth thickness measurement are the following.
1. The Chordal thickness
2. The constant Chord
3. The base tangent
4. Measurement over rollers.
Out of these, the first three utilize the vernier gear tooth.
The gear manufacturing methods.
Gears are generally made by one of the following two methods.
1. Reproducing method
2. Generating method
The sources of error in manufacturing of gears
1.
2.
3.
Error in the manufactured certify tool
Error in positioning the tool in relation to the work
Error in the relative motion of tool and blank during the generating operation.
The Classification of gears.
1) High speed gears
2) High power gears
3) Precision gears
The possible type of error in gears
Adjacent pitch error, cumulative pitch error, profile error, tooth to tooth composite error single and double flank, total composite error - single and double flank, total composite errorsingle and double flank, tooth thickness error, cyclic error, periodic error, run out radial run out ,
Eccentricity, Arial run out, undulation, undulation height, wavelength of an undulation, tooth
alignment error.
Sampling length :
Sampling length is the length over which the surface texture in measured. Sampling
lengths are given in the appropriate Indian and other countries National Standards.
Primary texture : This refers to the roughness of a surface, as opposed to its waviness
(secondary texture)
87
The function and operating of stylus - type surface texture measuring instrument.
Stylus is a fine point, usually diamond, drawn over the surface. The reference plane is
usually generated by a shoe or skied following the crest of the surface. Straight line or radius
attachments may also be fitted. Movement of the diamond stylus are amplified electronically and
traced on a moving chart. An integrating meter also can be used in indicate the Ra value direct.
Disadvantages of the stylus type of instrument.
Its bulk, complexity, relative fragility, high initial COSA limitation to a section of surface.
Statement of roughness.
The roughness statement should include the following information’s.
1.
2.
3.
4.
Range of "Ra" value (or) "N" values
Sampling length
Direction of lay
Production process
Surface finish differs from surface integrity
Surface finish refers to the quality finish or roughness over the surface while surface
integrity refers to the continuity of the plane, that h, there should be no discontinuity of the plane
is the surface is integral.
The basis of selecting a sampling length
The length over which the study is made will affect the value of "Ra", if the waveness is to
fully included, the examination must be over atlas one waveness wavelength. The wavelength for
different processes vary and now standardized based on the experience.
Hence, the sampling length also varies.
"AARH" as applied to surface texture
Average Arithmetic Roughness Height. Its significance is same as C.L.A. or Ra value. The
term is mostly used in Oil Industry Piping material.
Real surface :
It is the surface limiting the body and separating it from the surrounding surface.
Geometrical Surface :
88
It is the Surface prescribed by the design or by the process of manufacture neglecting the
errors of form and surface roughness.
Effective Surface :
It is the close representation of real surface obtained by instrumental means.
Surface texture :
Repetitive or random deviations form the normal surface which form the pattern of the
surface. Surface texture include roughness, waveness, lay and flows.
Flows :
Flows are irregularities which occurs at one place or at relatively infrequent or widely
varying intervals in a surface like scratches, cracks, random blemishes etc.
The methods of measuring surface finish
1. Surface Inspection (or) comparison method
2. Direct Instrument
a) Touch Inspection
b) Visual Inspection
c) Scratch Inspection
d) Microscopic Inspection
e) Surface photograph
f) Micro - Interferometer
g) Wallace surface Dynamometer
h) Reflected light Intensity
Squarness of a try-square .
The term "Squarness" of a try-square refers to the accuracy of the right angle formed by the
outer edges of the blade and stock.
The reversal method used to test the squareness error of an engineer's square.
In the several method for testing the squareness of an engineer in square, a double edged
straight edge is arranged vertical. The square in placed on either side of the straight edge, keeping
in base at equal distance in bulk the cases. Then, the slips are so adjusted which can be just
inserted between the straight -edge and the square at the top of other side. If the straight edge is
not exactly vertical than the till of the straight edge will add to the squareness error when the
square is on one side and subtract from it on the other side. The mean of the apparent errors on
89
both sides then gives the true squareness error.
The reversal method in very accurate. The straight edge need not be exactly vertical and
provided each edge is straight, it need not be parallel, the parallelism error must be checked and
allowed for.
The various error in threads, and their effects.
Errors in threads : In the case of plain shafts and holes, there is only one dimension which has to
be considered (i.e diameter) and errors on this dimension if exceed the permissible tolerance, will
justify the rejection of part. While in the case of screw threads there are at least five important
elements which require consideration and error in any one of these can cause rejection of the
thread. In routine production all of these five elements (major diameter, minor diameter, effective
diameter, pitch and angle of the thread form) must be checked and methods of gauging must be
able to cover all these elements.
Errors on the major and minor diameters will cause interference with the mating thread. Due to
errors in these elements, the root section and wall thickness will be less, also the flank contact will
be reduced and ultimately the component will be weak in strength. Errors on the effective
diameter will also result in weakening of the assembly due to interference between the blanks.
Similarly pitch and angle errors are also not desirable as they cause a progressive lightening
and interference or assembly. These two errors have a special significance as they can be precisely
related to the effective diameter.
Now will consider come errors in detail and some terms.
Drunken Thread : This is the one having erratic pitch, in which the advance of the helix is
irregular in one complete revolution of the thread.
Thread drunkenness is a particular case of a periodic pitch error recurring at intervals of one
pitch. In such a thread, the pitch measured parallel to the thread is not but to a true helix. If the
screw thread be regarded as an inclined plane wound around a cylinder and if the thread be on
wound from the cylinder. (i.e development of the thread are taken) then the drunkness can be
visualized. The helix will be a curve in the case of drunken thread and not a bright line as shown
in fig.
True Thread
Drunken Thread
Pitch
Helix angle
90
II x Mean Dia
It is very difficult to determine such errors and moreover they do not have any great effect on
the working unless the thread is of very large size.
Pitch Errors in Screw Threads : Generally the threads are generated by a point cutting tool. In this
case, for pitch to be correct, the ratio of the linear velocity of tool and angular velocity of the work
must be correct and this ratio must be maintained constant, otherwise pitch errors will occur. If
there is some error in pitch, then the total length of thread engaged will be either too great or too
small, the total pitch error in overall length of the thread being called the cumulative pitch error.
Various pitch errors can be classified as,
1.
Progressive pitch Error : This error occurs when the tool work velocity ratios incorrect
though it may be constant. It can also be due to pitch errors in the lead screw of the lathe or other
generating machine.
The other possibility is by using an incorrect gear or an approximate gear train between work
and lead screw e.g while metric threads are cut with an inch pitch lead screw and a translatory
gear is not available. A graph between the cumulative pitch error and the length thread is
generally a straight line in case of progressive pitch error.
2.
periodic Pitch Error : this repeats itself at regular intervals along the thread. In this case,
successive portions of the thread are either longer or shorter than the mean. This type of error
occurs when the tool work velocity ratio is not constant. This type of error also results when a
thread is cut from a lead screw which lacks squareness in the abutment causing the lead screw to
move backward and forward once in each revolution. Thus the errors due to these cases are pitch
increases to a maximum, then reduces and through normal value to minimum and so on. The
graph between the cumulative pitch error and length of thread for this error will, therefore be of
sinusoidal form.
3.
Irregular Errors : These arise from distributes in the machining setup variations in the
cutting properties of material etc. thus they have no specifics causes and correspondingly no
specific characteristics also.. these errors could be summarized as follows.
91
Erratic Pitch : This is the irregular error in pitch and varies irregularly in magnitude over different
lengths of thread.
Progressive Error : When the pitch of a screw is uniform, but is shorter or longer than its nominal
value, it is said to have progressive errors.
Periodic Error : If the errors vary in magnitude and recur at regular intervals, when measured
from thread to thread along the screw are referred to as periodic errors.
Effect of pitch errors :
An error in pitch virtually increases the effective diameter of a bolt or screw and decreases the
effective diameter of a nut. The meaning of the virtual change in effective diameter is that if any
screw is perfect except for pitch error. It will not screw easily into a perfect ring gauge of same
nominal size until its effective diameter is reduced.
For White worth thread, if sp is the error in pitch then the virtual increase (decrease) in the
effective diameter of the thread in case of bolt (nut) is given by the relation.
Virtual change in effective diameter = 1.921 X ςp. Similarly errors in flank angles also require a
corresponding reduction in the effective diameter if the screw is to fit a perfect ring gauge of the
same nominal size.
It ςθ1 and ςθ2 are the errors flank angles in degrees (regardless of sign), the corresponding
virtual change (increase or decrease) in effective diameter of the thread in case of a bolt or nut is
given by (for Withworth thread) ςE=0.0105 X p (ςθ1+ ςθ2), where p is the normal pitch.
It is assumed that the maximum pitch error over the length of engagement is equally disturbed at
each end of engagement. Increase in effective diameter will obviously be the vertical movement of
flanks necessary to produce coincidence.
It may be mentioned here that effect, of long or short pitch will be same, i.e increase of the
interference between the mating threads, so each will lead to increase in effective diameter nut.
In ∆ABC
ABC = θ = half the angle of thread
Cot θ = BC / AC = (ςEd/2)/( θ p/2), or ςEd = ςp cot θ
Increase in effective diameter = ςp X cot θ.
Since cot 55/2 = 1.921 (for Whitworth), its effect is nearly doubled when the equivalent increase
in effective diameter is calculated.
Similarly the effect of pitch error will be reduce the effective diameter of the screw.
92
Angle Errors : Angle errors on threads may be either due to errors on one or both flanks. Any
error in angle of thread results in interface between the bolt and nut and to accommodate it, the
effective diameter of nut has to be increased. Thus like pitch errors, the angle errors also increase
the virtual effective diameter of a bolt and decrease that of a nut. Assuming that one of the pairs is
correct, it is possible to satisfactorily assemble the thread pairs by modifying the effective
diameter. The effective diameter of an incorrect bolt must be decreased to permit a correct mating
thread to make and similarly the effective diameter of an incorrect nut must be increased.
If (ςθ1+ ςθ2) be equivalent to the errors in the adjoining flank angles of any thread, then the
corresponding correction = Cp((ςθ1+ ςθ2 )
Where C = 0.0100 for unified thread = 0.0105 for Whitworth thread = 0.0091 for British associated
threads = 0.0115 for ISO metric thread p = basic pitch of thread, (ςθ 1+ ςθ2 ) = sum of errors in
adjacent flank angles in degrees (regardless of signs of the errors)
Diameter Errors : Errors of major, minor and pitch diameter and their mutual non-concentricity
give rise to interference and strain in the joint. More forces is required for fitting.
Measurement of Various elements of thread : The methods discussed here are from the point of
view of measurement of gauges, but they can obviously be applied to precise work, threading
tools, taps and hobs etc. we will be dealing with the measurement of most important six elements
i.e major, minor and effective diameters, pitch angle and form of thread.
Measurement of major diameter in screw threads.
Measurement of diameter in screw threads : for the measurements of major diameter of external
threads, a good quality hand micrometer is quite suitable. In taking readings, a light pressure
must be used as the anvils make contact with the gauge at points only and otherwise the errors
due to compression can be introduced. It is however, also desirable to check the micrometer
reading on a cylindrical standard of approximately the same size, so that the zero error etc, might
not come into picture.
For greater accuracy and convenience, the major diameter is measured by bench micrometer.
This instrument was designed by N.P.L to estimate some deficiencies inherent in the normal hand
micrometer. It uses constant measuring pressure and with this machine the error due to pitch
error in the micrometer threads avoided. In order to that all measurements be made at the same
pressure, a fiducial indicator is used in place of the all measurements machine there is no
provision for mounting the work piece between the centers and it is to be held in hand. This is so
because, generally the centers of the work piece are not true with its diameter. This machine is
used as a comparator in order to avoid any pitch errors of micrometers, zero error setting etc. a
calibrated setting cylinder is used as the setting standard.
The advantage of using cylinder as setting standard and not slip gauges etc. is that it gives
93
greater similarity of contact at the anvils. The diameter of the setting cylinder must be nearly same
as the major diameter. The cylinder is held and the reading of the micrometer is noted down. This
is then replaced by threaded work piece and again micrometer reading is noted for the same
reading of fiducial indicator. Thus, if the size cylinder is approaching that of major or diameter,
then for a given reading the micrometer thread is used over a short length of travel and any pitch
errors it contains are virtually eliminated.
If D1
R1
R2
=diameter of setting cylinder
=reading of micrometer on setting cylinder
=Micrometer reading on thread, then major diameter = D1 +(R – R1)
In order to determine the amount of taper, the readings should be taken at various positions
along the thread and to detect the ovality, two or three readings must be taken at one plane in
angular positions.
Major diameter of internal threads: The measurement of the elements of an internal threads is
more cumbersome. Since it is difficult to approach the elements of internal thread, an indirect
approach is followed by making a cast of the thread. The main art thus lies in obtaining a perfect
cast, because once good cast is available the various elements can be measured as for external
threads.
Cast may be made by plaster of paris, dental wax, or sulphur. The part whose internal thread is
to be measured is first cleaned and brushed with a fine oil. The part is then mounted between two
wooden blocks whose upper surface lie about half way up the ring. Cast materials is then poured
to depth less than the radius of part to permit easy removal of cast without screwing it out. After
the plaster is set, it should be taken out without rotating, but by pulling up the middle portion of
the cast. It may be mentioned that taking out of sulphur cast is easier than the plaster. Oiling is not
necessary in case of sulphur cast.
Measurement of minor diameter in screw threads.
Measurement of Minor diameter : This is also measured by a comparative process using small
Vee-pieces which make contact with root of the thread. The Vee pieces are available in several
sizes having suitable radii at the edges. The included angle of the root of the thread. To measure
the minor diameter by Vee pieces is suitable for only Whitworth and B.A threads which have a
definite radius at the root of the thread. For other threads, the minor diameter is measured by the
94
projector or microscope.
The measurement is carried out on a floating carriage diameter measuring machine in which
the threaded work piece is mounted between centers and a bench micrometer is constrained to
move at right angles to the axis of the center by a Vee ball side. The method of the application of
vee pieces in the machine is shown diagrammatically in fig. the dimension of vee piece play no
important function as they are interposed between the micrometer faces and the cylindrical
standard reading is taken.
It is important while taking readings, to ensure that the micrometer be located at right angles to
the axis of the screw being measured. The selected vee are placed head is then advanced until the
pointer of the indicator is opposite the zero marl, and note being made of the reading of the
micrometer is taken.
If reading on setting cylinder with Vee pieces in position = R1 and reading on thread = R2 and
diameter of setting cylinder = D1 then minor diameter = D1 +(R2 – R1).
Readings may be taken at various positions in order to determine the taper ovality.
Before proceedings to
the measurement of
effective diameter, the screw diameter measuring machine is first described in brief here. The
machine is shown. Also refer this figure. For schematic sketch. If consists of three main units. A
base casting carries a pair of centers, on which the threaded work piece is mounted. Another
carriage is mounted on it and is exactly at 90 to it.. On this is provided another carriage capable of
moving towards the centers. On this carriage one head having a large thimble enabling reading
upto 0.002mm is provided. Just opposite to it is affixed anvil which is spring loaded and its zero
position is indicated by a fiducial indicator. Thus the micrometer elements are exactly
perpendicular to the axes of the centers as the two carriages are located perpendicular to each
other. On the fixed carriage the centers are supported in two brackets fitted on either end. The
distance between the two centers the second carriage is adjusted depending upon the length of the
thread job. After job is fitted between the centers the second carriage is adjusted in correct position
to take measurements and is located in position. The third carriage is then moved till the fiducial
indicator is against the set point. The readings are noted from the thimble head. It is now obvious
that the axes of the indicator is specially designed for this class of this work and has only one
index line. Against which the pointer is always to be set. This ensures constant measuring
pressure for all readings. Sufficient friction is provided by the conical pegs to restrain the
movement of carriage along the line of centers. The upper carriage is free to float on balls and
enables micrometer readings to be taken on a diameter without restraint. Square ness of the
95
micrometer to the line centers can be adjusted by rotating the pegs in the first carriage which is
made eccentric in its mounting.
Above the micrometer carriage, two supports are provided for supporting the wires and vee
pieces for measurement of effective diameter etc.
Minor diameter of internal threads : minor diameter of internal threads can be measured
conveniently by the following methods.
i) Using taper parallels : The taper parallels are pairs of wedges having radiuses and parallel
outer edges. The diameter across their outer edges can be changes by sliding them over each other
shown in fig. the taper parallels are inserted inside the thread and adjusted until firm contact is
established with the minor diameter. The diameter over the outer edges is measured with a
micrometer. This method is suitable for smaller diameter threads.
ii) Using rollers : For threads bigger than 10mm diameter, precision rollers are inserted inside the
thread and proper slip gauge inserted between the rollers as shown in fig.
So that firm contact is
then the length of slip gauges
rollers.
obtained. The minor diameter is
plus twice the diameter of
Effective diameter measurement in screw threads by micrometer.
The effective diameter or the pitch diameter can be measured by any of the following methods.
i) Micrometer method
ii) One wire, two wire or three wire (or rod) method.
Thread micrometer method : the thread micrometer resembles the ordinary micrometer, but it
has special contacts to suit the end screw thread form that is to be checked. In this micrometer, the
end of the spindle is pointed to the Vee thread form with a corresponding vee recess in the fixed
anvil. When measuring threads only, the angle of the point and the side of vee-anvil i.e the flanks
of the threads should come into contact with the screw thread.
96
If correctly adjusted, this micrometer gives the pitch diameter.
This value should agree with that obtained by measurement by outside diameter and pitch
from the following relation.
Pitch dia = D-0.6403p (in case of Whitworth thread) where 0.6403p = depth of thread, D = outside
dia p = pitch.
Limitations of thread micrometer : The micrometer must be set to a standard thread plug. If not
done so in the first instance, there will be error due to helix angle of the thread being measured.
When setting the instrument to a standard plug gauge it will be observed that the reading is not
exactly zero, as previously inferred, when the spindle and anvil are brought together.
For correct results it is necessary to use a separate thread micrometer for every size of screw
thread to be gauged, otherwise there will be a small amount of error inherent in thread
micrometer.
A big advantage of thread micrometer is that is the only method which shows the variation for
the drunken thread.
One-wire method of measuring effective diameter of screw threads.
One wire method : In this method, one wire is placed between two threads at one side and on the
other side anvil of the measuring micrometer contacts the crests as shown in fig. First the
micrometer reading is noted on a standard gauge whose dimension is nearly same as to be
obtained by this method. Actual measurement over wire on one side and threads on other side =
size of gauge ± difference in two micrometer readings.
This method is used for measuring effective diameter of counter pitch threads, and during
97
manufacture of threads.
The difficulty with his method is that the micrometer axis may not remain exactly at right angles
to the thread axis.
Two wire method : The effective diameter of a screw thread may be ascertained by placing two
wires or rods of identical diameter between the flanks of the thread, as shown in fig. and
measuring the distance over the outside of these wires. The effective diameter E is then calculated
as
E = T + P, where
T
M
= Dimension under the wires = M -2d
=Dimension over the wires, d = diameter of each wire
The wires used are made of hardened steel to sustain the wear and tear in use. These are given
a high degree of accuracy and finish by lapping to suit different pitches.
Dimension T can also we determined by placing wires over a standard cylinder of diameter
greater that the diameter under the wires and noting the reading R1 and then taking reading with
wires over the gauge, say R2 then = S-(R1-R2)
P = It is a value which depends upon the dia of wire and pitch of the thread.
If P = pitch of the thread, then
P = 0.9605p – 1.1657d (for whitworth thread) P = 0.866p-d (for metric thread)
Actually p is a constant value which has to be added to the diameter under the wires to give the
effective diameter. The expression for the value P in terms of P (pitch), d (diameter of wire) and x
(thread angle) can be derived as follows.
Since BC lies on the effective diameter line,
1
pitch  12 p
2
d cosecx/2
OP 
2
d (cosecx/2-1)
PA 
2
P
PQ  QC cot x / 2  cot x / 2
4
p cotx/2 d (cosecx/2-1)
AQ  PQ  AP 

4
2
AQ is half the value of P
BC 
p
x
x 

P value =2AQ= cot  d  cos ec  1
2
2
2 

98
Two wire method can be carried out only on the diameter measuring machine described for
measuring the minor diameter, because alignment is not possible by 2 wires and can be provided
only by the floating carriage machine. In the case of three wore method, 2 wires on one side help
in aligning the micrometer square to the thread while the third placed on the readings.
A simplified diagram of this measuring machine is shown in fig. as already pointed out the
machine ensures that the axis of the micrometer is maintained at 90 to the axis of the screw under
test. The lower slide (wrongly indicated as lower side ) is capable of movement parallel with the
axis of thread while the top slide moves at 90 to thread axis.
Three wire method of measuring effective diameter.
Three wire method : This method of measuring the effective diameter is an accurate method, in
this three wires or rods of known diameter are used one on one side and two on the other side.
This method ensures the alignment of micrometer anvil faced parallel to the thread axis. This
wires may be either held in hand or hung from a stand so as to ensure freedom to the wires to
adjust themselves under micrometer pressure.
99
M = distance over wires, E=effective diameter, r=radius of the wires, d=diameter of wires, h=height
of the center of the wire rod from the effective diameter, x=angle of thread.
From fig. AD = AB cosec x/2 = r cosec x/2
CD = H/2 cotx/2 = cotx/2
h=AD-CD
r=cosecx/2 – p/4 cotx/2
distance over wires = M=E+2h+2r
=E+2(r cosec x/2 – p/4 cot x/2) + 2r
=E+2(1+ cosec x/2 – p/2 cot x/2)
M=E+d(r cosec x/2 – p/ cot x/2
i) In case of Whitworth thread :
x=55, depth of thread =0.64p, so that, E=D-0.64p and cosecx/2=2.1657, cotx/2=1.921
M=E+d(1+cosecx/2)-p/2cotx/2=D-0.64p+d(1+2.1657)-p/2(1.921) = D+3.1657d – 1.605p
M=D+3.1657d-1.6p, where D=outside dia
ii) In case of metric thread:
depth of thread = 0.6495p
so, E=D-0.6495p, x=60, cosec x/2=2; cotx/2 = 1.732
M=D-0.6495p+d(1+2)-p/2(1.732)=D+3d-(0.6495+0.866)p=D+3d-1.5155p
We can measure the value of M practically and then compare with the theoretical values with
help of formula derived above. After finding correct value of M and knowing d, E can be found
out.
If the theoretical and practical values of M(i.e measured over wires) differ, then this error is due
to one or more of the quantities appearing in the formulas.
Effect of lead angle on measurement by 3 wire method. If the lead angle is large (as with
warms; quick traversing lead screw, etc) then error in measurement is about 0.0125mm when lead
angle is 4.5 for 60 single thread series.
For lead angles above 4.5 compensation for rake and compression must also be considered.
There is no recommendation for B.S.W threads.
Rake correction in U.S Standard.

cot x / 2
x S2
x
x
E  m
 x 1  cos ec  cos cot 
2n
2 2
2
2

100
Where x/2 = half the included angle of threads, E = effective diameter, M=actually measured
diameter over wires, n=number of threads/inch, d=diameter of wire, s=tangent of the helix angle in
thread.
Best size wire: The wire is of such diameter that it makes contact with the flanks of the thread on
the effective diameter or pitch line. Actually effective diameter can be measured with any
diameter wire which makes contact on the true flank of the thread. Bu the values so obtains will
differ from those obtained with best size wires if there is any error in angle or form of thread. It is
recommended that for this condition the wire touches the flank at mean diameter line within ± 1/5
of flank length (refer solved problem) with best size wire, any error on the measured value of
simple effective diameter due to error in thread form or angle is minimized.
It can be shown that size of best wire diameter
d
p
2 cos x / 2
With best size wire, P value = d (cosecx/2+1)cotx/2
 1  sin x / 2  cos 2 x / 2 
p 1  sin x / 2
d
  d (1  sin x / 2)  .
sin x / 2
2 cos x / 2


Measurement of effective diameter of tapered threads: The measurement of the effective
diameter of taper threads is not made perpendicular to the axis, but at an angle depending on the
taper. The measurement is made at a given point or distance from the end of the thread, and in the
three wire method, the single wire is placed at this point. The other two wires are placed in two
opposite grooves and care must be taken to ensure that the micrometer or measuring anvils make
contact with each of the three wires.
The formula for the effective diameter of the taper thread is :
cot x / 2
E  ( M  d ) sec h 
 d cos ecx / 2
2n
Where E=effective diameter, M=measurement over the wires, d=diameter of the wires, h=half the
angle of taper, x/2=half the included angle of the thread form, n=number of threads per inch.
Effective Diameter measurement threads.
Thread comparator : In this case a pair of a ball tips engage the flanks of the threads in the work
and measure the effective diameter only.
The ball tip on the right is fixed at the end of a measuring jaw attached to a floating head in the
101
sliding brackets (B). the floating head has extension in contact with the spindle of the dial
indicator and the movement of floating head towards the indicator is constrained by a spring.
(The set up in fig does not show the ball tips)
The instrument is set to a reference standard, with the dial pointer a zero. To use the gauge, the
floating head is retracted to insert the ball tips in the internal threads of the work, and released to
allow the tips to engage the flanks of the thread under the pressure of the spring. The dial
indicator then shows the deviation from the nominal size to which the gauge is set. The
instrument may be used on work in the machine, or on the working bench. The fixed head (A)
carrying the left hand ball tip is adjusted by a fine screw to set gauge to the reference standard.
The reference standard is built up from slip gauges as shown in fig. the two end pieces have Vjaws of an angle of vee corresponding to the thread i.e 60 degree or 55 degree.
The dimension J1 are marked on the pieces, and are the depths from the face to the apex points of
the vees. Assuming the effective diameter and pitch of the thread to be known, the distance S is
found from the formula.
S=X+y-Z
Where, X = mean effective diameter
Y = Depth of the thread from apex to the apex of the V form
The value of y depends on the V-form, angle of the thread, and is equal to 0.9605p for 55 threads
and 0.866p for 60 threads.
Z = J1 + J2 i.e, constants for the end gauge pieces.
The assembled slips are set in a holder with a slip equal to half the pitch, bench one end piece to
compensate for the helix angle.
102
The reference gauge thus assembled is ready for setting the comparator. Ball tips must be of
suitable size for the thread. The size is not critical provided the ball point first the thread so as to
bear o the flack near the mean pitch line.
For threads from 4 to 7 t.p.i a ball of 0.095 inch dia is used, from 7 to 12 t.p.i 0.060 inch diameter
and from 12 to 20 t.p.i. 0.035 inch diameter balls are used. A pair of V-jaws, 55 or 60 covers all
pitches from 4 to 20 t.p.i. The method of calculating the value of S from the effective diameter
excluded the radius OY at the creset and root of the thread, as the form is considered to extend to
the apex of the vee. In some cases it may be necessary to accept the major diameter as it may be
the basic dimension of the thread, and the form at the root of the thread must then be taken into
account.
P
r
For metric threads, S=D+0.2165p-Z; for whitworth threads, S=D+0.3202p-Z.
Layman’s method of finding the effective diameter (internal thread) is by taking the impression
of threads with the help of wax or any other material, say sulphur. Sulphur is mostly used because
it can be used many times.
The checking of thread form by optical projection method.
Checking the “Thread form “ and “Angle by optical projection of thread”. This method is
applicable only to external threads because internal threads cannot be projected.
The standard type of projector is used, consisting of a projector lamp, a condenser lens or
collimator, the projection lens and the screen.
The screw thread to be examined is placed in the parallel beam of light between the condenser
lens and the projector lens.
The modern projectors are quipped with work holding pictures, the projection lamp and the
lenses situated on top of the cabinet, and the screen at the front. The light rays from the lens are
directed downwards into the cabinet, and hence to the screen by a system of prisms and mirrors,
bringing every thing within the reach of the operator.
103
The enlarged image of the thread form appears on the ground –glass screen on which is
mounted the template or drawing of the form made to scale equal to the magnification of the lens.
This way the two forms (i.e ideal and projected) are compared.
One of the difficult I projecting screw thread is the fact that form is specified on an axial plane. So
we must consider the correction for it.
Referring to fig. the normal pitch p is less than the axial pitch P and is given by the relation; p = P
cosθ; where θ is the helix angle.
Referring to fig.
IfA =
half the included angle of thread on the axial plane.
X=
B=
tan A 
half the included angle of the thread on normal plane
full depth of thread to apex and
0.5P
0.5P cos 
; tan X 
B
B
0.5 p 

 or tan X 

B 

Or we say tan X = tan A cosθ
Values of A and θ are known 2X is the included angle 2X and then compare it to the theoretically
calculated value 2X=2tan-1 (tan A cos θ )
The included angle can be determined by two ball method.
The measurement of pitch of screw threads.
Measurement of pitch : The accuracy of pitch in any form of thread is very important. Therefore it
is very important to able to measure this element of thread to high degree of accuracy, at least
double that of the effective diameter measurement. The measurement must be made in such a way
that other features or dimensions e.g diameter and thread angle do not influence the result.
104
External Threads :
1.
For less accurate methods, the zees pitch or lead measuring instrument may be used. It
utilizes contact members having two ball points which are applied to the effective surface of the
thread. These points are aligned parallel to the thread axis either by a thread pin at the back or a
special back rest having a plane face parallel to the thread axis. The instrument is adjusted to zero
before making a measurement, with the aid of a special micrometer gauge supplied for the
purpose, or buying a standard plug gauge. Upon applying the instrument to the thread it registers
the pitch deviation from the standard measurement. The scale of the indicator has a range of ±
0.1mm and each division reads to 0.01mm. The measuring accuracy of the indicator is ± 0.003mm.
2.
The pitch of external threads can be measured by using screw pitch or profile gauge. Such a
gauge consists of series of thread forms with varying pitch. The one which coincides perfectly
with the thread under test gives the pitch. The accuracy of measurement depends on the method
of sighting used to judge the perfect ness.
3.
A more accurate method is the microscope method. Screw threads can be inspected and
their profile angles and linear pitches checked with the aid of a goniometric microscope. The parts
to be gauged are usually held between centers and illuminated from below, their silhouettes
appearing in the field of the viewing eyepiece. Effective pitch diameters can also be measured by
this method.
The method of measuring pitch is shown in fig. the microscope has two reticules that can be
oriented to the slopes of the thread and the point of intersection of these is used as the measuring
reference. The movement of the longitudinal carriage is read off the linear scale, the micrometer
microscope being employed for this purpose.
The linear measuring accuracy is within 0.001mm and for angles, it is 10 sec of arc.
A comparatively simple, method
of testing the pitch of a
screw thread with the cooke tool room microscope fitted with its projection screen is as follows.
The screw to be checked is mounted in a cradle under the microscope objective and the
necessary adjustments made to project the sharp enlarged image of the thread on the screen. The
appropriate thread form on the microscope thread template is then brought into coincocide with
the projected image, as shown in fig. and a reading of the lon-gitudinal table micrometer screw
taken; this can be done to an accuracy of 0.0025mm. The table is then moved by means of the
micrometer screw until the image of the next thread on the screen under inspection fills the
template profile and the reading of the micrometer again taken. The difference between the
readings gives the measured pitch of the screw. The procedure is repeated for each in individual
105
thread in order to find the separate pitch error, if any. Finally, the difference between the initial
and last readings of the micrometer when divided by the number of threads that have been
measured enables the “mean pitch” of the screw to be estimated.
For still more accurate purpose it is necessary to employ a special screw pitch measuring
machine by which the actual pitch error of individual threads can be measured. The Pitter and
Matrix are typical examples of pitch measuring machines.
The Pitter screw measuring machine employs various stylus points to suit screw threads that
are to be checked. The screw under measurement is held stationary between centers on the
machine. The indicator unit, carrying the stylus which bears on the flanks of each thread
successively, is carried on a slide which is mounted on balls. The slide is actuated by means of a
micrometer. The act of rotating the micrometer spindle causes the slide to move in relation to the
fixed centers. i.e causes the indicator to move in relation to the work being measured. The stylus
which is mounted on a leaf spring, falls in and out of each thread; the pointer of the indicator
reads zero (it is adjusted to read zero in the first groove) when this stylus is in a central position in
each successive thread. The micrometer reading is taken each time the indicator reads zero; these
readings then shown the pitch error of each thread of the screw ordinary pitches whilst special can
be provided for.
It may be mentioned that is small hand wheel below the micrometer actuates screw for the
purpose of moving the indicator in relation to the slide so as to bring the stylus opposite to the
screw to be tested in any position between the centers. The total travel of the micrometer is 25mm.
As the pitch of the micrometer screw is checked accurately when the machine is inspected and a
106
curve of errors is provided, it is possible to attain a high standard of precision in measuring
screws. The pitch errors are extremely small, being of the order of 0.002mm for a thread. A test
screw is also supplied with the machine and a chart of itch error for this screw.
The metric pitch measuring machine operates on a similar principle to the pitter machine. It is
robust in construction and sensitive in measurement, revealing pitch accuracies of 0.0025mm for
all thread forms. In this machine refer fig. a micrometer head is provided on the headstock which
is fixed on the base. The rotation of micrometer head produces movement of the longitudinal
carriage along the bed of the base.
Another carriage carrying the indicating and amplifying units comprising a radiuses stylus and
visual scale allowing a zero reading to be taken, and also capable of moving at 90 longitudinally
and locked in any position. A weight ensures a unidirectional thrust at all times. The micrometer
screw of 40 t.p.i has a 50 mm traverse and also has a compensator for any small residual pitch
errors. In operation, the screw thread to be checked is placed between centers and the correct
stylus mounted in the indicating head.
When the test screw is in position between the centers, and the correct stylus chosen i.e the one
which makes contact at or near the diameter, the carriage carrying the indicating unit is traversed
until the stylus is located in the first thread of the test screw and the indicator of coincident with
the fiducial line; the second carriage is then locked. The stylus, by virtue of an ingenious mounting
device, is capable of free movement riding up and down the thread flanks on linear movement of
the screw thread by rotation of micrometer head. The stylus is now traversed along the thread,
pitch by pitch, reading being taken each time the indicator is set to zero. The micrometer can be
fitted with a series of graduated dials that can be changes quickly. With the proper dial for the
pitch that is to be measure the readings of the error obtained from the displacement of the lines on
the disc which is graduated in (0.002 mm) divisions. It is after making this test, to the turn to first
thread and repeat the readings, and the micrometer should read zero again.
107
Additional description of pitch measuring machines: To correct any error pitch of the
micrometer screw a compensator bar is provided.
The instrument is checked periodically with a master reference screw which is placed between
centers and measured for the pitch over full range of micrometer. In this case variation in the
reading is taken to indicate errors in the micrometer screw, and the compensator bar modified
accordingly.
The micrometer screw has 40 t.p.i and with a graduated dial of 250 divisions numbered every
10 divisions, the instrument is read as on ordinary micrometer calibrated to 0.0001inch. the
micrometer dial may be replaced by any one of the five alternative dials to simplify the
measurement of the threads of certain pitches. Each of the dials is marked with a number of
divisions to suit a range of pitches as follows.
Dial No.of div
6
A
9
7
B
11
C
8
13
D
19
25
E
20
For measurement
6,12,24,48,15,30,60 t.p.i
4,5,9,18,36 t.p.i
7,14,28,56,5,10,20,40, t.p.i
11,2 t.p.i
4,8,16,32t.p.i
13,26 t.p.i
19 t.p.i
(Each 0.002mm numbered every fifth division pitch multiples of
0.025mm)
Dial C is for British association, metric or non-standard pitches. Dial E is for metric machines
only. The provision of a dial marked to suit a particular pitch simplifies pitch measuring, a
division on the dial is opposite the zero mark for nominal pitch each thread. Any variation of the
division from the zero may then be read directly to 0.0001” on either side of the zero line.
Stylus points are available to suit any particular thread. Care should be taken to make the stylus
point touch the thread at or near the pitch line. The stylus holder is pivoted to allow the stylus
point to follow in and out of the threads, as the carriage is moved along, and is adjustable for
pressure.
108
Expression for the best size wire.
The best size wire is one, in which case the wire makes contact with the thread flank. i.e the
contact points of the wires should be, on the pitch line or effective diameter. In other words, OP is
perpendicular to the flank position of the thread. Let half the included angle of thread be x.
Then in ∆OAP, sin POA
AP
AP
SinPOA 
, or sin (90 -x)=
OP
OP
AP
AP
OP 

 AP sec x
sin(90  x) cos x
Since AP = r, and wire diameter = 2r=2AP sec x
As AP lies on the pitch line, AP=p/4 (where p = pitch of the thread)
2p
p
dp 
sec x  sec x
4
2
Problem 1: Derive an expression from first principles for the limits of diameter for ‘best size’ wires
for measuring threads of BA form in terms of pitch
Best wire size is d
p
x
sec
2
2
here x=included angle of the thread
d
p
1
 47 30  p
= sec 
 0.5465 p
 
2
 2  2 0.9150
1
(a) upper limit/lower limit:
5
1
flank length   BF
5
109
Refer fig please note that point B could not be shown in fig. Actually B lies on line OF such that AB
┴OF. Point C lies on inter section of line AD and OF).
BF = CE + BC + EF = CE + 2BC
BC = (OA sin x/2) tan x/2
= [(0.1808p + 0.2682p). sin 23 45] X tan 23 45 = 0.0378p
Hence upper limit for best wire size = 0.5465p + 0.0378p = 0.5843p and lower limit for best wire
size = 0.5465p – 0.0378p = 0.5087p.
Two corrections applied in the measurement of effective diameter by the method of wires
The two corrections applied are : i) Rake correction, and ii) Compression correction.
i) Rake Correction : The rake correction becomes necessary because in the determination of
formula for effective diameter by three wires method, a plane axial section of the thread had been
considered and it is assumed that the wore touches each flank of the thread in this plane. This
assumption is true for angular grooves with zero helix angle, but not for screw threads which
have a helix; and in the later case wire lies on parallel to the helix at the radius of the point of
contact. The points of contact on opposite flanks will lie on opposite sides of the mean axial plane.
As a result of this, the wire lies slightly father from the thread axis than what has been assumed
and a correction has to be applied to the effective diameter as measured and calculate. This
correction is different effective diameters being measured.
A general formula for calculating rake correction is
C=
cosx/2cotx/2 l2 2
A (1  A sin x / 2  A2 sin 2 X / 2)
2
2
d
Where C = Rake correction, X/2 = Half the included angle of thread, l=Lead of thread,
D = diameter of wire A= Constant
d
Constant 
T+d
Where T = Diameter under the wires.
This correction is always subtracted from the measured diameter.
110
ii) Compression Correction: As the micrometer exerts some force on the wires while measuring
the effective diameter of threads, some degree of comparison takes place and as a result the
diameter observed is less. This correction, is therefore added to the value of diameter obtained.
This correction is more pronounced on fine threads and those whose included angle is small e.g
B,A threads, for measuring forces upto about 350gm. The correction is within 0.0025mm for thread
diameter down to about 3.5mm and only 0.005mm at 1 mm diameter for larger threads, for the
some measuring force, the compression is less and can be ignored.
Formula for determining compression correction is
E 2/3
=0.001 1/3 mm.
E
Various errors in gears.
Gear errors. Various possible types of error on spur, helical, bevel and worm gears are described
below:
(i) Adjacent pitch error
(ii) Cumulative pitch error
Actual pitch – design pitch.
Actual length between corresponding flanks of teeth not adjacent
to each other-design length.
(iii) Profile error
The maximum distance of any point on the tooth profile form and
normal to the design profile when the two coincide at the
reference circle.
(iv) The tooth to tooth
The range of difference composite error – single flanks between
the displacement
(Refer Fig. 15.13a)
at the pitch circle of a gear and that of a master gear meshed with
it at fixed centre when moved through a distance corresponding
to one pitch with only the driving and driven flanks in contact.
(v) The total composite
The range of difference errors – single flank
between
the
displacement at the pitch circle of a gear and that of a master gear
meshed with it at fixed centre distance when moved through one
revolution with it at fixed centre distance when moved through
one revolution with only the driving and driven banks in contact
(Refer Fig.15.3a).
(vi) The tooth to tooth
The range of variation in composite error – double
the
minimum centre flank
distance between a gear and a master
gear when rotated through a distance corresponding to the pitch
of the teeth (Refer Fig. 15.13a)
(vii)The total composite
The range of variation in error-double flank.
The minimum
centre distance between gear and a master gear when the gear is
rotated through one revolution (Refer Fig.15.13b)
(viii) The tooth thickness error Actual tooth thickness measured along the surface of the reference
cylinder – design tooth thickness.
(ix) Cyclic error
An error occurring during each revolution of the element under
consideration.
111
(x) Periodic error
(xi) Run out
(xii) Radial run out
(xiii) Eccentricity
(xiv) Axial run-out (wobble)
(xv) Undulation
(xvi) Undulation height
(xvii) Wave length of an
(xviii) Tooth alignment error
An error occurring at regular intervals not necessarily
corresponding to one revolution of the component.
It is the total range of reading of a fixed indicator with the contact
point applied to a surface rotated, without axial movement about
a fixed axis.
It is the run – out measured along a perpendicular to the axis of
ration.
It is half the radial run-out.
It is the run- out measured parallel to the axis of rotation, at a
specified distance from the axis.
A periodical departure of the actual tooth surface from the design
surface (Refer Fig. 15.13b).
The normal distance between two surface from the design surface
(Refer Fig. 15.13c)
The distance between two undulation
adjacent crests of an
undulation (Refer Fig. 15.13c)
The distance of any point on a tooth trace from the design tooth
trace passing through a selected reference point on that tooth
(Refer Fig.15.13c)
The presence of these errors caused interference in efficient
Operation of gears. These result in non-smooth and noisy
Operation which ultimately affect the working life.
Various Gear Measurements.
For proper inspection of gear, it is essential to pay attention to the raw material, each
process in the production cycle, machining the blanks, heat treatment, the cutting and surface
finish of the teeth.
The gear blank should be tested for dimensional accuracy (face width, bore, hub, length,
and outside diameter), and eccentricity As outside diameter forms the datum from where the
tooth thickness is measured, it forms an important item to be controlled. Concentricity of the
blanks is also essential and the side faces should be true to the bore. On very precise gears details
like tip radius, shape of root provided and surface finish are also measured.
Concentricity of teeth is an important item and should be checked to ensure that the set up and
equipment is in good order. If teeth are not concentric then fluctuating velocity will be noticed on
the pitch line while transmitting motion. This also leads to inaccuracy of parts when being used
for indexing purposes. Tooth concentricity can be checked by (i) mounting the gear between the
bench centres, placing a standard roller in each tooth space and then using a dial indicator, (ii)
using a projector in which case the teeth are brought against a stop and each image of tooth on
screen should coincide with a line on the screen (iii) using a gear testing fixture fitted with a
spring loaded slide and dial indicator, in which case the spring exerts a constant pressure on the
112
mating teeth and the movement of the dial indicator, in which case the spring exerts a constant
pressure on the mating teeth and the movement of the dial indicator gives the measure of the
eccentricity of teeth.
Good alignment of each tooth on a gear is essential, as otherwise the load will not be distributed
evenly over its face. If teeth of a gear be machined poorly, it is quite probable that the load may be
carried by one edge only introducing high bearing stresses. Tooth alignment can be checked by
placing a standard roller in the tooth space and checking for parallelism off a surface plat. In the
other method, the teeth on one gear are lightly marked with Prussian blue and mounted in a
testing machine having a master gear. The contacts made on the mating gear give good idea of
tooth alignment.
Hardness of gear tooth should be tested to ensure that heat treatment is proper and that the
desired harness due to provision of adequate thickness and grain size have been attained.
The method employed for measuring and testing of gears depends upon various factors,
such as the precision of gears, method of manufacturing equipment available etc.
The accuracy of any gear mainly depends upon the cutter accuracy and the setting of the
machine. Thus for most of the gears, optical projection and rolling tests will suffice. But in
manufacture of high precision gear, it is necessary to determine the accuracy of individual
elements e.g., tooth thickness, pitch of teeth and form of teeth etc.
Accuracy of measurement. While the accuracy of measuring of gear depends upon the measuring
equipment available, it must be emphasized that there are some in-built limitations in the gear
itself, such as the inability of a gear to its own axis of rotation. Thus if the reference circle of gear
is eccentric, it would be reflected in pitch error. Similarly the errors in tooth surface finish such as
undulation would jeopardize the validity of a signal point measurement on a tooth flank.
The inspection of gear is mainly of two types (a) Analytical, and (b) functional. By
analytical inspection of gears we mean that all the individual elements of the gear teeth are
checked. This method is slow and tedious and not of much use for industry. The discrete error
values of pitch, tooth profile etc. cant give a true overall assessment of the accuracy of a gear. It is
not easy to asses accurately how these elemental values combine in practice to give a prescribed
performance under operational conditions. How ever this method is of great understanding of the
subject to student. Nevertheless it may be stressed that all errors in pitch profile cause variations
in the uniformity of rotary motion and the errors in tooth alignment or helix angle result in the
concentration at small areas instead of being distributed uniformly.
The analytical inspection of the gears consists in determination of the following teeth
elements in which the errors are caused due to manufacturing errors.
(A) Profile. (B) Spacing. (C) Pitch (D) Run out or eccentricity or concentricity. (E)
Thickness of tooth (F) Lead. (G) Backlash.
The functional type of inspection consists of carrying out the running test of gear with
113
another gear which is more accurate and is known as control gear or master gear, to determine
composite vibration, noise level, or variation in action. If a pair of gears work together at the
designed speed and under load with little noise, they are considered satisfactory for many
purposes. If drive is noisy, then individual elements have to be measured. However master gear
has to be measured on elemental basis only.
Rolling Tests
This is the most commonly used test under production conditions. This consumes much
less time and gives quite accurate results. In rolling test, the gear to be tested is actually compared
with a hardened and ground master gear. This test is generally performed on a most commonly
used machine Parson Gear Tester. This test reveals any errors in tooth form, pitch and
concentricity if pitch line, When two gears are in mesh with each other, then any of the above
errors will cause the variation of centre distance. This fact is utilized for testing the errors in gear
by this machine.
It essentially consists of a base. Two carriages, one fixed and the other movable are
mounted on the base. The position of the fixed carriage can be adjusted in order to accommodate
a wide range of diameters. While in use, this fixed carriage is locked in one position. The
movable carriage is spring loaded towards the fixed carriage. Two spindles are mounted in a
parallel plane on each carriage and these are made to suit the bore of the gears.
The distance between the centre of two spindles is adjusted to be equal to the centre
distance by slip gauges. A dial gauge is made to rest against the movable carriage and its reading
is adjusted at zero at this time. The master gear is mounted on the spindle on fixed carriage and
gear to be tested on the movable carriage. The gears when in mesh are then rotated by hand and
the variations in the dial gauge readings are observed. If it falls outside the set limits, then gear is
rejected. The variations might also be recorded by some electrical pick up in which the movement
of carriage is first converted into electrical impulse which is magnified further and trace of
variation obtained on a graph paper. The trace obtained will be depicting the compound errors
i.e., all errors like eccentricity and tooth form errors etc., which occur together and the trace will be
as shown in Fig.15.8.
The machine could also be used to carried out more complex tests by suitable modification in
its operation, e.g., by locking the movable carriage at the running centre distance of the gears, and
by fixing the master gear, the black flash can be determined by setting a dial gauge at the pitch
line of the production gear. It is also possible to check the gears for smooth running at this setting
and this is very essential for gears. This is judged by the noise produced.
114
For these tests, if master gear is not available, then any two mating gears are mounted on
the spindle and they are tested twice at relative angular positions of 1800 to each other so that any
compensating errors in one angular position in gears are also revealed.
Measurement of tooth thickness by gear tooth Vernier method.
Measurement of tooth thickness. The permissible error or the tolerance on thickness of
tooth is the variation of actual thickness of tooth from its theoretical value. The tooth thickness is
generally measured at pitch circle and is therefore, the pitch line thickness o tooth. It may be
mentioned that the tooth thickness is d as the length of an arc, which is difficult to measure
directly. In most of the cases, it is sufficient to measure the chordal thickness i.e., the chord joining
the intersection of the tooth profile with the pitch circle,. Also the difference between chordal
tooth thickness and circular tooth thickness is very small for gear of small pitch. The thickness
measurement is the most important measurement because most of the gears manufactured may
not undergo checking of all other parameters, but thickness measurement is a must for all gears.
There are various methods of measuring the gear tooth thickness.
(i) Measurement of tooth thickness by gear tooth venire caliper. (ii) Constant chord
method. (iii) Base tangent method. (iv) Measurement by dimension over pins.
The tooth thickness can be very conveniently measured by a gear tooth venire. Since the
gear tooth thickness varies from the tip of the base circle of the tooth, the instrument must be
capable of measuring the tooth thickness at a specified position on the tooth. Further this is
possible only when there is some arrangement to fix that position where the measurement is to be
taken. The tooth thickness is generally measured at pitch circle and is, therefore, referred to as
pitch-line thickness of tooth. The gear tooth vernier has two vernier scales and they are set for the
width (w) of the tooth and the depth (d) from the top, at which w occurs.
Considering one gear tooth, the theoretical of values of w and d can be found out which
may be verified by the instrument. In Fig. 15.14, it may be noted that w is a chord ADB, but tooth
thickness is specified as an arc distance AEB. Also the distance d adjusted on instrument is
slightly greater than the addendum CE, w is therefore called chordal thickness and d is called the
chordal addendum.
In Fig.15.14, w = AB = 2AD
115
Now, AOD =  = 3600/4N, where N is the number of teeth,
W = 2AD = 2xAO Sin  = 2R Sin 360/4N (N = pitch circle radius)
Module m =
 w2
and
d 
P.C.D
2R
N .m.

, R 
No. of teeth N
2
Nm
 360 
 90 
Sin 
  N .m.Sin   ---- (1)
2
 4N 
N
Also from Fig 15.14, d = OC –OD
But OC = OE + addendum = R + m = (Nm/2) + m
Nm
 90 
OD  RCos 
Cos  
2
N
Nm
Nm
 90  Nm  2
 90  
m
Cos   
1   Cos    --- (2)

2
2
2  N
N
 N 
Any error in the outside diameter of the gear must be allowed for when measuring tooth
thickness.
In the case of helical gears, the above expressions have to be modified to take into account
the change in curvature along the pitch line. The virtual number of teeth Nv for helical gear =
N/cos3 
Hence in Eqs. (1) and (2), N can be replaced by N/cos3  and m by mn (normal module).
w 

Nmn
 90

Sin  Cos 3   , and
3
Cos 
N

Nmn  2Cos 3 
 90

1
 Cos  Cos 3   

3
Cos  
N
N

these formulae apply when backlash is ignores. On mating gears having equal tooth thickness
and without addendum modifications, the circular tooth thickness equals half the circular pitch
minus half the backlash.
Gear Tooth Caliper.
It is used to measure the thickness of gear teeth at the pitch line or chordal thickness of
teeth and the distance from the top of a tooth to the chord. The thickness of a tooth at pitch line
and the distance from the top of a
tooth to the chord. The thickness
of a tooth at pitch line and the
addendum is measured by an
adjustable tongue, each of which
is adjusted independently by
adjusting screw on graduated
bars. The effect of zero errors
116
should be taken into consideration.
This method is simple and inexpensive. However it needs different setting for a variation
in number of teeth for a given pitch and accuracy is limited by the least count of instrument. Since
the wear during use is jaws, the caliper has to be calibrated at regular intervals to maintain the
accuracy of measurement.
The constant chord method and Base pitch method of measuring gear tooth thickness.
Constant Chord Method. In the above method, it is seen that both the chordal thickness and
chodral addendum are dependent upon the number of teeth. Hence for measuring a large
number of gears for se, each having different number of teeth would involve separate calculations.
Thus the procedure becomes laborious and time – consuming one.
The constant chord method does away with these difficulties. Constant chord of a gear is
measured where the tooth flanks touch the flanks of the basic rack. Are straight and inclined to
their centre line at the pressure angle as shown in Fig. 15.16.
Also to pitch line of the rack is tangential to the pitch circle of the gear and, by definition,
the tooth thickness of the rack along this line is equal to the are tooth thickness of the gear round
its pitch circle. Now, since the gear tooth and rack space are in contact in the symmetrical position
at the points of contact of the flanks, the chord is constant at this position irrespective of the gear
of the system in mesh with rack. This is the property utilized in the constant chord method of the
gear measurement.
The measurement of tooth thickness at constant chord simplified the problem for all
number of teeth. If an involutes tooth is considered symmetrically in close mesh with a basic rack
form, then it will be observed that regardless of the number of teeth for a given size of tooth (same
module), the contact always occurs at two fixed point A and B. AB is known as constant chord.
The constant chord is d as the chord joining those points, on opposite faces of the tooth, which
117
make contact with the mating teeth when the centre line of the tooth lie on the line of the gear
centers. The value of AB and its depth from the tip, where it occurs can be calculated
mathematically and then verified by an instrument, The advantage of the constant chord method
is that for all number of teeth (of same module) value of constant for all gears of the meshing
system. Secondly it readily lends itself to a form of comparator which is more sensitive than the
gear tooth venire.
In Fig 15.16, PD = PF = are PF = ¼  circular pitch =
Since line
ÐCAP=Φ
AP
is
the
line
of
action,
1  P C  D 

 1/ 4    m
4
N
i.e.it
is
tangential
to
the
base
circle,
in right angled ΔAPD,=PDcosΦ=  π/4  mcosΦ
in triangle PAC,AC=APcosΦ=  π/4  mcos 2Φ
c=constant chord=2AC=  π/2  mcos 2 Φ
where  is the pressure angle (from Fig.15.16)
For helical gear, constant chord = (  / 2 ) m cos 2  n
Where mn = normal module i.e. module of cutter used and  n=normal pressure angle.
π
 π

mcosΦsinΦ=m 1- cosΦsinΦ   4 
4
 4
.......
Now PC = m 
 π

 For helical gear,d=m n 1- 4 cosΦ n sinΦ n  



m
m
sin  cos  
sin 2.........  5 
Also height of AB above pitch line = PC=
4
8
Base pitch. This is d as the circular pitch of the teeth measured on the base circle. In Fig.15.17,AB
represents the portion of a gear base circle, CD and EF the sides of two teeth, FD being the base
pitch. From the property of involutes if any line as GH is drawn to cut the involutes and tangential
to the base circle, the GH=FD.
Thus base pitch could also be d as equal to the linear distance between a pair of involutes
measured along a common generator.
Base circumference =
2 RB
 Basepitch  2 RB / N
If  is the pressure angle, then
 cos    P.C.D./ 2  cos 
RB = P.C.R.
 Basepitch  (2 N )   P  C  D  / 2   cos 
  m cos 
118
This is the distance between tangents to the curved portions of any two adjacent teeth and
can be measured either with a height gauge or on an enlarged projected image of the teeth. This
principle is utilized in ‘David Brown’ tangent comparator and it is the most commonly used
method.
Base pitch measuring instrument. This instrument has three tips. One is the fixed measuring tip,
other one is the sensitive tip whose position can be adjusted by a screw and the further movement
of it is transmitted through a leverage system to the dial indicator.; and the third tip is the
supplementary adjustable stop which is meant for the stability of the instrument and its position
can also be adjusted by a screw. The distance between the fixed and sensitive tip is set to the
equivalent to the base pitch of the gear with the help of slip gauges. The properly set-up
instrument is applied to the gear so that all the three tips contact the tooth profile. The reading on
dial indicator is the error in the base pitch.
Base tangent method.
The Base Tangent Method. (‘David Brown’ tangent comparator). In this method, the span of a
119
convenient number of teeth is measured with the help of the tangent comparator. This uses a
single venires caliper and has, therefore the following advantages over gear tooth venires scales:
(i) The measurements do not depend on two venires readings, each being function of the
other.
(ii) The measurement is not made with an edge of the measuring jaw with the face.
Consider a straight generator (edge) ABC being rolled back and forth along a base circle
(Fig.15.19). Its ends thus sweep out opposed involutes A2 AA1 and C2 CC1 respectively. Thus the
measurements made across these opposed involutes by span gauging will be constant (i.e. AC =
A1C1=A2 C2 = A0 C0) and equal to the are length of the base circle between the origins of involutes.
Further the position of the measuring faces is unimportant as long as they are parallel and on an
opposed pair of the true involutes. As the tooth from is most likely to conform to a true involutes
at the pitch point of the gear, it is always preferable to choose a number of teeth such that the
measurements is made approximately at the pitch circle of the gear.
The value of the distance between two opposed involutes, or the dimension over parallel faces is
equal to the distance round the base circle between the points where the corresponding tooth
flanks cut i.e. ABC in fig.15.19. It can be derived mathematically as follows:
The angle between the points A and C on the pitch circle where the flanks of the opposed
involutes teeth of the gear cut this circle can be easily calculated.
Let us say that the gear has got ‘N’ Number of teeth and AC on pitch circle corresponds to
‘S’ number of teeth. (Fig.15.20);  Distance AC = (S – ½)pitches
 Angle subtended by AC   S  1/ 2  2 / N radians.
Angles of arcs BE and B D.
In volute function of pressure angle    tan   
 1  2
 AngleofarcBD   S  
 2  tan    
 2 N

BD = Angle of arc BD  Rb

1  2

 S  2   N  2  tan       RP cos  becauseRb  RP cos  




mN

1  2

mN 
cos   S  
  tan      becauseRP 
2
2 N
2 


 S 

 Nm cos  

 tan    
 N 2N

As already d, length of arc BD = distance between two opposed involutes and thus it is.
120
 S

 Nm cos   tan    

2 N N 

It may be noted that when backlash allowance is specified normal to the tooth flanks this
must be simply subtracted from this derived value.
Tables are also available which directly give this value for the given values of S,N and m.
This distance is first calculated and then set in the ‘David Brown’ tangent comparator
(Fig.1521) with the help of slip gauges. The instrument essentially consists of a fixed anvil and a
movable anvil. There is a micrometer on the moving anvil side and this has a very limited
movement on either side of the setting. The distance is adjusted by setting the fixed anvil at
desired place with the help of looking ring and setting tubes.
Composite Method of Gear Checking.
Composite testing of gears consists in measuring the variation in centre distance when a
gear is rolled in tight mesh (double flank contact) with a specified or mast gear. In composite gear
checking two types of checking’s are made :
(a)
Total Composite Variation, (b) Tooth to Tooth Composite Variation.
Total composite variation is the centre distance variation in one complete revolution of the gear
being inspected; whereas tooth to tooth composite variation is the centre distance variation as the
gear is rotated through any increment of 360º/N.A uniform tooth to tooth variation shows profile
variation whereas a sudden jump indicates the pitch variations.
Composite type of checking takes care of all the errors in the gears. It is specially very much
suited for large gears as it also ensures control over the tooth spacing. The composite method of
checking is very much suitable for checking worn gears.
Tolerance for Composite Errors. The following table gives the tolerance on total composite
errors and tooth to tooth composite error.
Here factor F  M  0.25 D
Master Gears. Master gears are made with sufficient accuracy capable of being used as the
basis for comparing the accuracy of other gears. These are mostly used in composite errors
determination in which the master gears are rotated in close mesh (double flank) or in single
contact with the gears under test. These can also be used for calibration of gear checking
instruments used in shop-floor Master gears are generally of two types; i.e. Master gears type A
used for checking precision gears of accuracy class up to 7and type B master gears used for
checking gears from 8 to 12. Master gears are made from chromium –manganese tool steel or good
quality gauge steel and are hardened to 62HRC These are properly stabilized to relieve internal
stresses. The master gears should preferably have lower module values because with coarse
pitches the master gear would have either a very few teeth or else it will be quite big making it
121
difficult to handle besides high-production cost.
Class or Grade of
Gear
Total Composite
Error in Microns
Tooth or Tooth
Composite Errors in
Microns
1
2
3
4
5
6
7
8
9
10
11
12
4+0.32F
6+0.30F
10+0.08F
16+1.25F
25+2.0 F
40+3.2 F
56+4.5 F
71+5.6 F
90+7.1 F
112+9.0F
140+11.2F
180+14.0F
2+0.16F
3+0.224F
4+0.32 F
6+0.45 F
9+0.56 F
12+0.90F
16+1.25F
22+1.8F
28+2.24F
36+2.8F
45+3.55F
56+4.50F
Parkinson Gear Tester. The principle of this device is to mount a standard gear on a fixed vertical
spindle and the gear to be tested on another similar spindle mounted on a sliding carriage,
maintaining the gears in mesh by spring pressure. Movement of the sliding carriage as the gears
are rotated are indicated by a dial indicator, and these variations are a measure of any
irregularities in the form of a waxed circular chart and records made of the gear variation in
accuracy of mech.
Fig. shows a gear tester for testing spur gears. (Testers are available for bevel, helical and worm
gears also)The gears are mounted on the two mandrels, so that they are free to rotate without
measurable clearance. The left spindle can be moved along the table and clamped in any desired
position. The right mandrel slide is free to move, running on steel balls, against sprint pressure
and it has a limited movement. The two mandrels can be adjusted so that their axial distance is
equal to the designed gear. Centre distance. The spring pressure can be regulated. There are also
screws for limiting the movement of the sliding carriage. A scale is attached to one carriage and a
vernier to the other; this enables centre distances to be measured to within 0.025mm. The dial
122
indicator on the right contacts the right end of the sliding carriage and therefore indicates any
radial variations of the gear under test as the gears are rotated.
When the waxed paper recorder is fitted, the chart makes a revolution for each one of the
gears mounted on the sliding carriage. As the char moves or rotates, the line traced records the
movements of the floating carriage, a circle is drawn at the same time as the record. The figures
shown in Fig. 15.28 are reproduction of a few typical charts with a reduced scale and the radial
errors magnified about 50 times. The gear shown by No.1 record is a fully satisfactory one, that at
No.2 is a moderate gear at No.3 is an unsatisfactory one.
It may be noted that the method described above is dual flank method, i.e., both tooth
flanks come in contact which is seldom the case in actual practice. The chart records obtained by
this test do not give a clear indication of true cumulative pitch error. This test is an expedient test
for accepting or rejecting a gear but not for finding out detailed causes for rejection. It is used
mainly to detect poor tooth form caused by worn or inaccurate cutting tool, and pitch circle
eccentricity arising from inaccurate centering of the gear blank prior to tooth cutting, etc.
Technically more correct method of mesh testing is single –flank method in which, instead
of measuring centre distance variation the angular variation is measured. The mesh tester is a
complex system and more costly. The simplest machine of this type consist of two shafts each
carrying a gear and a plain disc having diameter equal to the nominal pitch diameter of the gear.
One shaft has a rotary joint between the gear and its associated pitch disc. An indicator is used to
measure angular variation between the gear and disc on this shaft. In use, the two discs are
brought into frictional contact so that one can drive the other without slip. This method is not
popular because it requires these manufacture of two very accurate pitch discs for every gear pair
of different size. Present day’s single – flank mesh testers do not require different pitch discs. The
two shafts carrying the gears are fitted with radial gratings having angular band of accurately
spaced clear radial lines (one line for one minute of arc). When two such gratings (inclined at very
small angle ) rotate in close proximity, interference bands known as Moire fringes are formed
moving in radial direction which generate electric pulses. These pulse trains are continuously
phase –compared to provide a detailed chart record of gear transmission errors.
123
Base circle dia. Range
Max. outside dia. Of gear
Module range(DP)
Helix angle range
Max gear width
Additional vertical probe travel
Setting accuracy of base circle
Adjustable error magnification
Of electronic printer
Steady Centre Attachment
Center distance
Throat depth
Fig. Gear testing centre.
0.550mm
600mm
0.2-20
0-90º
150mm
150mm
1μm
100x,200x,500x,1000x,2000x
20-570mm
300mm
124
Calculation of the dimension of the maximum chord over four teeth when the gear under
inspection has the following specifications:
No. of teeth = 32; module =4, Pressure angle = 20º
Shift of the tool into the gear to provide back flash = 0.25mm.
Solution. In this case the cutting tool is moving into the blank by o.25mm more, so the tooth
thickness will get reduced. Hence, the correction needed on one side of tooth is
 0.25 tan   0.25 tan 200  0.6010mm
and distance over 4 teeth for theoretical gear is
 S

cos   tan    

2 N N 

  20

 3

N.m.  32  4  cos 20  tan 20 


180
2  32 32 

 42.42
And distance for the actual gear
=42.42-2  0.0190=42.382mm.
21. Calculation of the dimension over pins in the following case. Also indicate the diameter of
the pins to be used. N=31,m=3,  =20º.
Solution. Best in diameter
  / 2.m cos    / 2  3  cos 200  4.426mm
From Fig.15.34,P>C>D.=mN=AC=3  31=93mm
360
 5.80 ,  5.8 / 2  2.90 , andangleCBA  900
And
2  31
CB  AC cos   93  cos 2.9  92.87

 Dimension over pin =92.87+4.426=97.296mm.
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Construction and working principle of Tomlinson Surface meter.
The Tomlinson Surface Meter. This instrument was designed by Dr. Tomlinson. This instrument
uses mechanical –cum-optical means for magnification (Fig.11.8).
The diamond stylus on the surface finish recorder is held by spring pressure against the
surface of a lapped steel cylinder. The stylus is also attached to the body of the instrument by a
lead spring and its height is adjustable to enable the diamond to be positioned conveniently. The
lapped cylinder is supported on one side by the stylus and on the other side by two fixed rollers as
shown in Fig. 11.
The stylus is restrained from all motions except the vertical one by the tensions in coil and
leaf spring. The tensile forces in these two springs also keep the lapped steel cylinder in position
between the stylus and a pair of fixed rollers. A light spring steel arm is attached to the horizontal
lapped steel cylinder and it carries at its tip a diamond scriber which bears against a smoked glass.
When measuring surface finish, body is traversed across the surface by a screw rotated by a
synchronous motor. Any vertical movement of the stylus caused by the surface irregularities,
causes the horizontal lapped steel cylinder to
roll. By its rolling, the light arm attached to its end provides a magnified movement on a smoked
126
glass plate. This vertical movement coupled with the horizontal movement produces a trace on
the glass magnified in vertical direction and there being no magnification in horizontal direction.
The smoke glass trace is the, further projected at 50or 100 magnification for examination. This
instrument is comparatively cheap one and gives reliable results.
The Taylor-Hobson Talysurf.
The talysurf is an electronic instrument working on carrier modulating principle. This
instrument also gives the same information as the previous one records the static displacement of
the stylus and is dynamic instrument like profilometer.
The measuring head of this instrument consists of a diamond stylus of about 0.002mm tip
radius and skid or shoe which is drawn across the surface by means of a motorized driving unit
(gearbox), which provides three motorized speeds giving respectively 20and 100 horizontal
magnification and a speed suitable for average reading. A natural position in which the pick-up
can be traversed manually is also provided. In this case the arm carrying the stylus forms an
armature which pivots about the centre piece of E- shaped stamping as shown in Fig. 11.9 On two
legs of (outer pole pieces ) the E-shaped stamping there are coils carrying an a.c. current. These
two coils with other two resistances form an oscillator.; As the armature. Is pivoted about the
central leg any movement of the stylus causes the air gap to vary and thus the amplitude of the
original a. c. current flowing in the coils is modulated. The output, of the bridge thus consists of
modulation only as shown in Fig. 11.9 This is further demodulated so that the current now is
directly proportional to the vertical displacement of the stylus only.
The demodulated output is caused to operate a pen recorder to produce a permanent
record and a meter to give a numerical assessment directly. In recorder of this statement the
marking medium is an electric discharge through a specially treated paper which blackens at the
127
point of the stylus, so this has no distortion due to drag and the record strictly rectilinear one.
Now-a-days microprocessors have made available complete statistical multi-trace systems
measuring several places over a given area and can provide standard deviations and average over
area-type readings and complete surface characterization. These systems lend themselves to
research applications where specialized programming can achieve auto correlation, power
spectrum analysis and peak curvature.
Various methods of analysis of surface traces.
Analysis of Surface Traces.
A numerical assessment is assigned to indicate the degree of smoothness (roughness) a
number of ways. In practice three roughness measures have shown themselves to be particularly
useful.
1. Maximum Peak to Valley Height of Roughness. This is obviously the most common
measure of roughness but is not by any means a complete definition of roughness, e.g. the two
cases in fig11.13peak to valley height is same, but frequencies of irregularities are different and
second surface is more rough in comparison to first one but since, this is a relatively simple
method of analysis, this will be a satisfactory measure there it is desired to control the cost of
finishing for checking the rough machining. This method is also very advantageous in cases where
the condition of surface is likely to exert an important influence on such properties as fatigue
resistance and it is intended to clear the surface of the irregularities left by a previous operation.
2. Root Mean Square Value (R.M.S. Value). This measure was in use previously and now – adays superseded by Centre Line Average measure, as latter has the properties of bring easily
measured. R.M. S. blue is d as the square lot of the mean of the squares the ordinates of the surface
measured from a mean line.
Referring to Fig. 11.14, be selected length L is divided to n equal parts. Ordinates corrected
at the points 1,2, 3,4,………,n, whose heights are (by)
h1 , h2 , h3 , h4 ,......., hn
thenhr ,m, s.
h1  h22  h32  ......  hn2

n
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3. Centre Line Average Method (C.L.A. Value). This is d as the average height from a mean line
of all ordinates of the surface regardless of the sign.
Thus referring to Fig.11.14, C.L.A. =
h1  h2  h3  h4  .......hn
n
But of find C.L.A. value like this will be laborious job. Also by this method, spacing chosen
may be such that important ordinates are likely to be missed.
Things can be much simplified by using a plain meter which can find out the area of any
curve. Referring to Fig. 11.15, let us say that somehow or other the mean line is exactly known.
The C.L.A. value
A1  A2  A3  ....... A

L
L
One has to take care of units carefully to find the C.L.A. value in micron.
=
How to determine Mean Line. For it first the mean line is estimated by eye-judgement. Then total
area above and below the assumed mean line are measured and a correction is applied to the
assumed mean line to get the correct mean line. Error [(  A (above) -  A (below)]/L is applied to
the assumed mean line to get the correct, mean line. Thus in Fig.11.16,x’y’ is assumed mean line.
Thencorrection 
( A1 A3  A5  A7 )  ( A2  A4  A6  A8 )
and this correction added to the assumed line
L
algebraically gives the actual mean line. The C.L.A. value can be found out as described
previously.
“Talysurf” has got built in arrangement for integrating the areas and the average value is
directly given.
129
C.L.A. value does not give any idea regarding the greatest extent and the nature of the
surface irregularities It is likely to give identical values for surface of vastly different
characteristics. So this is the main disadvantage of C.L.A value, but when the characteristics of a
surface have been found out to be satisfactory and such conditions are produced which do not
allow the surface to change radically in manufacturing, then C.L.A. value provides a workable
control.
The procedure for determing flatness.
Procedure for determining flatness (Fig.7.5). The procedure for determining flatness is as
follows:
(1) Carry out the straightness test already described on all the lines AB,BC,AC etc., and
tabulate the readings up to the cumulative error column.
(2) Let a plane passing through the points A,B and D be assumed to be an arbitrary plane,
relative to which the heights of all other points may be determined. For it, the ends of lines AB,
AD and BD are corrected to zero and thus the height of points A, B and D are zero.
(3) The height of point I is determined relative to the arbitrary plane ABD=000. As I is the midpoint of line AC also, all the points on AC can be fixed relative to the arbitrary plane by
assuming A=0 and correcting Ion AC to coincide with the mid-point. A hint could be taken
here that Cis twice as far from A as the mid-point, the correction for C will be double that of I.
(4) Point C is now fixed relative to the arbitrary plane and points Band Dare set at zero, all
intermediate points on BC and DC can be corrected accordingly.
(5) The positions of Hand G, E and F are known, so it is now possible to fit in lines HG and EF.
This also provides a check on previous evaluation since the mid-point of these lines should
coincide with the known position of mid-point I.
130
In this way, the height of all the points on the surface relative to the arbitrary plane ABD are
known.
One thing to be noted here is that according to definition of flatness error, departure from
flatness is determined by the minimum separation of a pair of parallel planes which will just
contain all the points on the surface. Here it is possible to determine two points at either extreme
of the reference plane to the separation but the reference plane chosen may not be the best plane.
Therefore, in order to determine the minimum separation some correction has to be made. The
calculation for a final correction to determine for a final correction to determine the minimum
separation of a pair of parallel planes which just contain all the points on the surface is made by
graphical method as given below.
The various points on the surface have been determined with reference to ABD as reference
plane as described previously. Two points on opposite sides having maximum positive and
maximum negative values are selected and jointed together by a line xx. Let these points in Fig.7.6
be R and. Draw a line yy parallel to xx to represent the plane ABD as shown in fig 7.6 set of to
scale the height of all points relative to YY by taking projections from all the points on the surface.
In fig 7.6, Projections from all points have not been shown for the sake of clarity. Next by
inspection, draw a closest pair of parallel lines zz, which will contain all of the points. It may be
noted that one line will have two points on it, and the other line, one point only. The distance
between these two lines is a measure of the error in flatness. Although it is not exact value but for
practical purpose it gives sufficiently accurate results.
The optical flatness testing method for very flat and polished surface has already been
discussed in the chapter of interferometry.
Devices used for measurement of roundness.
Devices for measurement of roundness. The most commonly used devices for measurement of
roundness are:
(1) Diametral. (2) Circumferential confining gauge – shaft is confined in a ring gauge and rotated
against a set indicator probe. (3) Rotating on centres. (4) V-Block.(5) Three-point probe (120º
spacing )Accurate spindle.
(a) Part fixed, exterior spindle with probe rotates, (b) probe fixed, Part rotates with spindle.
1.Diametral Method. In this method, the measuring plungers are located 180º apart and the
diameter is measured at several places. This method is suitable only when the specimen is
elliptical or has an even number of lobes. Diametral check does not necessarily disclose effective
size or roundness. This method is unreliable in determining roundness.
2.Circumferential confining Gauge. Fig. 7.35 shows the principle of this method. It is useful for
inspection of roundness in production. How ever, this method requires a separate highly
131
accurate master for each size part to be measured. The clearance between part and gauge is
critical to reliability. This technique does not allow for the measurement of other related
geometric characteristics, such as concentricity, flatness of shoulders, etc. The values obtained
are dependent on the shape of the specimen.
3. Rotating on centres. (Refer Fig.7.36). Some parts, (such as shafts ) may be inspected for
roundness while mounted on centres. In this case, reliability is dependent on many factors like
angles of centres, alignment of centres, roundness and surface condition of the centres and centre
holes, and run out of piece. Out-of-straightness of the part will cause a doubling run out effect and
appear to be roundness error.
Any or all of these factors may combine, creating a high degree of uncertainty as to exact nature of
the error.
For workshop purpose, the V-block method is quite accurate as it is capable of indicating
normal requirements of accuracy. However for very precise job where more reliable and more
accurate results are desired, the second method is recommended which is quicker and also
eliminates the effects of angle of the block and the number of lobes on part, but of course, is a very
costly one.
4. Assessment using a V-block. The set up employed for assessing the circularity error (lobing) by
using a V-block is shown in Fig.7.37, i.e., the vee-block is placed on a surface plate and the work to
be checked is placed upon it. A sensitive dial indicator is firmly fixed in a stand and its feeler
made to rest against the surface of the work. The work is rotated to measure the rise and fall of the
work-piece. For determining the number of lobes on the work – piece is first tested in a 60ºV-block
and then in a 90º V-block. The number of lobes is then equal to the number of times the indicator
132
pointer deflects during rotation of the work piece through 360º. The idea of testing the work –
piece in two V-blocks is that when an elliptically shaped part is rotated on a V-block is that when
an elliptically shaped part is rotated on a V-block of angle 60º, no change in reading is indicated,
whereas if the same part is rotated on a90º angle Vee –block, two maximum and two minimum
readings are indicated on the indicator.
The method of determination of the circularity error by V-block has certain limitations and,
therefore, the following points should be born in mind.
(a)The error of circularity measured on a V-block is greatly affected by the following factors:
(i) Angle of V-block very much influences in the determination of circularity error, i.e. if the
circularity error is say ∆e, then it is possible that the indicator shows no variation, or same as ∆e,
or twice ∆e ,or thrice ∆e, or some other value for each position of the instrument when V-blocks of
different, angles are used, This is because of the fact that as the angle of V changes the place where
the work- piece rests also changes, Ultimately it will be noted that the same work – piece rests at
higher place in V-block of smaller angle and at lower place in V-block of larger angle and thus the
indicator will show different readings for same work-piece kept in same position on different
angle V-blocks.
(ii) Position of the instrument, i.e. whether measured from top or bottom.
(iii) Number of lobes on the rotating part (e.g., elliptical, triangular, quadrilateral, pentagonal
etc.)
(b)
The instrument’s position should be in the same vertical plane as the point of contact of the
part with the V-block. If the error is measured at a point far from the V-block, The error of
circularity will be influenced by the radial run out of the part.
(c)
A leaf spring should always be kept below the indicator plunger and the surface of the part,
otherwise readings are likely to be affected by minute undulations of the surface, such as surface
roughness.
It is obvious that with different angle of V-blocks, dial indicator shows different readings
for the same work-piece placed in the same position. If this problem is studied further by
analyzing an elliptical work piece on different angle V-blocks, it will be found that some solution
133
can be arrived at. Let us consider an elliptical work piece whose major axis if 2∆more than the
minor axis as shown in Fig.7.38.
We will place this work –piece on different angle V-blocks first with major axis placed
along the direction of dial movement and then with minor axis along the direction of dial –
movement. This is so because the work-piece has two number of lobes.
It may be noted that it is possible to take dial readings both from top as well as bottom.
Consider the case when work-piece is placed at flat. Surface in two positions as shown in Fig.7.39.
It will be noted that the error of circularity when measured from top = 2∆ and when measured
134
from bottom =0, whereas the actual error of circularity in the work-piece =∆.
Similarly, if the work-piece is placed on a V-block of angle 120º it will be found by
calculation or otherwise that the error of circularity in this case when measured from bottom
=0.42∆.
In the same way, it will be found that when work-piece is tested on the 108º V-block, the
circularity error measurement when measured from top=1.38∆ and 0.62∆ if measured from
bottom. The corresponding values for 90º and 60º V-block will be ∆, ∆ and 0, 2∆ respectively.
Thus for an elliptical work-piece which has got 2 numbers of lobes, the ratio of circularity
error measurement by dial indicator on different V-blocks and the actual error is as given below
such values of the constant k=
Measured value of error of circularity
Actual value of error of circularity
can be determined for different shapes of work –pieces, i.e. having different number of lobes.
V-Block. (a) Fixed angle. Depending on the number of lobes on a part, the following angles of Vblocks are recommended for measurement of correct roundness by V-block method.
Lobes
Three-point out of roundness
Five – lobed part
Seven – lobed part
Angle of V-block
60º
180º
128º
34
(b)
Adjustable V-Block. It is usually difficult to ascertain the number of lobes of a part and
have large number of fixed angle V-Blocks. V-block which can be adjusted to correct angle to
show out-of roundness is better choice.
V-Block method is limited in the determination of roundness of part because it is suitable only
when the number of lobes is known and is uniformly arranged, which is never the case.
Various terms used in screw threads.
Screw thread terminology.
1. Screw Thread. A screw thread is a continuous helical groove of specified cross-section
produced on the external or internal surface of a cylinder or a cone.
2. Multiple Start Thread. This is produced by forming two or more helical grooves, equally
spaced and similarly formed in an axial section on a cylinder. This gives a quick traverse
without sacrificing core strength.
3. Crest. Crest is the prominent part of thread i.e. top surface joining the two sides of thread.
4. Root. Root is the bottom of the groove between the sides of two adjacent threads.
135
5. Flank. The straight surface between the crest and root (which connects the corresponding point
on the next (adjacent) thread is called pitch of the thread.
6. Pitch. The distance measured parallel to the axial from a point on a thread to the
corresponding point on the next (adjacent) threads is called pitch of the thread.
7. Lead. Lead is the distance through which a screw advances axially in one complete revolution.
For a single start thread. It can also be d as a distance measured radically between the major
and minor diameters.
8. Depth of thread. It is the distance between the crest and root of the thread measured
perpendicular to the axis of the thread. It can also be d as a distance measured radially
between the major and minor diameters.
9. Thread Angle (included angle). It is the angle included between the flanks or slopes of a
thread measured in an axial plane.
10. Flank angle. The angle made by the flank of a thread with the perpendicular to the thread axis
is called flank angle. It is equal to half the thread angle.
11. Lead Angle. On a straight thread, lead angle is the angle made by the helix of the thread at the
pitch line with plane perpendicular to the axis.
12. Helix Angle. On a straight thread, the helix angle is the angle made by the helix of the thread at
the pitch line with the axis.
13. Major diameter. It is the diameter of an imaginary c0-axial cylinder which would touch the
crests of an external thread or roots of an internal thread. It is also called as external diameter,
core diameter, outside diameter or full diameter of external threads.
14. Minot diameter (Core diameter or root diameter). It is the diameter of an imaginary co-axial
cylinder which would touch the roots of an external thread or crests of an internal thread.
15. Effective diameter (pitch diameter). It is the diameter of an imaginary co-axial which intersects
the flanks of the threads such that the width of the threads (metal) and widths of the spaces
between the threads are equal, each being half the pitch.
16. Virus effective diameter (functional diameter). The functional diameter of an external thread is
the pitch diameter of the enveloping thread of perfect thread elements having full depth of
engagement but clear at crests and roots, and of specified length.
When added to (for external threads) the pitch diameter, the cumulative effects of deviations
from specified profile for a specified length of engagement gives the functional diameter.
Various methods of radius measurement.
To find out the Radius of Circle of any job having a portion of a Circle:
This method requires the use of surface plate, Vernier Caliper, C-clamp and two pins of equal
size. This method could be best applied to jobs like cap of a bearing. The job is first clamped to
surface plate with the help of C-clamp. It should be clamped in such a way that central position of
the circular part is in contact with the surface plate as far as possible. Then two pins of equal
diameter are placed on each side of the work as shown in figure and the reading over the balls is
taken with the Vernier caliper. Let the reading be / let the diameter of pins be d and radius of job
R.
136
Let ‘O’ be the assumed centre of the circle. Then in rt. d OAB. In figure
OB2 = OA2 + AB2
2
2
2
d 
d   1 d 

or  R+    R    
2 
2   2 

d
d2
(1  d)2
or R 2 
 Rd  R  2  Rd 
4
2
4
1
or 2Rd= (1  d)2
4
(1-d)2 (1  d)2
and R =

4  2d
8d
To find out the Radius of a Concave surface
i)
ii)
iii)
When the edges are well-d
When the edges are rounded up.
When the edges are well-d, his method is applicable to those parts which have large radius
to curvature. This required the use of a surface plate, angle plate, height gauge, depth
micrometer, slip gauges and a C-clamp.
The part to be tested is kept one surface plate and with the help of a depth micrometer the
maximum depth of the cavity is determined. Let is be h. Next the part is kept in such a way that
cavity is resting against an angle plate and the part is then clamped in this position. The hole is
then measured from edge to edge with a height gauge having a sharp scribing arm. Let the
maximum dreading, i.e. diameter of
the hold be d (fig).
137
Let O be the assumed centre of the cavity and R the radius of curvature.
Then in rt. d OAB,
OA2 = AB + BO2
2
or
 d
R     (R  h)2
 2
d2
=
 R 2  h2  2Rh
4
2
2
or
 d
2Rh =    h2
 2
2
 d
2
 2 h
d2 h
R=  

 .
2h
8h 2
ii) When he edges are rounded up. When the edges of the cavity are rounded up, then the radius
of curvature can be measured by a depth micrometer and slip gages. The width of the depth
micrometer base is measured with the help of slip gauges. Let is be d, then it is placed in the cavity
ill it fully rests in the cavity, its frame touching all the sides of cavity (fig). The measuring tip is
then lowered down till it touches the base. The reading is then noted on the thimble and let it be h.
now the case is similar to previous one and the radius of curvature R can be found out be the same
formula.
Other method to note down d and h is by using a heavy steel block, a steel ball and slip
gauges as shown in figure in this method, the steel ball is placed in the cavity and the heavy steel
block also put into the cavity. The space between the block and ball is filled up by a suitable length
of slip gauges so that L lock is just touching the sides of cavity.
Here length of block is d and length of slip gauges and diameter of ball constitute h. The
formula for finding the radius of curvature remains the same.
Working principle of profilometer
Profilometer: Profilometer is an indicating and recording instrument used to measure roughness
in microns. The principle of the instrument is similar to gramophone pick up. It consists of two
138
principal units: a tracer and an amplifier. Tracer is a finely pointed stylus. It is mounted in the pick
up unit which consists of an induction coil located in the field of a permanent magnet. When the
tracer is moved across the surface to be tested, it is displaced vertically up and down due to the
surface irregularities. This causes the induction coil to move in the field of the permanent magnet
and induces a voltage. The induced voltage is amplified and recorded.
This instrument is best sited of measuring sauce finish of deep bores.
Straightness and the various methods of measurement of straightness.
The tolerance on the straightness of a line is d as the maximum deviation in relation to the
reference straight line going the two extremities of the line under examination.
A line is said to be straight over a given length, if the distance of its points from two planes
perpendicular to each other and parallel to the generation direction of the line remains within the
specified tolerance limits.
The straightness error of a line is d as the distance ‘e’ between two lines drawn parallel to
the mean true line and enveloping the actual contour by passing through the highest and lowest
points on the measured line as shown in figure.
The mean true line should be chosen such that it passes through the maximum number of
points measured and the sum of the areas above it must be equal to the sum of areas below it.
The maximum straightness error can then the graphically determined by measuring the
normal distance (e) between the two straight lines drawn parallel to the mean true line,
139
enveloping all measured points.
For measuring the straightness of a line and its error, the following instruments are used.
(i)
(ii)
(iii)
Straight edge
Spirit level
Auto-collimator
Measurement of straightness
(i)
By using a spirit level. The most convenient method of testing straightness of a surface of
any length to a high degree of accuracy is by using spirit level or auto-collimator.
A straight line is drawn on the surface whose straightness is to be checked. A sensitive
spirit level. Fitted with two feet at a convenient distance apart is moved along this line in steps
equal to the pitch distance between centre lines of the feet. For each position, the reading is noted.
Variations in the bubble position represent angular variations in the surface and these are
converted into differences in high of the feet above or below the starting point.
(ii) Auto collimator method. The main principle of this method is same as that of the spirit level
method. In this method a block fitted with feet at convenient distance apart and carrying a plane
reflector is moved along the surface in steps equal to the pitch of the feet. Angular variations at
each position are used to plot the graph of errors.
When testing vertical surface an optical square may be interposed so that auto collimator
can be used in the horizontal position. This is usually more convenient that arrange the instrument
with its axis vertical.
A particular feature of this method is that it can be used for vertical side of horizontal slide
ways where the level cannot be used.
(ii) Straight edge method. This is simplest method of testing straightness of a surface. A straight
edge of know accuracy is applied to the surface to be tested and degree of contact is determined
by marking, feelers or light gap. The more accurate method of measuring straightness by a
straight edge is wedge method.
A straight edge is supported at the points for minimum deflection on two unequal piles of
140
slip gauges so that it is at a slight inclination to the surface to be tested. The distance between the
supports is divided into number of equal parts and marked on the straight edge. If both straight
edge and surface are perfectly straight, the gap at each point will very uniformly.
Assume that the slip gauges used have values 10mm and 10.1 mm as shown in the figure.
Let the distance between the slip values be divided into 5 numbers of equal parts. The gap at each
 0.1 
point will, therefore, vary by 0.02mm 
 now we can determine the value of pile of slip
 5 
required for exact contact at each position. Eg. At the first position it is 10 mm; at the second
position it will be 10.02 mm; at the third it will be 10.04 mm and so on. Insert the lip gauges of
appropriate value at each marked position. If there is no error, the slip will make contact with both
the surfaces exactly at the marked positions. If however, there are errors in straightness, the slips
will not fit exactly at their marked positions, but will be displaced one way or other along the
straight edge by amounts proportional to the errors.
This is very sensitive method of measurement and can be made as sensitive as desired by
choosing a small wedge angle and large number of measuring positions. Care must be taken to see
that the slips do not wring to the surface otherwise the whole sensitivity will be lost.
Various methods of measurement of roundness.
The most commonly used methods of measurement of roundness are :
1.Using V block and Dial indicator
2.Roundness measuring machine
3.Bench center method
1. V-block and dial indicator method. A very simple and most commonly used method of
measuring out of roundness is by using a V block and dial indicator. The set up employed for this
purpose
is
as
shown in figure.
141
The V-block is placed on the surface plate and the work to be checked is placed upon it.
A sensitive dial indicator is firmly fixed in a stand and its feeler made to rest against the
surface of the work. The work is rotated about the diameter to be checked the dial indicator
records any variation in dimensions due to out-of-roundness.
This method converts the diameter measurement to a chordal-height variation, and
presents a new set of measurement peculiarities which are dependent upon the included angle of
the V-block and the number of lobes present on the circumstance of the work piece to be
measured.
Plotting Polar Graph
The ideal about the actual shape of the work piece can be obtained by actually plotting the
polar graph. Equally spaced 12 markings (at angles of 30) are made on the face of the work piece
to be measured. The work piece is properly cleaned and then placed on the V-block against a rigid
block with a steel ball in between as shown in figure the dial indicator is placed just above the
work piece so that it touches the work piece nearly at the centre of the V-block. The work piece is
then rotated such the marking on the work piece is below the indicating plunger. The readings of
the dial indicator are noted down for all the markings. This procedure is repeated three times to
take the average value.
For plotting the polar graph, a suitable scale is chosen depending upon the maximum value
of the reading. Then a circle of diameter nearly four times the maximum reading of the dial
indicator is drawn and divided into twelve equal numbers of angular divisions as shown in figure.
Inside the outer circle, another concentric circle of suitable diameter is drawn. Then the values of
the indicator are plotted in radial direction taking the smaller circles as the reference circle in order
that both the positive and negative readings are plotted with the prepared graph.
For obtaining the actual profile of the work piece in individual points are then joined by
straight lines. The error is measured as the radial distance between the minimum inscribing circle
for the profile obtained. This is done by hit and trial method such that this distance is minimum.
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The actual value of the error of roundness is given by,
Error =
measured error from polar graph
k
where, k is a constant, value of which depends upon the shape of the workpiece and angle
of V-block (as indicated in table).
For determining the number of lobes (for selecting the constant value k from the table, the
work piece is first tested in a 60 V-block and then in a 90 V-block). The number of lobes is then
equal to the number of times the indicator pointer deflects during rotation of the work piece
through 360 the reason for testing the work piece part is rotated on a V-block of angle 60, no
change in reading is indicated, whereas if the same part is rotated on a 90 V-block, two maximum
and two minimum readings are indicated on the indicator.
Work on an axis against a fixed indicator can be use to obtain results of less precision. In
this type the work is placed on a circular table with its centre set, as from a fixed base, is placed
with its plunger in contact with the edge of the disc.
This method is more accurate a record of the exact profile of the job is made automatically
and thus the waviness is also superimposed upon the profile of the job. A permanent polar chart
record is usually provided and the method leads itself to standardization. The sophisticated
machines have the provision to check concentricity roundness, alignment, squareness, parallelism
and flatness.
2. Bench centre method. In this method bench centres and a precision mechanical (dial gauge), air
or electronic indicator may be used to measure out of roundness of a work piece on a radial basis.
The accuracy of the result is, however, effected by shape and angle of centres and the centre holes,
lubrication of centre etc. in the part under test.
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Alignment tests conducted on a lathe.
1. Test for level of installation
(a) In longitudinal direction (b) In transverse direction
Measuring instruments. Spirit level, gauge block to suit the guide ways of the lathe bed.
Procedure. The gauge block with the spirit level is placed on the bed ways on the front position,
back position and in the cross wise direction. The position of the bubble in the spirit level is
checked and the readings are taken.
Permissible error. Front guide ways 0.02 mm/meter convex only. Rear guide ways, 0.01 to 0.02
convexity. Bed level in cross-wise direction  0.02 meters. Straightness of slide ways (for machines
more than 3m turning length only measurement s taken by measuring taught wire and
microscope or long straight edge). Tailstock guide ways parallel with movement of carriage
0.02mm/m. no twist is permitted.
The error in level may be corrected by setting wedges at suitable points under the support feel or
pads of the machine.
3. Straightness of saddle in horizontal plane.
Measuring instruments. Cylindrical test mandrill (600 mm
long), dial indicator.
Procedure. The mandrel is held between centres. The dial indicator is mounted on the
saddle. The spindle of the dial indicator is allowed to touch the mandrel. The saddle is then
moved longitudinally along the length of the mandrel. Readings are taken at different places
Permissible error. 0.02 mm over length of mandrel.
4.Alignment of both the centres in the vertical plane.
Measuring instruments. Cylindrical mandrel 600mm long, dial gauge.
144
Procedure. The test mandrel is held between centres. The dial indicator is mounted on the saddle
in vertical plane as shown in figure. Then the saddle along with the dial gauge is traveled
longitudinally along the bed ways, over the entire length of the mandrel and the readings are
taken at different places.
Permissible error 0.02 mm over 600 mm length of mandrel (tail stock centre is to lie higher only).
5.True running of taper socket in main spindle.
Instruments required. Test mandrel with taper shank and 300 mm long cylindrical measuring
part, dial gauge.
Procedure. The test mandrel is held with its taper shank in a head stock spindle socket. The dial
gauge is mounted on the saddle. The dial gauge spindle is made touch with the mandrel. The
saddle is then traveled longitudinally along the bed ways and readings are taken at the points A
and B as shown in figure.
Permissible error. Position A, 0.01 mm, position B 0.02 mm.
6. Parallelism of main spindle to saddle movement.
(a) Ina a vertical plane (b) In horizontal plane
Measuring instruments. Test mandrel with taper shank and 300 mm long cylindrical measuring
part, dial gauge.
Procedure. The dial gauge is mounted on the saddle. The dial gauge spindle is made to touch the
mandrel and the saddle is moved to and fro. It is checked in vertical as well as in horizontal plane.
Permissible errors. (a) 0.02/300 mm mandrel rising towards free and only. (b) 0.02/300 mm
mandrel inclined at fee end towards tool pressure only.
7. Movement of upper slide parallel with main spindle in vertical plane.
Measuring instrument. Test mandrel with taper shank and 300mm long cylindrical measuring
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part, dial gauge.
Procedure. The test mandrel is fitted into the spindle and a dial gauge clamped to the upper slide.
The slide is traversed along with the dial gauge plunger on the top of the stationery mandrel.
Permissible error-0.02 mm over the total movement of the slide.
8. True running of locating cylinder of main spindle.
Measuring instrument. Dial gauge.
Procedure. The dial gauge is mounted on the bed, touching at a point on main spindle.
The main spindle is rotated by hand and readings of dial gauge are taken.
Permissible error -0.01 mm.
9. True running of head stock centre.
Measuring instrument. Dial indicator.
Procedure : Tailstock sleeve is fed outwards. The dial gauge is mounted on the saddle. Its spindle
is touched to the sleeve at one end and then saddle is moved to and fro, it is checked in H.P. and
V.P. also.
Permissible error. (a) 0.01/100 mm (Tailstock sleeve inclined towards tool pressure only). (b)
0.01/100 mm (Tailstock sleeve rising towards free end only).
10. Parallelism of tail stock sleeve taper socket to saddle movement (a) in V.P (b) in H.P.
Measuring instruments. The mandrel with taper shank and a cylindrical measuring part of 300mm
length, dial gauge.
Procedure. Test mandrel is held with its taper shank in a tail stock sleeve taper socket. The dial
146
gauge is mounted on spindle. The dial gauge spindle is made touch with the mandrel. The saddle
is the traversed longitudinally along the bed way and readings are taken.
Permissible error.
(a) 0.03/300 mm (mandrel rising towards free and only)
(b) 0.03/300 mm (mandrel inclined towards tool pressure only)
Various alignment test on a milling machine.
Alignment tests on milling machine.
(1) Flatness of work table.
(a) in longitudinal direction
(b) in transverse direction.
Measuring instruments spirit level.
Procedure. A spirit level is placed directly on the table at points about 25 to 30 cm apart, at A B C
for longitudinal tests and D E and F for the transverse test.
The readings are noted.
Permissible error.
Direction A – B – C  0.04 mm
Direction D – E – F  0.04 mm
(2) Parallelism of the work table surface to the main spindle.
Measuring instrument. Dial indicator test mandrel 300 mm long, spirit level.
Procedure. The table is adjusted in the horizontal plane by a spirit level and is then set in its mean
position longitudinally. The mandrel is fixed in the spindle taper. A dial gauge is set on the
machine table, and the feeler adjusted to touch the lower surface of the mandrel. The dial gauge
readings at (A) and (B) are observed, the stand of the dial gauge being moved while the machine
table remains stationery.
Permissible error. 0.02/300 mm.
(3) Parallelism of the clamping surface of the work table in its longitudinal motion.
Instruments. Dial gauge, straight edge.
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Procedure. A dial gauge is fixed to the spindle. The gauge spindle is adjusted to touch the table
surface. The table is then moved in longitudinal direction and readings are noted. If the table
surface is uneven it is necessary to place a straight edge on its surface and the dial gauge feeler is
made to rest on the top surface of the straight edge.
Permissible error. 0.02 up to 50 mm length of traverse, 0.03 up to 1000 mm and 0.04 above 1000
mm length of traverse.
(4) Parallelism of the cross (transverse) movement of the worktable to the main spindle.
(a) in a vertical plane
(b) in horizontal plane
instruments. Dial gauge, test mandrel with taper shank.
Procedure. The table is set in its mean position. The mandrel is held in the spindle. A dial gauge
field to the table is adjusted so that its spindle touches the surface of the mandrel. The table is
moved cross-wise and the error is measured in the vertical plane and also in the horizontal plane.
Permissible error. 0.02 for the overall traverse movement of the work table.
(5) rue running of internal taper of the main spindle.
Instrument 300mm long test mandrel, dial gauge
Procedure. The test mandrel with its taper shank is held in the main spindle. Dial gauge is kept
scanning the periphery of the mandrel. Spindle is rotated and dial gauge readings are noted at
different points say A and B as shown.
Permissible error. A: 0.01 mm, position B: 0.02 mm.
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(6) Squareness of the centre T-slot of worktable with main spindle.
Instruments. Dial gauge, special bracket.
Procedure. To check the perpendicularity of the locating slot and the axis of the main spindle. The
table should be arranged in the middle position of its longitudinal arranged in the middle position
of its longitudinal movement, and a bracket with a tenon at least 150 mm long inserted in the
locating slot, as shown in figure.
A dial gauge should be fixed in the spindle taper, the feeler being adjusted to touch the
vertical face of the bracket. Observe the reading on the dial gauge when the bracket is near one
end of the table, the swing over the dial gauge and move the bracket so that the corresponding
readings can be taken near the other end of the table.
(7) Parallelism of the T-slot with the longitudinal movement of the table.
Instrument. Dial gauge special bracket.
Procedure. The general parallelism of the T-slot with the longitudinal movement of the table is
149
checked by using 150 mm long braked having a tennon which enters the slot. The dial gauge is
fixed to the spindle taper and adjusted so that its feeder touches the upper surface of the bracket.
The table is then moved longitudinally while the bracket is held stationary by the hand of the
operator and dial gauge deviations from parallelism are noted down.
Permissible error. 0.0125 mm in 300 mm.
(8)
Parallelism between the main spindle and guiding surface of the
overhanging arm.
Instruments. Dial gauge, mandrel
Procedure. The overhanging arm is clamped in its extreme extended position. The dial gauge is
fixed to the arbor support.
The feeler of the dial gauge is adjusted to touch the top or ride of the test mandrel. The
arbor support can then be moved along the overhanging arm and the deviations from parallelism
observed on the dial gauge.
Tests on shaping machine.
The use of shaping machine is to create flat surfaces accurately. Therefore, the chief
requirements of the shaping machine are that it should cut straight, parallel and face flat.
The important alignment tests on shaping machine are described below:
1. Straightness and flatness of the table.
The straightness and flatness of the table is the fundamental requirement of the shaping
machine to produce accurate work pieces.
Instruments. Spirit level, gauge block.
Procedure. The table is brought in the central position. The spirit level is placed over the gauge
block at several points on the table parallel to and perpendicular to the direction of the table
feed and in all the positions the bubble in the spirit level must be central.
2. Parallelism of top surface of table to its transverse movements.
Instruments. Dial gauge, straight edge.
150
Procedure. The table is brought to one side end. Dial gauge is then moved in transverse
direction below dial gauge and readings are taken.
3. Parallelism of table top to ram movement (parallelism of the table feed under the tool)
Instrument. Dial gauge, straight edge.
Procedure. The ram is brought to the end of its edge. The dial gauge is placed on the table top
in the direction of movement of the ram. The ram is then moved backward and forward and
reading are taken.
Permissible error. 0.015 per 300 mm.
4. Trueness and parallelism of vertical ways of column.
Instruments. Dial gauge.
Procedure. The table is brought to its lowest position. The dial gauge is placed on the table so
that its feeler will touch the vertical ways of the column as shown in figure.
The table is then moved up and if the side ways are perfectly parallel and leveled straight, the
dial gauge touching to it will not shows any
5. The accuracy, squareness, and parallelism of T-slots on the label.
Instrument. Dial indicator, angle plate.
Procedure. The angle is inserted in the slot lengthwise and the dial gauge is set in the adjacent
parallel slot as shown in the figure the dial gauge is adjusted so that its feeler just touches the
angle plate. The reading is adjusted to zero and then the dial indicator is moved through the slot
lengthwise and the deflection
is noted.
Checking accuracy of T - slots
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Various alignment tests on pillar type drilling machine.
Before carrying out the alignment tests, the machine is properly leveled in accordance with the
manufacturers instructions.
The various tests performed on pillar drilling machine are:
Instruments. Straight edge, two gauge blocks; feeler gauges.
1. Flatness of clamping surface of base. The test is performed by placing a straight edge on two
gauge block on the base plate in various positions and the error is noted down by inserting feeler
gauges.
Permissible error. The error should not exceed 0.1/1000mm clamping surface and the surface
should be concave only.
2. Flatness of clamping surface of table
The test is performed in the same manner as test (1), but not on the label. The permissible error
is also same.
3. Perpendicularity of drill guide to the table base plate.
Instruments. Frame level.
The squareness (perpendicularity) of drill head guide to the table is tested.
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(a) In a vertical plane passing through the axes of both spindle and column, and
(b) In plane at 90 to the plane at (a).
The test is performed by placing the frame level (with graduations from 0.03 to 0.05 mm) on
guide column and table and the error is noted by noting the difference between the readings of the
two levels.
Permissible error. The error should not exceed 0.25/1000mm guide column for (a) and the guide
column should be inclined at the upper end towards the front, and 0.15/1000mm for (b).
For testing the perpendicularity of drill guide to the base plate the test is similar as above, the only
difference being that the frame level is to be placed on the base instead of a table.
4. Perpendicularity of spindle sleeve with base plate.
This test is performed in both the place as specified in test (3) and in the similar manner. The
only difference is that the frame levels are to be placed on spindle sleeve and base plate.
Permissible error. The error (i.e. the difference between the readings of the two levels) should not
exceed 0.25/1000mm for plane (a) and the sleeve should be inclined towards column only, and
0.15/100mm for plane (b).
5. True running of spindle taper
Instruments: Test mandrel, dial gauge
Procedure: The test mandrel is placed in the tapered hole of spindle and a dial indicator is fixed on
the table and its feeler made to scan the mandrel. The spindle is rotated slowly and readings on
indicator noted down.
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Permissible error. The error should not exceed 0.03/100mm for machines with taper up to Morse
No.2 and 0.04/300mm for machines with taper larger than Morse No.2.
6. Parallelism of the spindle axis with its vertical movements.
Instruments. Test mandrel, dial gauge.
Procedure. This test is performed into two planes (A) and (B) at right angles to each other. The test
mandrel is fitted into the taper hole of the spindle and the dial gauge is fixed on the table with its
feeler touching the mandrel. The spindle is adjusted in the middle position of its travel. The
spindle is moved in upper and lower directions of the middle position of its travel. The spindle is
moved in upper and lower directions of the middle position with slow vertical feed mechanism
and the readings of the dial gauge are noted down.
Possible error. For plane (A) and (B) both 0.03/100 mm, 0.05/300mm.
7. Squareness of clamping surface of table to its axis.
Instruments. Dial gauge.
Procedure. The dial indicator is mounted in the tapered hole of the spindle and its feeler is made
to touches the surface of table. The table is then moved slowly and the readings of dial gauge
noted down.
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Permissible error. The permissible error should not exceed 0.05/300am diameter.
8. Squareness of the spindle axis with table.
Instruments. Straight edge, dial gauge.
Procedure. This test is performed by placed the straight edge in position AA’ and BB’. The work
table is arranged in the middle of its vertical travel. The dial gauge is mounted in the tapered hole
of the spindle and its feeler is made to touch the straight edge first at A and readings are taken.
Then the spindle is rotated by 180 so that the feeler touches at point A’ and again the reading is
taken. The difference of these two reading is the error in squareness of spindle axis with table.
Similar readings are taken by placing the straight edge is position BB’.
Permissible error: The permissible errors are 0.08/300mm with lower end of spindle inclined
towards column only for set up AA’ and 0.05/300mm for set up BB’.
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UNIT – IV
LASER AND ADVANCES IN METROLOGY
Interferometer and types of interferometer.
Interferometer is optical instruments used for measuring flatness and determining the lengths of
slip gauges by direct reference to the wavelength of light.
Types :
1.
2.
3.
4.
NPL flatness interferometer
Michelson interferometer
Laser interferometer
Zesis gauge block interferometer
Common source of light used for interferometer.
a) Mercury 198
b) Cad minus
c) Krypton 86
d) Helium
e) Hydrogen
f) Laser mixed radiations
Crust and trough
The light is a form of energy being propagated by electromagnetic waves, which is a sine curve.
The high point of the wave is called crust and the low point is called trough.
Wavelength
The distance between two crust and two trough is called the wavelength.
156
Alignment test on machine tools
The alignment test is carried out to check the grade of manufacturing accuracy of the machine
tool.
Various geometrical checks made on machine tools.
1. Straightness of guide ways and slide ways of machine tools.
2. Flatness of machine tables and slide ways.
3. Parallelism equidistance and alignment of the Slide ways.
4. True running and alignment of shaft and spindle.
5. The pitch error or load of lead screw
6. Pitch errors of gears.
7. Distinguish between a geometrical test and practical test on a machine tool.
The alignment test is carried out to check the grade of manufacturing accuracy of the machine
tool.
Performance test consist of checking the accuracy of the finished component.
Alignment test consist of checking the relationship between various machine elements when the
machine tool is idle.
Performance test consists of preparing the actual test jobs on the machine and checking the accuracy
of the jobs produced.
Necessary conditions for interference of light waves
The following conditions should be satisfied. To observe the phenomenon of sustained or
continuous interference of light waves,
1. Two sources of light should be coherent, ie.
a) The two sources of light should continuously emit waves of same wave length or frequency.
b) For obtaining interference fringes, the amplitude, of the two interfering wave trains should be
equal or very nearly equal.
c) The two sets of wave trains from the two sources should either have the same phase or a
constant different phase.
2. Two sources should be very narrow.
3. Emitting a set of interfering beans should be very close to each other.
157
Interferometer measurement and effect
The line of single for viewing the bands should be nearly perpendicular to the reference
surface of the optical flat. It viewing angle varies by 5 degree, then no error in product. However,
when the viewing angle in bigger, then the actual fringes will be read less and errors of around
15%, 40% and 100% may occur with viewing angles eg 30 degree, 45 degree and 60 degree
respectively.
Monochromatic light in used for interferometer work
As the white light contains a whole spectrum of wavelengths and since the pitch of the
interference fringes will be different for each, the interference fringes formed will be mixture of all
and it becomes very difficult to distinguish the various dark and light fringes. The whole pattern
looks quite blurred and as the an gap between optical flat and the surface to be tested increases, it
becomes absolutely impossible to distinguish the dark and light fringes at any one point.
In the case of monochromatic light, the spread of wave length is very small and thus fringes
are formed at considerable separations of optical flat and surface. The interference fringle pattern
in much more clearly d.
Advantages of light std. of wavelength
Light standard s the length in terms of a std. which is not only constant, but also,
reproducible anywhere in the world. This is the major criterion for any standard. It does not
depend on reference to some particular and possibly whether able piece of metal. It become
possible because at constant pressure and temperature, each pure color of light from a vaporizing
element has a particular and constant wavelength, and with the adventure nuclear physics, it was
possible to obtain pure isotopes of various elements, serving as very pure mono chromatic light
source.
Advantages of using laser beam in interferometer
The laser provides a source of wherence and truly mono chromatic light. Non-laser light is
in coherent and does not exactly follow the sinusoidal wave, but is subject to small random
variations. The property of wherence in laser beam enables it to be projected in a narrow pencil of
beam (with out any scatter).
Various factor responsible for "Renaissance" of optics.
1. An enormoces increase in imaging performance due to computer - assisted optics design
correction and assembly.
2. The availability of new optical media.
158
3.
4.
5.
6.
The discovery and application of the laser.
The development of holography and Coherent optics.
The development of fiber - optics wave - guider.
Material structuring within micrometers.
"Flatness' as applied to metrology
Flatness is the minimum distance between the two parallel planes that cover all the
irregularities of the surface.
State the characteristic of the surface
The surface must be reflective in order to respond to interferometer measurement.
Advantages of laser as a light source in interfermetric measurement
The light emitted in coherent and highly monochromatic enabling interference fringes to be
produced over long distances as opposed to short distances with a conventional discharge lamp.
The light is of an intensity which enables the fringes produced to be readily detected by suitable
photo-cells, and the signal - to - noise ratio in such that counting speeds up to a million cycles per
second are possible. Further, the light in produced as a narrow parallel beam which eases the
problem of producing the optical components in an interferometer system.
Fundamental difference between a flatness interferometer and light interferometer
The fundamental difference between a flatness interferometer and light interferometer is
that the later incorporates a constant deviation prism which splits the light into number of parallel
beams each hawing a difference and closely d wavelength of known value.
Light sources are used in interferometer
Mercury, mercury 198, cadmium, krypton, krypton86, thallium, sodium, Helicem, neon, Gas laser.
Interferometer
It is an optical instrument used for measuring flatness and determining the length of slip
gauges by direct reference to the wavelength of light.
Types of interferometer
Michelson interferometer, twyman - green interferometer, NPL flatness interferometer.
159
CMM
It is a three dimensional measurements for various components. These machines have precise
movement is x-y-z co-ordinates which can be easily controlled and measured. Each slide in three
directions is equipped with a precision linear measurement transducer which gives digital display
and sense positive and negative direction.
Position accuracy.
It is s as difference between positions read out of machine along an individual axis and value of
a reference length measuring system. Three parameters are needed for position accuracy. Position
accuracy of x axis, y axis and z axis are measured.
Axial length measuring accuracy and volumetric length measuring accuracy.
Axial length measuring accuracy:
It Is d as difference between the reference length of gauges aligned with a machine axis and the
corresponding measurement results from the machine.
Volumetric length measuring accuracy:
It is s as difference between the reference length of gauges, freely in space and the corresponding
measured results from the machine.
Types of co-ordinate measuring machine.
Cantilever type : easy to load and unload, but mechanical error may occur due to sag or
deflection.
Bridge type : More difficult to load but mechanical errors are less.
Horizontal bore mill : It is used for large and heavy work pieces.
Vertical bore mill : It is very slow to operate but highly accurate.
Spherical co-ordinate measuring machine : Both linear and rotary axes are incorporated. It can be
used to measure various features of parts like cane, cylinder, hemisphere etc.
CNC, CMM
A numerical control system can be used with CMM to do calculations while measuring
complex parts. Error can be stored in memory while doing calculations. For automatic calibration
of probe, determination of co-ordinate system, calculation, evaluation and recording etc. special
software are incorporated.
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CMM software.
Measurement of diameter, center distance, and length can be measured as follows.
i)
Measurement of plane and spatial curves
ii) Minimize CNC programme
i)
Data communications
ii)
Digital input and output command
iii)
Interface to CAD software
Machine vision.
Machine vision can be d as a means of simulating the image recognition and analysis
capabilities of the human system with electronic and electromechanical techniques.
Four basic types of machine vision system
i) Image formation
ii) Processing of image
iii)
Analyzing the image
iv)
Interpretation of image
Advantages of machine vision system.
i) Reduction of tooling and fixture cash
ii) Elimination of need for precise part location
iii)
Integrated automation of dimensional verification
iv)
Defect detection
Gray scale analysis.
In these techniques, discrete areas or windows are formed around only the portions of the
image to be inspected. For determining if brackets are present, high intensity lighting is positions
so that a bracket, when the bracket is missing no shadow will be cash. When the bracket is present,
a large number of darker pixels can be observed in the window due to the cast shadow then when
a bracket is missing. A contrast threshold between the dark and light pixel value area can be set.
This type of discrete area analysis is a powerful tool can be used for inspection of absence, currant
part assembly, orientation, part, integrity etc.
Advantages of CMM.
I. The inspection rate is increased
II. Accuracy is reduced
III. Operator’s error can be minimized. Skill of the
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IV. operator is reduced.
V. Reduction in calculating, recording and set up time
VI. No need of GO / NOGO gauges
VII. Reduction of scrap and good part rejection.
Mention the disadvantages of CMM.
I.
II.
III.
IV.
V.
The table and probe may not be perfect alignment
The stylus may have run out
The stylus moving in z-axis may have some perpendicularity errors
Stylus while moving in x and y direction may not be square to each other
There may be errors in digital system
Mention the application of CMM.
I.
II.
III.
IV.
V.
CMM’s to find application in automobile, machine tool, electronics, space and many other
large companies
These are best suited for the test and inspection of test equipment, gauges and tools
For aircraft and space vehicles of hundred percent inspections is carried out by using CMM
CMM can be used for determining dimensional accuracy of the component
CMM can also be used for sorting tasks to achieve optimum pacing of components within
tolerance limit.
Past process metrology incorporated CNC machines
The process of measuring the work pieces during machining and automatically updating the
machine tool offsets in the control system to maintain the dimensional quality of the work piece
machined without any manual intervention is called post process metrology. The post process
metrology set up can reduce the cost and time of production.
Features of a flexible inspection system.
i)A powerful computer serves as a real time processor to handle part dimensional data and as a
multi programming system to perform such tasks as manufacturing process control.
ii)The terminal provides interactive communications with personal computer where the
programmes are stored.
iii)Input devices microprocessor based gauges and other inspection devices are used in CMM.
i) Co-ordinate measuring machine equipped with a laser probe ii) Virtual measuring system.
i)A CMM equipped with a laser probe can convert a part of physical model into a digitize file.
Such a file can be compared with other file and can be manipulated by designers to improve
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quality. Manufactures can verify that each finished part measures exactly as designed.
ii)Virtual measuring system uses a microscope system to examine as electronic replica of the
surface texture of part. Such a system is non-contact 3-D surface measurement system and provide
image of the surface. The images are processed on a PC using vertical scanning interferometer and
vision analysis software to produce 2D-profuile, 3-D plots and counter plots
It generates statistics for average roughness, average profile height, reduced peak height, cares
roughness depth, reduced valley depth and a number of other parameters. It also determines the
depth, spacing and angle of groove in a hared surface optical probe of a cylinder bore can be
rotated 360 degrees and moved vertically along the cylinder wall.
Three important field of machine vision system.
1.
Inspection : It is the ability of an automated vision system to recognize well d pattern and if
these pattern match these stored in the system, makes machine vision ideal for inspection of raw
materials, parts, assemblies etc.
2.Part Identification : It is the ability of part recognition provides positive identifications of an
object for decision making purposes.
3.Guidance and control : Machine vision systems are used to provide sensor feedback for real
time guidance and control ranging from visual serving of industrial robots and weld seam
tracking to calculation of geometric off sets for part processing and assembly operations.
Application of machine vision system.
I.
II.
III.
IV.
V.
This can be used to replace, machine for applications like welding, machining to maintain
relationship between tool and work.
Machine vision systems are used for printed circuit board
These are used for weld seam tracking, robot guidance and control, inspection of
microelectronic devices and tooling, on line inspection in machining operation, online
inspection of a assembling maintaining high speed packaging.
This is for the recognition of object from its image
Achieve 100% accuracy.
Steps involved in producing software for engineering metrology
i)Precise and detailed definition of geometrical form
ii) Specification of the measurement procedure
iii) Mathematical modeling of the measurement
Measuring machine.
It is a machine which is used for measurement of length over the other faces of length bar
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or any other long member with end, that may be rounded, or flat and parallel.
Measuring machine
Length bar measuring machine, new all measuring machine, universal measuring machine,
optical projection comparator, microscopes, optimeter, co-ordinate measuring machine, optical
probe, and etc.
Co-ordinate measuring machine (CMM)
Computerization in manufacturing has become so common that the introduction of
computerized co-ordinate machiners has revolutionized quality control in metal working.
A Co-ordinate measuring machine consists, in essence of a mean of moving a probe within
a 3-D rectangular Co-ordinate systems. This probe provides on electrical signal when contact with
the manufactured component in established, enabling the special Co-ordinates of selected contact
points to be accurately recorded.
Advantages of Co-ordinate measuring machines.
Flexibility :
CMM are flexible in that use, in the sense that they are not designed for any single or
particular task. Speed of measurement.
Component alignment and the establishment of appropriate reference points are very time
consuming with conventional inspection techniques, these procedures are greatly simplified with
computer assisted / controlled CMM's.
Improved accuracy:
All measurements on a CMM are taken from a common geometrically fixed measuring
system, eliminating the introduction of errors that can result from set up changes.
Reduced operator influence:
The use of digital readouts eliminates the subjective interpretation of reading common with
dial or vernier type measuring devices. Further more, operator "feel" ins avoided with toughtrigger prober.
In this manner, computer assisted / controlled CMMS have effectively deskilled the
measurement aspect of quality assurance.
Method by which the plate can be produced if the dimensions are produced using polar coordinates.
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The operation is that of boring the six holes.
Using the Co-ordinate method, it would be necessary for calculate of dimensions, A, B, C,
D, E, F, and G in Fig.
If the machine is filled with a circular table, the note may be bored from the centre of the
circle, and the only dimension required will be the diameter of the pitch circle H of the holes and
the angular spacing between them is 60 degree. It is recommended that the central note J in
provided for setting purpose, which in known as a reference note and simplifies checking of the
jig after manufacture. For checking the chord K should be given as this proves useful whatever
method of boring in employed.
Electronic gauging.
It is a transducer equipment using non-contracting sensors or probes to cover many
engineering problems of precision measurement. The operation relies on the electrical
capacitance, between the sensor and test surface, and one, two or six channels can be provided.
Component checked by Electronic gauging system.
This is essentially a differential measurement one sensor monitoring a shaft position which
will provide a changing datum should the shaft be warped. The second sensor responds to the
combined eccentricities due to the shaft and the disc. The measuring instrument, can be arranged
to read the differences between these two quantities.
CMM
CMM- Co-ordinate measuring machine It can be utilised to measure length and diameters
of both plain and the readed work tapers and the pitch of the screw the reads to a high degree of
accuracy.
Optical projection comparator (or) machine
It is a measuring instrument, which projects an enlarged image or shadow of the
components being measured on the screen, where it is compared to a master drawing. By this
device, complicated shaped parts can be easily checked.
Essential elements of an optical projection comparator
1) Source of light, 2) Collimating or Condensing lens, 3) Projection lens 4) Screen
Type of optical projection comparator
Horizontal projector, vertical projector, cabinet projector, Bausch and comp projector, and
societe Genevoise projector.
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Optical measuring instrument and types
It is a measuring equipment, where the lever in amplified by using light beam.
1. Vertical optimeter
2. Horizontal optimeter
3. Tool maker's microscope
Accuracy specification in CMM
There are two type of accuracies d in connection with CMM
a. Geometrical accuracy :
It is determined by independent measurement because they make major contribution to
overall accuracy of machine. It concerns the straightness, squareness of axis, and position
accuracy.
b. Total Measuring accuracy:
It is determined by utilising the entire machine system as applied to master gauges. It
concerns with the axis measuring accuracy and volumetric length measuring accuracy.
Machine vision system.
It can be d as a means of simulating the image recognizion and analysis capabilities of the
human eye\brain system with electronic and electro-mechanical techniques.
Human vision system.
In human vision system, eye senses the image and brain analysis the information and takes
action on the basis of analysis.
Basic steps in machine vision system
There are four basic steps in machine vision system.
a. Image formation
b. Processing of image in a form suitable for analysis by computer.
c. Interpretation of image and decision making.
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Machine vision systems.
The machine vision system could be used for Inspection, part identification, guidance and control.
Inspection
The ability of an automated vision system to recognise well d patterns and determine if
third pattern match those stored in the system makes machine vision ideal for inspection of raw
material, parts assemblies and etc.
Application of machine vision system.
Machine vision system can be used to replace human vision for applications like welding,
machining to ensure correct relationship in maintained between tool and workpiece, assembly of
parts to analys the position of parts so that other parts can be correctly aligned for insertion or
some other form of mating.
It is frequency used for printed circuit board inspection to ensure minimum conductor
width and spacing between conductor and many other features. These are used for weld seam
tracking, robot guidance and control, inspection of micro-electronic devices and tooling, on-line
inspection in machining operation, on-line inspection in machining operation, on-line inspection
of assemblies, monitoring high speed packaging equipment etc.
Application of computer in metrology.
Computers can be advantageously applied in the field of engg. metrology for tasks like
processing of acquired data, control of calibration equipment, in co-ordinate measuring machine,
etc.
Computer find extensive applications in the field of roundness measurement, form and
surface texture measurement.
Advantages of computer for processing of acquired data and control
I.
A particular measurement sequence is strictly adhered to since computer accepts the
information in a sequential manner and also provides necessary guidance to operator in this
regard.
II. Inspection time in reduced, considerably.
III. Calculation of final result in available immediately on completion of the last measurement.
IV. Rejected readings can be repeated.
V. Scope for copying and calculation errors is virtually eliminated.
VI. The checking of the result in made much more simple.
VII. Time for calibration is reduced considerably.
VIII. New operator can be trained quickly and they need not be highly qualified.
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Different methods of dimensional measurement using layer.
Laser techniques are used for measurement of dimensions in the following ways.
a. Scanning laser gauges.
b. Photo diode array imaging
c. Diffraction pattern system.
d. Laser triangulation sensors
e. Interferometers.
f. Holography
Advantages and disadvantages of analog image sensors
Advantages :
Resolution, low lighting, contrast, sensitivity, capability to preprocess cost.
Disadvantages :
Poor linearity image drift and image burn.
Working principle and the steps involved machine vision system.
The machine vision system involves following four basic steps.
Image
formation
Processing of image in a form suitable for analysis by computer
Defining and analysing the characteristics of image
Interpretation of image and decision making.
We will now discuss these four steps in more details.
Image
formation. For formation of image suitable light source is required. It may consist of
incandescent light, fluorescent tube, fiber-optic bundle, arc lamp, or strobe light. Laser beam is
used for triangulation system for measuring distance. Polarised or ultraviolet light is used to
reduce glare or increase contrast. It is important that light source is placed correctly since it
influences the contrast of the image. Selection of proper illumination technique, (viz, back
lighting, front lighting-diffused or directed bright field, or directed dark field, or polarised,
structured light) is important. Back lighting is suited when a simple silhouette image is required
to obtain maximum image contrast.
Front lighting is used when certain key features on the surface of the object are to be inspected.
If a three-dimensional feature is being inspected, side lighting or structured lighting may be
required.
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The proper orientation and fixturing of part also deserve full attention.
An image sensor like vidicon camera, CCD or CID camera is used to generate the electronic
signal representing the image. The image sensor collects light from the scene through a lens and
using a photosensitive target, converts it into electronic signal. Most image sensors generate
signals representing two-dimensional arrays (scans of the entire image).
Vidicon Camera used in closed – circuit television systems can be used for machine vision
systems. IN it, an image is formed by focussing the income light through a series of lenses onto
the photoconductive face plate of the vidicon tube. An electron beam within the tube scans the ph
to conductive surface and produces an analog output voltage proportional to the variations in
light intensity for each scan line of the original scene.
It provides a great deal of information of a scene at very fast speeds. However they tend to
distort the image due to their construction and are subject to image burn-in on the photo
conductive surface. These are also susceptible to damage by shock and vibration.
Solid State Cameras. These are commonly used in machine vision systems. These employ
charge coupled device (CCD) or change injected device (CID) image sensors. They contain matrix
or linear array of small, accurately spaced photo sensitive elements fabricated on silicon chips
using integrated circuit technology, Each detector converts the light falling on it, through the
camera lens, into analog electrical signal corresponding to light intensity. The entire image is thus
broken down into an array of individual picture elements (pixels).
Typical matrix array solid state cameras may have 256 x 256 detector elements per array.
Solid-state cameras are smaller, rugged and their sensors do not wear out with use. They exhibit
less image distortion because of accurate placement of the photodetectors. CCD and CID differ
primarily in how the voltages are extracted from the sensors.
ii) Image processing : The series of voltage levels available on detectors representing light
intensities over the area of the image need processing for presentation to the microcomputer in a
format suitable for analysis. A camera may typically from an image 30 times per sec i.e. At 33 m
sec intervals. At each time interval the entire image has to be captured and forzen for processing
by an image processor. An analog to digital converter is used to convert analog voltage of each
detector into digital value.
If voltage level for each pixel is given either 0 or 1 value depending on some threshold
value, it is called Binary System. On the other hand gray scale system assigns upto 256 different
values depending on intensity to each pixel. Thus in addition to black and white, many different
shades of gray can be distinguished. This thus permits comparison of objects on the basis of
surface characteristics like texture, color, orientation, etc. All of which produce subtle variations
in light intensity distributions. Gray scale systems are used in applications requiring higher
degree of image refinement. For simple inspection tasks, silhoutte images are adequate and
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binary system may serve the purpose. It may be appreciated that gray-scale system requires huge
storage processing capability because a 256 x 256 pixel image array with upto 256 different pixel
values will require over 65000-8 bit storage locations for analysis, at a speed of 30 images per
second. The data processing requirements can thus be visualised. It is, therefore, essential that
some means be used to reduce the amount of data to be processed. Various techniques in this
direction are :
a) Windowing. This technique is used to concentrate the processing in the desired area of interest
and ignoring other non-interested part of image. An electronic mask is created around a small
area of an image to be studied.
Thus only the pixels that are not blocked out will be analysed by the computer.
a) Image Restoration. This involves preparation of an image in more suitable form during
the pre-processing stage by removing the degradation suffered. The image may be degraded
(blurring of lines/ boundaries; poor contrast between image regions, presence of background
noise, etc.) due to motion of camera / object during image formation, poor illumination /poor
placement, variation in sensor response, poor contrast on surface, etc.).
The quality may be improved, ( i ) by improving the contrast by constant brightness
addition,( ii ) by increasing the relative contrast between high and low intensity elements by
making light pixels lighter and dark pixels darker (contrast stretching ) or ( iii ) by fourier domain
processing.
Other techniques to reduce processing are edge detection and run length encoding. In
former technique, the edges are clearly found and d and rather than storing the entire image, only
the edges are stored. In run-length encoding, each line of the image is scanned, and transition
points form black to white or vice versa are noted, along with the number of pixels between
transitions. These data are then stored instead of the original image, and serve as the starting
point for image analysis.
iii) Image Analysis. Digital image of the object formed is analysed in the central processing
unit of the system to draw conclusions and make decisions. Analysis is done by describing and
measuring the properties of several image features which may belong to either regions of the
image or the image as a whole. Process of image interpretation starts with analysis of simple
features and then more complicated features are added to it completely. Analysis is carried for
describing the position of the object, its geometric configuration, distribution of light intensity
over its visible surface, etc.
Three important taks performed by machine vision systems are measuring the distance of
an object from a vision system camera, determining object orientation, and defining object
position.
The distance of an object from a vision system camera can be determined by stadimetry
(direct imaging technique, in which distance is judged by the apparent size of an object in the field
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of view of camera after accurate focussing), or by triangulation technique, or by stereo vision
(binocular vision technique using the principle of parallax).
The object orientation can be determined by the methods of equivalent ellipse (by
calculating an ellipse of same area as the image of object in two- dimensional plane, and
orientation of object being d by the major axis of the ellipse), the connecting of three points
(defining orientation by measuring the apparent relative position of three points of image), light
intensity distribution (determining orientation based on relative light intensity), structured light
method (in which the workpiece is illuminated by the structured light and the three dimensional
shape and the orientation of the part are determined by the way in which the pattern is distored
by the part).
Image can be interpreted by analysis of the fundamental geometric properties of twodimensional images. Usually parts tend to have distinct shapes that can be recognized on the
basis of elementary features. For complex three-dimensional objects, additional geometric
properties need to be determined, including descriptions of various image segments (process
being known as feature extraction). In this method the boundary locations are determined and the
image is segment into distinct regions and their geometric properties determined. Then these
image regions are organised in a structure describing their relationship.
An image can also be interpreted on the basis of difference in intensity of light in different
regions. Analysis of subtle changes in shadings over the image can add a great deal of
information about the three-dimensional nature of the object.
Advantages and Limitations of computer in processing
The advantages of using computer for processing of acquired data and control are as under :
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A particular measurement sequence is strictly adhered to since computer accepts the
information in a sequential manner and also provides necessary guidance to operator in this
regard.
Inspection time is reduced considerably
The calculation of final result in available immediately on completion of the last
measurement.
Rejected readings can be repeated straight away, before the set up is disturbed.
Scope for copying and calculation errors is virtually eliminated.
The checking of the result is made much more simple.
Time for calibration is reduced considerably.
New Operation can be trained quickly and they need not be highly qualified.
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The limitations on use of computers for this application could be :
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Computer adheres to a given criteria rigorously and thus all the qualifying requirements and
ability of operator in accepting / rejecting a reading need to be told to computer clearly
without any ambiguity.
Sometimes a number may be entered incorrectly due to transposing error or key-bounce.
Strict control is needed over the use, amendment and copying of programme tapes to ensure
that unauthorised modifications are not made.
Checking procedure to ensure correct loading of program from tape needs to be followed.
Measurement process gets remote from the operator.
It is difficult to locate the source of problem by normal operator.
While the effects of drifts, environment influences are hidden or not noticed; but operator
may not get that confidence.
While human eye and memory are extremely good at detecting drifts and averaging high
frequency noise on signals, careful programming has to be undertaken to give a computer a
similar facility.
Co – ordinate Measuring Machines (CMM) – Principle.
These machine have precise movements in x-y-z coordinates which can be easily controlled
and measured. Each slide in three directions is equipped with a precision linear measurement
transducer which gives digital display and sense +vd/ -ve direction. These are manufactured in
both manual and computer-controlled models and come in a wide range of sizes to accommodate
a variety of applications. The measuring head incorporates a probe tip, which can be of different
kinds like taper tip, ball tip etc. Various type of CMMs are shown in Fig. 17.11. The cantilever
type is easiest to load and unload, but is most susceptible to mechanical error because of sag or
deflection in y -axis beam. Bridge type is more difficult to load but less sensitive to mechanical
errors. Horizontal boring mill type is best sited for large heavy workpieces. Vertical bore mill
type is highly accurate but usually slower to operate. A floating bridge type machine is also
available in which the complete bridge can slide in y-direction on the slides. It has the
compromises of both cantilever and bridge type, and is thus fast to operate, simple in alignment,
and rugged construction affords consistent accuracy.
For measuring the distance between two holes, the workpiece is clamped to the worktable
and aligned with the machine's three mutually perpendicular x, y and z measuring slides. The
tapered-probe tip is then seated in first datum hole and the probe position digital readout is set to
zero. The probe is then moved to successive holes, at each of which the digital readout represents
the coordinate part print hole location with respect to the datum hole. Machine is also equipped
with automatic recording and data processing units which are essential when complex geometric
and statistical analysis is to be carried out. In fact, in modern machines, automatic on -line
processing of measurement data is possible when the part is still on the worktable.
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In a special coordinate measuring machine, both linear ( x and z axes) and rotary axes are
incorporated. The machines can measure various features of parts whose shapes are objects of
revolutions like cones, cylinders and hemispheres.
R-0 machines having motions of their measuring head in R, 0 and
inspecting parts that are basically spherical.
direction are used for
As it is impossible to manufacture a mechanically perfect machine it is important to be able
to analysee the geometry errors associated with each individual CMM and determine their effects
on the machine's measurement accuracy. The result of such analyses can be used to compensate
for these effects and thus provide a high degree of accuracy that could not otherwise be achieved.
The prime advantage of co-ordinate measuring machine is the quicker inspection coupled
with accurate measurements.
The co-ordinate measuring machine with mechanical gauge makes use of two-axis X and Y
positioning tables to bring the work to the probe that engages the holes to be inspected.
Some machines are equipped with an optical comparator as well as travel dial indicator.
Present day co-ordinate measuring machines are three-axis digital read-out type and work
up with an accuracy of 10 microns and resolution of 5 microns. These utilise a measuring element
called inductory data element which uses inductive coupling between conductors separated by a
small air gap. As this element is not subjected to wear, it does not develop inaccuracy. It does not
require reference standards or any other external device for its operation. The workpiece is
aligned by a probe and by a switching adjustment on the worktable.
Many machines utilize More fringe concept for measurement.
Some coordinate measuring machines are available with accessories like optical viewing
screen, (optical comparator), microscope attachment for the inspection of thin, soft, or delicate
workpieces, and automatic print out. Some machines, it addition to measuring in three axes, are
also designed to permit the checking of angularity, roundness, taper, and concentricity. Provision
of rotary table makes such co-ordinate measuring machine more versatile because setting of a part
need not be changed and all areas can be approached due to positioning of rotary table. The
errors likely to occur in multiple set-ups are thus avoided.
Some co-ordinate measuring machines utilise electronic indicator probe (mounted on the
end of the spindle) which can reach over and under the workpiece to check squareness in a single
set up. Some machines are provided with linear air bearings on the horizontal slide motions to
achieve finer slide position resolution.
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Important Features of Co-ordinate Measuring Machines (CMM)
In order to meet the requirement of faster machines with higher accuracies, the stiffness to
weight ratio has to be high in order to reduce dynamic forces. To give maximum rigidity to
machines without excessive weight, all the moving members, the bridge structure, Z- axis
carriage, and Z – column are made of hollow box contraction.
Principles of kinematic design are used in the three master guide ways and probe location.
Even whole machine with its massive granite worktable is supported on a three-point suspension.
A map of systematic errors in machine is build up and fed into the computer system so that
error compensation is built up into the software.
All machines are provided with their own computers with interactive dialogue facility and
friendly software.
Thermocouples are incorporated throughout the machine and interfaced with the computer
to be used for compensation of temperature gradients and thus provide increased accuracy and
repeatability.
With the advent of three-axis programming, computers enable CMM to measure threedimensionally object from variable datums.
The real benefit of today's CMM is its total flexibility and programmability, which makes it
capable of handling virtually any measuring requirement within its physical size limit, thus
rendering dedicated or specially designed gauging unnecessary.
Design improvements allied to a rapid growth in software for 3 and 4 axis movements
enable CMMS to measure straight line relationships between basic features, i.e., hole centre
distances, etc. and also a variety of form measurements, such as turbine blades, cam profiles etc.
Accuracy Specification for Co-ordinate Measuring Machines.
Two types of accuracies are d in connection with coordinate measuring machines; viz
geometrical accuracy (determined by independent measurement because they make major
contribution to overall accuracy of machine)and ii) total measuring accuracy (determined by
utilising the entire measuring machine system as applied to master gauges ).
Geometrical accuracy concerns the straightness of axes, squareness of axes, and position
accuracy. Total measuring accuracy concern s axial length measuring accuracy, and volumetric
length measuring accuracy.
Straightness of axes : Straightness of axes is d as deviation from a straight line in two
orthogonal planes for each axis of movement, and thus following six measurement parameters
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need to be considered : Straightness of x-axis measured in y and z direction ; of y -axis in x and z
direction; of z-axis in x and y directions. Measurement is effected against a suitable straightness
reference e.g. Laser beam and taking at least 10 readings at different points in each direction over
full travel of each axis. Straightness is d as the distance A (deviation bandwidth) between the two
parallel lines containing the two graphs (Refer Fig. 17.13).
Squareness of axes: It is d as deviation from 90o of the straightness bandwidth lines of two
orthogonal axis movements. Three measurement parameters (squareness between x and y axes,
between y and z axes, and between x and z axes). Measurement is effected against a suitable
squareness reference, e.g. Laser beam, taking at least 10 measurements over full travel of each axis.
Squareness is then d as the deviation from 90o of the angle between the straightness bandwidth
lines of two axes and is given as an absolute value in arc seconds (Refer Fig. 17 .14).
Position accuracy :
It is d as difference between position readout of machine along an
individual axis and value of a reference length measuring system. Following three measurement
parameters are needed for position accuracy. Position accuracy of x axis, of y axis, and of z axis.
Measurement is effected along one measuring line for each machine axis located approximately at
centre of measuring travel of remaining two axes. For this purpose, a suitable reference length
measuring system, e.g. Laser interferometer, is aligned to each machine axis within a permissible
deviation of 1 arc minute (minimum 20 points measured over full travel of each axis). Fig. 17.15
shows a typical deviation record in which position accuracy F is d as the distance between the two
parallel lines containing the two graphs for the two directions.
Axial Length Measuring Accuracy : It is d as difference between the reference length of gauges,
freely oriented in space, and the corresponding measured results from the machine. Three
reference gauges are measured, their lengths corresponding to approximately 1/3, 1/2 and ¾ of full
travel of respective axis (upto a maximum of 1000 mm). Length measuring accuracy G is d as the
absolute value of the difference between the calibrated length of the gauge block and the actual
measured value.
Volumetric Length Measuring Accuracy : It is d as difference between the reference length of
gauges, freely oriented in space, and the corresponding measured results from the machine.
Three reference gauges are measured, their lengths corresponding to approximately 1/3, ½ and ¾
of the full travel of the longest axes (upto maximum of 100 mm). Volumetric length measuring
accuracy M is d as the absolute value of the difference between the calibrated length of the gauge
block and the actual measured values.
Performance of CMM.
In evaluating the performance of a coordiante measuring machine, the following major aspects
need consideration.
1.Definition and measurements of "geometrical accuracies", such as positioning accuracy,
straightness and squareness.
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2.Master gauge measurement methods to "total measuring accuracy" in terms of "axial
length measuring accuracy, volumetric length measuring accuracy, and length measuring
repeatability, i.e., the coordianted measuring machine has to be tested as complete system.
Measuring systems can be characterised by the combination of "mode of operation" and
probe type. Modes include free floating manual, driven manual, and direct computer
controlled. Probe types are passive, switching, proportional and nulling. The CMM is
tested in the mode and with the probe that is commonly used.
3.Since environmental effects have great influence, explicit specification on environmental
conditions for the accuracy testing, including thermal parameters, vibrations and relative
humidity are required.
It is usually difficult to establish a quantitative relationship between any particular
environmental specification and the effect in machine's performance. Thus it is better to what
level of environmental enfluence is acceptable, and maintain those conditions.
The thermal effects dominate the environmental influences affecting a CMM. The sources
of thermally induced errors include deviations of surrounding air temperature from 20oC,
temperature gradients, radiant energy (e.g. Sunlight), utility air temperature, and self-heating in
machines with drive motors. Thermal effects may take the form of differential expansion between
the workpiece and the machine scale system, drift between a workpiece origin and the machine
scale system origin, and distortion of the machine structure leading to significant changes in the
calibration and adjustment of the machine. The dominant effect of vibration is to degrade the
repeatability of a machine. If the indicated relative motion between the machine table and the ram
exceeds 50% of the working tolerance for repeatability, the vibration environment is deemed
unacceptable.
It is important that suitable performance tests capable of testing the machine as a complete
system are performed. It may be mentioned that use of parametric testing (straightness,
squareness, angular motion) does not test the system performance test is carried out by measuring
a mechanical artifact which provides some similarity between the machine testing and actual
measurement of workpieces. Such testing must sample throughout the work zone. For
performance test, linear displacement accuracy is checked by a step bar or a laser interferometer.
These measurements are made along three orthogonal lines through the centre of the work zone to
provide a thorough sampling of many combinations of x, y, and z errors that occur throughout the
work zone of a machine.
Using the socketed ball bar provides a means of sweeping out the surface of a (nearly)
perfect hemispheres with a physical object (ball). The CMM is used to measure the location of the
centre of this ball at many locations on the hemisphere. The actual measurement data is compared
to an ideal hemisphere simply by recording the range of the length of the ball bar computed from
the data. The procedure calls for moving the socket defining the centre of the hemisphere to
several locations in the work zone and repeating the measurements. Three different lengths of the
bar also are used. The performance is specified independently for the different lengths.
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Three Dimensional Measuring Machine
3-D measuring machines are very useful in modern sophisticated industry. These
machines are designed for 3-dimensional calibration of certifiable accuracy. Fig. 17.16 shows the
schematic diagram of such a machine. Such a machine is adaptable for computer control. Laser
interferometers are provided as scales. A cooling system is incorporated to reduce the
temperature rise when the machine is in operation. The workpiece (gauge) is mounted on the
table which moves to provide the x-measurement. y-motion is obtained by movement of the large
carriage (carrying probe on z-slide) across the bridge. z slide mounted on y-carriage moves
vertically up and down. Axes movement is controlled by stepping motors attached to leadscrews. The three carriages are mounted upon double-V ways, the x and y slides with roller
bearings and the z-slide with plain ways.
Fig. 17.16 shows a typical y-z measuring machine. The axi-symmetric part is centered upon
the rotary table or the "c" axis. The rotary table is mounted on the horizontal (y) slide. The
electronic gauge stylus is typically a ball-tipped, single axis, linear varible displacement
transducer (LVDT) carried and positioned by the vertical (z) slide. The axis of the LVDT is
typically mounted at a 45 degree angle with respect to the y and z axes. A correction is provided
for the cosine error introduced when the direction of travel of LVDT is not normal to the part
surface.
Displacement accuracy is achieved by laser interferometers operating in helium shielded
pathways. The interferometers are located in strict accordance with the Abbe principle, i.e., the
extension of the laser interferometer axis passes through the centre of the stylus ball at its null
position (the centre of stylus ball being "functional point"). Refer Fig. 17.17.
On the y-axis slide, two laser interferometers suitably separated are provided. The
difference in readings between these two lasers is used as a servo input to drive a piezoelectric
crystal that supports one end of the y-axis table, thereby correcting the angular motion or pitch of
the table.
Straightness accuracy is achieved by mounting straight edges parallel to each slide to
measure and correct for slide way straightness errors. For instance any error in the straightness of
travel of z-slide will cause unwanted movement in the y direction. The LVDT gauge head that
contacts the straight edge detects this movement and corrects it by zero shifting the y-slide.
Similarly when nonstraighness of y-slide travel is detected, the z-axis is zero shifted in the proper
direction to correct the travel.
However stiff a machine may be made, it deflects and distorts owing to the effects of
changing and moving loads on the structure. The metrology system must therefore be made
independent of the machine base, i.e., the external forces upon the metrology system must be
constant. The metrology base is thus designed so as not to be influenced by the machine base
(Refer Fings. 17.17 & 17.18). The frame is supported on kinematic mounts inside the machine
base. The plane of the supports is coincident with the bending neutral axis of the machine base,
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and its influence on the metrology frame is thereby minimised. The metrology frame houses the
laser, laser pathways and remote interferometers and also supports the two straight edges.
Because of low coefficient of expansion of granite, it is chosen for building the machine
base. The base is supported on three pneumatic isolators. The metrology frame is built of steel
because temperature controlled oil shower is included.
For stability of the laser ( which depends on the stability of the medium in the pathways ),
helium at a pressure slightly above atmospheric pressure ( Maintained at constant value by a
regulator ) is provided in path ways. The effect of helium pressure change on the laser
wavelength is taken into account.
y-axis and z-axis slides ride on and are guided by hydrostatic bearings. A portion of each
bearing is evacuated and the evacuated section acts like a vacuum chuck to hold the bearing
against the way (similar to preloading the bearing). The balance of the bearings are externally
compensated to enhance the stiffness. The slide drive system (Fig. 17.19) can be considered as a
rack and pinion drive without gear teeth. The capstan is connected directly to the drive motor.
The steel traction bar is squeezed between the capstan and the idler roller. One end of the traction
bar is fastened to the slide with spherical bearing. A coil spring supports the weight of the bar at
the opposite end. Both the capstan and the idler are supported on hydrostatic bearings.
This type of drive system has minimum cost, minimum heat generation, maximum
stiffness, minimum sliding friction, maximum linearity of displacement, no backlash, high
reliability, compactness and minimum influence on slide straightness.
The thermal environment of the measuring machine and the part is controlled by
showering adequate quantity of oil controlled at 25oC. The shower is carefully sculptured to
maintain machine temperature and to minimise splash. The primary advantages of liquid shower
are its greater heat removal capability and the fact it is easily directed to the critical areas of the
machine and workpiece surfaces. Liquids also have higher heat capacity than gases and
accordingly it is possible to remove heat with corresponding lower temperature differences.
Principle and working of Michelson interferometer.
Michelson Interferometer. This is the oldest type of interferometer, which has subsequently been
modified in several respects and lot of sophistication introduced. However, Michelson using this
interferometer, established exact relationship between meter and red wavelengths of cadmium
lamp; so understanding of its working will be of interest to all.
The basic Michelson interferometer consists of a monochromatic light source, a beam splitter
and two mirrors. It relies on the principle of constructive and destructive interference as one
mirror remains fixed and the other is moved.
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In schematic form, Michelson interferometer is shown in Fig. 6.16, which utilizes
monochromatic (or single wavelength) light from an extended source. This light falls on a beam
Splitter (which is a plain parallel plate having a semi-transparent layer of silver at its back)
which splits the light into two rays of equal intensity at right angles. One ray is transmitted to
Mirror M1 and other is reflected through beam splitter to Mirror M2. From both these mirrors, the
rays are reflected back and these reunite at the semi-reflecting surface from where they are
transmitted to the eye as shown in Fig. 6.06.
Mirror M2 is fixed and the reflected ray from M1 serves as reference beam, Mirror M1 is movable,
i.e., it is attached to the object whose dimension is to be measured.
If both mirrors are at same distance from beam splitter, then light will arrive in phase and
observer will see bright spot due to constructive interference. If movable mirror shifts by quarter
wavelength, then beam will return to observer 180 out of phase and darkness will be observed
due to destructive interference.
Each half wavelength of mirror travel produces a change in the measured optical path of one
wavelength and the reflected beam from the moving mirror shifts through 360  phase change.
When the reference beam reflected from the fixed mirror and the beam reflected from the moving
mirror rejoin at the beam splitter, they alternately reinforce and cancel each other as the mirror
moves. Thus each cycle of intensity at the eye represents /s of mirror travel.
It may be noted that when monochromatic light source is used then fringes can be seen over a
range of path difference that may vary from a few to a million wavelengths, depending on the
source. However, when white light is used, then fringes can be seen only if both ray paths are
exactly equal to a freq. wavelengths in total length in glass and air. The lengths themselves are not
important, but only their differences affect fringe formation. So when white light source is used
then a compensator plate is introduced in the path of mirror M1 so that exactly the same amount of
glass is introduced in each of the paths. (In the path of mirror M 2, the glass was coming due to
rays passing through beam splitter back surface). The various sophistications which have
undergone to improve the Michelson’s basic apparatus are:
(i)
(ii)
(iii)
Use of laser as the light source, which means that the measurements can be made over
longer distances; and also the beam laser compared to other monochromatic sources has
exact and pure wavelength thus enabling highly accurate measurements.
Mirrors are replaced by cube-corner reflectors (ratio-reflectors) which reflect light
parallel to its angle of incidence regardless of retro reflector alignment accuracy.
Instead of observing the interference phenomenon by eye, photocells are employed
which convert light-intensity variations in voltage pulses which are processed by
electronic instruments to give the amount and direction of position change.
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Single Frequency DC Interferometer System.
It is much improved system over the Michelson simple interferometer. It uses a single
frequency circular polarized laser beam. On reaching the polarizing beam splitter, the beam splits
into two components. The reflected beam being vertically polarized light and the transmitted
beam being horizontally polarized light. These two beams referred to as reference are and
measurement are respectively travel to their retro reflectors and are then reflected back towards
the beam splitter.
The recombined beam at beam splitter consists of two superimposed beams of different
polarization; one component vertically polarized having traveled around reference arm and other
component horizontally polarized having traveled around the measurement arm. These two
beams being differently polarized do not interface. The recombined beam then passes through a
quarter wave plate which causes the two beams to interfere with one another to produce a beam
of plane polarized light. The angular orientation of the plane of this polarized light depends on the
phase difference between the light in the two returned beams.
The direction of plane of polarization spin is dependent on the direction of movement of the
moving retro reflector. The beam after quarter wave plate is split into three polarization sensitive
detectors. As the plane of polarized light spins, each detector produces a sinusoidal output wave
form. The polarization sensitivity of the detectors can be set so that their outputs have relative
phases of 0, 90, and 180. The outputs of there detectors can be used to distinguish the direction
of movement and also the distance moved by the moving retro reflector attached to the surface
whose displacement is to be measured.
For linear measurements (positional accuracy of velocity), the retro reflector is attached to the
body moving along the linear axis. For angular measurement. For pitch and yaw), the angular
beam splitter is placed in the path between the laser head and the angular reflector. In this way it
is possible to measure flatness, straightness, rotatory axis calibration. Arrangements also need to
be made for environmental compensation because the refractive index of the air varies with
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temperature, pressure and humidity. Heterodyne interferometer, an a.c. device avoids all the
problems encountered in above d.c. device, i.e. effect of intensity level change of source, fringe
contrast changes and d.c. level shifts which can cause fringe miscounting.
Interferometer is now an established and well developed technique for high accuracy and high
resolution measurement.
Twyman – Green Specialization of Michelson Interferometer.
In the Michelson interferometer shown in Fig. 6.18, the rays actually describe a cone, giving rise to
various types of fringe patterns which may be hard to interpret.
Twynman-Green modified Michelson interferometer utilizes a pin-hole source diaphragm and
collimating lenses. In this way, all rays are rendered parallel to the central rays and thus all rays
describe the same path . All modern tow-beam interferometers are based on this arrangement. The
mirrors M1 and M2 are arranged perpendicular to the optical axis. If mirror M1 is kept fixed, and
M2 is moved slowly exactly parallel to itself, the observer will note periodic changes in the
intensity of the field being viewed, from bright to dark for every /2 movement of the mirror. In
fact intensity variation is found to be sinusoidal. It may also be noted that if one of the mirrors is
even slightly inclined to the optical axis then parallel fringes will be seen moving parallel to
themselves by just one fringe for every \2 (half the wavelength of the light source used) mirror
motion. Usually it is quite difficult to count such fringes by eye. However, photo detectors
connected to high speed counters can do this job very accurately (accuracy of one part in million
being obtainable). It is possible to calibrate the output of counter directly ion terms of the linear
movement of the mirror M2, but several conditions must be met to achieve these results.
Fringe counting interferometer.
A simple arrangement of fringe counting system based on Kosters prism is shown in Fig.6.19.
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With the use of Koster’s prism, the two interfering paths can be arranged parallel instead of at
right angles. At big advantage is using Koster’s prism, is that if slight vibrations exist, then
vibration tends to affect the arms equally and the annoying effect of vibration is nullified. In order
to be able to count the fringes, the following must be taken care of:
(i) It has been indicated that mirror should travel exactly parallel to itself and no machines have
ways sufficiently straight to maintain uniform fringe fields. The recent trend is to use corner-cube
reflectors which are not all sensitive to their own orientation and return the reflected ray exactly
parallel to the incident beam.
(ii) It is observed that the wavelength of light source is modified by the refractive index of air
which is dependent on pressure, temperature and humidity of air (wavelength is fixed only in
vacuum). The slight changes in wavelength may be immaterial in case of flatness or from
measuring systems, but not in fringe counting and gauge block interferometers. So pressure,
temperature and humidity should be measured and correction factors applied for. If optical paths
are longer then the air currents between optical elements exert more and more influence; and the
system should, therefore, be properly shielded with insulating, and radiation reflecting
enclosures.
(iii) It has already been indicated that the signal strength becomes poor if the path difference
between the rays corresponding to two mirror systems is high. Thus it limits the range of
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movement of movable mirror because its movement means change in path length. It is found that
using cooled mercury 198 lamps, speeds of 12.5 mm/sec. are possible when path lengths are nearly
equal, but the traversing speed has to be reduced to 0.0025 mm/sec., when path difference is about
250 mm due to poor signal to noise ratio.
Construction and working of AC interferometer
This article is based on a similar article appearing in magazine “Machine Design” Vol. 47 No.4.
The measuring capacity in interferometers with lamp as source of light is limited because it is not
possible to maintain the sharpness of interference fringes beyond certain distance due to the size
of the lamp. Laser interferometer uses A..C. laser as the light source and thus enables the
measurements to be made over longer distance because it is possible to maintain the quality of
point interference fringes over long distances when lamp is replaced by a laser source. It must be
understood that white light emitted by a lamp is combination of waves at different frequencies but
laser generates a continuous train of light waves, resulting into high coherence. Laser represents a
source of intensely monochromatic optical energy, which can be collimated into a directional
beam, Also laser beam wavelength is exact and pure for highly accurate measurements. It utilizes
the principles of both optical techniques and digital electronics; and is a highly accurate and
versatile measuring system that can cope with industrial environments. In case of AC laser
interferometer (ACLI) position information is carried as phase deviation rather than as a signal
amplitude deviation, thus giving a much improved signal to noise ratio over amplitude
modulation, because the noise sources that affect signal amplitude have little effect on phase. In
this way, ACLI is much more tolerant of environmental factors that attenuate the intensity of a
laser beam, such as dust, smoke, air turbulence etc. It requires no warm-up time or standby
power.
Thus ACLI has the following advantages: high repeatability and resolution of displacement
measurement (0.1m), high accuracy,, long-range optical path (60m), easy installation, and no
change in performance due to ageing or wear and tear. A single laser source can be used for as
many as six simultaneous measurements in different axes. However, it is very much expensive;
since the basic instrument measures physical displacement in terms of wavelength instead of
traditional units, conversion instrumentation is required for conventional read out. Highest
possible accuracy is obtainable only by compensating changes in air pressure and temperature
which affect wavelength of the laser beam.
operation of AC Interferometer.
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It uses two frequency laser system, thus overcoming the shortcoming of d.c. laser
interferometer. Whereas the d.c. system mixes out of phase light beams of the same frequency, the
a.c. system mixes beams of two different frequencies thus permitting the distance information to
be carried on a.c. waveform. Use is made of the fact that the AC amplifiers are insensitive to d.c.
variation of a.c. inputs.
Two frequency Zee man laser generates light of two slightly different frequencies with opposite
circular polarizations. These beams get split up by beam splitter B 1; one part travels towards B2
and from there to external cube corner where the displacement is to be measured. It may be noted
that mirror is not employed here like Michelson Interferometer, because mirror alignment is a
critical procedures. Thus interferometer, instead, uses cube-corner reflectors (retro reflectors)
which reflect light parallel to its angle of incidence regardless of retro reflector alignment
accuracy. Beam splitter B2 optically separates the frequency f1 which alone is sent to the movable
cube-corner reflector. The second frequency f2 (optically separated) from B2 is sent to a fixed
reflector which then rejoins f1 at the beam splitter B2 to produce alternate light and dark
interference flicker at about 2 Mega cycles per second. Now if the movable reflector (external cube
corner) moves, then the returning beam frequency will be Doppler-shifted slightly up or down by
∆f1. Thus the light beams moving towards photo-detector P2 have frequencies f2 and (f1 ± ∆f1) and
P2 changes these frequencies into electrical signal. (Photocells convert light-intensity variations
into voltage pulses which can be processed by electronic instruments to give the amount and
direction of position change).
Photo detector P1 receives signal from beam splitter B1 and changes the reference beam
frequencies f1 and f2, into electrical signal. An A..C. amplifier A1 separates frequency difference
signal [(f2- (f1 ± ∆f1). The pulse converter extracts ∆f1, one cycle per half wavelength of motion. The
up-down pulses from the pulse converter are counted electronically and displayed in analog or
digital form on the indicator. It may be noted that output in case of ACLI is in the form of pulses,
whereas in d.c. systems, the output is in the form of a sinusoidal wave, the amplitude (intensity) of
which depends upon laser aging, air turbulence or air pollutant and thus the change of amplitude
leads to improper triggering and counting errors (Refer Fig. 6.32).
1) Counter operating, if amplitude wave is above counter trigger level.
2) Counter disabled by small amplitude change of sinusoidal wave.
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Principle Heterodyne Interferometer Technique.
Simple d.c. fringe counting techniques suffer from problems of intensity level changes in source
and also on account of motion of source or object. Fringe contrast changes and d.c. level shifts
result in miscounting of the fringes. Heterodyne interferometer is an a.c. device and the problems
of d.c. fringe counting techniques are overcome. In this type of interferometer, a zeeman laser
source emits two closely spaced orthogonal polarization frequencies separated by around 1 MHz.
A beam splitter placed in front of laser source separates off part of the signal
from both polarizations which are mixed on detector D1 to provide a reference beat f1-f2. The
transmitted component travels up to polarizing beam splitter where it is splitter. Part of it travels
to reference fixed arm and other to measurement arm connected with target movement. The two
signals are recombined at the polarizing beam splitter and detected by detector D 2. If target is
stationary, the detected beam is f1-f2. When it moves, then detected beat is f1-f2 ∆f. The reference
and Doppler-shifted beats are counted by two independent counters and subtracted to give ∆ f.
Integration of the count over time t measures 2d/.
Dual-frequency Laser Interferometer.
This instrument is used to measure displacement, high-precision measurement of lengths,
angles, speeds and refractive indices as well as derived static and dynamic quantities. It operates
on heterodyne principle. The two resonator modes (frequencies f1 and f2) are generated in a laser
tube such that f1-f2=640MHz. These are controlled so that their maxima are symmetrical to the
atomic transition. This permits a long reliable stability. The frequency stability of He-Ne laser is
responsible for outstanding performance of the interferometer.
An amplitude beam splitter branches off part of the laser output create a reference beam, which
an optical fibre cable relays to a photo detector 1. This detects the beat signal of 640MHz frequency
difference produced by the heterodyning of the two modes. The other portion of the light serves
185
as measuring beam. Via an interferometer arrangement it is directed to a movable measuring
mirror and a stationary reference mirror, which reflects it on to a photo-detector 2. The two
frequencies in the measuring beam are separated by a polarization-sensitive beam splitter so that
the measuring mirror receives light of frequency f1 only, whereas the light that strikes the
reference consists exclusively of frequency f2. With the measuring mirror at rest, detector 2 also
senses the laser differential frequency of f1-f2 = 640MHz. If the measuring mirror is being displaced
at a speed v, the partial beam of frequency f1 reflected by it is subjected to a Doppler shift df1;
where df1 = (2v)1.
Accordingly, detector 2 now receives a measuring frequency of f1-f2 ± df1 (+ df1 or – df1) depending
on the direction of movement of the measuring mirror. The reference frequency f 1-f2 and the
measuring frequency f1-f2 ± df1 are compared with each other by an electronic counting chain. The
result is the frequency shift ± df1 due to the Doppler effect, a measure of the wanted displacement
of the measuring mirror. In a fast, non-hysteric comparator, the
Doppler frequency df1 is digitized and then fed to a counter, which registers the number of zero
passages per unit time.
The forward and return movements of the measuring mirror can be distinguished by out
coupling the measuring signal f1—f2 ± df1 at ‘n’ phase angles, via a delay line and feeding to ‘n’
mixers. The mixers are connected with the reference signal f1—f2 (common feeding point for all
mixers). Thus n Doppler frequencies get shifted in phase by /n at the mixer outputs. They are
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symmetrical relative to zero. After comparison they are made available to low-frequency counting
logic as TTL signals. The n phase angles and their tolerances are implemented by the geometry of
the delay line.
This system can be used for both incremental displacement and angle measurements. Due to
large counting range it is possible to attain a resolution of 2.nm in 10 m measuring range. Means
are also provided to compensate for the influence of ambient temperature, material temperature,
atmospheric pressure and atmospheric humidity fluctuations.
Different light sources used for interferometer and their characteristics.
A wide variety of light sources is available for interferometer work but the selection of
proper source for any application depends on the requirements of results to be obtained by
interferometer, cost and convenience. For simple applications like testing of surface geometry,
where the difference between interfering paths is of the order of a few wavelengths only, tungsten
lamp with a filter, transmitting only a narrow band of wavelengths would be adequate.
However, sophisticated applications require the use of light sources such as mercury 198,
cadmium, krypton 86, thallium, sodium, helium, and neon and gas lasers. In these sources, the
discharge lamp is charged with one particular element and contains means to vaporize them. The
atoms of these elements are excited electrically so that they emit radiation at certain discrete
wavelengths.
Characteristics of various light source are summarized below:
i)
Mercury. It is les expensive source having high intensity, and green line can be easily
isolated with filters. Since natural mercury contains several isotopes, each isotope emits
light whose wavelength is very slightly different from each other. As a result, natural
mercury light source radiates a mixture of wavelengths which can be treated as
monochromatic only for short path difference.
ii)
Mercury 198. It is a pure isotope produced by neutron bombardment of gold. It is
considered to be one of the best sources of very sharply d wavelengths, and fringes are
visible with path difference up to 500 mm. Light is emitted when mercury 198 is excited by
microwave produced electric field. It is the international secondary standard of
wavelength.
iii)
Cadmium. This is the only natural material producing a spectral line (red) almost
completely symmetrical, having useful path difference of about 200 mm. Cadmium 114 is
the official secondary international standard of length.
iv)
Krypton. It has the advantage of being easily excited, so used in some instruments. It is not
as monochromatic as Krypton 86 because natural krypton is a mixture of isotopes. It can be
used up to path difference of 375 mm.
v)
Krypton 86. Krypton 86 lamp produces spectral lines of different wavelengths and,
therefore, a fairy elaborate monochromatic is required to separate them. Further its
excitation takes place at very very low temperatures, therefore, this lamp is used only in
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standardizing laboratories. Next to laser, this enables the fringes to be observed with
maximum path difference (about 800 mm).
The orange-red line of krypton 86 isotope, produced under specified conditions, and at a
temperature of 63.3 K temperature of nitrogen triple point, is the new basic international standard
of length-meter being d as exactly 1,650,763.73 wavelengths of this source, measured in vacuum.
vi)
vii)
viii)
ix)
x)
Thallium. As 95% of its light is emitted at one green wavelength, it can be used over a
reasonable path difference without the use of my filter.
Sodium. It is used only in applications where interference path difference does not exceed a
few hundred wavelengths. Usually yellow sodium light is used which contains two
separate but closely spaced lines of equal intensity; and because of this the interference
fringes wash out fad because of this the interference fringes wash out for higher path
difference.
Helium. Orange line of helium is used where path difference is not great.
Neon. As conventional neon lamp has too many closely spaced lines (in red part of the
spectrum) and not sharply d, it does not find many applications. Neon in gas laser,
however, has assumed a uniquely important role.
Gas lasers. In metrology work gas lasers which produce highly monochromatic and intense
light (1000 times more intense than others) are used to great advantage, enabling
interference fringes to be observed with enormous path differences, up to 100 million
wavelengths. (It may be noted that high-power, intermittently operating ruby laser is not of
interest in metrology). Gas lasers are produced by exciting (by an electric discharge or a
high-frequency field) a mixture of neon and helium
UNIT – V
MEASUREMENT OF POWER, FLOW AND TEMPERATURE RELATED
PROPERTIES
Force.
The mechanical quantity which changes or tends to change the motion or shape of a body
to which it is applied is called force.
Load cells
Load cells are devices used for force measurement through indirect methods.
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Principle of working of load cells.
Force applied to the elastic member of the cell results in a proportional displacement or strain is
sensed by calibrated mechanical or electromechanical means.
Principle of working of load cells.
Force applied to the elastic member of the cell results in a proportional displacement or strain is
sensed by calibrated mechanical or electromechanical means.
Devices used to measure force
1. Scale and balance
a. Equal arm balance
b. Unequal arm balance
c. Pendulum scale
2. Elastic force meter – Proving ring
3. Load cell
a. Strain gauge load cell
b. Hydraulic load cell
c. Pneumatic load cell
Basic principle of elastic force meter.
When a steel ring is subjected to a force across it’s diameter, it deflects. This deflection is
proportional to applied force when calibrated.
Basic principle of equal arm balance.
It works on the principle of moment comparison. The beam of the equal arm balance is in
equilibrium when clockwise rotating moment is equal to anticlockwise rotating moment.
Basic principle of hydraulic load cell.
When a force is applied on a liquid medium contained in a confined space, the pressure of
the liquid increases. The increase in pressure of liquid is proportional to the applied force.
Instruments used for the measurement of torque.
2.Optical torsion meter
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3.Electrical torsion meter
4.Strain gauge torsion meter
5.Mechanical torsion meter
Basic principle of Mechanical torsion meter.
When a shaft is connected between a driving engine and driven load, a twist occurs on the
shaft between its ends. This angle of twist is measured and calibrated in terms of torque.
Types of strain gauges.
1.Unbonded strain gauge
2.Bonded strain gauge
3.Fine wire strain gauge
4.Metal foil strain gauge
5.Piezo-resistive strain gauge
unbonded strain gauge.
These strain gauges are not directly bonded on to the surface of the structure under study.
Hence they are termed as unbonded strain gauges.
bonded strain gauge.
These strain gauges are directly bonded on to the surface of the structure under study.
Hence they are termed as unbonded strain gauges.
Gauge factor.
It is the ratio of change in resistance to the change in length.
Few materials used in binding of strain gauges.
1.Ceramic cement
2.Epoxy resin
3.Nitrocellulose.
Need for using strain gauge in wheatstone network circuits.
The need for the strain gauge in wheatstone network circuit is that the change in resistance
due to strain in the gauges can neither be measured or made to give an output which can easily
displayed or recorded.
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Strain gauge rosettes
The arrangement of strain gauges in the shape of rose is referred to as a strain gauge rosette.
Purpose of temperature measurement
1.
2.
3.
It is one of the most common and important measurements.
In process industries which involve chemical operations.
In studying the temperature of molten metal in foundries.
Instruments used to measure temperature.
1.
2.
3.
4.
5.
Bimettalic thermometers
Resistance thermometers
Thermistors
Thermocouples
Pyrometer
Thermistor
It is a bulk semiconductor resistance temperature sensor.
Two distinct instruments commonly referred to as pyrometers.
1. Total radiation Pyrometers.
2. Optical pyrometers.
Applications of bimetallic thermometer.
1. Bimetallic thermometer is used in control devices.
2. Used for process applications such as refineries, oil
burners, tyre vulcanizers, etc.
Principle of pressure thermometer
When liquids, gases or vapours are heated they expand and when they are cooled they
contract. This is the basic behind the construction of pressure thermometers.
Principle of bimetallic thermometer.
When a bimetallic helix fixed at one end free at the other end is subjected to temperature
changes, the free end of the bimetallic helix deflects proportional to change in temperature. This
deflection becomes a measure of change in temperature.
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Advantages of bimetallic thermometer.
1. Their accuracy is between  2% to  5% of the scale.
2. Simple, robust, inexpensive.
Basic principle of resistance thermometers
When an electric conductor is subjected to temperature change the resistance of the
conductor changes. This change in resistance of the conductor becomes a measure of the change in
temperature when calibrated.
Advantages of thermistors
1. Fairly good operating range (100C to 300C).
2. Have ability to withstand electrical and mechanical
stresses.
Metal used for thermocouple wire.
1. Chromel - constantan
2. Iron – constantan
3. Chromel – Alumel
4. Copper – constantan
5. Platinum – Rhodium
Quantity meter and flow meter.
Quantity meter measures the rate of flow by measuring the total quantity of fluid over a
period of time and dividing it by the time considered.
Flow meter measures the actual flow rate.
Advantages of venturimeter.
1. Low head loss about 10% of differential pressure head.
2. High co-efficient of discharge.
3. Capable of measuring high flow rates in pipes having very large diameter.
4. Characteristics are well established so they are extensively used in process and other industries.
Two types of hot wire anemometer.
1. Constant current type
2. Constant temperature type.
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Pyrometer
Three definitions
 “Any instrument used for measuring high temperatures by means of the radiation emitted
by a hot object”
 “A thermometer designed to measure high temperatures”
 “A device measuring the temperature of an object by means of the quantity and character
of the energy which it radiates”
Types of pyrometers
There are two types of pyrometers
(i)Optical Pyrometer
1892 introduced by Lechatelier, which it measured radiation from dull red to white hot Used for
measuring kiln and furnace temperature
Today an optical pyrometer is used in which the color of an electrically heated filament is matched
visually to that of the emitted radiation. Based on the principle of using the human eye to match
the brightness of the hot object to that calibrated inside the instrument
It is made from a small magnifying optical device. Filters that reduce wavelength to 0.65-0.66 and
other filters reduce intensity. These restrictions prevent the device from measuring object that are
glowing (700 C)
(ii)Radiation Pyrometer
Non-contact temperature sensors measure temperature from the amount of thermal
electromagnetic radiation received from a spot on the object of measureMeasures the rate energy
emission per area unit.
Absolute, gauge and differential pressures - zero reference
Although pressure is an absolute quantity, everyday pressure measurements, such as for tire
pressure, are usually made relative to ambient air pressure. In other cases measurements are made
relative to a vacuum or to some other ad hoc reference. When distinguishing between these zero
references, the following terms are used:

Absolute pressure is zero referenced against a perfect vacuum, so it is equal to gauge
pressure plus atmospheric pressure.

Gauge pressure is zero referenced against ambient air pressure, so it is equal to absolute
pressure minus atmospheric pressure. Negative signs are usually omitted.

Differential pressure is the difference in pressure between two points.
193
The zero reference in use is usually implied by context, and these words are only added when
clarification is needed.
Atmospheric pressure is typically about 100 kPa at sea level, but is variable with altitude and
weather. If the absolute pressure of a fluid stays constant, the gauge pressure of the same fluid
will vary as atmospheric pressure changes. For example, when a car drives up a mountain, the tire
pressure goes up. Some standard values of atmospheric pressure such as 101.325 kPa or 100 kPa
have been d, and some instruments use one of these standard values as a constant zero reference
instead of the actual variable ambient air pressure. This impairs the accuracy of these instruments,
especially when used at high altitudes.
Use of the atmosphere as reference is usually signified by a (g) after the pressure unit e.g. 30 psi g,
which means that the pressure measured is the total pressure minus atmospheric pressure. There
are two types of gauge reference pressure: vented gauge (vg) and sealed gauge (sg).
34. What are the different units of pressure
Pressure Units
pound-force
per
square inch
(psi)
pascal
(Pa)
bar
(bar)
technical
atmosphere
(at)
1 Pa
≡ 1 N/m2
10−5
1.0197×10−5
9.8692×10−6
7.5006×10−3
145.04×10−6
1 bar
100,000
≡ 106 dyn/cm2
1.0197
0.98692
750.06
14.5037744
1 at
98,066.5
0.980665
≡ 1 kgf/cm2
0.96784
735.56
14.223
1 atm
101,325
1.01325
1.0332
≡ 1 atm
760
14.696
1 torr
133.322
1.3332×10−3
1.3595×10−3
1.3158×10−3
≡ 1 Torr;
≈ 1 mmHg
19.337×10−3
1 psi
6.894×103
68.948×10−3
70.307×10−3
68.046×10−3
51.715
≡ 1 lbf/in2
atmosphere
(atm)
torr
(Torr)
Static and dynamic pressures
Static pressure is uniform in all directions, so pressure measurements are independent of direction
in an immovable (static) fluid. Flow, however, applies additional pressure on surfaces
perpendicular to the flow direction, while having little impact on surfaces parallel to the flow
direction. This directional component of pressure in a moving (dynamic) fluid is called dynamic
pressure. An instrument facing the flow direction measures the sum of the static and dynamic
pressures; this measurement is called the total pressure or stagnation pressure. Since dynamic
pressure is referenced to static pressure, it is neither gauge nor absolute; it is a differential
pressure.
While static gauge pressure is of primary importance to determining net loads on pipe walls,
194
dynamic pressure is used to measure flow rates and airspeed. Dynamic pressure can be measured
by taking the differential pressure between instruments parallel and perpendicular to the flow.
Need of calibrating a pressure gauge
Pressure gauges are either direct- or indirect-reading. Hydrostatic and elastic gauges measure
pressure are directly influenced by force exerted on the surface by incident particle flux, and are
called direct reading gauges. Thermal and ionization gauges read pressure indirectly by
measuring a gas property that changes in a predictable manner with gas density. Indirect
measurements are susceptible to more errors than direct measurements.
Various direct methods of measurement of force.
Force is very basic engineering parameter the measurement of which can be done in many
ways as follows:
(i)
(ii)
Direct Methods: Involves a direct comparison with a known gravitational force on a
standard mass, say by a balance.
Indirect Methods: Involves the measurement of effect of force on a body, such as
acceleration of a body of known ma subjected to force.
(i) Direct Methods
(a) Use of Analytical Balance
Analytical balance consists of an arm that rotates about a pivot. Two forces W 1 W2 (or)
weights are added at the two ends as shown in figure.
Let W1 be the know force and W2 be the unknown. Let ‘G’ be the gravity center of the arm
and WG be its weight. When W1 = W2, the arm is unbalanced. This unbalance is indicated by angle
the pointer making with the vertical.
195
For equilibrium, the requirement is
WG.XG = W1 W1 – W2 W2
(b) Use of Pendulum Scale
This uses the Principle of multiple leverage. The input, a direct force or a force Proportional
to weight is transmitted from a suitable agency and applied to the lord rod. As the load is applied,
the sectors rotate about A (Figure) moving the counter weights outward. This movement increases
the counterweight effective moment until the load and balance moments are equalized. Motion of
the equalizer bar is converted to indicator movement by a rack and pinion.
Indirect methods of measurement of force (i) Acceleration method (ii) Using elastic loaded
members (iii) Using cantilever elastic member.
(a) Use of Acceleration
A force will make a body accelerate. By measuring the acceleration, the force may be
determined, from the equation F=ma, when m – mass of the body used. To measure acceleration,
accelerometers are used.
196
(b) Use of Elastic Loaded Members
This uses the principle of finding strain produced in a body to measure the force applied.
For measuring displacement, strain gauges are mounted as shown in figure. The body is subjected
to a force and the gauges measure the strain so produced.
From basic mechanics of materials, force F produces a displacement  
Where
l – Length of the specimen
A – Cross-sectional area
E – Young’s modulus
F
AE
F
2 , 4 
AE
And strain 1,  2 
 being poison’s ratio. If the output of the circuit is e, it is given by
197
Fl
AE
V.GF
(1   2  3   4 )
4
V.GF
F
e=
(l   )
2
AE
e=
(c) Use of Cantilever Elastic member
In a cantilever beam, if the point of application of load is known, the bending moment
caused by it can be interpreted as force applied.
It is established that due to force, F, deflection of a cantilever at a length ‘l’ from the point of
application of force, is given as
W I3

3 EI
where E – Young’s modulus of beam material,
bd3
I – Moment of inertia of beam section =
12
From bending equation,
Moment at section x Mx  x x z (z-section modulus)
bd2
6

Strain  x is given by  x  x
E
6.Fl1
i.e.,
x 
E.bd2
Mx   x x
Gauges R1, R3 measure tensile strain and
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R2, R4 measure compressive strain.
Indirect methods of measurement of force (i) Using proving Rings (ii) Using load cells.
(i) Use of proving Rings
Proving rings are steel rings used for calibration of material testing machines in situations
where, due to their bulkness, dead weight standards cannot be used.
P ring is a circular ring of rectangular section and may support tensile or comprehensive force
across its diameter.
 the change in radius in the direction of force, is given by
K

16
3
  4  F.d
  
 2   EI
where d is the outer diameter of the ring and
K is stiffness.
Deflection of the ring is measured using a precision micrometer. To get precise measurements,
one edge of the micrometer is mounted on a vibrating reed which is plucked to obtain a vibratory
motion. The micrometer contact is then moved forward until a noticeable damping of the
vibration is observed.
199
Maximum deflection is typically of the order of 1% of the outside diameter of the ring. Proving
rings are normally used for force measurement within the range of 2 kN to 2 mN.
(ii) Use of Load Cell
Force transducers intended for weighing purposes are called load cells. Instead of using total
deflection as a measure of load, strain gauge load cells measure load in terms of unit strains. A
load cell utilizes an elastic member as the primary transducer and strain gauges as secondary
transducer. Figure shows one such load cell arrangement.
Working of a DC Dynamometer for the measurement of torque.
Mechanical Dynamometer:
These come under the absorption type. An example for this kind is prony brake.
In Prony brake, mechanical energy is converted into heat through dry friction between the
wooden brake blocks and the flywheel (pulley) of the machine. One block carries a lever arm. An
arrangement is provided to tighten the rope which is connected to the arm. Rope is tightened so as
to increase ht frictional resistance between the blocks and the pulley.
200
If
F – Load applied and
Power dissipated P 
2NT 2NFr

60
60
r - Lever arm
N – Speed of flywheel (rpm)
Torque T = F.r
The capacity of Prony brake is limited because:
1. Due to wear of wooden blocks, friction coefficient varies. So, unsuitable for large powers
when used for long periods.
2.To limit temperature rise, cooling is to be ensured.
D.C. Dynamometer
D.C. dynamometer is usable as an absorption as well as transmission dynamometer. So, it
finds its use in I.C. Engines, steam turbines and pumps. A d.c. dynamometer is basically a d.c.
motor with a provision to run it as a d.c. generator where the input mechanical energy, after
conversion to electrical energy, can either be dissipated through a resistance grid or recovered for
use. When used as an absorption dynamometer it acts as d.c. generator. (figure) Cradling in
trunnion bearings permits the determination of reaction torque.
201
The torque is measured by measuring a balancing force (by means of a load cell, for
example) at a fixed known torque arm. When used as a transmission dynamometer it performs as
a d.c. motor. It then measures the torque and power input to the machine, for example, a pump
that absorbs power.
Its good performance at low speeds and ease of control makes it an efficient means of torque
measurement.
Working of a eddy current or inductor dynamometer for the measurement of torque.
Eddy Current or Inductor Dynamometers:
This is an example for absorption type dynamometers.
Principle: When a conducting material moves through a magnetic flux field, voltage is generated,
which causes current to flow. If the conductor is a wire forming a part of a complete circuit will be
caused to flow through that circuit, and with some form of commutating device a form of a.c. or
d.c. generator may result.
An eddy current dynamometer is shown in figure. It consists of a metal disc or wheel
which is rotated in the flux of a magnetic field. The field if produced by field elements or coils
excited by an external source and attached to the dynamometer housing which is mounted in
trunnion bearings. As the disc turns, eddy currents are generated. Its reaction with the magnetic
field tends to rotate the complete housing in the trunnion bearings. Water cooling is employed.
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Measuring instruments used for temperature measurement and the working of bimetallic
thermometers.
Temperature measuring instruments may be classified on the basis of:
1.
Nature of change produced in the temperature sensing elements.
2.
Electrical and non-electrical operation principle.
3.
Temperature range of the instrument.
Classification based on the Nature of Change Produced.
1. Glass thermometers
2. Pressure gauge thermometers
3. Differential expansion thermometers
4. Electrical resistance thermometers
5. Thermo couples
6. Optical pyrometers
7. Radiation pyrometers
8. Fusion pyrometers
9. Calorimetric pyrometers
Based on Electrical and non-electrical Principles
1. Primarily electrical or electronic in nature
2. Not primarily electrical or electronic in nature.
Bimetallic Thermometers:
Principle Involved : These use the principles of metallic expansion when temperature changes.
A bimetallic strip is shown in figure which is straight initially. When temperature changes,
its shape also changes into an arc.
Fig. Deformation of bimetallic Strip
203
The displacement of the free end can be converted into an electric signal through use of
secondary transducers like variable resistance, inductance and capacitance transducers. Figure
shows a strip of bimetal in the form of a spiral. The curvature of the strip varies with temperature.
This causes the pointer to deflect. A scale is provided which has been calibrated to show the
temperature directly.
This kind of spiral is mostly used in devices measuring ambient temperature and airconditioning thermostats.
Advantages of Bimetallic Thermometers
1. Simple
2. Inexpensive
3. Accuracy of  0.5% to 2%
Limitations
1. Not usable above 400C because of possibility of warping
Application Areas of Bimetal Thermometers
1. Refineries
2. Vulcanizers
3. Oil burners, etc.
204
Working of thermocouples and thermistors
i) Thermocouples
Principles Involved : When heat is applied to the junction of two dissimilar metals, an e.m.f. is
generated. (Figure)
The e.m.f. produced E can be written as,
E = k. 
Where  - Difference in temperature of two junctions
This means that the e.m.f. produced is directly proportional to the temperature difference.
So, if the conjunction is maintained at constant temperature the thermocouple reading will be a
direct measure of temperature. (figure)
ii) Thermistors:
Thermistor is a temperature sensitive variable resistor made of a ceramic like
semiconducting material. They are made of metal oxides and their mixtures like oxides of cobalt,
copper, nickel, etc. Unlike metals, thermistors respond negatively to temperature. They behave as
resistors with a high negative temperature coefficient of resistance. Typically, for each 1 C rise in
temperature, the resistance of a thermistor decreases by about 5%. This high sensitivity to
temperature changes makes the thermistor useful in precision temperature measurements. The
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resistance of thermistors vary from 0.5 to 0.75M . Variation of resistivity with temperature is
shown in figure.
The temperature vs resistance relation is given by
l 1
R  R0e   
 T T0 
Where
R – Resistance at temperature TK
R0
- resistance at temperature T0K
B – Constant (3400 K to 4600 K)
Thermistors come in different configurations some of which are shown in figure.
Application Area of Thermistor
1. Measurement of thermal conductivity
2. Measurement of gas composition
3. Measurement of flow and pressure of liquids.
206
Flow is measured using Orifice meter and Venturi meter.
i) Orifice Meter:
Let
a1 – Area at section I-I
a0 – Area of orifice
Cd – Discharge coefficient
Then, Flow rate Q 
Cd  a1  a0
A 21  a2o
ii) Venturimeter:
This is just like an orifice meter. It has three distinct parts, namely convergent cone, throat
and divergent cone. A manometer measures the pressure difference between two sections as
shown in figure.
Let
Then, Q =
a1
A2
x
Cd
-
Area at the inlet (1-1)
Area at the section (2-2)
Pressure head difference
Discharge coefficient
Cd  a1  a2 2 g x
a21  a22
207
Flow is measured using Rotameter and Pitot tube.
i) Rotameter:
A rotameter is a variable area type flow meter. It consists of a vertical tapered tube with a
float which is free to move within the tube. The fluid goes from the bottom to the top. When no
fluid flows, the float rests at the bottom of the tube. The float is made of such a diameter that it
completely blocks the inlet. When flow starts in the pipeline and fluid reaches the float, the
buoyant effect of fluid makes the float lighter. The float passage remains closed until the pressure
of the flowing material plus the buoyance effect exceeds the downward pressure due to the float
weight. Thus, depending on flow, the float assumes a position. Thus the float gives the reading of
flow rate.
ii) Pitot Tube:
Principle: “Transformation of kinetic energy of a liquid into potential energy in the form of a static
head”.
Figure shows a pitot tube installed in a pipeline where it acts like a probe. The tube consists of two
concentric tubes, the inner tube with its open ends ‘faces’ the liquid.
208
The outer tube has a closed end and has four to eight holes in its wall. The pressure in the
outer tube is the static pressure in the line. Total pressure is sum of static pressure and the
pressure due to the impact of fluid.
If
P
Ps

Velocity v =
-
Pressure at inlet (Stagnation pressure)
Static pressure
Density, then
2 / (P  P0 ), from which flow rate is determined.
Hydraulic and Pneumatic systems for the measurement of force.
Hydraulic and Pneumatic Systems:
If a force is applied to one side of a piston or diaphragm, and a pressure, either hydraulic or
pneumatic, is applied to the other side, some particular value of pressure will be necessary to
exactly balance the force. Hydraulic and pneumatic load cells are based on this principle.
For hydraulic systems, conventional piston and cylinder arrangements may be used.
However, the friction between piston and cylinder wall and required pickings and seals is
unpredictable, and thus good accuracy is difficult to stain. Use of the floating piston with a
diaphragm-type seal practically dominates this variable.
Figure shows a hydraulic cell in section. This cell is similar to the type used in some
materials-testing machines. The piston does not actually contact a cylinder wall in the normal
sense, but a thin elastic diaphragm, or bride ring, of steel is used as the positive seal, which allows
small piston movement. Mechanical stops prevent the seal from being overstrained.
When force acts on the piston, the resulting oil pressure is transmitted to some form of
pressure – sensing system such as the simple Bourdon gage. If the system is completely filled with
fluid, very small transfer or flow will be required. Piston movement may be less than 0.002 in at
full capacity. In this respect, at least, the system will have good dynamic response; however,
overall response will be determined very largely by the response of the pressure sensing element.
Very high capacities and accuracies are possible with cells of the type. Capacities to
5,000,000 Ibf (22.2MN) and accuracies of the order of  ½ % of reading or  1/10% of capacity.
209
Whichever is greater, have been attained. Since hydraulic cells are somewhat sensitive to
temperature change, provision should be made for adjusting the zero setting. Temperature
changes during the measuring process cause errors of about ¼ % per 10F change.
Pneumatic load cells
Pneumatic load cells are quite similar to hydraulic cells in that the applied load is balanced
by a pressure acting over a resisting area, with the pressure becoming a measure of the applied
load. However, in addition to using air rather than liquid as the pressurized medium, these cells
differ from the hydraulic ones in several other important respects.
Pneumatic load cells commonly use diaphragms of a flexible maternal rather than pistons
and they are designed to regulate the balancing pressure automatically. A typical arrangement is
shown in figure.
Air pressure is supplied to one side of the diaphragm and allowed to escape through a
position – controlling bleed valve. The pressure under the diaphragm, therefore, is controlled both
by source pressure and bleed valve position. The diaphragm seeks the position that will result in
just the proper air pressure to support the load, assuming that the supply pressure is great enough
so that its value multiplied by the effective area will at least support the load.
We see that as the load changes magnitude, the measuring diaphragm must change its
position slightly. Unless care is used in the design, a nonlinearity may results, the cause of which
may be made clear by referring to figure.
210
As the diaphragm moves, the portion between the load plate and the fixed housing will
alter position as shown. If it is assumed that the diaphragm is of a perfectly flexible material,
incapable of transmitting any but tensile forces, then the division of vertical load components
transferred to housing and load plate will occur at points A or A’, depending on diaphragm
position. We see then tat the effective area will change, depending on the geometry of this portion
of the diaphragm. If a complete semicircular roll is provided, as shown in figure (b) this effect will
be minimized.
Since simple pneumatic cells may tend to be dynamically unstable, most commercial types
provide some form of viscous damper to minimize this tendency. Also additional chambers and
diaphragms may be added to provide for tare adjustment. Single-unit capacities to 80,000 Ibf (356
kN) may be obtained, and by use of paralleled units practically any total load or force may be
measured. Errors as small as 0.1% of full scale may be expected.
Working of pressure thermometers with a neat sketch.
Pressure Thermometers:
Figure shows the essentials of the practical pressure thermometer. The necessary parts are
bulb A, tube B, pressure – sensing gage C, and some sort of filling medium. Pressure
thermometers are called liquid-filled, gas – filled, or vapor filled, depending on whether the filling
medium is completely liquid, completely gaseous, or a combination of a liquid and its vapour. A
primary advantage of these thermometers is that they can provide sufficient force output to
permit the direct of recording and controlling devices. The pressure-type temperature – sensing
system is usually less costly than other systems. Tubes as log as 200ft may be used successfully.
Expansion (or contraction) of bulb A and the contained fluid or gas, caused by temperature
change, alters the volume and pressure in the system. In the case of the liquid-filled system, the
sensing device C acts primarily as a differential volume indicatory, with the volume increment
serving as an analog of temperature. For the gas-or vapour-filled systems, the sensing device
211
serves primarily as a pressure indicator, with the pressure providing the measure of temperature.
In both cases, of course, both pressure and volume change.
Ideally the tube or capillary should serve simply as a connecting link between the bulb and
the indicator. When liquid or gas-filled systems are used, the tube and its filling are also
temperature – sensitive, and any difference from calibration conditions along the tube introduces
output error. This error is reduced by increasing the ratio of bulb volume to tube volume.
Unfortunately, increasing bulb size reduces the time response of a system, which may introduce
problems of another nature. On the other hand, reducing tube size, within reason, does not
degrade response particularly because, in any case, flow rate is negligible. Another source of error
tht should not be overlooked is any pressure gradient resulting from difference in elevation of
bulb and indicator not accounted for by calibration.
Temperature along the tube is not a factor for vapour-pressure systems, however, so long
as a free liquid surface exists in the bulb. In this case, Dalton’s law for vapours applies, which
states that if both phases (liquid and vapour) are present, only one pressure is possible for a given
temperature. This is an important advantage of the vapour-pressure system. In many cases,
though, the tube in this type of system will be filled with liquid, and hence the system is
susceptible to error caused by elevation difference.
Principle and working of thermistors.
Resistance elements sensitive to temperature are made of metals generally considered to be
good conductors of electricity. Examples are nickel, copper, platinum and silver. A temperature –
measuring device using an element of this type is commonly referred to as a resistance
thermometer, or a resistance temperature detector, abbreviated RTD. Of more recent origin are
elements made from semiconducting materials having large – and usually negative – resistance
212
coefficients. Such materials are usually some combination of metallic oxides of cobalt, manganese,
and nickel. These devices are called thermistors.
One important difference between these two kinds of material is that, whereas the
resistance change in the RTD is small and positive (increasing temperature causes increased
resistance), that of the thermistor is relatively large and usually negative. In addition, the RTD
type provides nearly a linear temperature – resistance relation, whereas that of the thermistor is
nonlinear. Still another important difference lies in the temperature ranges over which each may
be used. The practical operating range for the thermistor lies between approximately - 100 C to
275C (-150F to 500F). The range for the resistance thermometer is much greater, being from
about - 260C to 1000C (-435 F to 1800F). Finally, the metal resistance elements are more time
stable than the semiconductor oxides; hence they provide better reproducibility with lower
hysteresis.
Resistance Thermometers (RTDs)
Evidence of the importance and reliability of the resistance thermometer may be had by
recalling that the International Temperature Scale of 1990 specifies a platinum resistance
thermometer as the interpolation standard over the range from -259.35C to 961.78C (-484.52F to
1763.20F).
Certain properties are desirable in material used for resistance thermometer elements. The
material should have a resistivity permitting fabrication in convenient sizes without excessive
bulk, which would degrade time response. In addition, its thermal coefficient of resistivity should
be high and as constant as possible, thereby providing an approximately linear output of
reasonable magnitude.
The material should be corrosion – resistant and should not undergo phase changes in the
temperature range of corrosion – resistant and should not undergo phase changes in the
temperature range of interest. Finally, it should be available in a condition providing reproducible
and consistent results. In regard to this last requirement, it has been found that to produce
precision resistance thermometers, great care must be exercised in minimizing residual strains,
requiring careful heat treatment subsequent to forming.
As is generally the case in such matters, no materials is universally acceptable for
resistance-thermometer elements. Undoubtedly, platinum, nickel, and copper are the materials
most commonly used, although others such as tungsten, silver and iron have also been employed.
The specific choice normally depends upon which compromises may be accepted. The
temperature – resistance relation of an RTD must be determined experimentally. For most metals,
the result can be accurately represented as

R(T)  R0 1  A  T  To   B  T  T0  2

where
R(T) = the resistance at temperature T,
213
R0
= the resistance at a reference temperature T0
A and B = temperature coefficients of resistance depending on material.
Over a limited temperature interval (perhaps 50C for platinum) a linear approximation to
the resistance variation may be quite acceptable.
R(T) = R0 (1+ A(T – T0))
But for the highest accuracy, a high – order polynomial fit is required.
The resistance element is most often a metal wire wrapped around an electrically insulating
support of glass, ceramic or mica. The latter may have a variety of configurations, ranging from a
simple flat strip, as shown in figure to intricate “bird-cage” arrangement (3). The mounted element
is then provided with a protective enclosure. When permanent installations are made and when
additional protection from corrosion or mechanical abuse is required, a well or socket may be
used, such as shown in figure.
More recently, thin films of metal-glass slurry have been used as resistance elements. These
films are deposited onto a ceramic substrate and laser trimmed. Film RTDs are less expensive than
the wire RTDs and have a larger resistance for a given size; however, they are also somewhat less
stable (4). Resistance elements similar in construction to foil strain gages are available as well. The
resistance grid is deposited onto a supporting film, such as Kapton, which may then be cemented
to a surface. These sensors are generally designed to have low strain sensitivity and high
temperature sensitivity. Table describes characteristic of several typical commercially available
resistance thermometers.
The use of a pyrometer, it’s working principle and Applications
A pyrometer is a non-contacting device that intercepts and measures thermal radiation, a process
known as pyrometry. This device can be used to determine the temperature of an object's surface.
The word pyrometer comes from the Greek word for fire, "πυρ" (pyro), and meter, meaning to
214
measure. Pyrometer was originally coined to denote a device capable of measuring temperatures
of objects above incandescence (i.e. objects bright to the human eye).
Principle of operation
A pyrometer has an optical system and detector. The optical system focuses the thermal radiation
onto the detector. The output signal of the detector (Temperature T) is related to the thermal
radiation or irradiance j* of the target object through the Stefan–Boltzmann law, the constant of
proportionality σ, called the Stefan-Boltzmann constant and the emissivity ε of the object.
This output is used to infer the object's temperature. Thus, there is no need for direct contact
between the pyrometer and the object, as there is with thermocouple and Resistance temperature
detector (RTDs).
Applications
Pyrometer are suited especially to the measurement of moving objects or any surfaces that can not
be reached or can not be touched.
In Industry: Temperature is a fundamental parameter in metallurgical furnace operations.
Reliable and continuous measurement of the melt temperature is essential for effective control of
the operation. Smelting rates can be maximized, slag can be produced at the optimum
temperature, fuel consumption is minimized and refractory life may also be lengthened.
Thermocouples were the traditional devices used for this purpose, but they are unsuitable for
continuous measurement because they rapidly dissolve.
Over-the-bath Pyrometer: Continuous pyrometric measurement from above the bath surface is
still employed, but is known to give poor results because of emissivity variations, interference by
gases and particulate matter in the intervening atmosphere, and dust accumulation on the optics.
Tuyère Pyrometer: The Tuyère Pyrometer is an optical instrument for temperature measurement
through the tuyeres which are normally used for feeding air or reactants into the bath of the
furnace.
Different types of pressure measuring instruments
Many instruments have been invented to measure pressure, with different advantages and
disadvantages. Pressure range, sensitivity, dynamic response and cost all vary by several orders of
magnitude from one instrument design to the next. The oldest type is the liquid column (a vertical
tube filled with mercury) manometer invented by Evangelista Torricelli in 1643. The U-Tube was
invented by Christian Huygens in 1661.
Hydrostatic Gauges
Hydrostatic gauges (such as the mercury column manometer) compare pressure to the hydrostatic
force per unit area at the base of a column of fluid. Hydrostatic gauge measurements are
215
independent of the type of gas being measured, and can be designed to have a very linear
calibration. They have poor dynamic response.
Piston Gauges
Piston-type gauges counterbalance the pressure of a fluid with a solid weight or a spring. Another
name for piston gauge is deadweight tester. For example, dead-weight testers used for calibration
or tire-pressure gauges.
Liquid column
The difference in fluid height in a liquid column manometer is proportional to the pressure
difference.
Liquid column gauges consist of a vertical column of liquid in a tube whose ends are exposed to
different pressures. The column will rise or fall until its weight is in equilibrium with the pressure
differential between the two ends of the tube. A very simple version is a U-shaped tube half-full of
liquid, one side of which is connected to the region of interest while the reference pressure (which
might be the atmospheric pressure or a vacuum) is applied to the other. The difference in liquid
level represents the applied pressure. The pressure exerted by a column of fluid of height h and
density ρ is given by the hydrostatic pressure equation, P = hgρ. Therefore the pressure difference
between the applied pressure Pa and the reference pressure P0 in a U-tube manometer can be
found by solving Pa − P0 = hgρ. If the fluid being measured is significantly dense, hydrostatic
corrections may have to be made for the height between the moving surface of the manometer
working fluid and the location where the pressure measurement is desired.
Based on the use and structure following type of manometers are used
1.
Simple Manometer
2.
Micromanometer
3.
Differential manometer
4.
Inverted differential manometer
McLeod gauge
A McLeod gauge isolates a sample of gas and compresses it in a modified mercury manometer
until the pressure is a few mmHg. The gas must be well-behaved during its compression (it must
not condense, for example). The technique is slow and unsuited to continual monitoring, but is
capable of good accuracy.
Useful range: above 10-4 torr (roughly 10-2 Pa) as high as 10−6 Torr (0.1 mPa),
0.1 mPa is the lowest direct measurement of pressure that is possible with current technology.
Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other
pressure-controlled properties. These indirect measurements must be calibrated to SI units via a
direct measurement, most commonly a McLeod gauge.
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Aneroid Gauges
Aneroid gauges are based on a metallic pressure sensing element which flexes elastically under
the effect of a pressure difference across the element. "Aneroid" means "without fluid," and the
term originally distinguished these gauges from the hydrostatic gauges described above.
However, aneroid gauges can be used to measure the pressure of a liquid as well as a gas, and
they are not the only type of gauge that can operate without fluid. For this reason, they are often
called mechanical gauges in modern language. Aneroid gauges are not dependent on the type of
gas being measured, unlike thermal and ionization gauges, and are less likely to contaminate the
system than hydrostatic gauges. The pressure sensing element may be a Bourdon tube, a
diaphragm, a capsule, or a set of bellows, which will change shape in response to the pressure of
the region in question. The deflection of the pressure sensing element may be read by a linkage
connected to a needle, or it may be read by a secondary transducer. The most common secondary
transducers in modern vacuum gauges measure a change in capacitance due to the mechanical
deflection. Gauges that rely on a change in capacitances are often referred to as Baratron gauges.
Bourdon Gauges
A Bourdon gauge uses a coiled tube, which, as it expands due to pressure increase causes a
rotation of an arm connected to the tube. In 1849 the Bourdon tube pressure gauge was patented
in France by Eugene Bourdon.
The pressure sensing element is a closed coiled tube connected to the chamber or pipe in which
pressure is to be sensed. As the gauge pressure increases the tube will tend to uncoil, while a
reduced gauge pressure will cause the tube to coil more tightly. This motion is transferred through
a linkage to a gear train connected to an indicating needle. The needle is presented in front of a
card face inscribed with the pressure indications associated with particular needle deflections. In a
barometer, the Bourdon tube is sealed at both ends and the absolute pressure of the ambient
atmosphere is sensed. Differential Bourdon gauges use two Bourdon tubes and a mechanical
linkage that compares the readings.
In the following illustrations the transparent cover face of the pictured combination pressure and
vacuum gauge has been removed and the mechanism removed from the case. This particular
gauge is a combination vacuum and pressure gauge used for automotive diagnosis:

the left side of the face, used for measuring manifold vacuum, is calibrated in centimetres of
mercury on its inner scale and inches of mercury on its outer scale.

the right portion of the face is used to measure fuel pump pressure and is calibrated in
fractions of 1 kgf/cm² on its inner scale and pounds per square inch on its outer scale.
Diaphragm Gauges
A pile of pressure capsules with corrugated diaphragms in an aneroid barograph.
A second type of aneroid gauge uses the deflection of a flexible membrane that separates regions
of different pressure. The amount of deflection is repeatable for known pressures so the pressure
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can be determined by using calibration. The deformation of a thin diaphragm is dependent on the
difference in pressure between its two faces. The reference face can be open to atmosphere to
measure gauge pressure, open to a second port to measure differential pressure, or can be sealed
against a vacuum or other fixed reference pressure to measure absolute pressure. The deformation
can be measured using mechanical, optical or capacitive techniques. Ceramic and metallic
diaphragms are used.
Useful range: above 10-2 Torr (roughly 1 Pa)
For absolute measurements, welded pressure capsules with diaphragms on either side are often
used.
Shape:

Flat

corrugated

flattened tube

capsule
Bellows Gauges
In gauges intended to sense small pressures or pressure differences, or require that an absolute
pressure be measured, the gear train and needle may be driven by an enclosed and sealed bellows
chamber, called an aneroid, which means "without liquid". (Early barometers used a column of
liquid such as water or the liquid metal mercury suspended by a vacuum.) This bellows
configuration is used in aneroid barometers (barometers with an indicating needle and dial card),
altimeters, altitude recording barographs, and the altitude telemetry instruments used in weather
balloon radiosondes. These devices use the sealed chamber as a reference pressure and are driven
by the external pressure. Other sensitive aircraft instruments such as air speed indicators and rate
of climb indicators (variometers) have connections both to the internal part of the aneroid chamber
and to an external enclosing chamber.
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