Metrology and Instrumentation
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Samir Mekid, PhD, is Professor of Mechanical Engineering and Founding Director of the Interdisciplinary Research Center for Intelligent Manufacturing and Robotics at King Fahd University of Petroleum and Minerals in Saudi Arabia. He has worked as a design engineer with Caterpillar and is a Chartered Engineer registered with IMechE.
Content
Preface xiii
Acknowledgments xv
About the Author xvii
1 Fundamental Units and Constants in Metrology 1
1.1 Introduction 1
1.2 Current Definitions of the Main SI Units 6
1.3 New Definition of Seven Base Units of the SI 6
1.4 Derived International System (SI) Units 7
1.5 SI Conversion 7
1.6 Fundamental Constants 8
1.7 Common Measurements 9
1.8 Principles and Practices of Traceability 10
1.8.1 Definition of Traceability 10
1.8.2 Accreditation and Conformity Assessment 11
Multiple Choice Questions of this Chapter 12
References 12
2 Scales of Metrology 13
2.1 Introduction to Practical Metrology across All Scales 13
2.2 Nanometrology 14
2.2.1 Introduction and Need in Industry 14
2.2.2 Definition of Nanometrology 15
2.2.3 Importance of Nanometrology in Science and Technology 15
2.3 Standards 18
2.4 Micrometrology 22
2.4.1 Introduction and Need in Industry 22
2.4.2 Definition of Micrometrology 22
2.4.3 Examples of Micrometrology of Microparts 22
2.5 Macroscale Metrology 23
2.5.1 Standards 25
2.6 Large-Scale Metrology and Large-Volume Metrology 29
2.6.1 Introduction and Need in Industry 29
2.6.2 Definition 30
2.6.3 Verification Standards 32
2.7 Instruments Techniques 34
2.7.1 Large Coordinate Measuring Machines 35
2.7.2 Laser Trackers 35
2.7.3 Theodolite 35
Multiple Choice Questions of this Chapter 37
References 37
3 Applied Math and Statistics 39
3.1 Introduction 39
3.2 Scientific and Engineering Notation 39
3.3 Imperial/Metric Conversions 40
3.4 Ratio 41
3.5 Linear Interpolation 42
3.6 Number Bases 42
3.7 Significant Figures, Rounding, and Truncation 43
3.8 Geometry and Volumes 44
3.8.1 Perimeter 44
3.8.2 Volume and Area 44
3.9 Angular Conversions 44
3.10 Graphs and Plots 45
3.11 Statistical Analysis and Common Distributions 47
3.11.1 Definition of Measurement Data 47
3.11.2 Statistical Measurements 47
3.11.3 Statistical Analysis of Measurements 47
3.11.4 Probability 48
3.11.5 Sample and Population 49
3.11.6 Formulation of Mean and Variance for Direct Measurements 49
3.11.7 Mean and Variance Based on Samples 50
3.11.8 The Standard Deviation of the Mean 51
3.12 Formulation of the Standard Uncertainty and Average of Indirect Measurements 52
3.12.1 How to Determine the Measured Value and Random Error? 52
3.12.2 Repeated Measurements of One Single Quantity 52
3.12.3 Normal Distribution 53
3.12.4 Student's t-distribution 55
Multiple Choice Questions of this Chapter 60
4 Errors and their Sources 61
Introduction 61
4.1 Definition of the Error and Their Types 61
4.1.1 Systematic Errors 62
4.1.2 Random Errors 63
4.1.3 Components of Motion Error Assessment 63
4.2 Measurement Characteristics 63
4.2.1 Characterization of the Measurement 63
4.2.2 Resolution, Error Uncertainty, and Repeatability 64
4.2.3 Model of Measurement 67
4.3 Propagation of Errors 69
4.4 Sources of Errors 73
4.4.1 Static Errors and Dynamic Errors 73
4.5 Error Budget 77
4.5.1 Components of the Error Budget 77
4.5.2 Example of Error-Budget Table 78
4.6 Error Elimination Techniques 79
4.6.1 Methods 79
4.7 Model of Errors in CNC Using HTM 81
4.8 Case Study of Errors Budget 87
4.8.1 Description of the Designed System 87
4.8.2 Error Modeling and Experimental Testing 88
4.9 Solved Problems 96
Multiple Choice Questions of this Chapter 97
References 97
5 Measurement and Measurement Systems 99
5.1 Introduction 99
5.2 What Can Be Standard in a Measurement? 101
5.3 Definitions of Key Measurement Components 102
5.3.1 Measurement System 102
5.3.2 Measurement System Analysis 103
5.3.3 Measurement Process 103
5.4 Physical Measurement Process (PMP) 103
5.5 Difference between Number and an Analysis Model 104
5.6 Measurement Methods 105
5.6.1 Metrology and Measurement 105
5.6.2 Metrological Characteristics of Measuring Instruments 108
5.7 Instrumentation for Measurement 109
5.7.1 Background 109
5.7.2 Measurement Instrumentations 109
5.7.3 Digital Measuring Device Fundamentals 109
5.8 Non-Portable Dimensional Measuring Devices 110
5.8.1 Laser Interferometry, Application to CNC Machines 110
5.8.2 Coordinate Measuring Machine (CMM) 118
5.9 Metrology Laboratory Test for Students 140
Multiple Choice Questions of this Chapter 146
References 146
6 Tolerance Stack-Up Analysis 149
6.1 Introduction 149
6.1.1 Importance of Tolerance Stack-Up Analysis 149
6.1.2 Need for Tolerance Stack-Up Analysis in Assemblies 151
6.1.3 Manufacturing Considerations in Engineering Design 151
6.1.4 Technical Drawing 152
6.1.5 Definitions, Format, andWorkflow of Tolerance Stack-Up 153
6.2 Brief Introduction to Geometric Dimensioning and Tolerancing (GD&T) 156
6.2.1 Notation and Problem Formulation 156
6.2.2 Dimension Types 157
6.2.3 Coordinate Dimensioning 158
6.2.4 Tolerance Types 160
6.2.5 Characteristics of Features and Their Tolerances 162
6.3 Tolerance Format and Decimal Places 164
6.4 Converting Plus/Minus Dimensions and Tolerances into Equal-Bilaterally Toleranced Dimensions 165
6.5 Tolerance Stack Analysis 167
6.5.1 Worst-Case Tolerance Analysis 169
6.5.2 Rules for Assembly Shift 169
6.5.3 Worst-Case Tolerance Stack-Up in Symmetric Dimensional Tolerance 171
6.5.4 Worst-Case Tolerance Stack-Up in Asymmetric Dimensional Tolerance 173
6.6 Statistical Tolerance Analysis 173
6.6.1 Definition of Statistical Tolerance Analysis 173
6.6.2 Worst-Case Analysis vs RSS (Root-Sum Squared) Statistical Analysis 175
6.6.3 Second-Order Tolerance Analysis 176
6.6.4 Cases Discussions 176
6.6.5 Understanding Material Condition Modifiers 178
Appendix A from ISO and ASME Y14 Symbols 188
Multiple Choice Questions of this Chapter 189
References 189
7 Instrument Calibration Methods 191
7.1 Introduction 191
7.2 Definition of Calibration 191
7.3 Need for Calibration 192
7.4 Characteristics of Calibration 193
7.5 Calibration Overall Requirements and Procedures 195
7.5.1 Calibration Methods/Procedures 195
7.6 Calibration Laboratory Requirements 197
7.7 Industry Practices and Regulations 198
7.8 Calibration and Limitations of a Digital System 199
7.9 Verification and Calibration of CNC Machine Tool 201
7.10 Inspection of the Positioning Accuracy of CNC Machine Tools 202
7.11 CNC Machine Error Assessment and Calibration 207
7.12 Assessment of the Contouring in the CNC Machine Using a Kinematic Ballbar System 219
7.13 Calibration of 3-axis CNC Machine Tool 221
7.14 Calibration of a Coordinate Measuring Machine (CMM) 225
7.14.1 CMM Performance Verification 225
7.14.2 Accreditation of Calibration Laboratories 226
Section 1: Scope and Description 231
Section 2: Calibration Requirements 232
Section 3: Preliminary Operations 232
Section 4: Calibration Process 233
Section 5: Data Analysis 234
Section 6: Calibration Report 234
Multiple Choice Questions of this Chapter 235
References 235
8 Uncertainty in Measurements 237
8.1 Introduction and Background 237
8.2 Uncertainty of Measurement 238
8.3 Measurement Error 238
8.4 Why Is Uncertainty of Measurement Important? 239
8.5 Components and Sources of Uncertainty 239
8.5.1 What Causes Uncertainty? 239
8.5.2 Uncertainty Budget Components 240
8.5.3 The Errors Affecting Accuracy 240
8.6 Static Errors and Dynamic Errors 241
8.7 Types of Uncertainty 241
8.8 Uncertainty Evaluations and Analysis 242
8.9 Uncertainty Reporting 243
8.10 How to Report Uncertainty 245
8.11 Fractional Uncertainty Revisited 247
8.12 Propagation of Uncertainty 247
Multiple Choice Questions of this Chapter 252
References 252
9 Dimensional Measurements and Calibration 255
9.1 Length Measurement 255
9.2 Displacement Measurement 255
9.3 Manual Instruments 260
9.3.1 Caliper 260
9.3.2 Vernier Caliper 261
9.3.3 Micrometer 262
9.3.4 Feeler Gauge 262
9.3.5 Liner Measurement Tool 263
9.3.6 American Wire Gauge 263
9.3.7 Bore Gauge 263
9.3.8 Telescopic Feeler Gauge 264
9.3.9 Depth Gauge 265
9.3.10 Angle Plate or Tool 265
9.3.11 Flat Plate 266
9.3.12 Dial Gauge 266
9.3.13 Oil Gauging Tapes 267
9.3.14 Thread Measurement 267
9.3.15 Planimeter 267
9.4 Diameter and Roundness 269
9.4.1 How to Measure a Diameter? 269
9.4.2 Roundness 270
9.5 Angular Measurements 276
9.5.1 Line Standard Angular Measuring Devices 277
9.5.2 Face Standard Angular Measuring Devices 277
9.5.3 Measurement of Inclines 279
9.5.4 Optical Instruments for Angular Measurement 280
9.6 Metrology for Complex Geometric Features 282
9.6.1 Edge Detection Techniques Using a CCD Camera 282
9.6.2 Full Laser Scanning for Reverse Engineering 283
9.7 Measurement Surface Texture 285
9.7.1 Geometry of Surface 285
9.7.2 Surface Integrity 286
9.7.3 Specification of Surfaces 286
9.7.4 Sampling Length 287
9.7.5 Instruments and Measurement of Roughness 290
Multiple Choice Questions of this Chapter 291
References 291
10 Mechanical Measurements and Calibration 293
10.1 Importance of Mechanical Measurements 293
10.2 Mechanical Measurements and Calibration 293
10.3 Description of Mechanical Instruments 294
10.3.1 Mass Measurements 294
10.3.2 Force Measurements 295
10.3.3 Vibration Measurements 295
10.3.4 Volume and Density 296
10.3.5 Hydrometers 298
10.3.6 Acoustic Measurements 298
10.4 Calibration of Mechanical Instruments 300
10.4.1 When Is Equipment Calibration Needed? 300
10.4.2 When Is There No Need for Calibration? 301
10.4.3 Process of Equipment Calibration 301
10.5 Equipment Validation for Measurement 301
10.5.1 Is There a Need of Equipment Validation? 302
10.5.2 Features and Benefits of Validation 302
10.5.3 Process of Validation of Equipment 302
10.6 Difference between Calibration and Validation of Equipment 303
10.7 Difference between Calibration and Verification 303
10.8 Calibration of Each Instrument 304
10.8.1 Mass Calibration 304
10.8.2 Force Calibration 304
10.8.3 Pressure Calibration 304
10.8.4 Vibration Measurements 306
10.8.5 Volume and Density 307
10.8.6 Hydrometers 308
10.8.7 Acoustic Measurements 308
Multiple Choice Questions of this Chapter 308
References 308
11 Thermodynamic Measurements 309
11.1 Background 309
11.2 Scale of Temperature 309
11.2.1 Ideal Gas Law 310
11.2.2 Vacuum 310
11.2.3 Gas Constants 310
11.3 Power 312
11.4 Enthalpy 312
11.5 Humidity Measurements 312
11.6 Methods of Measuring Temperature 313
11.7 Temperature Measured through Thermal Expansion Materials 314
11.7.1 Liquid-in-Glass Thermometer 314
11.7.2 Bimetallic Thermometer 314
11.7.3 Electrical Resistance Thermometry 315
11.7.4 Resistance Temperature Detectors 316
11.7.5 Examples for Discussion 318
11.7.6 Thermistors 320
11.8 Thermoelectric Temperature Measurement or Thermocouples 321
11.8.1 Basic Thermocouples 321
11.8.2 Fundamental Thermocouple Laws 322
11.9 Thermocouple Materials 323
11.9.1 Advantages and Disadvantages of Thermocouple Materials 324
11.9.2 Thermocouple Voltage Measurement 325
11.10 Multi-Junction Thermocouple Circuits 326
11.11 Thermopiles 327
11.12 Radiative Temperature Measurement 327
Multiple Choice Questions of this Chapter 329
References 329
12 Quality Systems and Standards 331
12.1 Introduction to Quality Management 331
12.2 Quality Management 332
12.2.1 Total Quality Management (TQM) 332
12.2.2 Quality Management System (QMS) 333
12.2.3 TQM Is Essential to Complete TQS 333
12.2.4 ISO-Based QMS Certification 333
12.3 Components of Quality Management 334
12.3.1 Quality System (QS) 334
12.3.2 Quality Assurance (QA) 335
12.3.3 Quality Control (QC) 335
12.3.4 Quality Assessment 335
12.4 System Components 336
12.4.1 Quality Audits 336
12.4.2 Preventive and Corrective Action 336
12.4.3 Occupational Safety Requirements 337
12.4.4 Housekeeping Practices 338
12.5 Quality Standards and Guides 338
Multiple Choice Questions of this Chapter 339
References 340
13 Digital Metrology Setups and Industry Revolution I4.0 341
13.1 Introduction 341
13.1.1 What Is a Digital Measurement? 341
13.1.2 Metrology and Digitalization 341
13.1.3 Implementation Strategy 343
13.2 Data Acquisition 343
13.3 Setup Fundamentals for Measurement and Data Acquisition 344
13.3.1 Length Measurement in Open Loop 344
13.3.2 Thermal Measurement and Data-Acquisition Considerations 345
13.3.3 Data Transfer to Cloud 349
13.3.4 Internet of Things (IoT) Metrology 349
13.3.5 Closed-Loop Data Analysis- (In-Process Inspection) 350
13.4 Digital Twin Metrology Inspection 352
Multiple Choice Questions of this Chapter 354
References 354
Index 357
1
Fundamental Units and Constants in Metrology
"When you can measure what you are speaking about and express it in numbers, you know something about it."
-Lord Kelvin (1883). Source: Public Domain.
1.1 Introduction
Metrology is the science of measurement with various applications. It is derived from the Greek words metro - measurement and Logy - science. The BIMP (Bureau of Weights and Measures in France) defines metrology as "the science of measurement embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology."
Five pivots define the functions of metrology:
- To establish the units of measurements;
- To replicate these units as standards;
- To guarantee the measurement uniformity;
- To develop measurement methods;
- To investigate the accuracy of methods-related errors.
Based on this, the objectives of metrology are:
- Selection of proper measuring instrument;
- Proper measuring standards;
- Minimizing inspection cost;
- Defining process capabilities;
- Standardization;
- Maintaining accuracy and precision during inspection or as component of an instrument over time of use [1].
Therefore, two types of metrology exist:
- Deterministic, or industrial, metrology.
- Legal, or scientific, metrology.
Measurement is the process of revealing a single or multiple values to the characteristics of an object or property by conducting experiments to determine the value of this particular property. These properties may be physical, mechanical, or chemical, such as length, weight, force, strain, volume, angle, and molls.
Figure 1.1 Simplified methodology producing measurement results.
Metrology also includes precision, repeatability, and accuracy, which refers to how accurate the measured value is. It establishes a well-known understanding of the measuring process and the related units that are critical in connecting various human activities and ensures that these measurements are linked to reference standards, which is commonly referred to as traceability. For as long as civilization has existed, measurements have been taken. It is necessary for a country's economic and social development. It provides precise measurements that have an impact on the economy, health, safety, and general well-being. It could also be a legal problem. As a result, the topic is always in demand.
This chapter will introduce the fundamental units and constants in metrology through conversions between units and systems. To put measurements into context, a complete methodology of the act of measurement beginning with the object to measure and ending with the result that constitutes the information needed for the object is required. The complete process is summarized in Figure 1.1. The figure depicts a simplified methodology for producing measurement results with minimal conditions such as the units to be known, the calibration of the measurement instruments, and the uncertainty of such measurements. This is to cast the majority of the aspects that engineers conducting measurements must be aware of. A dimension is a non-numerical measure of a physical variable. The unit is used to associate a quantity or measurement with a dimension.
Example 1.1 The mass of an object is a primary dimension, while 15 kg is associated with the quantity 15 of mass with the unit of kg. We need a comparison with some precise unit value to measure the quantity of anything. Body parts (Figure 1.2) and natural surroundings were used by early humans to provide suitable measuring instruments. Elementary measures became essential in the primitive human societies for tasks such as building dwellings, making clothing, bartering for food, and exchanging raw materials.
Figure 1.2 Vitruvian man by Leonardo da Vinci showing nine historical units of measurement.
Source: Wikimedia Commons
- According to early Babylonian and Egyptian transcripts, length was first measured with the forearm (cubit), hand (palm and span), and finger (digit).
- The cycles of the celestial bodies such as the sun, moon, and others were used for time measurements.
- Plant seeds were used for the sake of establishing volume measurement, while with the expansion of scales for weighing, seeds and stones became standards. As sample, the carob seed was the base measure for the carat, which is still used as a mass unit in the gemstone industry.
As trade and commerce expanded, it became necessary to standardize measurement systems across many countries. This decreased the possibility of disagreements arising from measurement system misunderstandings.
The international system of units, known as the SI (from French "Système International") unit system, distinguishes physical units into two classes as shown below:
- Base or primary units; and
- Derived units.
These two categories cover the most commonly used units, such as time, temperature, length, mass, pressure, and flow rate. The National Institute of Standards and Technology (NIST) [2] introduced the SI units, which can be found at this hyperlink: SI units (https://physics.nist.gov/cuu/Units/). For more information on the SI units, visit the website of the international standards organization known as the Bureau International des Poids et Mesures (BIPM).
Table 1.1 Primary units.
Measurement Units Symbol Description Unit of length meter m One meter is equal to the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second. Unit of mass kilogram kg One kilogram is equal to the unit of mass presented by the international prototype of the kilogram in Figure 1.2. Since 2019, the new definition based on Planck's constant has been used. Unit of time second s One second is equal to the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. Unit of electric current ampere A One ampere is defined as follows: the constant current if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, will produce between these conductors a force equal to 2 × 10-7 newton per meter of length. Unit of thermodynamic temperature kelvin K One kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Unit of amount of substance mole mol One mole is the amount of substance of a system containing as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Unit of luminous intensity candela cd One candela is the luminous intensity within one direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and having a radiant intensity of 1/683 watt per steradian in that direction.
As will be demonstrated later, each measurement unit has a primary quantity that is used by convention. Each primary quantity has only one primary unit. As a result, every primary unit can be decomposed or recomposed further. Table 1.1 shows primary units of different kinds of physical quantities, symbols, and their descriptions. Figure 1.3 depicts the kilogram prototype safely conserved in Paris as a reference unit of kg kept constant in quantity for comparison. The following section discusses derived units, which are shown in Table 1.2.
Figure 1.3 The standard kilogram for mass.
Table 1.2 Derived units.
Derived quantity Si derived new unit Symbol SI units SI base units Force newton N mkgs-2 Pressure, stress pascal Pa N/m2 m-1kgs-2 Energy, work, quantity of heat joule J Nm m2kgs-2 Power watt W J/s m2kgs-2 Electric charge coulomb C sA Electromotive force volt V m2kgs-3A-1 Electric capacitance farad F C/V m-2kg-1s4A2 Electric...