Applied Metrology for Manufacturing Engineering

Ammar Grous

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848211889
• eBook ISBN: 9781118622599
• Edition: 1
• Topic: Tecnologia e ingegneria
• Subtopic: Ingegneria industriale

Applied Metrology for Manufacturing Engineering, stands out from traditional works due to its educational aspect. Illustrated by tutorials and laboratory models, it is accessible to users of non-specialists in the fields of design and manufacturing. Chapters can be viewed independently of each other. This book focuses on technical geometric and dimensional tolerances as well as mechanical testing and quality control. It also provides references and solved examples to help professionals and teachers to adapt their models to specific cases. It reflects recent developments in ISO and GPS standards and focuses on training that goes hand in hand with the progress of practical work and workshops dealing with measurement and dimensioning.

Chapter 1

Fundamentals of Error Analysis and their
Uncertainties in Dimensional Metrology
Applied to Science and Technology

1.1. Introduction to uncertainties in dimensional metrology

In the field of applied science, measurements are not accurate as they are always subject to errors due to various causes, both human and material. Qualifying an error to later quantify an uncertainty proves that the validity of the measurement result is doubted. Therefore, evaluating uncertainties of measurements generating errors is quite a complex task. To “buoy” the influencing factors on which the type of measurement depends, first we develop the mathematical principles relevant to this domain [GUI 00, 04, MUL 81, NIS 94, TAY 05].

On reading the International Vocabulary of Metrology (VIM) and the Guide to the Expression of Uncertainty in Measurement (GUM) [NIS 94, VIM 93] concerning several specific areas of metrology (see ISO 1087-1, 2000, §3.7.2), we note that the definition given for “error” and “uncertainty” is poorly understood and even truncated. For example, in the VIM from 2004 to 2006, there was no fundamental difference in the basic principles of measurements, whether they were carried out in physics or engineering. As the uncertainty in the measurement increases from classical or true value approach (forevermore unknown) toward uncertainty approach, it leads to the reconsideration of the measurement concepts. We know that both the instruments and the measurements do not provide “this” true value. Therefore, it is possible to differentiate two categories of errors. They should be considered differently in terms of propagation of errors. However, as no justified rule underlies the combination between systematic and random errors, it results in total error, which characterizes the measurement result. The estimated upper limit of the total error is named as uncertainty.

The components of measurement uncertainty are conventionally [VIM 93] grouped into two categories. The first one, type A, is estimated using statistical methods, and the second, type B, is estimated using other methods. It is a priori based on laws. In fact, the person operating is responsible for assessing the sources of errors. Although the manufacturers provide data such as the class of the device, the standard, and the resolution, we should have sound knowledge based on experience. Combination of both categories A and B gives the compound uncertainty U_c( y).

GUM [GUM 93], corrected in 1995, provides a definition for the type B approach of uncertainty. It emphasizes mathematical processing of uncertainty using an explicit measurement model where the measurand is characterized by a unique value. The objective of uncertainty approach in measurement is not to determine the true value but to evaluate the errors. There are several types of measurement errors, such as parallax error, setting zero reference of the device, technique errors, errors in reading the instrument, and even human errors due to various effects such as temperature, dilation, and relative humidity. Therefore, it is difficult to define uncertainty solely based on the standard deviation. We should also consider the parameters given by the manufacturer (Mitutoyo in our study). Moreover, even the most refined measurement cannot reduce the interval to a single value due to the inherently finite amount of information defining the measurand: it is then agreed, in the VIM, that a definitional uncertainty imposes a limitation lower than any measurement uncertainty. The interval is then represented by a measured value, which results from the instrumental manipulations.

The VIM third edition of 2008 provides more concise definitions of the terminologies used in metrology. In other fields of engineering, the work is based on reliability indices [GRO 94, GRO 95]. To quantify the probability of assembled structures failure, the Monte Carlo simulation approach plays an important role in metrology. It is one of the reasons we completed this book dedicated to dimensional metrology using a dimensioning approach based on a cross-welded structure.

Similar to the VIM, in the GUM [GUI 00, NIS 94] the objective of measurements is to establish the probability that certain measured values are consistent with the definition of the measurand. The reader will easily notice that the terminology is rather less common in experimental sciences. Nevertheless, measurement, measuring, measurand, true value and so on are terms that should not be used inappropriately. The terms given in the VIM third edition, and their formats, are consistent with the frame rules for terminology outlined in international standards ISO 704, ISO 1087-1, and ISO 10241. For further information, the reader can refer to them. The word mesurage has been used to describe the act of measurement. The word mesure occurs in various occasions in the VIM. Other terms include appareil de mesure, unité de mesure, and méthode de mesure (respectively, measuring instrument, unit of measurement, and measurement method in English). In general, the usage of French word mesurage for mesure is not permissible.

In addition, the quantity of influence is not subjected to measurement, even when it affects the measurement result (e.g. the temperature of a micrometer). Quantities of influen...

Table of contents

• Cover
• Title Page
• Copyright
• Chapter 1: Fundamentals of Error Analysis and their Uncertainties in Dimensional Metrology Applied to Science and Technology
• Chapter 2: Fundamentals of Dimensional and Geometrical Tolerances According to ISO, CSA (Canada), and ANSI (USA)
• Chapter 3: Measurement and Controls Using Linear and Angular Standards
• Chapter 4: Surface Control
• Chapter 5: Opto-Mechanical Metrology
• Chapter 6: Control of Surface States
• Chapter 7: Computer-Aided Metrology-CAM
• Chapter 8: Control of Assembly and Transmission Elements
• Chapter 9: Control of Materials Hardness Testing
• Chapter 10: Overall Summary
• Glossary
• Appendix 1
• Appendix 2
• Appendix 3
• Appendix 4
• Appendix 5
• Appendix 6
• Index