L7 measurement system

Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
MECHANICAL MEASUREMENTS AND METROLOGY
(Course Code:18ME36B)

TEXT BOOKS
• Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006.
• Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill.
• Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009
REFERENCE BOOKS:
• Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford
University Press..
Further Reference:
 National Programme on Technology Enhanced Learning (NPTEL)
http://nptel.ac.in/courses/112104121/1

MECHANICAL MEASUREMENTS AND METROLOGY
CHAPTER 7: Measurement system
MODULE 4

Learning Objectives
Explain basic definitions in measurements

Module 4
Measurement systems
Definition, Significance of measurement, Generalized measurement system, Static
characteristics- Accuracy, Precision, Calibration, Threshold, Sensitivity, Hysteresis,
Repeatability, Linearity, Loading effect, Dynamic characteristics- System response,
Time delay. Errors in measurement, Classification of errors.

Introduction
Why Make Measurements?
• Designing physical systems
• Measurements for commerce
• Verifying / validating the functionality of the parts/components

Measuring process
Measurement is defined as the quantification of a physical variable using a
measuring instrument.

Generalized measurement system
Elements of a generalized measurement system

Primary detector–transducer stage
• Primary detector–transducer stage senses the input signal.
• Transform the signal into its analogous signal.

Intermediate modifying stage
• The input signal is modified and amplified by signal conditioning and processing
devices before passing it to the output stage.
• Signal conditioning (noise reduction and filtering) is to enhance the condition of
the signal.
• The signal is processed by means of integration, differentiation, addition,
subtraction, digitization, modulation. etc.
• Output should be analogous to the input.

Output or Terminating stage
• The output stage provides a value of the i/p measured being analogous to o/p.
• The output is either indicated or recorded by a scale and pointer, digital display,
CRO, for subsequent evaluations
• Recording may be in the form of chart or a computer printout.
• Other methods of recording include punched paper tapes, magnetic tapes, or
video tapes, photographs etc.

Examples of the three stages of a generalized measurement system

BASIC DEFINITIONS
Hysteresis in Measurement Systems
• The value of the quantity being measured
should remain same whether the
measurements have been obtained in an
ascending or a descending order.
Hysteresis is due to the presence of dry friction
& the properties of elastic elements.

BASIC DEFINITIONS
Linearity in Measurement Systems
• A measuring instrument is said to be linear, if it
uniformly responds to incremental changes,
i.e. the o/p = i/p, over a specified range.
The maximum deviation of the o/p from the i/p

BASIC DEFINITIONS
Resolution in Measurement Systems
• A Resolution is the smallest change in a physical property that an instrument can
sense / detect reliably
• Resolution is the closeness of the reading of the measuring quantity with the true
value / standard.
E.g.: Weighing machine

BASIC DEFINITIONS
Threshold
• Minimum value of the input signal required to detect the output.
• Minimum value of the input is defined as the threshold of the instrument.
• Minimum value of the input below which no output can be detected.

BASIC DEFINITIONS
Drift
• The gradual shift in the indication or record of the instrument over an extended
period of time.
• The variation caused in the output of an instrument.
• This variation is not due any change in the input.
• Drift is due to internal temperature variations and lack of component stability.

BASIC DEFINITIONS
Zero Stability
• The ability of an instrument to return to the zero reading after the input signal
comes back to the zero value after the variations due to temperature, pressure,
vibrations, magnetic effect, etc., have been eliminated.

BASIC DEFINITIONS
Loading effect
• The incapability of a measuring system to measure, record, or control the input
in an undistorted form.
• It may occur in any of the three stages of measurement.

BASIC DEFINITIONS
System Response
• The characteristics of a measuring instrument is to transmit the input signal with
all the relevant information.
• The behaviour of the measuring system under the varying conditions of input
with respect to time is known as the dynamic response.

BASIC DEFINITIONS
System Response
Two types of dynamic inputs:
1. Steady-state periodic quantity: Magnitude has a definite repeating time cycle.
2. Transient magnitude: The time variation of the transient magnitude does not
repeat

BASIC DEFINITIONS
Dynamic Characteristics
1. Speed of response
2. Measuring lag
Retardation type
Time delay type

BASIC DEFINITIONS
1. Speed of response:
The speed with which the measuring instrument responds to the changes in the
measured quantity.

BASIC DEFINITIONS
2. Measuring lag:
The time when an instrument begins to respond to a change in the measured
quantity.
• Lag is normally due to the natural inertia of the measuring system.

BASIC DEFINITIONS
1. Retardation type: measurement system responds instantaneously after the
changes in the input have occurred.
2. Time delay type: measuring system begins to respond after a dead time to the
applied input.
Dead time: the time required by the measuring system to begin its response to a
change in the quantity to be measured.

ERRORS IN MEASUREMENTS
• Measurements obtained are not completely accurate, as they are associated
with uncertainty.
• To analyse the measurement data, we need to understand the nature of
errors associated with the measurements.
• To investigate the causes or sources of the errors in measurement and
subsequently eliminate them.

1. Systematic errors / Controllable errors
2. Random errors

• If error the error deviates by a fixed amount from the true value.
• These errors are controllable in nature.
E.g.: Zero error
measurement of length using a scale.
measurement of current with inaccurately calibrated ammeters.
• Systematic errors cannot be eliminated by taking a large number of readings
and then averaging them out.

Cause of systematic errors;
1. Calibration errors
2. Ambient conditions
3. Deformation of workpiece
4. Avoidable errors

• A small amount of variation from the nominal value will be present in length
standards like slip gauges and engraved scales.
• Errors are due to Inertia and hysteresis effects.
• Calibration curves are used to minimize such variations
1. Calibration errors

• It is essential to maintain the ambient conditions at internationally accepted
values of standard temperature (20 ºC) and pressure (760 mmHg) conditions.
• A small difference of 10 mmHg, results errors in the measurement.
E.g.: An increase in temperature of 1 ºC results in an increase in the length of C25
steel by 0.3 μm.
• For error-free results, a correction factor for temperature has to be provided.
2. Ambient conditions

• The stylus pressure applied during measurement affects the accuracy.
• Due to stylus pressure and elastic deformation and changes in workpiece shape
may occur.
3. Deformation of workpiece

• Datum errors
• Reading errors
• Errors due to parallax effect
• Effect of misalignment
• Zero errors
4. Avoidable errors
These include the following;

Transducer
• Transfer efficiency
• Primary and Secondary transducers
• Electrical transducers
• Mechanical transducers
• Electronic transducers
• Relative comparison of each type of transducers

Transducer
• Detector or sensing element.
• The transducer, may be electrical, mechanical, optical, magnetic, piezoelectric, etc.
• Converts the sensed information (i/p) into convenient form.
• Device that converts one form of energy into another form.

Transfer efficiency
• The ratio of information sensed and delivered by the sensor, is transfer efficiency.

CLASSIFICATION OF TRANSDUCERS
1. Primary and secondary transducers
2. Based on the principle of transduction
3. Active and passive transducers
4. Analog and digital transducers
5. Direct and inverse transducers
6. Null and deflection transducers

Primary and Secondary Transducers
1. Sensing or detecting element /Primary transducer
The function of this element is to respond to / sense a physical change
2. Transduction element / Secondary transducer
The function of a transduction element is to transform the output from the sensing
element to an analogous electrical output.

Primary detector transducer stage with primary and secondary transducers

Primary detector
transducers(Mechanical)

Based on Principle of Transduction
• Based on how the input quantity is transduced into output i.e. capacitance,
resistance, and inductance values.
1. Capacitive: Capacitor microphone, Capacitive pressure gauge, dielectric gauge
2. Resistive: Resistance Strain gauge, RTD, Photoconductive cell, thermistor
3. Inductive: Magnetic circuit, Reluctance pickup, Differential transformer

Active and Passive Transducers
1. Active transducers or self-generating type: They develop their own voltage or
current output.
• The energy is derived from the physical quantity being measured.
E.g.: thermocouples, photovoltaic cells.
Active transducer
Passive transducer
2. Passive transducers or External powered type: They need external / auxiliary source
of power supply. E.g.: Resistive, Capacitive and Inductive ( LVDT)

Analog and Digital Transducers
• Based on the output generated.
• The output generated is a continuous function of time or is in discrete form.
Analog: Input quantity is converted into an analog output.
E.g.: LVDT, strain gauge, thermocouple, and thermistor
Digital: Input quantity is converted into an electrical signal.
E.g.: shaft encoders, linear displacement transducers

Direct and Inverse Transducers
Direct: Transforms a non-electrical variable into an electrical variable.
E.g. Thermocouple
Inverse: Transforms an electrical quantity into a non-electrical quantity.
E.g.: Piezoelectric transducer
• Voltage is given as the input, and its dimensions are changed causing a
mechanical displacement.

Intermediate Modifying and Terminating devices

Intermediate Modifying and Terminating devices
The transduced signal is further modified and amplified by conditioning and
processing devices, so that the signal is appropriate before passing it on to the
output or terminating stage for display.

Inherent Problems in Mechanical Systems
Design problems arise when the signals from the primary–secondary transducers
are fed into mechanical intermediate elements and these mechanical
intermediate elements, like linkages, gears, cams, etc., are inadequate, in
handling dynamic inputs

Kinematic Linearity
• When linkages are used as a mechanical amplifier, it should be designed
in such a way that it provides the same amplification (gain).
• The gain should be linear, otherwise result in a poor amplitude response.

Mechanical Amplification
• Gain = Mechanical advantage

Reflected Frictional Amplification
• The effect of frictional force is amplified and is reflected back to the input as a
magnified load, proportion to the gain between the friction and the input.
• This effect is referred as the reflected frictional amplification.
• The total reflected frictional force is given by: Ftfr = ΣAFfr
Ftfr = Total reflected frictional force (in N) at the input of the
system.
A= Mechanical amplification or gain
Ffr = Actual frictional force (in N) at its source.

Reflected Inertial Amplification
• The effects of inertial forces are amplified and reflected back to the input in
proportion to the gain
• The total reflected inertial force is given by: Ftir = ΣA ΔFir
Ftir = Total reflected inertial force (in N) at the input of the system,
A = Mechanical amplification or gain
ΔFir = Increment of the inertial force (in N) at any point in the system.

Amplification of Backlash and Elastic Deformation
• The consequences of backlash is lost motion.
• Lost motion occurs when an input does not generate the analogous displacement
at the output, results in a positional error and contributes to the uncertainty.
• At the output, both backlash and elastic deformation result in lost motion, which is
amplified by an amount equal to the gain between the source and the output.

Temperature Problems
• Temperature variations adversely affect the operation of the measuring system
• It is extremely difficult to maintain a constant-temperature environmental
condition for a general-purpose measuring system.
• The only option is to accept the effects due to temperature variations and devise
the methods to compensate temperature variations.

ELECTRICAL INTERMEDIATE MODIFYING DEVICES

ELECTRICAL INTERMEDIATE MODIFYING DEVICES
• The major functions of intermediate modifying devices is to transduce
mechanical inputs into electrical signals.
• These signals will be modified or conditioned.
• Amplification of either voltage or power, is accomplished, depending on the
requirement of the terminating stage

Input Circuitry
• Active transducer does not require minimum circuitry for their operation.
• Passive transducer require minimum circuitry for their operation.

Input Circuitry
Common forms of input circuitry employed in transduction are:
 1. Simple current-sensitive circuits
 2. Ballast circuits
3. Voltage-dividing circuits
4. Voltage-balancing potentiometer circuits

Input Circuitry - Simple current-sensitive circuits

Input Circuitry
Simple current-sensitive circuits
Using Ohm’s law, the current indicated by the read-out circuit is given by the equation:

Input Circuitry
Simple current-sensitive circuits
• Maximum current flows when k = 0, i.e.
when the current will be ei/Rr.
• The output variation or sensitivity is
greater for higher value of transducer

Ballast Circuit
• An electrical ballast is a device placed in series with a load to limit the amount of current
in an electrical circuit.
• A ballast circuit is a modification of the current-sensitive circuit.
• A voltage-sensitive device is placed across the transducer in the circuit.
• Rb = ballast resistor.
• In absence of Rb, the indicator will not indicate any change with variation in Rt ;always
show full source voltage.
• It is necessary to incorporate some value of resistance in the circuit to ensure its proper
functioning.

Let e0 = the voltage across kRt
(transducer), the following equation
holds true:

Terminating devices
Presentation of processed data;
• Relative displacement
• Digital form
Relative displacement
• Scale and pointer
• Pen tracing on chart
Digital form
• Odometer
• Rotating drum mechanical counter

Cathode Ray Oscilloscope
A CRO is a voltage-sensitive device used to view, measure and analyze waveforms
Its advantage is that a beam of electrons with low inertia strikes the fluorescent
screen, generating an image that can rapidly change with varying voltage inputs to
the system.
The cathode ray tube (CRT) is the basic
functional unit of CRO.

Cathode Ray Tube
• The electron gun assembly comprises a heater, a cathode, a control grid, and accelerating anodes.
• When a cathode is heated, electrons are generated.
• The grid provides the control for of flow of electrons.
• The accelerating anodes, are positively charged, provides the striking velocity to the emitted
electron stream.
• The electron beam, gaining necessary acceleration, passes through horizontal and vertical
deflection plates, which provide the basic movements in the X and Y directions.
• In order to facilitate free movement of emitted electrons, vacuum is created within the tube.

Oscillographs
• The basic difference between a CRO and Oscillograph is;
• In CRO the output is visual in nature and in oscillograph it is traced on the paper.
Two types of oscillographs are;
1. Direct Writing-type Oscillographs
2. Light Beam Oscillographs

Direct Writing-type Oscillographs
• Consists of a stylus that traces an image on the moving paper by establishing
• direct contact.
• The stylus is current sensitive.
• A paper-transporting mechanism is required.
• The recording is by use of ink & moving the heated stylus on a paper.
• The recording is a time-based function of the input signal.
• As recording is by the movement of stylus on paper, a frictional drag is
created, which requires more torque.

Light Beam Oscillographs
• Consists of a paper drive mechanism, a galvanometer, and an optical system for
transmitting current-sensitive galvanometer rotation to a displacement, that can
be recorded on a photographic film or paper.
• The galvanometer of the oscillograph works on the D’Arsonval principle.
• The input depends on mass moment of inertia of the coil.
• Sensitivity of the oscillograph is a function of the number of turns in the coil.
• It is essential to keep the mass moment of inertia at a minimum level.

L7 measurement system

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