Theory and Design for Mechanical Measurements

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

1. Basic Concepts of Measurement Methods 1 1.1 Introduction 1 1.2 General Measurement System 2 1.3 Experimental Test Plan 4 Variables 5 Parameters 6 Noise and Interference 6 Random Tests 8 Replication and Repetition 12 Concomitant Methods 13 1.4 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 18 1.5 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 27 1.6 Presenting Data 27 Rectangular Coordinate Format 27 Semilog Coordinate Format 27 Full-Log Coordinate Format 28 1.7 Summary 28 References 28 Nomenclature 28 Problems 29 2. Static and Dynamic Characteristics of Signals 35 2.1 Introduction 35 2.2 Input-Output Signal Concepts 35 Classification of Waveforms 36 Signal Waveforms 38 2.3 Signal Analysis 39 Effects of Signal-Averaging Period DC Offset 42 41 vii

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 51 2.5 Fourier Transform and the Frequency Spectrum 57 Discrete Fourier Transform 59 2.6 Summary 64 References 64 Nomenclature 64 Problems 65 3. Measurement System Behavior 70 3.1 Introduction 70 3.2 General Model for a Measurement System Dynamic Measurements 70 Measurement System Model 72 3.3 Special Cases of the General System Model Zero-Order Systems 74 First-Order Systems 76 Second-Order Systems 87 3.4 Transfer Functions 96 3.5 Phase Linearity 98 3.6 Multiple-Function Inputs 99 3.7 Coupled Systems 101 3.8 Summary 104 References 104 Nomenclature 104 Problems 105 70 74 4. Probability and Statistics 109 4.1 Introduction 109 4.2 Statistical Measurement Theory 110 Probability Density Functions 110 4.3 Infinite Statistics 116 4.4 Finite Statistics 121 Standard Deviation of the Means 123 Pooled Statistics 125 4.5 Chi-Squared Distribution 126 Precision Interval in a Sample Variance 127 Goodness-of-Fit Test 129 4.6 Regression Analysis 131 Least-Squares Regression Analysis 132 4.7 Data Outlier Detection 138 4.8 Number of Measurements Required 140 4.9 Summary 143 References 143 Nomenclature 143 Problems 144

ix 5. Uncertainty Analysis 149 5.1 Introduction 149 5.2 Measurement Errors 149 5.3 Design-Stage Uncertainty Analysis 151 Combining Elemental Errors: RSS method 152 Design-Stage Uncertainty 152 5.4 Error Sources 155 Calibration Errors 156 Data-Acquisition Errors 156 Data-Reduction Errors 157 5.5 Bias and Precision Errors 157 Bias Error 157 Precision Error 158 5.6 Uncertainty Analysis: Error Propagation 159 Propagation of Error 159 5.7 Advanced-Stage and Single-Measurement Uncertainty Analysis 163 Zero-Order Uncertainty 164 Higher-Order Uncertainty 164 Mh-Order Uncertainty 165 5.8 Multiple-Measurement Uncertainty Analysis 170 Propagation of Elemental Errors 170 Propagation of Uncertainty to a Result 176 5.9 Summary 183 References 183 Nomenclature 184 Problems 184 6. Analog Electrica! Devices and Measurements 192 6.1 Introduction 192 6.2 Analog Devices: Current Measurements 192 Direct Current 192 Alternating Current 195 6.3 Analog Devices: Voltage Measurements 196 Analog Meters 197 Oscilloscope 197 Potentiometer 199 6.4 Analog Devices: Resistance Measurements 201 Ohmmeter Circuits 201 Bridge Circuits 203 6.5 Loading Errors and Impedance Matching 208 Loading Errors for A Voltage Dividing Circuit 209 Interstage Loading Errors 210 6.6 Analog Signal Conditioning: Amplifiers 213 6.7 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

6.8 Analog Signal Conditioning: Filters 221 Butterworth Filter Design 222 Bessel Filter Design 225 Active Filters 226 6.9 Grounds, Shielding, and Connecting Wires 226 Ground and Ground Loops 227 Shields 228 Connecting Wires 229 6.10 Summary 229 References 230 Nomenclature 230 Problems 230 7. Sampling, Digital Devices, and Data Acquisition 235 7.1 Introduction 235 7.2 Sampling Concepts 235 Sample Rate 236 Alias Frequencies 238 Amplitude Ambiguity 241 Selecting Sample Rate and Data Number 243 7.3 Digital Devices: Bits and Words 244 7.4 Transmitting Digital Numbers: High and Low Signals 246 7.5 Voltage Measurements 246 Digital-to-Analog Converter 247 Analog-to-Digital Converter 248 Digital Voltmeters 257 7.6 Data-Acquisition Systems 258 7.7 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 265 7.8 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 270 7.9 Digital Input-Output Communication 270 Serial Communications 271 Universal Serial Bus 273 Parallel Communications 274 7.10 Summary 278 References 278 Nomenclature 279 Problems 279

xi 8. Temperature Measurements 283 8.1 Introduction 283 Historical Background 283 8.2 Temperature Standards and Definition 284 Fixed-Point Temperatures and Interpolation 284 Temperature Scales and Standards 285 8.3 Thermometry Based on Thermal Expansion 287 Liquid-in-Glass Thermometers 287 Bimetallic Thermometers 288 8.4 Electrical Resistance Thermometry 289 Resistance Temperature Detectors 289 Thermistors 297 8.5 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 318 8.6 Radiative Temperature Measurements 322 Radiation Fundamentals 322 Radiation Detectors 323 Radiative Temperature Measurements 325 Optical Fiber Thermometers 326 8.7 Physical Errors in Temperature Measurement 327 Insertion Errors 327 Recovery Errors in Temperature Measurement 335 8.8 Summary 337 References 337 Nomenclature 338 Problems 339 9. Pressure and Velocity Measurements 345 9.1 Introduction 345 9.2 Pressure Concepts 345 9.3 Pressure Reference Instruments 348 McLeod Gauge 348 Barometer 349 Manometers 350 Deadweight Testers 354 9.4 Pressure Transducers 356 Bourdon Tube 357 Bellows and Capsule 358 Diaphragms 360 9.5 Pressure Transducer Calibration 364 Static Calibration 364 Dynamic Calibration 364

xii 9.6 Pressure Measurements in Moving Fluids 366 Total Pressure Measurement 367 Static Pressure Measurement 368 9.7 Design and Installation: Transmission Effects 369 Gases 370 Liquids 372 Heavily Damped Systems 373 9.8 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 383 9.9 Summary 383 References 383 Nomenclature 384 Problems 384 10. Flow Measurements 389 10.1 Introduction 389 10.2 Historical Comments 389 10.3 Flow Rate Concepts 390 10.4 Volume Flow Rate Through Velocity Determination 392 10.5 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 411 10.6 Insertion Volume Flow Meters 412 Electromagnetic Flow Meters 413 Vortex Shedding Meters 414 Rotameters 416 Turbine Meters 418 Positive-Displacement Meters 418 10.7 Mass Flow Meters 419 Thermal Flow Meter 419 Coriolis Flow Meter 420 10.8 Flow Meter Calibration and Standards 423 10.9 Summary 425 References 425 Nomenclature 425 Problems 426 11. Strain Measurement 429 11.1 Introduction 429 11.2 Stress and Strain 429 11.3 Resistance Strain Gauges 432

xiii Metallic Gauges 432 Semiconductor Strain Gauges 436 11.4 Strain Gauge Electrical Circuits 438 11.5 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 453 11.6 Optical Strain Measuring Techniques 454 Basic Characteristics of Light 455 Photoelastic Measurement 456 Moire Methods 457 11.7 Summary 460 References 460 Nomenclature 461 Problems 461 12. Metrology, Motion, Force, and Power Measurements 466 12.1 Introduction 466 12.2 Dimensional Measurements: Metrology 466 Historical Perspective 466 Principles of Linear Measurement 467 Optical Methods 473 12.3 Displacement Measurements 474 Potentiometers 474 Linear Variable Differential Transformers 474 12.4 Measurement of Mass 477 12.5 Measurement of Acceleration and Vibration 482 Seismic Transducer 482 Transducers for Shock and Vibration Measurement 488 12.6 Velocity Measurements 489 Linear Velocity Measurements 489 Velocity from Displacement or Acceleration 489 Moving Coil Transducers 492 Angular Velocity Measurements 492 12.7 Force Measurement 496 Load Cells 496 12.8 Torque Measurements 500 Measurement of Torque on Rotating Shafts 501 12.9 Mechanical Power Measurements 502 Rotational Speed, Torque, and Shaft Power 502 Cradled Dynamometers 503 12.10 Summary 504 References 506 Nomenclature 506 Problems 506

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