Theory and Design for Mechanical Measurements

Theory and Design for Mechanical Measurements merges time-tested pedagogy with current technology to deliver an immersive, accessible resource for both students and practicing engineers. Emphasizing statistics and uncertainty analysis with topical integration throughout, this book establishes a strong foundation in measurement theory while leveraging the e-book format to increase student engagement with interactive problems, electronic data sets, and more. This new Seventh edition has been updated with new practice problems, electronically accessible solutions, and dedicated Instructor Problems that ease course planning and assessment. Extensive coverage of device selection, test procedures, measurement system performance, and result reporting and analysis sets the field for generalized understanding, while practical discussion of data acquisition hardware, infrared imaging, and other current technologies demonstrate real-world methods and techniques. Designed to align with a variety of undergraduate course structures, this unique text offers a highly flexible pedagogical framework while remaining rigorous enough for use in graduate studies, independent study, or professional reference.

Preface v 1 Basic Concepts of measurement methods 1 1.1 Introduction 1 1.2 General Measurement System 2 Sensor and Transducer 2 Signal-Conditioning Stage 3 Output Stage 4 General Template for a Measurement System 4 1.3 Experimental Test Plan 5 Variables 6 Noise and Interference 8 Randomization 9 Replication and Repetition 13 Concomitant Methods 14 1.4 Calibration 14 Static Calibration 14 Dynamic Calibration 14 Static Sensitivity 15 Range and Span 15 Resolution 16 Accuracy and Error 16 Random and Systematic Errors and Uncertainty 16 Sequential Test 19 Hysteresis 19 Random Test 19 Linearity Error 19 Sensitivity and Zero Errors 21 Instrument Repeatability 21 Reproducibility 21 Instrument Precision 21 Overall Instrument Error and Instrument Uncertainty 22 Verification and Validation 22 1.5 Standards 22 Primary Unit Standards 22 Base Dimensions and Their Units 23 Derived Units 25 Hierarchy of Standards 28 Test Standards and Codes 29 1.6 Presenting Data 30 Rectangular Coordinate Format 30 Semilog Coordinate Format 30 Full-Log Coordinate Format 30 Significant Digits 30 Summary 33 Nomenclature 34 References 34 2 Static and Dynamic Characteristics Of Signals 35 2.1 Introduction 35 2.2 Input/Output Signal Concepts 35 Generalized Behavior 36 Classification of Waveforms 36 Signal Waveforms 38 2.3 Signal Analysis 39 Signal Root-Mean-Square Value 40 Discrete Time or Digital Signals 40 Direct Current Offset 41 2.4 Signal Amplitude and Frequency 42 Periodic Signals 43 Frequency Analysis 45 Fourier Series and Coefficients 48 Fourier Coefficients 48 Special Case: Functions with T = 2π 49 Even and Odd Functions 49 2.5 Fourier Transform and the Frequency Spectrum 55 Discrete Fourier Transform 56 Analysis of Signals in Frequency Space 60 Summary 62 References 63 Suggested Reading 63 Nomenclature 63 3 Measurement System Behavior 64 3.1 Introduction 64 3.2 General Model for a Measurement System 64 Dynamic Measurements 65 Measurement System Model 66 3.3 Special Cases of the General System Model 68 Zero-Order Systems 68 First-Order Systems 69 Second-Order Systems 79 3.4 Transfer Functions 88 3.5 Phase Linearity 90 3.6 Multiple-Function Inputs 91 3.7 Coupled Systems 93 3.8 Summary 95 References 95 Nomenclature 96 Subscripts 96 4 Probability and Statistics 97 4.1 Introduction 97 4.2 Statistical Measurement Theory 98 Probability Density Functions 98 4.3 Describing the Behavior of a Population 103 4.4 Statistics of Finite-Sized Data Sets 107 Standard Deviation of the Means 110 Repeated Tests and Pooled Data 113 4.5 Hypothesis Testing 114 4.6 Chi-Squared Distribution 117 Precision Interval in a Sample Variance 118 Goodness-of-Fit Test 119 4.7 Regression Analysis 121 Least-Squares Regression Analysis 121 Linear Polynomials 124 4.8 Data Outlier Detection 126 4.9 Number of Measurements Required 127 4.10 Monte Carlo Simulations 129 Summary 131 References 132 Nomenclature 132 5 Uncertainty Analysis 133 5.1 Introduction 133 5.2 Measurement Errors 134 5.3 Design-Stage Uncertainty Analysis 136 Combining Elemental Errors: RSS Method 137 Design-Stage Uncertainty 137 5.4 Identifying Error Sources 140 Calibration Errors 141 Data-Acquisition Errors 141 Data-Reduction Errors 142 5.5 Systematic and Random Errors and Standard Uncertainties 142 Systematic Error 142 Random Error 143 Other Ways Used to Classify Error and Uncertainty 144 5.6 Uncertainty Analysis: Multi-Variable Error Propagation 144 Propagation of Error 145 Approximating a Sensitivity Index 146 Sequential Perturbation 149 Monte Carlo Method 151 5.7 Advanced-Stage Uncertainty Analysis 151 Zero-Order Uncertainty 152 Higher-Order Uncertainty 152 Nth-Order Uncertainty 152 5.8 Multiple-Measurement Uncertainty Analysis 157 Propagation of Elemental Errors 157 Propagation of Uncertainty to a Result 163 5.9 Correction for Correlated Errors 168 5.10 Nonsymmetrical Systematic Uncertainty Interval 170 Summary 172 References 172 Nomenclature 172 6 Analog Electrical Devices and measurements 174 6.1 Introduction 174 6.2 Analog Devices: Current Measurements 174 Direct Current 174 Alternating Current 178 6.3 Analog Devices: Voltage Measurements 179 Analog Voltage Meters 179 Oscilloscope 179 Potentiometer 181 6.4 Analog Devices: Resistance Measurements 182 Ohmmeter Circuits 182 Bridge Circuits 182 Null Method 184 Deflection Method 185 6.5 Loading Errors and Impedance Matching 188 Loading Errors for Voltage-Dividing Circuit 189 Interstage Loading Errors 190 6.6 Analog Signal Conditioning: Amplifiers 193 6.7 Analog Signal Conditioning: Special-Purpose Circuits 196 Analog Voltage Comparator 196 Sample-and-Hold Circuit 197 Charge Amplifier 197 4–20 mA Current Loop 199 Multivibrator and Flip-Flop Circuits 199 6.8 Analog Signal Conditioning: Filters 201 Butterworth Filter Design 202 Improved Butterworth Filter Designs 203 Bessel Filter Design 208 Active Filters 209 6.9 Grounds, Shielding, and Connecting Wires 211 Ground and Ground Loops 211 Shields 212 Connecting Wires 213 Summary 213 References 214 Nomenclature 214 7 Sampling, Digital Devices, and Data Acquisition 215 7.1 Introduction 215 7.2 Sampling Concepts 216 Sample Rate 216 Alias Frequencies 218 Amplitude Ambiguity 221 Leakage 221 Waveform Fidelity 223 7.3 Digital Devices: Bits and Words 223 7.4 Transmitting Digital Numbers: High and Low Signals 226 7.5 Voltage Measurements 227 Digital-to-Analog Converter 227 Analog-to-Digital Converter 228 Successive Approximation Converters 232 7.6 Data Acquisition Systems 237 7.7 Data Acquisition System Components 238 Analog Signal Conditioning: Filters and Amplification 238 Components for Acquiring Data 241 7.8 Analog Input–Output Communication 242 Data Acquisition Modules 242 7.9 Digital Input–Output Communication 246 Data Transmission 247 Universal Serial Bus 248 Bluetooth Communications 248 Other Serial Communications: RS-232C 249 Parallel Communications 249 7.10 Digital Image Acquisition and Processing 252 Image Acquisition 252 Image Processing 253 Summary 256 References 256 Nomenclature 256 8 Temperature measurements 258 8.1 Introduction 258 Historical Background 258 8.2 Temperature Standards and Definition 259 Fixed Point Temperatures and Interpolation 259 Temperature Scales and Standards 260 8.3 Thermometry Based on Thermal Expansion 261 Liquid-in-Glass Thermometers 262 Bimetallic Thermometers 262 8.4 Electrical Resistance Thermometry 263 Resistance Temperature Detectors 264 Thermistors 271 8.5 Thermoelectric Temperature Measurement 276 Seebeck Effect 276 Peltier Effect 277 Thomson Effect 277 Fundamental Thermocouple Laws 278 Basic Temperature Measurement with Thermocouples 279 Thermocouple Standards 280 Thermocouple Voltage Measurement 287 Multiple-Junction Thermocouple Circuits 289 Applications for Thermoelectric Temperature Measurement: Heat Flux 291 Data Acquisition Considerations 294 8.6 Radiative Temperature Measurements 297 Radiation Fundamentals 297 Radiation Detectors 299 Radiometer 299 Pyrometry 300 Optical Fiber Thermometers 301 Narrow-Band Infrared Temperature Measurement 302 Fundamental Principles 302 Two-Color Thermometry 303 Full-Field IR Imaging 303 8.7 Physical Errors in Temperature Measurement 304 Insertion Errors 305 Conduction Errors 306 Radiation Errors 308 Radiation Shielding 310 Recovery Errors in Temperature Measurement 311 Summary 313 References 313 Suggested Reading 313 Nomenclature 314 9 Pressure and Velocity measurements 315 9.1 Introduction 315 9.2 Pressure Concepts 315 9.3 Pressure Reference Instruments 318 McLeod Gauge 318 Barometer 319 Manometer 320 Deadweight Testers 324 9.4 Pressure Transducers 325 Bourdon Tube 326 Bellows and Capsule Elements 326 Diaphragms 327 Piezoelectric Crystal Elements 330 9.5 Pressure Transducer Calibration 331 Static Calibration 331 Dynamic Calibration 331 9.6 Pressure Measurements in Moving Fluids 333 Total Pressure Measurement 334 Static Pressure Measurement 335 9.7 Modeling Pressure–Fluid Systems 336 9.8 Design and Installation: Transmission Effects 337 Liquids 338 Gases 339 Heavily Damped Systems 340 9.9 Acoustical Measurements 341 Signal Weighting 341 Microphones 342 9.10 Fluid Velocity Measuring Systems 345 Pitot–Static Pressure Probe 346 Thermal Anemometry 348 Doppler Anemometry 350 Particle Image Velocimetry 352 Selection of Velocity Measuring Methods 353 Summary 354 References 354 Nomenclature 355 10 Flow measurements 357 10.1 Introduction 357 10.2 Historical Background 357 10.3 Flow Rate Concepts 358 10.4 Volume Flow Rate through Velocity Determination 359 10.5 Pressure Differential Meters 361 Obstruction Meters 361 Orifice Meter 364 Venturi Meter 366 Flow Nozzles 368 Sonic Nozzles 373 Obstruction Meter Selection 374 Laminar Flow Elements 376 10.6 Insertion Volume Flow Meters 377 Electromagnetic Flow Meters 377 Vortex Shedding Meters 379 Rotameters 381 Turbine Meters 382 Transit Time and Doppler (Ultrasonic) Flow Meters 383 Positive Displacement Meters 384 10.7 Mass Flow Meters 386 Thermal Flow Meter 386 Coriolis Flow Meter 387 10.8 Flow Meter Calibration and Standards 391 10.9 Estimating Standard Flow Rate 392 Summary 393 References 393 Nomenclature 393 11 Strain measurement 395 11.1 Introduction 395 11.2 Stress and Strain 395 Lateral Strains 397 11.3 Resistance Strain Gauges 398 Metallic Gauges 398 Strain Gauge Construction and Bonding 400 Semiconductor Strain Gauges 403 11.4 Strain Gauge Electrical Circuits 404 11.5 Practical Considerations for Strain Measurement 407 The Multiple Gauge Bridge 407 Bridge Constant 408 11.6 Apparent Strain and Temperature Compensation 409 Temperature Compensation 410 Bridge Static Sensitivity 412 Practical Considerations 413 Analysis of Strain Gauge Data 413 Signal Conditioning 416 11.7 Optical Strain Measuring Techniques 418 Basic Characteristics of Light 418 Photoelastic Measurement 419 Moiré Methods 421 Fiber Bragg Strain Measurement 422 Summary 424 References 424 Nomenclature 424 12 Mechatronics: Sensors, Actuators, and Controls 426 12.1 Introduction 426 12.2 Sensors 426 Displacement Sensors 426 Measurement of Acceleration and Vibration 430 Velocity Measurements 437 Angular Velocity Measurements 441 Force Measurement 444 Torque Measurements 447 Mechanical Power Measurements 448 12.3 Actuators 450 Linear Actuators 450 Pneumatic and Hydraulic Actuators 452 Rotary Actuators 455 Flow-Control Valves 455 12.4 Controls 457 Dynamic Response 460 Laplace Transforms 460 Block Diagrams 463 Model for Oven Control 464 Proportional–Integral (PI) Control 468 Proportional–Integral–Derivative Control of a Second-Order System 469 Summary 474 References 474 Nomenclature 474 Chapter Homework Problems P-1 A Property Data and Conversion Factors A-1 B Laplace Transform Basics A-8 B.1 Final Value Theorem A-9 B.2 Laplace Transform Pairs A-9 Reference A-9 Glossary G-1 Index I-1