III. METROLOGY
THERE IS MEASURE IN ALL THINGS.
HORACE
SATIRES, BOOK I, 35 B.C.
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UNITS OF MEASUREMENT
Introduction
Metrology is the science of measurement. The word metrology derives from two
Greek words: matron (meaning measure) and logos (meaning logic). With today’s
sophisticated industrial climate the measurement and control of products and
processes are critical to the total quality effort. Metrology encompasses the
following key elements:
&
The establishment of measurement standards that are both
internationally accepted and definable
&
The use of measuring equipment to correlate the extent that product
and process data conforms to specification (expressed in recognizable
measurement standard terms)
&
The regular calibration of measuring equipment, traceable to
established international standards
Units of Measurement
There are three major international systems of measurement: the English, the
Metric, and the System International D`unites (or SI). The U.S. has effectively
retained the English System as a remanent of British colonial influence.
The metric and SI systems are decimal-based, the units and their multiples are
related to each other by factors of 10. The English system, although logical to us,
has numerous relic defined measurement units that make conversions difficult.
Most of the world is now committed to the adoption of the SI system. The SI system
was established in 1968 and the U.S. officially adopted it in 1975. The transition is
occurring very slowly. The final authority for standards rests with the internationally
based system of units. This system classifies measurements into seven distinct
categories:
1.
Length (meter). The meter is the length of the path traveled by light in
vacuum during a time interval of 1/299,792,458 of a second. The speed of
light is fixed at 186,282.3976 statute miles per second, with exactly 2.540
centimeters in one inch.
2.
Time (second). The second is defined as the duration of 9,192,631,770
periods of the radiation corresponding to the transition between the two
hyperfine levels of the ground state of the cesium - 133 atom.
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Units of Measurement (Continued)
3.
Mass (kilogram). The standard unit of mass, the kilogram is equal to the
mass of the international prototype which is a cylinder of platinum iridium
alloy kept by the International Bureau of Weights and Measures at Sevres
(near Paris, France). A duplicate, in the custody of the National Institute of
Standards and Technology, serves as the standard for the United States. This
is the only base unit still defined by an artifact.
4.
Electric current (ampere). The ampere is that constant that, if maintained in
two straight parallel conductors of infinite length, of negligible circular cross
section, and placed one meter apart in vacuum, would produce between these
conductors a force equal to 2 x 10 -7 Newtons per each meter of length.
5.
Temperature (Kelvin). The Kelvin, unit of thermodynamic temperature, is the
fraction 1/273.16 of the thermodynamic temperature of the triple point of
water. It follows from this definition that the temperature of the triple point
of water is 273.16 K (0.01 C). The freezing point of water at standard
atmospheric pressure is approximately 0.01 K below the triple point of water.
The relationship of Kelvin, Celsius and Fahrenheit is shown below.
Temp F = 1.8 (Temp C) + 32
Temp C = (Temp F - 32) ÷ 1.8
Temp K = Temp C + 273.15
KELVIN
CELSIUS
FAHRENHEIT
WATER BOILS
373.15(
100(
212(
WATER FREEZES
273.15(
0(
32(
ABSOLUTE ZERO
0(
-273.15(
-459.67(
Table 3.1 Relationship of the Three Common Temperature Scales
6.
Light (candela). The candela is defined as the luminous intensity, in a given
direction, of a source that emits monochromatic radiation of frequency 540
x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per
steradian.
7.
Amount of substance (mole). The mole is the amount of substance of a
system which contains as many elementary entities as there are atoms in
0.012 kilogram of carbon 12. The elementary entities must be specified and
may be atoms, molecules, ions, electrons, other particles or specified groups
of such particles.
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III. METROLOGY
UNITS OF MEASUREMENT
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UNITS OF MEASUREMENT
SI System Units
Listed below is a table of the SI system units:
QUANTITY MEASURED
UNIT
SYMBOL
FORMULA
FUNDAMENTAL UNITS
AMOUNT OF SUBSTANCE
LENGTH
MASS
TIME
ELECTRIC CURRENT
TEMPERATURE
LUMINOUS INTENSITY
MOLE
METER
KILOGRAM
SECOND
AMPERE
DEGREE KELVIN
CANDELA
mol
m
kg
s
A
K
cd
SUPPLEMENTARY UNITS
PLANE ANGLE
SOLID ANGLE
RADIAN
STERADIAN
rad
sr
DERIVED UNITS
AREA
VOLUME
FREQUENCY
DENSITY
VELOCITY
ANGULAR VELOCITY
ACCELERATION
ANGULAR ACCELERATION
FORCE
PRESSURE
KINEMATIC VISCOSITY
DYNAMIC VISCOSITY
WORK, ENERGY, QUANTITY OF HEAT
POWER
ELECTRIC CHARGE
VOLTAGE (ELECTROMOTIVE FORCE)
ELECTRIC FIELD STRENGTH
ELECTRIC RESISTANCE
ELECTRIC CAPACITANCE
MAGNETIC FLUX
INDUCTANCE
MAGNETIC FLUX DENSITY
MAGNETIC FIELD STRENGTH
MAGNETOMOTIVE FORCE
LUMINOUS FLUX
LUMINANCE
ILLUMINATION
SQUARE METER
CUBIC METER
HERTZ (ONE CYCLE PER SECOND)
KILOGRAM PER CUBIC METER
METER PER SECOND
RADIAN PER SECOND
METER PER SECOND SQUARED
RADIAN PER SECOND SQUARED
NEWTON
NEWTON PER SQUARE METER
SQ METER PER SECOND
NEWTON-SECOND PER SQ METER
JOULE
WATT
COULOMB
VOLT
VOLT PER METER
OHM
FARAD
WEBER
HENRY
TESLA
AMPERE PER METER
AMPERE
LUMEN
CANDELA PER SQ METER
LUX
m2
m3
Hz
kg/m3
m/s
rad/s
m/s2
rad/s2
N
N/m2
m2/s
N # s/m2
J
W
C
V
V/m
6
F
Wb
H
T
A/m
A
lm
cd/m2
lx
(s-1)
(kg # m/s2)
(N # m)
(J/s)
(A # s)
(W/A)
(V/A)
(A # s/V)
(V # s)
(V # s/A)
(Wb/m2)
(cd # sr)
(lm/m2)
Table 3.2 SI System Units Symbols and Formulas
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Methods Used in Dimensional Measurement
METHOD
DESCRIPTION
Direct measurement
An instrument such as a micrometer provides a
direct dimensional reading.
Mechanical indicator
An instrument such as a dial indicator
mechanically amplifies a small dimensional
reading onto a larger dial scale.
Electronic comparator
The instrument electronically amplifies a small
dimension onto a larger scale.
Pneumatic gage
The relative escape of air by pressure or flow
regulation against a work piece is measured on
a dimensionally graduated scale.
Optical comparator
A beam of light is directed upon the part to be
inspected, and the resulting shadow is
magnified by a lens system, and projected upon
a viewing screen by a mirror. The image can
then be inspected by comparing it with a master
silhouette having tolerance limits.
Interferometer
An actual measurement is accomplished by the
interference interaction of light waves that are
180( out of phase.
Coordinate measuring machine (CMM)
Computer controlled measurements are taken
on three mutually perpendicular axes. A CMM
is often used for layout before machining and
inspection after machining.
Table 3.3 Description of Dimensional Measurement Methods
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Measuring Instruments
Overview
The terms measuring tool and measuring instrument are used interchangeably in
this text. Some very basic tools are reviewed but other commonly used tools are
described in summary form only. The reader is advised to seek other sources, such
as Griffith (1992), Farago (1982) and Kennedy (1987), for a more in-depth treatment
of specific instruments. See the references at the end of this Section. In a
subsequent portion of this Section, the causes of error in measurement are
discussed. It is worthwhile to study the possible errors related to each tool.
Tool Care
Measuring instruments are typically expensive and should be treated with care to
preserve their accuracy and longevity. Some instruments require storage in a
customized case or controlled environment when not in use. Even sturdy hand
tools are susceptible to wear and damage. Hardened steel tools require a light film
of oil to prevent rusting. Care must be taken in the application of oil since dust
particles will cause buildup on the gage's functional surfaces. Measuring tools
must be calibrated on a scheduled basis as well as after any suspected damage.
Tools should be examined frequently for wear on the measuring surfaces. The
military standard covering the care and calibration of gages is MIL-STD-120. This
standard was last revised in 1950, but it is still useful as a reference for modern
gaging.
Reference/Measuring Surfaces
A reference surface is the surface of a measuring tool that is fixed. The measuring
surface is movable. Both surfaces must be free from grit or damage, secure to the
part and properly aligned for an accurate measurement.
Transfer Tools
Transfer tools have no reading scale. An example, discussed later in this Section,
is spring calipers. Jaws on these instruments measure the length, width or depth
in question by positive contact. The dimension measurement is then transferred to
another measurement scale for direct reading. There are a number of measuring
devices that may be used to transfer measurements from a reference piece to a part
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INSTRUMENTS AND TOOLS
surface.
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Variable Gages
Variable measuring instruments provide a physical measured dimension. Examples
of variable instruments are line rules, vernier calipers, micrometers, depth
indicators, runout indicators, etc... Variable information provides a measure of the
extent that a product is good or bad, relative to specifications. Variable data is often
useful for process capability determination and may be monitored via control charts.
Attribute Gages
Attribute gages are fixed gages which typically are used to make a go, no-go
decision. Examples of attribute instruments are master gages, plug gages, contour
gages, thread gages, limit length gages, assembly gages, etc... Attribute data
indicates only whether a product is good or bad (in most cases, it is known in what
direction the product is good or bad). Attribute gages are quick and easy to use but
provide minimal information for production control.
The Steel Rule
The steel rule is a widely used factory measuring tool for direct length measurement.
Steel rules and tapes are available in different degrees of accuracy and are typically
graduated on both edges. See the drawing below.
Figure 3.4 A Typical Steel Rule
The fine divisions on a steel rule (thirty-seconds on the one above) establish its
discrimination. Steel rules commonly discriminate to one thirty-second inch, one
sixty-fourth inch or one-hundredth inch.
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Use of the Steel Rule
The steel rule typically has discriminations of 1/32, 1/64, or 1/100 of an inch.
Obviously, measurements of .001" or greater should be performed with other tools
(such as a digital vernier caliper).
For maximum accuracy, the rule should measure a part with both butted firmly
against a rigid flat surface. The end of a rule may be worn, rounded or damaged
which produce errors in measurement. If a flat surface is not available the 1" mark
may be used as a reference point. Diagramed below are the correct and incorrect
methods of measurement.
Incorrect
Correct
Figure 3.5 Use of a Flat Surface with a Steel Rule
Hook Rules
Steel rules may be purchased with a moveable bar or hook on the zero end which
serves in the place of a butt plate. These rulers may be used to measure around
rounded, chamfered or beveled part corners.
Figure 3.6 Steel Rule with Hook Attachment
The hook attachment becomes relied upon as a fixed reference. However, by its
inherent design, it may loosen or become worn. The hook should be checked often
for accuracy.
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Spring Calipers
Spring calipers are transfer tools that perform a rough measurement of wide,
awkward or difficult to reach part locations. These tools usually provide a
measurement accuracy of approximately 1/16 inch.
Although these calipers are referred to as spring calipers, there are different
varieties (spring joint, firm joint, lock joint, etc...) which describe the type of
mechanical joint that connects the two sides of the unit.
A spring caliper measurement is typically transferred to a steel rule by holding the
rule vertically on a flat surface. The caliper ends are placed against the rule for the
final readings . See the diagram below.
Inside Calipers
Outside Calipers
Figure 3.7 Spring Caliper Applications
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Gage Blocks
Near the beginning of the 20th century, Carl Johansson of Sweden, developed steel
blocks to an accuracy believed impossible by many others at that time. His
objective was to establish a measurement standard that not only would duplicate
national standards, but also could be used in any shop. He was able to build gage
blocks to an accuracy within a few millionths of an inch.
When first introduced, gage blocks or "Jo" blocks as they are popularly known in
the shop, were a great novelty. Seldom used for measurements, they were kept
locked up and were only brought out to impress visitors.
Today gage blocks are used in almost every shop manufacturing a product requiring
mechanical inspection. They are used to set a length dimension for a transfer
measurement, and for calibration of a number of other tools.
The American National Standard for gage blocks, ANSI B89. 1.9 -1973, distinguishes
three basic gage block forms - rectangular, square and round. The rectangular and
square varieties are in much wider usage. Generally, gage blocks are made from
high carbon or chromium alloyed steel. Tungsten carbide, chromium carbide and
fused quartz are also used.
All gage blocks are manufactured with tight tolerances on flatness, parallelism and
surface smoothness. Gage blocks may be purchased in 4 standard grades:
FEDERAL ACCURACY GRADES
ACCURACY
IN LENGTH
NEW DESIGNATION
OLD DESIGNATION
0.5
AAA
± .000001
1
AA
± .000002
2
A+
+ .000004
- .000002
3
A&B
+ .000008
- .000004
Table 3.8 Gage Block Grades
Master blocks are 0.5 or 1 grade
Inspection blocks are 1 or 2 grade
Working blocks are 3 grade
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Gage Blocks (Continued)
Gage blocks should always be handled on the non-polished sides. Blocks should
be cleaned prior to stacking with filtered kerosene, benzene or carbon tetrachloride.
A soft clean cloth or chamois should be used. A light residual oil film must remain
on blocks for wringing purposes.
Block stacks are assembled by a wringing process which attaches the blocks by a
combination of molecular attraction and the adhesive effect of a very thin oil film.
Air between the block boundaries is squeezed out. The sequential steps for the
wringing of rectangular blocks is shown below. Light pressure is used throughout
the process.
Hold Crosswise
Swivel the
Pieces
Slip into
Position
Finished
Stack
Figure 3.9 Illustration of the Wringing of Gage Blocks
Wear Blocks
For the purpose of stack protection, some gage manufactures provide wear blocks.
Typically, these blocks are .050-inch or .100-inch thick. They are wrung onto each
end of the gage stack and must be calculated as part of the stack height. Since wear
blocks "wear" they should always be used with the same side out.
Gage Block Sets
Individual gage blocks may be purchased up to 20" in size. Naturally, the length
tolerance of the gage blocks increases as the size increases. Typical gage block
sets vary from 8 to 81 pieces based upon the needed application.
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Gage Block Set Contents
Listed below are the contents of a typical 81 piece set:
Ten-thousands blocks (9)
0.1001, 0.1002 . . . . . . . . . . . . . . 0.1009
One-thousands blocks (49)
0.101, 0.102 . . . . . . . . . . . . . . . . 0.149
Fifty-thousands blocks (19)
0.050, 0.100 . . . . . . . . . . . . . . . . 0.950
One inch blocks (4)
1.000, 2.000, 3.000, 4.000
Also included in the set, are two wear blocks that are either 0.050" or 0.100" in
thickness.
Minimum Stacking
A minimum number of blocks in a stack lessens the chance of unevenness at the
block surfaces. Stack up 2.5834" using a minimum number of blocks:
2.5834
- .1004 . . . . . (use this block)
2.483
- .133 . . . . . . (use this block)
2.350 . . . . . . (use 0.350 and 2.000 blocks)
This example does not consider the use of wear blocks.
Surface Plates
To make a precise dimensional measurement, there must be a reference plane or
starting point. The ideal plane for dimensional measurement should be perfectly
flat. Since a perfectly flat reference plane does not exist, a compromise in the form
of a surface plate is commonly used.
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Surface Plates (Continued)
Surface plates must possess the following important characteristics:
&
&
Sufficient strength and rigidity to support the test piece
Sufficient and known accuracy for the measurements required
Surface plates require appropriate care and maintenance:
&
&
&
&
&
The surface should be cleaned before use
The surface should be covered between uses
Work should be distributed to avoid concentrated wear
Move the test pieces and equipment carefully
A surface plate should not become a storage area
Cast Iron Vs. Granite
Surface plates are made of cast iron or granite. Each have merits:
Cast iron plates:
&
&
&
&
Usually weigh less per square foot of plate area
Are not likely to chip or fracture
Are acceptable for magnetic fixtures
Can provide a degree of wringability
Granite plates:
&
&
&
&
&
&
Are noncorrosive and require less maintenance
Do not burr or retain soft metals
Are cheaper per relative size
Have closer flatness tolerances
Have greater thermal stability
Are nonmagnetic
Surface Plate Usage
Surface plates are customarily used with accessories like: a toolmaker's flat,
angles, parallels, V blocks and cylindrical gage block stacks. Dimensional
measurements are taken from the plate up since the plate is the reference surface.
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