GATE INSTRUMENTATION ENGINEERING. Vol 3 of 5 ELECTRICAL AND ELECTRONIC MEASUREMENTS ANALYTICAL, OPTICAL AND BIOMEDICAL INSTRUMENTATION

Transcription

1 STUDY PACKAGE 1e GATE INSTRUMENTATION ENGINEERING Vol 3 of 5 BASICS OF MEASUREMENT SYSTEMS Transducers, Mechanical Measurement and Industrial Instrumentation ELECTRICAL AND ELECTRONIC MEASUREMENTS ANALYTICAL, OPTICAL AND BIOMEDICAL INSTRUMENTATION R. K. Kanodia Ashish Murolia NODIA & COMPANY

2 GATE Instrumentation Engineering Vol 3 of 5 RK Kanodia and Ashish Murolia Copyright By NODIA & COMPANY Information contained in this book has been obtained by author, from sources believes to be reliable. However, neither NODIA & COMPANY nor its author guarantee the accuracy or completeness of any information herein, and NODIA & COMPANY nor its author shall be responsible for any error, omissions, or damages arising out of use of this information. This book is published with the understanding that NODIA & COMPANY and its author are supplying information but are not attempting to render engineering or other professional services. MRP NODIA & COMPANY B - 8, Dhanshree Ist, Central Spine, Vidyadhar Nagar, Jaipur Ph : , enquiry@nodia.co.in Printed by Nodia and Company, Jaipur

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5 Preface The objective of this study package is to develop in the GATE aspirants the ability to solve GATE level problems of Instrumentation Engineering Paper. The highly increased competition in GATE exam from last few years necessitate an in-depth knowledge of the concepts for the GATE aspirants. There are lots of study packages available for GATE Instrumentation Engineering, which includes the theory and problem sets. But through this package our notion is to develop the problem solving approach rather than just introducing the theory and problem set. This study package fulfills all the requirements of a GATE aspirant to prepare for the exam. There is no special pre-requisite before starting this study package. Although it is always recommended to refer other standard text books to clear doubts in a typical problem. The study package is published in 5 different volumes that cover the different subjects of GATE Instrumentation Engineering Paper. As the weightage of General Aptitude and Engineering Mathematics in the Instrumentation Engineering paper are 15 % each, and the subjects are very much wide in the syllabus; these subjects are published in separate volumes to provide practice problem set on all the important topics of the subjects. Rest three volumes cover the core subjects of GATE Instrumentation Engineering. In the very first volume of this study package, General Aptitude is introduced. General aptitude is divided into two sections: verbal ability and numerical ability. Some important rules of grammar is introduced at the starting of verbal ability section, and then different types of verbal ability problems are given in separate chapters. At the end of each chapter answers of the problems are described with detailed theory and grammatical rule. The numerical ability part does not include theory as it is expected from an engineering students that they are very well known to the basic mathematical formulas of under 10th class. In numerical ability section, the chapters are organized such as to cover all types of problems asked in previous GATE papers. There is the detailed solutions available for each of the numerical ability problems such that even an average student can clear his/her doubts easily. In volume 2 of the study package, Engineering Mathematics is introduced. Each chapter of Engineering Mathematics introduces a brief theory with problem solving methodology and important formulas at the starting and then the problems are given in a graded manner from basic to advance level. At last, the solutions are given with a detailed description of formulas and concepts used to solve it. Volumes 3, 4 and 5 include the core subjects of instrumentation. The subjects with interrelated topics are taken in the same volume. Volume 3 includes the subjects:

6 Basics of Measurement Systems; Electrical & Electronic Measurement; Transducers, Mechanical Measurement and Industrial Instrumentation; Analytical, Optical & Biomedical Instrumentation. Volume 4 includes the subjects: Basics of Circuits, Analog Electronics, Digital Electronics. Volume 5 includes the subjects: Signals & Systems; Communication Systems; Control Systems and Process Control. For each of the subjects, the chapters are organized in a manner to cover the complete syllabus with a balanced number of problems on each topic. In starting of each chapter, a brief theory is given that includes formula, problem solving methodology and some important points to remember. There are enough number of problems to cover all the varieties, and the problems are graded from basic to advance level such that a GATE aspirant can easily understand concepts while solving problems. Each and every problems are solved with a good description to avoid any confusion or doubt. There are two types of problems being asked in GATE exam: MCQ (Multiple Choice Questions) and NAT (Numerical Answer Type questions). Both type of problems are given in this study package. Solutions are presented in a descriptive and step-bystep manner. The diagrams in the book are clearly illustrated. Overall, a very simple language is used throughout this study package to facilitate easy understanding of the concepts. We believe that each volume of GATE Study Package helps a student to learn fundamental concepts and develop problem solving skills for a subject, which are key essentials to crack GATE. Although we have put a vigorous effort in preparing this book, some errors may have crept in. We shall appreciate and greatly acknowledge all constructive comments, criticisms, and suggestions from the users of this book at rajkumar.kanodia@gmail.com We wish you good luck! Authors Acknowledgements We would like to express our sincere thanks to all the co-authors, editors, and reviewers for their efforts in making this project successful. We would also like to thank Team NODIA for providing professional support for this project through all phases of its development. At last, we express our gratitude to God and our Family for providing moral support and motivation. Authors

7 Syllabus General Aptitude (GA): Verbal Ability : English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. Numerical Ability : Numerical computation, numerical estimation, numerical reasoning and data interpretation. Section 1 : Engineering Mathematics Linear Algebra: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors. Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green s theorems. Differential equations: First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy s and Euler s equations, initial and boundary value problems, solution of partial differential equations: variable separable method. Analysis of complex variables: Analytic functions, Cauchy s integral theorem and integral formula, Taylor s and Laurent s series, residue theorem, solution of integrals. Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode and standard deviation, random variables, discrete and continuous distributions: normal, Poisson and binomial distributions. Numerical Methods: Matrix inversion, solutions of non-linear algebraic equations, iterative methods forsolving differential equations, numerical integration, regression and correlation analysis. Instrumentation Engineering Section 2: Electrical Circuits: Voltage and current sources: independent, dependent, ideal and practical; v - i relationships of resistor, inductor, mutual inductor and capacitor; transient analysis of RLC circuits with dc excitation. Kirchoff s laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power transfer and reciprocity theorems. Peak-, average- and rms values of ac quantities; apparent- active- nd reactive powers; phasor analysis, impedance and admittance; series and parallel resonance, locus diagrams, realization of basic filters with R, L and C elements. One-port and two-port networks, driving point impedance and admittance, open-, and short circuit parameters. Section 3: Signals and Systems Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function, frequency response of first and second order linear time invariant systems, impulse response of systems; convolution, correlation. Discrete time system: impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters. Section 4: Control Systems Feedback principles, signal flowgraphs, transient response, steady-state-errors, Bode plot, phase and

8 gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and lead-lag compensators, state-space representation of systems; time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo and stepper motors, servo valves; on-off, P, P-I, P-I-D, cascade, feedforward, and ratio controllers. Section 5: Analog Electronics Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of operational amplifiers; applications of opamps: difference amplifier, adder, subtractor, integrator, differentiator, instrumentation amplifier, precision rectifier, active filters and other circuits. Oscillators, signal generators, voltage controlled oscillators and phase locked loop. Section 6: Digital Electronics Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flip-flops, shift registers, timers and counters; sample-and-hold circuit, multiplexer, analog-to-digital (successive approximation, integrating, flash and sigma- delta) and digital-to-analog converters (weighted R, R-2R ladder and current steering logic). Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of number systems, 8-bit microprocessor and microcontroller: applications, memory and input-output interfacing; basics of data acquisition systems. Section 7: Measurements SI units, systematic and random errors in measurement, expression of uncertainty -accuracy and precision index, propagation of errors. PMMC, MI and dynamometer type instruments; dc potentiometer; bridges for measurement of R, L and C, Q-meter. Measurement of voltage, current and power in single and three phase circuits; ac and dc current probes; true rms meters, voltage and current scaling, instrument transformers, timer/counter, time, phase and frequency measurements, digital voltmeter, digital multimeter; oscilloscope, shielding and grounding. Section 8: Sensors and Industrial Instrumentation Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow (differential pressure, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters) temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer and semiconductor); liquid level, ph, conductivity and viscosity measurement. Section 9: Communication and Optical Instrumentation Amplitude-and frequency modulation and demodulation; Shannon s sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor and their characteristics; interferometer: applications in metrology; basics of fiber optic sensing. **********

9 Contents BASICS OF MEASUREMENT SYSTEMS 1 Characteristics of Measurement Systems 1.1 Introduction Measurement Methods Direct Measurement Methods Indirect Measurement Methods Measurement System Static characteristics of Measurement system Accuracy Precision Repeatability Reproducibility Tolerance Linearity Resolution Sensitivity Dead Zone Hysteresis Effect Threshold Range Dynamic characteristics of measurement systems Zero order instrument First order instrument Second order instrument 10 2 Error and Uncertainty Analysis 2.1 Introduction Errors in Measurement Absolute Error Relative Error Percentage Error Limiting error Relative Limiting Error Percentage Limiting Error Types of Errors Gross Errors Systematic Errors Random errors Statistical Analysis of Measurements Subject to Random Errors Gaussian Error Analysis Combination of errors Sum of Two Quantities Difference of Two Quantities Product of two Components Quotient Power of a Factor Composite Factors 34 3 Statistical Analysis of Data 3.1 Introduction Probability Joint Probability Conditional Probability 56

10 3.2.3 Statistical Independence Random Variable Discrete Random Variable Continuous Random Variable Transformation of random variables Multiple random variables Statistical average of random variable Mean or Expected Value Moments Variance Standard Deviation Characteristic Function Joint Moments Covariance Correlation Coefficient Some Important probability distributions Binomial Distribution Poisson Distribution Gaussian Distribution Rayleigh Distribution 64 4 Curve Fitting 4.1 Introduction Methods of curve fitting Fitting of A straight LIne Fitting of a parabola 92 ELECTRICAL & ELECTRONIC MEASUREMENTS 1 Electromechanical Indicating Instrument 1.1 Introduction pmmc instrument Construction and Working dc ammeters Shunt Resistor Ayrton Shunt dc voltmeter Multiplier Resistor Multirange Voltmeter Ohmmeter Series-Type Ohmmeter Shunt-Type Ohmmeter Multimeter 8 2 Measurement Of Resistance 2.1 Introduction Ammeter-voltmeter Method Ohmmeter Method Wheatstone Bridge Method 31 3 Measurement Of Inductance, Capacitance 3.1 Introduction Measurement of inductance Inductance Comparison Bridge Maxwell Bridge Hay Inductance Bridge Measurement of Capacitance De-sauty s Bridge 49

11 3.3.2 Schering Bridge Vector Impedance Meter Q-Meter 51 4 Electronic Instruments For Measuring Basic Parameters 4.1 Introduction Electronic voltmeter Analog Electronic Voltmeter AC Electronic Voltmeter DC Electronic Voltmeter Digital Electronic Voltmeter Resolution and Sensitivity of DVM Types of Digital Voltmeters Electronic Multimeter Analog Electronic Multimeter Digital Electronic Multimeter Measurement of Frequency Bridge Method Frequency Meter RF Power measurement RF Power Measurement Using Dummy Load Bolometer Bridge Method for RF Power Measurement Calorimetric Method for RF Power Measurement Shielding and grounding Grounding Shielding 89 5 Cathode Ray Oscilloscopes CRT Construction Deflection System Focussing System Astigmatism Time Base Generator Synchronising Circuit Blanking Circuit Delay Line CRO Probes Oscilloscope Techniques of Measurements Measurement of Voltage Measurement of Current Measurement of Frequency Measurement of Phase Angle Waveform Analysers 6.1 Introduction Signal Analysis Techniques Wave analyzer Frequency-Selective wave Analyzer Heterodyne Wave Analyzer Harmonic Distortion analyzer Tuned Circuit Harmonic Analyzer Heterodyne Harmonic Analyzer Fundamental Suppression Harmonic Distortion Analyzer Spectrum analyzer Filter Bank Spectrum Analyzer Swept Superheterodyne Spectrum Analyzer Spectra of Different Signals Introduction Basic CRO circuit 105

12 TRANSDUCERS, MECHANICAL MEASUREMENT & INDUSTRIAL INSTRUMENTATION 1 Electrical Transducers 1.1 Introduction Classification of Electrical Transducers Passive Transducers Active Transducers Resistive Transducer Resistance Thermometers Resistive Displacement Transducers Strain Gauge Inductive Transducers Operating Principle of Inductive Transducers Differential Transducers Capacitive Transducer Operating Principle of Capacitive Transducers Capacitive Thickness Transducer Capacitive Displacement Transducers Piezoelectric Transducer Measurement of Force Using Piezoelectric Transducer Equivalent Circuit of a Piezoelectric Transducer Loading Effect on Piezoelectric Transducer 16 2 Signal Conditioning For Electrical Transducer 2.1 Introduction Signal conditioning system Input circuits Power supplies Constant Voltage Potentiometer Circuit Constant Current Potentiometer Circuit Constant Voltage Wheatstone Bridge Circuit Constant Current Wheatstone Bridge Circuit Amplifiers Operational Amplifier Instrumentation Amplifier Chopper Amplifier Filters Low pass RC filter High-pass RC filter Active Filter 62 3 Measurement Of Translational And Rotational Motion 3.1 Introduction Measurement of Translational displacement Resistive Potentiometer Linear Variable Differential Transformer (LVDT) Capacitive Displacement Transducers Measurement of Translational Velocity Differentiation of Displacement Measurements Integration of the Output of an Accelerometer Measurement of Translational Acceleration 86

13 3.5 Measurement of Rotational Displacement Rotary Variable Differential Transformer Measurement of Rotational velocity Digital Tachometers Analogue Tachometers Differentiation of Angular Displacement Measurements Integration of the Output From an Accelerometer Measurement of rotational acceleration Measurement of vibration Vibration Measurement Seismic Device Force Balance Type Seismic Device Shock 93 4 Force, Torque And Vibration Measurement 4.1 Introduction Mass measurement Column Type Load Cell Cantilever Beam Type Load Cell Intelligent Load Cell Force measurement Balance Hydraulic Load Cells Pneumatic Load Cell Measurement of Force Using Accelerometers Torque measurement Transmission Dynamometers Driving Type Dynamometer Absorption dynamometer Temperature Measurement 5.1 Introduction Resistance devices Resistance Thermometers Thermistors Thermocouple Multiple Junction Thermocouple Circuit Non-electrical methods of temperature measurement Bimetallic Thermometers Liquid-in-glass Thermometer Pressure Thermometer Radiation methods of temperature measurement Total Radiation Pyrometer Selective radiation pyrometer Pressure Measurement 6.1 Introduction Important terms used in pressure measurement Classification of pressure measuring systems Manometers U-tube Manometer Cistern Manometer Inclined Tube Manometer Micromanometer Bourdon Tube pressure Gauge C-type Bourdon Tube Pressure Gauge Twisted Bourdon Tube 177

14 6.6 Diaphragm pressure gauge Bellow pressure gauge Pirani Gauge Thermocouple gauge Ionization gauge Flow Measurement 7.1 Introduction Flow measurement Differential Pressure Flowmeter Variable Area Flowmeter Turbine Flowmeter Ultrasonic Flowmeter Electromagnetic Flowmeter Laser Doppler Flowmeter Level measurement Dipsticks Float Gauge System Displacer System Capacitive Devices Indirect Level Measurement Measurement of ph values ph Probe Practical Range of ph Measurement Voltage Output of ph Probe Measurement of viscosity Viscosity Measurement by Placing Liquid between Parallel Plates Rotating Concentric Cylinder Method Industrial Viscosimeter Measurement of humidity Electrical Hygrometer Psychrometer Dew Point Meter 211 ANALYTICAL, OPTICAL & BIOMEDICAL INSTRUMENTATION 1 Analytical Instrumentation 1.1 Introduction Elements of analytical instrument Mass Spectrometer Operating Principle Components of Mass Spectrometer Types of Mass Spectrometers Ultraviolet and visible spectrometry Absorption Instruments Operating Principle of UV-Vis Absorption Spectrometer Construction of UV-Vis Absorption Spectrometer Infrared Spectroscopy Basic Components of Infrared Spectrophotometers Types of Infrared Spectrophotometers X-Ray Spectrometry X-Ray Generating Equipment Collimator Monochromator X-Ray Detector Nuclear Magnetic Resonance spectroscopy Construction of NMR Spectrometer Types of NMR Spectrometers 14 2 Optical Sources And Detectors

15 2.1 Introduction Optical Phenomenon Refraction and Refractive Index Reflection, Absorption and Transmittance Photometry Point Sources and Extended Sources Solid Angle Luminous Flux Luminous Intensity Luminance Radiometry Laws of Illumination Optical Sources Sunlight Incandescent Sources Fluorescent Sources Light Emitting Diode LASER Optical Detectors Photo-emissive Cells Semiconductor Photoelectric Transducers Interferometers Construction and Working of Michelson s Interferometer Formation of Interference Fringes Measurement with Michelson s Interferometer 38 3 Fiber Optics 3.1 Introduction Optical fibers Operating principle of optical fibers Total Internal Reflection Critical Angle Acceptance Angle Numerical Aperture Fiber optic sensors Pure Fibre Sensros Remote Optic Sensors Fiber optic detectors 58 4 Biomedical Instrumentation 4.1 Introduction Fundamentals of medical instrumentation Physiological System of Body Sources of Biomedical Signals Basic Medical Instrumentation System Biomedical recorders Electrocardiograph (ECG) Electroencephalograph (EEG) Electromyograph (EMG) Clinical Measurement Measurement of Heart Rate Measurement of Pulse Rate Blood Pressure Measurement Measurements of Temperature Measurements of Respiration Rate Ultrasonic imaging systems Physics of Ultrasonic Waves Medical Ultrasound Characteristic of Real Time Ultrasonic Imaging Systems Requirements of Real Time Ultrasonic Imaging Systems Biological Effects of Ultrasound X-Ray Computed tomography 84

16 4.6.1 Gantry Geometry Patient Dose in CT Scanners 84 **********

17 CHAPTER 1 Measurement of Translational and Rotational Motion 1.1 Introduction Instrumental techniques are available for the measurement of linear as well as rotational displacements. In this chapter, we will deal with the electrical transducers that is used to measure the translational and rotational motion. Following topics are covered in the chapter: Measurement of translational displacement using resistive potentiometer, LVDT, capacitive displacement transducer Different methods of measurement of translational velocity and acceleration Measurement of rotational displacement using RVDT Different methods of measurement of rotational velocity and acceleration Digital and analogue tachometers Vibration and shock measurement 1.2 Measurement of Translational displacement Translational displacement transducers are instruments that measure the motion of a body in a straight line between two points. Many different types of translational displacement transducer exist and these, along with their relative merits and characteristics, are discussed in the following sections Resistive Potentiometer Figure 3.1 shows the different types of potentiometer circuits. Circuit (a) provides dc output currents of range 4 20 ma or any other desired range; Circuit (c) is the usual variable potential divider, also known as single-ended potentiometer circuit, Circuit (d) is a push-pull potentiometer circuit. Circuits (b) and (d) develop bipolar outputs for bidirectional motion about the central point.

18 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 18 Measurement of Translational and Rotational Motion Chap 1 Figure 3.1: Different Circuits of Resistance Displacement Transducer Loading Effect If the voltmeter is electronic in nature, and has high input impedance, the loading effect will be negligible, with the ratio of Vo/ Ei of Figure 1.1(c) being the same as Rx/ Rp. For a linear transducer, Rx/ Rp is the same as the fractional value x, which is the ratio of the displacement given to the contactor, to its full-scale value. Hence under no-load conditions, x Rx Vo Rp Ei For the same position of contactor, the output voltage will be lower if R L, the resistance of voltmeter forming the load, is finite and this new value of V o l, if taken to represent the displacement, is given by Vol xl Ei With the true value being x, the error is given by error xl x Representing Rp/ RL by m, the percentage error can be obtained as 100^xl - xh 6 mx^1 xh@ 100 xl Linear Variable Differential Transformer (LVDT) LVDT is a passive inductive transformer. It works on the principle of variable-inductance.

19 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 19 Construction of LVDT Figure 3.2 shows the basic construction of an LVDT. The transformer consists of a single primary winding P 1 and two secondary windings S 1 and S 2 wound on a hollow cylindrical former. The secondary windings have an equal number of turns and are identically placed on either side of the primary windings. The primary winding is connected to an ac source. Figure 3.2: Construction of LVDT A movable soft iron core slides within the hollow former and therefore affects the magnetic coupling between the primary and the two secondaries. The displacement to be measured is applied to an arm attached to the soft iron core. The whole assembly is placed in a stainless steel housing and the end lids provide electrostatic and electromagnetic shielding. The frequency of the ac applied to the primary winding ranges from 50 Hz to 20 khz. Operation of LVDT Since the primary winding is excited by an ac source, it produces an alternating magnetic field which in turn induces ac voltages in the two secondary windings. In order to convert the output from S 1 to S 2 into a single voltage signal, the two secondaries S 1 and S 2 are connected in series opposition, as shown in Figure 3.3. Let the output voltage of the secondary winding S 1 is V S1 and that of secondary winding S 2 is V S2. Hence the output voltage of the transducer is the difference of the two voltages. i.e. V o V V S1 S2

20 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 20 Measurement of Translational and Rotational Motion Chap 1 Figure 3.3: Measurement of Translational Motion using LVDT When the core slides within the hollow former, the output voltage V o will also change. The amount of voltage change will be proportional to the amount of linear motion. Advantages of LVDT 1. Linearity: The output voltage of this transducer is practically linear for displacement upto 5 mm. 2. High output: It gives a high output, and therefore intermediate amplification devices are not required. 3. Infinite resolution: The change in output voltage is stepless. The effective resolution depends more on the test equipment than on the transducer. 4. Ruggedness: These transducers can usually tolerate a high degree of vibration and shock. 5. Less friction: There are no sliding contacts. 6. High sensitivity: The transducer possesses a sensitivity as high as 40 V/mm. 7. Low power consumption: Most LVDTs consume less than 1W of power. 8. Low hysteresis: This transducer has a low hysteresis, hence repeatability is excellent under all conditions.

21 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 21 Disadvantages of LVDT 1. Large displacements are required for appreciable differential output. 2. They are sensitive to stray magnetic fields. 3. The receiving instrument must be selected to operate on ac signals, or a demodulator network must be used if a dc output is required. 4. The dynamic response is limited mechanically by the mass of the core and electrically by the applied voltage. 5. Temperature also affects the transducer Capacitive Displacement Transducers The capacitive displacement transducer is fundamentally a proximity transducer, in the sense that the movable plate or electrode may be the conducting surface of any object in the vicinity of the fixed plate. If the transducer has a solid insulating material of dielectric constant ε, as shown in Figure 3.4(a), the capacitance is given by 0 C A 0 ε t x + ε 0 Figure 3.4: Capacitive displacement transducer If the air gap is decreased by T x, the capacitance increases by C which is given by 0 C0 + TC ε A t x0 Tx + ε So, the fractional change in capacitance is TC Tx N C0 x t N x T ^x0 + th where N is the sensitivity factor given as 1 + t N 1 x tx 0 + ε 0

22 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 22 Measurement of Translational and Rotational Motion Chap Measurement of Translational Velocity Translational velocity cannot be measured directly and therefore must be calculated indirectly by other means as described below Differentiation of Displacement Measurements Differentiation of position measurements obtained from any of the translational displacement transducers described in previous section can be used to produce a translational velocity signal. Unfortunately, the process of differentiation always amplifies noise in a measurement system. Therefore, if this method has to be used, a low-noise instrument such as a d.c. excited carbon film potentiometer or laser interferometer should be chosen. In the case of potentiometers, a.c. excitation must be avoided because of the problem that harmonics in the power supply would cause Integration of the Output of an Accelerometer Where an accelerometer is already included within a system, integration of its output can be performed to yield a velocity signal. The process of integration attenuates rather than amplifies measurement noise and this is therefore an acceptable technique. 1.4 Measurement of Translational Acceleration The only class of device available for measuring acceleration is the accelerometer. Most forms of accelerometer consist of a mass suspended by a spring and damper inside a housing, as shown in Figure 3.5. Figure 3.5: Structure of an Accelerometer The accelerometer is rigidly fastened to the body undergoing acceleration. Any acceleration of the body causes a force, F a, on the

23 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 23 mass, M, given by F a Mxp This force is opposed by the restraining effect, F s, of a spring with spring constant K, and the net result is that the mass is displaced by a distance x from its starting position such that Kx F s In steady state, when the mass inside is accelerating at the same rate as the case of the accelerometer, then we have F a F s or Kx Mxp or xp Kx (3.1) M This is the equation of motion of a second order system, and in the absence of damping, the output of the accelerometer would consist of non-decaying oscillations. A damper is therefore included within the instrument, which produces a damping force, F d, proportional to the velocity of the mass M given by F d Bxo This modifies the equation (3.1) to Kx + Bxo Mxp 1.5 Measurement of Rotational Displacement Rotational displacement transducers measure the angular motion of a body about some rotation axis. The various devices available for measuring rotational displacements are described in following sections. NOTE Rotational transducers are important not only for measuring the rotation of bodies such as shafts, but also as part of systems that measure translational displacement by converting the translational motion to a rotary form Rotary Variable Differential Transformer A Rotary Variable Differential Transformer (RVDT) is an electromechanical transducer used for measuring angular displacement and operates on the same principle as LVDT. It provides a variable ac output voltage that is linearly proportional to the angular displacement of its input shaft. When energized with a fixed ac source, the output signal is linear within a specified range over the angular displacement. Construction of RVDT The RVDT is similar in construction to the LVDT, except that a camshaped core replaces the core in the LVDT as shown in Figure 3.6.

24 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 24 Measurement of Translational and Rotational Motion Chap 1 Most RVDTs are composed of a wound, laminated stator and a salient two-pole rotor (core). The stator, containing four slots, contains both the primary winding and the two secondary windings. Some secondary windings may also be connected together. Figure 3.6: Construction of RVDT RVDTs utilize brushless, non-contacting technology to ensure long life and reliable, repeatable position sensing with infinite resolution. Such reliable and repeatable performance assures accurate position sensing under the most extreme operating conditions. Operation of RVDT Basic RVDT operation is provided by rotating an iron-core bearing supported within a housed stator assembly. A fixed alternating current excitation is applied to the primary stator coil that is electromagnetically coupled to the secondary coils. This coupling is proportional to the angle of the input shaft. The output pair is structured so that one coil is in-phase with the excitation coil, and the second is 180c out-ofphase with the excitation coil. Now, we consider the following cases to understand the operation of RVDT: CASE I When the rotor is in a position that directs the available flux equally in both the in-phase and out-of-phase coils, the output voltages cancel and result in a zero values signal. This is referred to as the null position. CASE II If the core is turned anticlockwise, the flux linking with one winding S 1, increases while the other S 2 decreases. Hence the output can be considered as a positive value. CASE III If the core is turned in clockwise direction, the flux linking with winding S 1 reduces, while that linked with winding S 2 increases, hence producing an out of phase output that is in the opposite direction that is a negative value.

25 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page Measurement of Rotational velocity The main application of rotational velocity transducers is in speed control systems. They also provide the usual means of measuring translational velocities, which are transformed into rotational motions for measurement purposes by suitable gearing. Many different instruments and techniques are available for measuring rotational velocity as presented below Digital Tachometers Digital tachometers are usually non-contact instruments that sense the passage of equally spaced marks on the surface of a rotating disc or shaft. As each mark is sensed, a pulse is generated and input to an electronic pulse counter. Instantaneous velocity can be calculated at each instant of time that an output pulse occurs, using the scheme shown in Figure 3.7. In this circuit, the pulses from the transducer gate the train of pulses from a 1 MHz clock into a counter. Control logic resets the counter and updates the digital output value after receipt of each pulse from the transducer. The measurement resolution of this system is highest when the speed of rotation is low. Figure 3.6: Scheme to Measure Instantaneous Angular Velocities In digital tachometers, various types of sensor are used, such as optical, inductive and magnetic ones. Optical Tachometers Digital tachometers with optical sensors are often known as optical tachometers. Optical pulses can be generated by photoelectric techniques Optical tachometers yield better accuracy than other forms of digital tachometer but are not as reliable because dust and dirt can block light paths.

26 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 26 Measurement of Translational and Rotational Motion Chap 1 Induction Tachometers Induction tachometers are a form of digital tachometer that use inductive sensing. They are widely used in the automotive industry within anti-skid devices, anti-lock braking systems (ABS) and traction control. Magnetostricitive Tachometers The rotating element in magnetostrictive tachometers has a very simple design in the form of a toothed metal gearwheel. The sensor is a solid-state, Hall-effect device that is placed between the gear wheel and a permanent magnet. When an inter-tooth gap on the gear wheel is adjacent to the sensor, the full magnetic field from the magnet passes through it. Later, as a tooth approaches the sensor, the tooth diverts some of the magnetic field, and so the field through the sensor is reduced. This causes the sensor to produce an output voltage that is proportional to the rotational speed of the gear wheel Analogue Tachometers Analogue tachometers are less accurate than digital tachometers but are nevertheless still used successfully in many applications. The a.c. tachometer has an output approximately proportional to rotational speed like, the d.c. tachogenerator. Mechanical structure of an analogue tachometer takes the form of a two-phase induction motor, with two stator windings and (usually) a drag-cup rotor, as shown in Figure 3.7. Figure 3.7: Working of AC Tachometer One of the stator windings is excited with an a.c. voltage and the measurement signal is taken from the output voltage induced in the second winding. The magnitude of this output voltage is zero when the rotor is stationary, and otherwise proportional to the angular velocity of the rotor. The direction of rotation is determined by the phase of the output voltage, which switches by 180 as the direction reverses.

27 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 27 Therefore, both the phase and magnitude of the output voltage have to be measured Differentiation of Angular Displacement Measurements Angular velocity measurements can be obtained by differentiating the output signal from angular displacement transducers. Unfortunately, the process of differentiation amplifies any noise in the measurement signal Integration of the Output From an Accelerometer In measurement systems that already contain an angular acceleration transducer, it is possible to obtain a velocity measurement by integrating the acceleration measurement signal. This produces a signal of acceptable quality, as the process of integration attenuates any measurement noise. 1.7 Measurement of rotational acceleration Rotational accelerometers work on very similar principles to translational motion accelerometers. They consist of a rotatable mass mounted inside a housing that is attached to the accelerating, rotating body. Rotation of the mass is opposed by a torsional spring and damping. Any acceleration of the housing causes a torque Jθ p on the mass. This torque is opposed by a backward torque due to the torsional spring and in equilibrium Jθ p Kθ or θ p Kθ J A damper is usually included in the systems to avoid undying oscillations in the instrument. This adds an additional backward torque Bθ o to the system and the equation of motion becomes Jθ p Bq o + Kq 1.8 Measurement of vibration Vibrations are very commonly encountered in machinery operation, and therefore measurement of the accelerations associated with such vibrations is extremely important in industrial environments. Vibrations normally consist of linear harmonic motion that can be expressed mathematically as X X sin( t) 0 ω

28 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 28 Measurement of Translational and Rotational Motion Chap 1 where X is the displacement from the equilibrium position at any general point in time, X 0 is the peak displacement from the equilibrium position, and ω is the angular frequency of the oscillations. The velocity v of the vibrating body can be obtained as v wx0cos( wt) and expression for the acceleration can be given as 2 α w 0 sin( wt) It is apparent that the intensity of vibration can be measured in terms of either displacement, velocity or acceleration. Acceleration is clearly the best parameter to measure at high frequencies. However, because displacements are large at low frequencies, it would seem that measuring either displacement or velocity would be best at low frequencies. In next section, we will learn the technique of vibration measurement Vibration Measurement Seismic Device A vibration measurement system requires other elements, as shown in Figure 3.8, to translate the accelerometer output into a recorded signal. The three other necessary elements are 1. Signal-conditioning element: It amplifies the relatively weak output signal from the accelerometer and also transforms the high output impedance of the accelerometer to a lower impedance value. 2. Signal analyser: It converts the signal into the form required for output. The output parameter may be either displacement, velocity or acceleration and this may be expresses as either the peak value, r.m.s. value or average absolute values. 3. Signal recorder: It must be chosen very carefully to avoid distortion of the vibration waveform. Figure 3.8: Vibration Measurement System In these devices the base of the device or transducer is attached to the object whose motion or vibration is to be measured, as shown in Figure 3.9. Inside the transducer, is a mass m supported on a spring of stiffness k and viscous damper, with damping coefficient c. The motion of the mass relative to the frame or base, gives an indication of the motion of the object and is the output of the instrument.

29 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 29 Figure 3.9: Seismic Device The acceleration response of seismic transducer is given by the equation, 2 ω nz 0 1 A ( 1 r ) + ( 2ξ r) where A 0 ω 2 x0, acceleration amplitude of the object r ww / n, frequency ratio ω n m k, undamped natural frequency ξ c, damping ratio 2 km ω circular frequency of motion of the moving object Force Balance Type Seismic Device 1.9 Shock These are similar to seismic devices except that there is no mechanical spring used here and the restoring force is provided by a feedback arrangement, as shown in Figure These types of motion measuring devices are used in inertial navigation systems. It is possible to get higher accuracy and increased stability as effects like hysteresis, non-linearity, temperature effects, etc. associated with mechanical springs are absent here. Shock describes a type of motion where a moving body is brought suddenly to rest, often because of a collision. This is very common in industrial situations and usually involves a body being dropped and hitting the floor. An instrument having a very high-frequency response is required for shock measurement, and for this reason, piezoelectric crystal-based accelerometers are commonly used.

30 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 30 Measurement of Translational and Rotational Motion Chap 1 Figure 3.10: Force Balance Type Seismic Device **********

31 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 31 EEXERCIS MCQ 1.1 An LVDT produces an output voltage of 2.6 V for displacement 0.4 mm. The sensitivity of LVDT is (A) 0.15 mm/v (B) 0.15 m/v (C) 6.5 V/mm (D) 6.5 V/m MCQ 1.2 The output of LVDT is 1.25 V at maximum displacement. At a load of 075. mω, the deviation of linearity is maximum and it is! V. The linearity at the given load is (A) 0.5% (B) 0.025V (C) 0.2%V (D) 1.25% MCQ 1.3 An LVDT has a secondary voltage of 5 V for a displacement of! mm. What is the output voltage for a displacement of 8 mm from its central position? (A) 0.2 V (B) 0.4 V (C) 0.32 V (D) 3.2 V MCQ 1.4 In a linear voltage differential transformer (LVDT) the output voltage is 1.8 V at maximum displacement. At a certain load the deviation from linearity is maximum and it is! V from a straight line through the origin. The linearity at the given load is (A)! 25% (B)!40% (C)! 025. % (D)!0. 4%

32 GATE STUDY PACKAGE INSTRUMENTATION ENGINEERING Set of 5 Books by NODIA Publication Page 32 Measurement of Translational and Rotational Motion Chap 1 NAT 1.5 The output of an LVDT is connected to a 4 V voltmeter through an amplifier whose amplification factor is 500. An output of 1.8 mv appears across the terminals of LVDT when the core moves through a distance of 0.6 mm. If the millivoltmeter scale has 100 divisions 1 and the scale can be read to 4 of a division, then the resolution of instrument will be MCQ 1.6 NAT 1.7 MCQ 1.8 NAT 1.9 mm An LVDT is used for measuring the deflection of a bellows. The sensitivity of LVDT is 40 V per mm. The bellows is deflected by mm by a pressure of 08. # 10 6 Nm / 2. The sensitivity of the LVDT in V per Nm / 2 is (A) 4# 10-6 (B) 625. # 10-6 (C) 5# 10-6 (D) # - The output of an LVDT is connected to a 5V voltmeter through an amplifier with a gain of 250. The voltmeter scale has 100 divisions and the scale can be read upto 1/5th of a division. An output of 2 mv appears across the terminals of the LVDT, when core is displaced through a distance of 0.5 mm. The resolution of instrument is The output of an LVDT is connected to a 5 V voltmeter through an amplifier whose amplification factor is 250. An output of 2 mv appears across the terminals of LVDT when the core moves through a distance of 0.5 mm. The millivoltmeter scale has 100 divisions. The scale can 1 be read to 5 of a division. The resolution of the instrument in mm is (A) 10-3 (B) 10-4 (C) 10-2 (D) None of these An accelerometer has a seismic mass of 0.05 kg and a spring constant of 3# 10 3 N/m. Maximum mass displacement is! 002. m (before the mass hits the stop). The maximum measurable acceleration is m

33 SALIENT FEATURES * Brief Theory * Methodology * Important Points * *MCQ * Numerical Answer Type Questions * Memory Based Questions * Detailed Solution for Each and Every Problem* Chap 1 Measurement of Translational and Rotational Motion Page 33 NAT 1.10 A seismic instrument has a natural frequency of 4 Hz and a damping ratio of If the system is excited by a frequency 6 Hz, the error due to the proximity of excited frequency with natural frequency of the instrument will be MCQ 1.11 MCQ 1.12 MCQ 1.13 MCQ 1.14 % A steel cantilever is 0.25 m long, 15 mm wide, and 3 mm thick. The modulus of elasticity for steel is 200 GN/ m 2. When a force of 22 N is applied at the free end, the value of deflection at the end will be (A) (B) 9.21 (C) (D) A body is dropped from a height of 10 m and suffers a shock when it hits the ground. If the duration of the shock is 5 ms, the magnitude of the shock will be (g is acceleration due to gravity) (A) 7 g (B) 200g (C) 286 g (D) None of these A variable reluctance type tachometer has 120 teeth on rotor. The speed of the shaft on which the rotor is mounted is 1500 rpm. What will be the frequency of the output pulses? (A) 25 pulse per second (B) 3000 pulses per second (C) 2 pulses per second (D) None of these A toothed rotor tachometer is used with a digital counter for measuring speed of rotation of the shaft on which the wheel is mounted. The gating period is 10 3 µ s and a reading of 0004 is obtained on the four digit display. If the number of teeth on rotor is 150, then the speed of shaft is (A) 150 (B) 4000 (C) 1600 (D) 100