MECHANICAL INSTRUMENTATION MODULE-1 LECTURE NOTES FOR FOURTH SEMESTER INSTRUMENTATION AND CONTROL ENGG. STUDENTS

1. IC 208 MECHANICAL INSTRUMENTATION
Module- 1
Binil Babu,
Asst. Professor
Department Mechanical Engineering
SNMIMT, MALIANKARA
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2. Contents
1 Mechanical Measurement 1
2 Definitions and basic concepts 1
3 Direct and Indirect comparison 1
4 The generalised Measurement System 2
4.1 Example of generalized measurement system . . . . . . . . . . . . . . . . . . . . . 3
5 Types of input quantities 4
6 Classification of errors 5
6.1 Gross errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6.2 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2.1 Instrumental errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2.2 Environmental Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6.2.3 Observational Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6.3 Random Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7 Uncertainty 8
7.1 Kline and Mclintock Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
7.2 Propagation of uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
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3. 1 Mechanical Measurement
Measurement is defined as the process or the act of obtaining a quantitative comparison between
a predefined standard and an unknown magnitude.Measurement means determination of anything
that exists in some amount.If those things that exist are related to mechanical engineering, then
the determination of such amounts are referred to as mechanical measurements.
2 Definitions and basic concepts
True value Standard or reference of known value or a theoretical value.
Accuracy Closeness to 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 Closeness of agreement between indications or measured quantity values obtained by
replicate measurements on the same or similar objects under specified conditions
Sensitivity - Sensitivity is the degree of response of an instrument to an incoming signal.
Repeatability - Repeatability is defined as the ability of a measuring system to produce the
same indicated output when the same measurand value applied to it consecutively under similar
conditions.
Reproducibility - Reproducibility is defined as the ability of a measuring system to produce
same indicated output when the same measurand value applied to it under different conditions
and instruments.
Resolution - It is the smallest increment of change in measured value that can be determined
from the instrument’s read out scale.
Calibration - At some point during the preparation of measuring system known magnitude
of input quantity must be feed into sensor transducer and system output behaviour must be
observed.Such comparison allows the magnitude of input. This process is called calibration.In
other words it is the process of establishing a relationship between input quantity and measurement
device.
3 Direct and Indirect comparison
(i) Direct method of measurement.
In this method the value of a quantity is 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 in sensitiveness in making judgement.
(ii) 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.
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4. Figure 1: Accuracy and Precision
4 The generalised Measurement System
ELEMENTS OF A GENERALIZED MEASUREMENT SYSTEM:
Most of the measurement systems contain three main functional elements are:-
• Primary sensing element
• Variable conversion element
• Data presentation element.
Figure 2: Generalized measurement system
Primary sensing element:
The quantity under measurement makes its first contact with the primary sensing element of
a measurement system.i.e., the measurand - (the unknown quantity which is to be measured) is
first detected by primary sensor which gives the output in a different analogous form.This output
is then converted into an electrical signal by a transducer - (which converts energy from one form
to another).The first stage of a measurement system is known as a detector
Transducer stage Variable conversion element:
The output of the primary sensing element may be electrical signal of any form; it may be
voltage, a frequency or some other electrical parameter.For the instrument to perform the desired
function, it may be necessary to convert this output to some other suitable form.
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5. Variable manipulation element:
The function of this element is to manipulate the signal presented to it preserving the original
nature of the signal.It is not necessary that a variable manipulation element should follow the
variable conversion element.Some non-linear processes like modulation, detection, sampling, fil-
tering, chopping etc. are performed on the signal to bring it to the desired form to be accepted by
the next stage of measurement system.This process of conversion is called signal conditioning.The
term signal conditioning includes many other functions in addition to variable conversion & vari-
able manipulation.In fact the element that follows the primary sensing element in any instrument
or measurement system is called signal conditioning element.When the elements of an instrument
are actually physically separated, it becomes necessary to transmit data from one to another. The
element that performs this function is called a data transmission element.
Data presentation element
The information about the quantity under measurement has to be conveyed to the personnel
handling the instrument or the system for monitoring, control, or analysis purposes.This function
is done by data presentation element.In case data is to be monitored, visual display devices are
needed.These devices may be analog or digital indicating instruments like ammeters, voltmeters
etc.
4.1 Example of generalized measurement system
Figure 3: Example of generalized measurement system
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6. 5 Types of input quantities
I According to time dependence
1. Static input quantity
If the input quantity is not changing with respect to time it is called static quantity.
2. Dynamic input quantity
If the input quantity is changing with respect to time it is called dynamic quantity.
(a) steady state periodic
Ramp input is an example for steady state input.The ramp input varies linearly
with time and the ramp response of the system is observed to give the steady state
error between the output and the input.
Figure 4: ramp input
(b) non repetitive or transient
Step input is an example for transient type input quantity.This is a an abrupt
change from one steady input value to another. The response of the system to it is
called the transient response and is a measure of how well the system can respond
to sudden changes.
Figure 5: step input
i. Single pulse/ aperiodic
ii. Continuous / random
Sine wave input is an example for continuous periodic input.The sine wave
input is used to provide the frequency response of the system. It shows how
the system responds to inputs of cyclic nature at different frequencies.
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7. Figure 6: Sine wave input
II Analog and Digital
Analog signal: Analog measurements vary with time in continuous manner over a range of
magnitudes.Such signals are analogous to a continuous physical process. An analog signal has
a value at every instant of time and is usually varies smoothly in magnitude.Eg.Speedometers
in automobiles.
Digital Signal: Digital signals changing in stepwise manner between two distant magnitude
like high and low voltage or an ON/OFF signal.Eg. Digital tachometer (measurement of
revolution of a shaft)
6 Classification of errors
The term error in a measurement is defined as:-
Error = Instrument reading true reading.
The measurement error is defined as the difference between the true or actual value and the
measured value. The true value is the average of the infinite number of measurements, and the
measured value is the precise value. Errors in measurement is classified as:-
1. Gross Errors
2. Systematic Errors
3. Random Errors
6.1 Gross errors
The gross error occurs because of the human mistakes. For examples consider the person using
the instruments takes the wrong reading, or they can record the incorrect data. Such type of error
comes under the gross error. The gross error can only be avoided by taking the reading carefully.
Eg.The experimenter reads the 31.5C reading while the actual reading is 21.5C.
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8. Figure 7: Classification of error
The following methods can be use to eliminate gross errors during measurement.
1. The reading should be taken very carefully.
2.Two or more readings should be taken of the measurement quantity. The readings are taken by
the different experimenter and at a different point for removing the error.
6.2 Systematic Errors
The systematic error comes under dynamic errors.Dynamic error is the error caused by the time
variations in the measurand.Its results from the inability of the system to respond truly to a time
variable measurement.The systematic error is also known as controllable errors. The systematic
errors are mainly classified into three categories.
1. Instrumental Errors
2. Environmental Errors
3. Observational Errors
Calibration errors,avoidable errors etc are also the examples for systematic error.
6.2.1 Instrumental errors
The following are the reasons for instrumental error:-
(a) Inherent Shortcomings of Instruments Such types of errors are inbuilt in instruments
because of their mechanical structure. They may be due to manufacturing, calibration or opera-
tion of the device. These errors may cause the error to read too low or too high.
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9. Eg If the instrument uses the weak spring then it gives the high value of measuring quantity.
The error occurs in the instrument because of the friction or hysteresis loss.
(b) Misuse of Instrument The error occurs in the instrument because of the fault of the
operator. A good instrument used in an unintelligent way may give an enormous result.
(c) Loading Effect It is the most common type of error which is caused by the instrument in
measurement work. For example, when the voltmeter is connected to the high resistance circuit
it gives a misleading reading, and when it is connected to the low resistance circuit, it gives the
dependable reading. This means the voltmeter has a loading effect on the circuit.
6.2.2 Environmental Errors
These errors are due to the external condition of the measuring devices. Such types of errors
mainly occur due to the effect of temperature, pressure, humidity, dust, vibration or because of
the magnetic or electrostatic field.The following precautions can be used to eliminate errors.
1.The arrangement should be made to keep the conditions as constant as possible.
2.Using the equipment which is free from these effects.
3.By applying the computed corrections.
6.2.3 Observational Errors
Such types of errors are due to the wrong observation of the reading. There are many sources
of observational error. For example, the pointer of a voltmeter resets slightly above the surface
of the scale. Thus an error occurs (because of parallax) unless the line of vision of the observer
is exactly above the pointer. To minimise the parallax error highly accurate meters are provided
with mirrored scales.
6.3 Random Errors
The error which is caused by the sudden change in the atmospheric condition, such type of error
is called random error. These types of error remain even after the removal of the systematic error.
Hence such type of error is also called residual error.
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10. 7 Uncertainty
Uncertainty in measurement is defined as the range about the measured value within which the
true value of measured quantity is estimated to lie with some level of confidence.
7.1 Kline and Mclintock Approach
A more precise method of estimating uncertainty was proposed by Kline and Mclintock. this
method is based on a careful specification of the uncertainties in the various primary experimental
measurements.For example certain pressure reading might be expressed as
p = 100kPa ± 1kPa
When plus or minus notation is used to designate the uncertainty the person making the
designation is stating the degree of accuracy with which he or she believes the measurement has
been made. This specification in itself uncertain because the experimenter is naturally uncertain
about the accuracy of these measurements.
If a very careful calibration of an instrument has performed recently with the standards of
very high precision, then the experimenter will be justified in assigning a much lower uncertainty
to measurements than if they were performed with a instrument of unknown calibration history.
To add a further specification of the uncertainty of a particular measurement Kline and Mclin-
tock propose that the experimenter specify certain odds for the uncertainty.Then the above equa-
tion of pressure can be expressed as p = 100kPa ± 1kPa (20 to 1)
In other words the experimenter is willing to bet with 20 to 1 odds that the pressure mea-
surement is within ±1kPa.It is important to note that the specification of such odds can only be
made by the experimenter based on the total laboratory experience.
7.2 Propagation of uncertainty
The uncertainty analysis in measurements when many variables are involved is done on the same
basis as is done for error analysis,when the results are expressed as standard deviation or proba-
bility error.Suppose a set of measurement is made and the uncertainty in each measurement may
be expressed with same odds the following method is used to find the uncertainty in measurement.
If X is a function of several variables, X = f(x1, x2, x3.......xn), where x1, x2......xn are indepen-
dent variables with same degree of odds.
Let Wx be the resultant uncertainty and wx1, wx2, wx3.......wxn be the uncertainties of indepen-
dent variables x1, x2.....xn respectively.the uncertainty in result is given by,
Wx =
∂X
∂x1
2
.wx1
2 +
∂X
∂x2
2
.wx2
2 + .........
∂X
∂xn
2
.wxn
2
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11. Problem: A certain resistor has voltage drop of 110.2 V and current of 5.3 A. The uncertainties
in measurements are ±0.2V and ±0.06 A respectively.Calculate the power dissipated in resistor
and the uncertainty in power.
Soln: Power, P = V X I
P = 110.2 X 5.3
P = 584 W
∂P
∂V
= I = 5.3 A
∂P
∂I
= V = 110.2 V
wV = ±0.2, wI = ±0.06
Substitute the values in Kline and Mclintock equation and find the uncertainty in power.
Answer is ±1.15% uncertainty in power.
Please practice more problems from Experimental methods for engineers by JP Holman.
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