ME111
Mechanical
Measurements
Lab.
Basic Concepts II
The Detector
▪ The measurement process requires
invariably a detector that responds to the
measured quantity by producing a
measurable change in some property of
the detector.
▪ The change in the property of the
detector is converted to a measurable
output that may be either mechanical
movement of a pointer over a scale or an
electrical output that may be measured
using an appropriate electrical circuit.
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The Transducer
▪ The action of converting the measured
quantity to a different form of output is
done by a transducer.
▪ The output may be manipulated by a
signal conditioner before it is
recorded or stored in a computer.
▪ If the measurement process is part of
a control application the computer can
use a controller to control the
measured quantity.
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Errors in Measurements
▪ Any measurement, however carefully
it is conducted, is subject to
measurement errors.
▪ These errors make it difficult to
ascertain the true value of the
measured quantity.
▪ If the spread in the data is small the
measurement is repeatable and may
be termed as being good.
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Types of Errors
The errors may be classified as:
1. Systematic errors.
2. Random errors.
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Systematic errors (Bias)
▪ Systematic errors due to faulty or improperly
calibrated instruments.
▪ These may be reduced or eliminated by careful choice
and calibration of instruments.
▪ Sometimes bias may be linked to a specific cause and
estimated by analysis. In such a case a correction
may be applied to eliminate or reduce bias.
▪ Bias is an indication of the accuracy of the
measurement. Smaller the bias more accurate the
data.
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Random Errors
▪ Random errors are due to non-specific causes like natural
disturbances that may occur during the measurement
process. These cannot be eliminated.
▪ The magnitude of the spread in the data due to the
presence of random errors is a measure of the precision of
the data.
▪ Smaller the random error more precise is the data. Random
errors are statistical in nature. These may be characterized
by statistical analysis.
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Accuracy & Precision
▪ The accuracy of an
instrument is a measure of
how close the output
reading of the instrument is
to the correct value.
▪ Precision is a term that
describes an instrument’s
degree of freedom from
random errors.
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Accuracy & Precision
▪ If a large number of readings
are taken of the same quantity
by a high precision instrument,
then the spread of readings will
be very small.
▪ High precision does not imply
anything about measurement
accuracy.
▪ A high precision instrument
may have a low accuracy.
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Accuracy & Precision
▪ The systematic error (Bias) appears
to vary with the temperature.
▪ The data points indicated by the full
symbols appear also to hug the
trend line. However the data points
do not lie on it. This is due to
random errors that are always
present in any measurement.
▪ Actually the standard thermocouple
would also have the random errors
that are not indicated in the figure.
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Example:
Yst "stasndard
random random
no. "n"
out put reading Y "measured out X-Xavg Y-Yavg (X-Xavg)^2 (X-Xavg)(Y-Yavg) Ycalc
bias bias %
error error %
(mv)"
put reading (mv)"
1
10
15
14
-20
-10.8
400
216
14.8
-0.8 -0.0571 1 0.0666667
2
20
20
21
-10
-3.8
100
38
19.8
1.2 0.05714 -1
-0.05
3
30
25
24
0
-0.8
0
0
24.8
-0.8 -0.0333 1
0.04
4
40
30
31
10
6.2
100
62
29.8
1.2 0.03871 -1 -0.033333
5
50
35
34
20
9.2
400
184
34.8
-0.8 -0.0235 1 0.0285714
150
124
1000
500
Σ(X-Xavg)^2 = 1000
R.E = R.E%= S.E = S.E%=
Σ X = 150
Σ Y = 124
Σ(X-Xavg)(Y-Yavg) = 500
Yc - Y R.E/ Y Yst - Y S.E/ Yst
Xavg= (Σ X/n)
30
Yavg= (Σ Y/n)
24.8
0.5
b1= Σ(X-Xavg)(Y-Yavg) /Σ(X-Xavg)^2 = 0.5
Y = b0 + b1 X
subs. In the equation by Xavg. and Yavg.-----------> b0 = 9.8 --------> Ycalc = 9.8 + 0.5 X
b0 = 9.8
X "Temp.
(ºC)"
Ycalc = 9.8+0.5*x
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Example:
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Factors Affecting Accuracy:
▪ Inaccuracy resulting from the presence condition of the instrument
▪ Intrinsic in accuracy of the instrument it self.
▪ Inaccurate installation of the instrument.
▪ Parllax effect: the apparent shifting of the pointer with respect to the sight
position, it is required to use a mirror under the pointer to avoid this error.
▪ The pointer vibration which is a result of the measured force variation near the
equilibrium point, the pointer is provided with a damper to minimize vibration.
▪ The free motion due to clearance between different elements.
▪ The environment temperature, a standard temperature for the instrument
indication (+ 20 ºC), which is the mean temperature in a laboratory at the
whole year.
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Instrument Calibration:
▪ Instrument must be calibrated to indicate its sensitivity and accuracy
▪ Calibration determined by loading the instrument till its maximum value and
gradually disloading it.
▪ Each load will give two calibrating readings which corresponds to the addition
and subtracting of friction force, (as the friction decrease the sensitivity
increase).
▪ Sensitivity of the apparatus is the linear motion of the indicating system with a
unit input.
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Repeatability & Reproducibility
▪ Repeatability describes the closeness of output readings
when the same input is applied repetitively over a short
period of time, with the same measurement conditions, same
instrument and observer, same location and same conditions
of use maintained throughout.
▪ Reproducibility describes the closeness of output readings
for the same input when there are changes in the method of
measurement, observer, measuring instrument, location,
conditions of use and time of measurement.
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Range or span
▪ The range or span of an instrument defines the minimum and
maximum values of a quantity that the instrument is designed
to measure.
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Sensitivity of measurement
▪ The sensitivity of measurement is a measure
of the change in instrument output that occurs
when the quantity being measured changes by
a given amount.
▪ Thus, sensitivity is the ratio:
▪ The sensitivity of measurement is therefore
the slope of the straight line drawn on Figure.
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Example (1)
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Threshold
▪ If the input to an instrument is gradually increased from
zero, the input will have to reach a certain minimum
level before the change in the instrument output reading
is of a large enough magnitude to be detectable.
▪ This minimum level of input is known as the threshold
of the instrument.
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Resolution
▪ When an instrument is showing a particular output
reading, there is a lower limit on the magnitude of
the change in the input measured quantity that
produces an observable change in the instrument
output.
▪ Using a car speedometer as an example, it has
subdivisions of typically 20 km/h. This means that
when the needle is between the scale markings,
we cannot estimate speed more accurately than to
the nearest 5 km/h. This figure of 5 km/h thus
represents the resolution of the instrument.
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Hysteresis Effects
▪ The figure illustrates the output characteristic of an
instrument that exhibits hysteresis.
▪ If the input measured quantity to the instrument is
steadily increased from a negative value, the
output reading varies in the manner shown in
curve (a).
▪ If the input variable is then steadily decreased, the
output varies in the manner shown in curve (b).
▪ The non-coincidence between these loading and
unloading curves is known as hysteresis.
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Hysteresis Effects
▪ Hysteresis is most commonly found in instruments that
contain springs, such as the passive pressure gauge and
the Prony brake (used for measuring torque).
▪ It is also evident when friction forces in a system have
different magnitudes depending on the direction of
movement, such as in the pendulum-scale massmeasuring device.
▪ Hysteresis can also occur in instruments that contain
electrical windings formed round an iron core, due to
magnetic hysteresis in the iron.
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Thank YOU