Theory and Design for Mechanical Measurements

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1 Theory and Design for Mechanical Measurements Third Edition Richard S. Figliola Clemson University Donald E. Beasley Clemson University John Wiley & Sons, Inc. New York / Chichester / Weinheim / Brisbane / Toronto / Singapore

2 1. Basic Concepts of Measurement Methods Introduction General Measurement System Experimental Test Plan 4 Variables 5 Parameters 6 Noise and Interference 6 Random Tests 8 Replication and Repetition 12 Concomitant Methods Calibration 13 Static Calibration 13 Dynamic Calibration 14 Static Sensitivity 14 Range 15 Accuracy 15 Precision and Bias Errors 15 Sequential Test 18 Random Test Standards 21 Basic Dimensions and Their Units 22 Derived Units 24 Force 24 Other Units 24 Electrical Dimensions 25 Hierarchy of Standards 26 Test Standards Presenting Data 27 Rectangular Coordinate Format 27 Semilog Coordinate Format 27 Full-Log Coordinate Format Summary 28 References 28 Nomenclature 28 Problems Static and Dynamic Characteristics of Signals Introduction Input-Output Signal Concepts 35 Classification of Waveforms 36 Signal Waveforms Signal Analysis 39 Effects of Signal-Averaging Period DC Offset vii

3 viii 2.4 Signal Amplitude and Frequency 44 Periodic Signals 45 Frequency Analysis 47 Fourier Series and Coefficients 49 Fourier Coefficients for Functions Having Arbitrary Periods Fourier Transform and the Frequency Spectrum 57 Discrete Fourier Transform Summary 64 References 64 Nomenclature 64 Problems Measurement System Behavior Introduction General Model for a Measurement System Dynamic Measurements 70 Measurement System Model Special Cases of the General System Model Zero-Order Systems 74 First-Order Systems 76 Second-Order Systems Transfer Functions Phase Linearity Multiple-Function Inputs Coupled Systems Summary 104 References 104 Nomenclature 104 Problems Probability and Statistics Introduction Statistical Measurement Theory 110 Probability Density Functions Infinite Statistics Finite Statistics 121 Standard Deviation of the Means 123 Pooled Statistics Chi-Squared Distribution 126 Precision Interval in a Sample Variance 127 Goodness-of-Fit Test Regression Analysis 131 Least-Squares Regression Analysis Data Outlier Detection Number of Measurements Required Summary 143 References 143 Nomenclature 143 Problems 144

4 ix 5. Uncertainty Analysis Introduction Measurement Errors Design-Stage Uncertainty Analysis 151 Combining Elemental Errors: RSS method 152 Design-Stage Uncertainty Error Sources 155 Calibration Errors 156 Data-Acquisition Errors 156 Data-Reduction Errors Bias and Precision Errors 157 Bias Error 157 Precision Error Uncertainty Analysis: Error Propagation 159 Propagation of Error Advanced-Stage and Single-Measurement Uncertainty Analysis 163 Zero-Order Uncertainty 164 Higher-Order Uncertainty 164 Mh-Order Uncertainty Multiple-Measurement Uncertainty Analysis 170 Propagation of Elemental Errors 170 Propagation of Uncertainty to a Result Summary 183 References 183 Nomenclature 184 Problems Analog Electrica! Devices and Measurements Introduction Analog Devices: Current Measurements 192 Direct Current 192 Alternating Current Analog Devices: Voltage Measurements 196 Analog Meters 197 Oscilloscope 197 Potentiometer Analog Devices: Resistance Measurements 201 Ohmmeter Circuits 201 Bridge Circuits Loading Errors and Impedance Matching 208 Loading Errors for A Voltage Dividing Circuit 209 Interstage Loading Errors Analog Signal Conditioning: Amplifiers Analog Signal Conditioning: Special Purpose Circuits 216 Analog Voltage Comparator 216 Sample and Hold Circuit 217 Charge Amplifier 217 Current Loop: 4-20 ma 219 Multivibrator and Flip-Flop Circuits 219

5 6.8 Analog Signal Conditioning: Filters 221 Butterworth Filter Design 222 Bessel Filter Design 225 Active Filters Grounds, Shielding, and Connecting Wires 226 Ground and Ground Loops 227 Shields 228 Connecting Wires Summary 229 References 230 Nomenclature 230 Problems Sampling, Digital Devices, and Data Acquisition Introduction Sampling Concepts 235 Sample Rate 236 Alias Frequencies 238 Amplitude Ambiguity 241 Selecting Sample Rate and Data Number Digital Devices: Bits and Words Transmitting Digital Numbers: High and Low Signals Voltage Measurements 246 Digital-to-Analog Converter 247 Analog-to-Digital Converter 248 Digital Voltmeters Data-Acquisition Systems Data-Acquisition System Components 259 Signal Conditioning: Filters and Amplification 259 Analog Multiplexers 262 A/D Converters 262 D/A Converters 262 Digital Input-Output 262 Central Processing Unit: Microprocessor 263 Memory 263 Central Bus 264 Buffers Analog Input-Output Communication 265 Data-Acquisition Boards 265 Single- and Differential-Ended Connections 267 Special Signal Conditioning Modules 269 Data-Acquisition Triggering 269 Data Transfer Digital Input-Output Communication 270 Serial Communications 271 Universal Serial Bus 273 Parallel Communications Summary 278 References 278 Nomenclature 279 Problems 279

6 xi 8. Temperature Measurements Introduction 283 Historical Background Temperature Standards and Definition 284 Fixed-Point Temperatures and Interpolation 284 Temperature Scales and Standards Thermometry Based on Thermal Expansion 287 Liquid-in-Glass Thermometers 287 Bimetallic Thermometers Electrical Resistance Thermometry 289 Resistance Temperature Detectors 289 Thermistors Thermoelectric Temperature Measurement 302 Seebeck Effect 303 Peltier Effect 304 Thomson Effect 304 Fundamental Thermocouple Laws 305 Basic Temperature Measurement with Thermocouples 306 Thermocouple Standards 307 Thermocouple Voltage Measurement 310 Multiple-Junction Thermocouple Circuits 316 Data Acquisition Considerations Radiative Temperature Measurements 322 Radiation Fundamentals 322 Radiation Detectors 323 Radiative Temperature Measurements 325 Optical Fiber Thermometers Physical Errors in Temperature Measurement 327 Insertion Errors 327 Recovery Errors in Temperature Measurement Summary 337 References 337 Nomenclature 338 Problems Pressure and Velocity Measurements Introduction Pressure Concepts Pressure Reference Instruments 348 McLeod Gauge 348 Barometer 349 Manometers 350 Deadweight Testers Pressure Transducers 356 Bourdon Tube 357 Bellows and Capsule 358 Diaphragms Pressure Transducer Calibration 364 Static Calibration 364 Dynamic Calibration 364

7 xii 9.6 Pressure Measurements in Moving Fluids 366 Total Pressure Measurement 367 Static Pressure Measurement Design and Installation: Transmission Effects 369 Gases 370 Liquids 372 Heavily Damped Systems Fluid Velocity Measuring Systems 374 Pitot-Static Pressure Probe 375 Thermal Anemometry 377 Doppler Anemometry 379 Selection of Velocity Measuring Methods 382 Laser Doppler Anemometers Summary 383 References 383 Nomenclature 384 Problems Flow Measurements Introduction Historical Comments Flow Rate Concepts Volume Flow Rate Through Velocity Determination Pressure Differential Meters 394 Obstruction Meters 394 Orifice Meter 397 Venturi Meter 399 Flow Nozzles 401 Sonic Nozzles 405 Obstruction Meter Selection 407 Laminar Flow Elements Insertion Volume Flow Meters 412 Electromagnetic Flow Meters 413 Vortex Shedding Meters 414 Rotameters 416 Turbine Meters 418 Positive-Displacement Meters Mass Flow Meters 419 Thermal Flow Meter 419 Coriolis Flow Meter Flow Meter Calibration and Standards Summary 425 References 425 Nomenclature 425 Problems Strain Measurement Introduction Stress and Strain Resistance Strain Gauges 432

8 xiii Metallic Gauges 432 Semiconductor Strain Gauges Strain Gauge Electrical Circuits Practical Considerations for Strain Measurement 442 The Multiple Gauge Bridge 442 Bridge Constant 443 Apparent Strain and Temperature Compensation 445 Construction and Installation 450 Analysis of Strain Gauge Data 450 Signal Conditioning 451 Uncertainties in Multichannel Measurements Optical Strain Measuring Techniques 454 Basic Characteristics of Light 455 Photoelastic Measurement 456 Moire Methods Summary 460 References 460 Nomenclature 461 Problems Metrology, Motion, Force, and Power Measurements Introduction Dimensional Measurements: Metrology 466 Historical Perspective 466 Principles of Linear Measurement 467 Optical Methods Displacement Measurements 474 Potentiometers 474 Linear Variable Differential Transformers Measurement of Mass Measurement of Acceleration and Vibration 482 Seismic Transducer 482 Transducers for Shock and Vibration Measurement Velocity Measurements 489 Linear Velocity Measurements 489 Velocity from Displacement or Acceleration 489 Moving Coil Transducers 492 Angular Velocity Measurements Force Measurement 496 Load Cells Torque Measurements 500 Measurement of Torque on Rotating Shafts Mechanical Power Measurements 502 Rotational Speed, Torque, and Shaft Power 502 Cradled Dynamometers Summary 504 References 506 Nomenclature 506 Problems 506

9 xiv Appendix A: A Guide for Technical Writing 509 Appendix B: Property Data and Conversion Factors 516 Glossary 523 Index 531

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