Geometric Tolerancing of Products

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2 Geometric Tolerancing of Products

3 Geometric Tolerancing of Products Edited by François Villeneuve Luc Mathieu

4 First published 2010 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Adapted and updated from Tolérancement géométrique des produits published 2007 in France by Hermes Science/Lavoisier LAVOISIER 2007 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc St George s Road 111 River Street London SW19 4EU Hoboken, NJ UK USA ISTE Ltd The rights of François Villeneuve and Luc Mathieu to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act Library of Congress Cataloging-in-Publication Data Geometric tolerancing of products / edited by Francois Villeneuve, Luc Mathieu. p. cm. Includes bibliographical references and index. ISBN Tolerance (Engineering) 2. Geometry, Descriptive. I. Villeneuve, Francois, II. Mathieu, Luc, TS172.G ' dc British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.

5 Table of Contents PART I. GEOMETRIC TOLERANCING ISSUES Chapter 1. Current and Future Issues in Tolerancing: the GD&T French Research Group (TRG) Contribution... 3 Luc MATHIEU and François VILLENEUVE 1.1. Introduction Presentation of the Tolerancing Resarch Group: objectives and function Synthesis of the approach and contributions of the group Languages for geometric specification Dimension chains in 3D Methods and tools Manufacturing dimensioning and tolerancing Uncertainties and metrology Research perspectives Media examples: centering and connecting rod-crank Conclusion Bibliography PART II. GEOMETRIC TOLERANCING LANGUAGES Chapter 2. Language of Tolerancing: GeoSpelling Alex BALLU, Jean-Yves DANTAN and Luc MATHIEU 2.1. Introduction Concept of the GeoSpelling language Geometric features Ideal features Non-ideal features Limited features... 29

6 vi Geometric Tolerancing of Products 2.4. Characteristic Intrinsic characteristic Situation characteristic Situation characteristic between ideal features Situation characteristic between limited and ideal features Situation characteristic between non-ideal and ideal features Situation characteristic between non-ideal features Operations Operations to identify the geometric features Evaluation operation Conditions Specifications on assemblies quantifiers Applications to part specification Applications to product specifications Conclusion Bibliography Chapter 3. Product Model for Tolerancing Denis TEISSANDIER and Jérôme DUFAURE 3.1. Introduction Objectives and stakes Cover the design cycle of the product Propose an environment of collaborative work Ensure the traceability of geometric specifications Proposal for a product model History General description of the IPPOP product model Basic entities definition of the product model Description of the connection links between basic entities Description of the decomposition and aggregation of basic entities Correspondence between tolerancing data and product model data Benefits of the IPPOP product model Description of the transfer principle Formalization of the geometric condition transfer activity Traceability of specifications Application on the centering device Description of the case studied Functional analysis of the centering device Transfer in preliminary design (stage 1) Transfers in embodiment design (stages 2 and 3)... 77

7 Table of Contents vii Transfer in detailed design (stage 4) Traceability of specifications of axis Conclusion Bibliography Chapter 4. Representation of Mechanical Assemblies and Specifications by Graphs Alex BALLU, Luc MATHIEU and Olivier LEGOFF 4.1. Introduction Components and joints Components, surfaces and datum features Joints Models of joints Models of contacts The requirements, technical conditions and specifications The requirements Technical conditions The specifications Manufacturing set-ups Displacements between situation features and associated loops Relative displacements The loops Loops with or without a coordinate system on the components The key elements The key deviations, surfaces, joints and components The loops and key sub-graphs Conclusion Bibliography Chapter 5. Correspondence between Data Handled by the Graphs and Data Product Denis TEISSANDIER and Jérôme DUFAURE 5.1. Introduction Correspondence between tolerancing graphs and the product data Kinematic graphs Graph of the elementary joints Closings of influential loops and traceability of specifications Correspondence between manufacturing set-ups and the data product Manufacturing graph of body Manufacturing set-up 10 of the body Conclusion

8 viii Geometric Tolerancing of Products PART III. 3D TOLERANCE STACK-UP Chapter 6. Writing the 3D Chain of Dimensions (Tolerance Stack-Up) in Symbolic Expressions Pierre BOURDET, François THIÉBAUT and Grégory CID 6.1. Introduction A reminder of the establishment of the unidirectional chain of dimensions by the Δl method Definition and properties The Δl model A reminder of the Δl method Establishment in writing of a chain of dimensions in 3D by the method of indeterminates in the case of a rigid body General points Model of the indeterminates Laws of geometric behavior of a mechanism with gaps and defects An example Consideration of the contact between parts in the mechanisms General theory Calculation of the distance between a point and a surface Utilization of the distance function expressed in the symbolic calculation Mechanisms composed of flexible parts, joints without gap (or imposed contact) and imposed effort General theory Utilization of a coordinate system on the parts Modeling of form defects and deformations Integration of flexibility of the parts The principle of writing an equation(s) for a mechanism composed of a single flexible part Conclusion Bibliography Chapter 7. Tolerance Analysis and Synthesis, Method of Domains Max GIORDANO, Eric PAIREL and Serge SAMPER 7.1. Introduction Deviation torsor and joint torsor Cartesian frame linked to a surface Deviation torsor Relative deviation torsor and absolute deviation torsor Joint torsor, kinematic torsor and clearance torsor

9 Table of Contents ix 7.3. Equations of loops Mechanism without clearance or deviation Taking into account the clearances and deviations Deviation and clearance domains Deviation domain Clearance domain Representation and properties of the domains Change of Cartesian frame Symmetry with regard to the origin Representation by polytopes Stacking of tolerances and sum of Minkowski Resulting clearance domain Zone corresponding to a domain Cases of axisymmetric systems Application to the analysis of simple chains Condition of assembly for one loop Application to a chain of dimension taking angular defects into account Application to a connecting rod-crank system Application to the synthesis of tolerances Condition of assembly, virtual state and domain Case of assemblies with parallel joints Notion of residual clearance domain and inaccuracy domain Condition of assembly for joints in parallel Taking elastic displacements into account Elastic deviation and joint torsor definition Elastic deviation torsors Elastic joint torsors Use rate and elastic domains Elastic clearance domain Elastic deviation domains Elastic domain duality Application to a simple assembly Assembly without clearances Assembly with clearances in joints Conclusion Bibliography Chapter 8. Parametric Specification of Mechanisms Philippe SERRÉ, Alain RIVIÈRE and André CLÉMENT 8.1. Introduction

10 x Geometric Tolerancing of Products 8.2. Problem of the parametric specification of complete and consistent dimensioning Model of dimensioning Case study Analysis of the coherence and completeness of dimensioning Generation of parametric tolerancing by the differential variation of the specification of dimensioning Generation of implicit equations of a parametric tolerancing Case study (continuation) Analysis and resolution of compatibility relations Problem of the specification transfer Expression of parametric tolerancing Relation between the variation intervals of specification parameters Interchangeability and clearance effect Case study Representation of parts Assembly representation Generation of the equation system associated with the mechanism Generation of compatibility relations Clearance effect calculation Conclusion Bibliography PART IV. METHODS AND TOOLS Chapter 9. CLIC: A Method for Geometrical Specification of Products Bernard ANSELMETTI 9.1. Introduction Input of a tolerancing problem Definition of nominal model External requirements Part positioning Setting up of parts Positioning tables Selection of positioning surfaces Virtual part assembly Tolerancing of positioning surfaces Generation of positioning requirements Generation of positioning tolerancing

11 Table of Contents xi 9.5. Generation of functional requirements Generation of proximity requirements Specification synthesis Principle Simple requirement Decomposition of complex requirements Tolerancing of the support Tolerance chain result Analysis lines method Application Statistical result Representation in Excel ranges Tolerance synthesis Variation of nominal models Quality optimization Effective method for maximizing tolerances Conclusion Bibliography Chapter 10. MECAmaster: a Tool for Assembly Simulation from Early Design, Industrial Approach Paul CLOZEL and Pierre-Alain RANCE Introduction General principle, 3D tolerance calculation Kinematic definition of the contact Calculation principle D chains of dimension results Tolerance definition Application to assembly calculation Preamble: definition of surfaces playing a part in the model Model definition Hyperstatism calculation and analysis Possible assembly configurations Quantification of functional conditions, choice of system architecture From model to parts tolerancing Choice of reference system Connections graph Identification of specifications: example Identification of numerical values: example Statistical tolerancing Industrial examples

12 xii Geometric Tolerancing of Products Aeronautic industry: structure Automotive industry: body structure assembly Automotive industry: mechanical assembly engine group Conclusion Bibliography PART V. MANUFACTURING TOLERANCING Chapter 11. Geometric Manufacturing Simulation Stéphane TICHADOU and Olivier LEGOFF Introduction Modeling of manufacturing set-up Analysis of a set-up Modeling of a set-up Chart of a set-up Representation of a process plan Approaches to geometric manufacturing simulation Formal approach to geometric manufacturing simulation Geometric manufacturing simulation with the CAM system Comparison of approaches Conclusion Bibliography Chapter 12. 3D Analysis and Synthesis of Manufacturing Tolerances Frédéric VIGNAT and François VILLENEUVE Introduction Manufacturing transfer, analysis and synthesis in 1D D manufacturing simulation model (MMP) Introduction The MMP From the manufacturing process to the MMP Determination of the positioning deviation Determination of machining deviations D analysis of the functional tolerances Definition of the virtual gauge and assembly properties Numerical analysis method in the worst case scenario D synthesis of manufacturing tolerances Functional tolerance transfer by splitting the inequation GapGP Determination of the surfaces concerned Proposition of a group of manufacturing tolerances

13 Table of Contents xiii Verification of the validity of tolerances and values chosen Conclusion Bibliography PART VI. UNCERTAINTIES AND METROLOGY Chapter 13. Uncertainties in Tolerance Analysis and Specification Checking Jean-Marc LINARES and Jean Michel SPRAUEL Introduction Proposal for a statistical model of real surfaces Nominal model and vector modeling Limits and impacts on tolerance analysis and metrology Definition: signature Proposal for a limited model and modeling by random vector Applications in metrology Independent variables and common components Application on a 2D line Extension to ordinary surfaces D point/line distance Extension to three fundamental distances Effect of the planning process of measurement Application to tolerance analysis Review of the principle of modeling Effect of the reference surface extent Effect of surface spacing Effect of shape defect on reference surfaces Effect of the choice of a reference system Conclusion Bibliography List of Authors Index

14 PART I Geometric Tolerancing Issues

15 Chapter 1 Current and Future Issues in Tolerancing: the GD&T French Research Group (TRG) Contribution 1.1. Introduction This book, entitled Geometric Tolerancing of Products, shows that especially in France a wealth of research work exists in this domain. This work highlights some difficult scientific stumbling blocks, the removal of which is of great importance in pursuing innovation in the development of industrial products. For many years this work has appeared limited, in terms of its response to specific problems concerning the different jobs in engineering (design, manufacturing methods, assembly methods, production and control). It is now, however, moving in new directions in the control of product/process integration, helping towards the development of the PLM (product life-cycle management) concept in companies. Even though the geometric performance of the means of production has progressed enormously over recent decades, geometric variations in the manufactured products exist and probably always will. Certainly the geometric defects observed have diminished in size but they are always there and play an important role in the quality and cost of products. Mastering these geometric variations throughout the product life cycle remains an undeniable performance Chapter written by Luc MATHIEU and François VILLENEUVE. Geometric Tolerancing of Products Edited by François Villeneuve and Luc Mathieu 2010 ISTE Ltd. Published 2010 by ISTE Ltd.

16 4 Geometric Tolerancing of Products factor for companies. Moreover, in the virtual and simulation era, it is no longer sufficient to design numerical models in CAD representing an ideal geometry. It is becoming increasingly crucial to make a realistic simulation of all of the behaviors, products, manufacturing, assembly, disassembly and control processes, and each of these in 3D. Finally, no model can be validated without being used in a real situation. The important recent developments in dimensional metrology, as much in mechanics as in optics, must also be employed in order to identify the parameters causing the deviations generated by manufacturing processes. These new challenges for the industrial world have greatly encouraged research into tolerancing and this activity is not new. It was initiated in France in the 1970s in the ENS de Cachan, by Professors Pierre Bourdet and André Clément, among others. Their work revealed research areas to others, thus leading to the creation of research groups across the whole country. The aim of this book is not only to propose a synthesis of the most recent research results of the different French research teams today, but also to offer a shared vision of examples in common resulting from a regular exchange of views that have animated meetings of the Tolerancing Research Group (TRG) since Presentation of the Tolerancing Resarch Group: objectives and function The first discussions about the creation of the Tolerancing Research Group (TRG) go back to April 2001 at the AIP-Priméca Colloquium, which takes place every two years at La Plagne. The TRG was officially created on April 24, 2001 at the Ecole Normale Supérieure of Cachan, during a work meeting on the occasion of the international seminar on computer-aided tolerancing of the International Academy for Production Engineering (CIRP). François Villeneuve from UJF Grenoble, University of Grenoble, and Luc Mathieu from CNAM Paris created this group, which they head to this day. One of the motivations for the creation of the TRG was the increasing interest in geometric tolerance and verification, or in other terms for tolerancing and measurement, as much in the research milieu as in the industrial one. This is in contrast to the fact that French research into tolerancing is particularly active all over the country. The first observations on this theme are that it: concerns an increasing number of research teams; reveals some difficult problems that are still poorly resolved; is the object of increasing demand for modeling by the industry; generates few tools in the systems assisted by computer (XAO); is the object of an international standardization, which is being restructured; is particularly well suited to PLM.

17 Issues in Tolerancing 5 The ambition of the TRG is to unite French research in the domain of tolerancing in these industrial and fundamental applications. These objectives consist of: comparing points of view on common scientific problems; exchanging solutions; bringing forward new research themes to respond to the needs of industry and others; promoting research into tolerancing and dimensional metrology in France; developing research in Europe and defending a certain French school; taking the responses proposed to the problems of tolerancing and metrology known to the industry; proposing solutions to the normalization organizations; producing collected written work in this domain, to respond to the diverse expectations of young researchers, industrialists, teachers and students. The TRG brings together 10 laboratories and about 30 experienced researchers. Since its creation, the group has worked on very specific subjects, prepared and presented in the framework of a predefined agenda, in order to profit fully from the in-depth exchanges and with a high level of science. Eighteen seminars over two days were organized: Lyon June 2001; Aix en Provence October 2001; Annecy March 2002; Bordeaux June 2002; Grenoble November 2002; Cachan March 2003; Metz November 2003; Annecy May 2004; St Ouen November 2004; Nantes May 2005; Grenoble November 2005; St Ouen May 2006; Aix November 2006; Cachan May 2007; St Ouen May 2008; Nantes November 2008; Bordeaux May 2009; and Metz November Minutes were taken for each meeting. The extent of this work led us to write this book: a synthesis of the knowledge mastered by researchers in the group and also a support for future research work. The method of work over the last nine years, where we have compared our opinions while working on case studies in common, has additionally enabled us to provide supportive homogenous examples throughout the different chapters of this book. These examples are presented in section Synthesis of the approach and contributions of the group Without trying to be exhaustive, the chapters of this book reflect the present state of knowledge and research in tolerancing in France. The domains of activity and research in tolerancing can be resumed thus (see Figures 1.1 and 1.2):

18 6 Geometric Tolerancing of Products The specification of products. This domain tries to define some geometric models for products with defects with the goal of building an unequivocal language of expression of the accepted limits for all people concerned by the control of geometric variations. This work is generally carried out in order to better structure the current standards and exchange language between XAO systems. The second facet of this activity is the determination of the assembly and part tolerances, starting from the conditions of aptitude for use, which can be expressed by functional requirements on the product. It also aims to determine the manufacturing specifications from the functional specifications of the components. This activity is called tolerance synthesis, or qualitative synthesis. Figure 1.1. Activity domains and research into tolerancing The simulation of the geometric behavior of assemblies with defects. This domain concerns the research into models of tolerance transfer, the optimization of methods and tools for an analysis of the geometric deviations and their consequences. Two types of problems are considered. First the direct problem if we study the consequences of the values of defects influencing the tolerance (tolerance analysis). Second, the inverse problem if we examine the distribution of the required value on influential components (quantitative tolerance synthesis). These tools generally have three objectives:

19 Issues in Tolerancing 7 - to simulate the possibility of assembling the product by evaluating the consequences of deviations of the components on the product and robustness of the assembly; - to simulate how the product functions under normal conditions of use to determine its aptitude for application; - to simulate the manufacturing process to verify the feasibility of the functional tolerances, and determine the control tolerances. The verification of the specifications or metrology. This research domain consists of finding the measurement equipment and algorithms for controlling and setting manufacturing and assembly equipment. It is important for the declaration of product conformity with respect to specifications in agreement with current standards, and for the validation of simulation models. This measurement equipment and algorithms must give accurate information on the real product situation associated with its uncertainties. Figure 1.2. Research branches into tolerancing and metrology domains

20 8 Geometric Tolerancing of Products The different branches of research in the domains of tolerancing are shown in Figure 1.2. This graph is inspired by the work of François Villeneuve and Frédéric Vignat in the PhD thesis of the latter [VIG 05]. It succinctly presents the contributions of the authors of this book, where the numbers in this figure indicate the chapters concerned Languages for geometric specification The second part of this book presents research into the language of geometric specification. It is necessary to talk of languages in the largest sense, because in the four chapters the following approaches are covered: first, GeoSpelling; second, the basis of future propositions in terms of international standards (ISO); third, the aspects of the product model for tolerancing; fourth, with the view to PLM and finally, the specifications using graphs. GeoSpelling (Chapter 2) is an answer to the need for an unequivocal language addressing the specification and verification of the products. Furthermore, it is important that it is unified for the macro- and micro-geometry of isolated parts and assemblies using the concepts of specification by dimension and by zone. This comes from the research work essentially led by Alex Ballu, Luc Mathieu and Jean- Yves Dantan. It was presented by French experts and adopted by the ISO GPS (International Organization for Standardization Geometric Products Specification) technical committee. In 2005, it was the subject of the ISO/TS document [ISO 05] The two important points of this model are, first, a model of parts with defects called the skin model, and second, a declarative approach to explicitly describe the quantity that is subject to tolerance or measure. Chapter 3 proposes a product model used on a data structure permitting the management of data useful for tools of dimension chains. It comes from the work on the IPPOP (Product Integration, Process and Organization for the amelioration of Performance in engineering) project, an exploratory project recognized by the National Network of Software Technologies. This project ran from December 2001 to June 2005, and the authors of this chapter participated in it. Its principle objective is to propose a collaborative work environment where the different jobs in the product life cycle can intervene in the tolerancing process. This environment must ensure the traceability of tolerances, and in particular for all transfers from initial functional requirements to disassembly at the end of the product s life, passing

21 Issues in Tolerancing 9 through the stages of manufacture and component inspection. This chapter is based on the research work of Jérôme Dufaure and Denis Teissandier. The representation of the mechanical assemblies and tolerances by graphs (see Chapter 4) aims at modeling the mechanism structure, links, functions, requirements and tolerances. It visualizes the mechanism cycles used to write the loop-closing equations for the displacements and also allows the representation of key cycles. A representation tool based on graphs was therefore proposed and synthesized by Alex Ballu, Luc Mathieu and Olivier Legoff. This chapter is emblematic of the work of the TRG, because it involves the work of a large part of the group, which has led to a shared notation. Other, slightly different graphs also appear in other chapters of this book, as it is very difficult to converge on a unique notation with consensus. The concepts evoked in Chapter 4 reflect the rich and animated collective work. Chapter 5 shows the relations that exist between the product model and the data manipulated by the graphs proposed in Chapter Dimension chains in 3D The third part of this book approaches the problem of the dimension chains in 3D. This expression is retained in this work because it is familiar to technologists (even though we would prefer to call it the transfer of specifications, tolerance analysis and synthesis). This part deals with the simulation of geometric deviations on the mountability of components in assembly and with respect to functional requirements. Rigid and non-rigid parts are considered. Three contributions cover the historical approach of the group in this domain. They share the characteristic of considering the problem of tolerance transfer from a 3D point of view when industrial and academic practices are still 1D. Chapter 6 covers the work initiated by Pierre Bourdet and Eric Ballot, which was further developed by François Thiébaut and Grégory Cid. It proposes the method of indeterminates, a 3D generalization of the Δl method, to establish in formal mathematical expressions the chains of minimal 3D dimensions permitting the correct functioning of a mechanism composed of rigid parts with deviations. This formal approach allows the systematic analysis of functional or assembly conditions. The small displacement torsor is the mathematical tool that subtends this method. The method of indeterminates can be extended to the case of an assembly of flexible parts submitted to effort or imposed displacements at the points of a mesh. The mathematical tools presented in this chapter are used again, at least in part, in Chapter 7, analyzing the approaches by domains, Chapter 10, presenting the tool MECAmaster, and Chapters 11 and 12, examining 3D tolerancing in

22 10 Geometric Tolerancing of Products manufacturing. As the small displacement torsor tool was originally developed for metrology in 3D, we have a good example of coherent models for PLM here. The method of tolerance analysis and synthesis in 3D, i.e. the domains presented in Chapter 7, is based on a similar model to that of the previous chapter. This chapter is the synthesis of a work initiated by Max Giordano, later associated with Eric Pairel and Serge Samper. Only the intrinsic deviations of the surfaces and position and orientation of the surfaces with respect to each other are modeled and quantified in the form of a small displacement torsor called the deviation torsor. The gap in the link is expressed in the form of the gap torsor. The loop relations coming from assembly of the parts are constrained by the inequations applied to the gap and deviation torsor components. All of the values of these components together constitute a domain in the space of small displacements. In the same way, for a link with a gap, we define a domain of displacements allowed by the gap. Relating the gap domains and deviation domains enables the analysis and synthesis of tolerances. Chapter 8 covers the notion of tolerance transfer from a parametric point of view, i.e. with a vectorial parametric transformation of the surfaces and links of a mechanism. The deviations of the mechanism are seen as a variation of the characteristic parameters of each link, which are different to the two former chapters where the surface deviations are limited by tolerance zones. The method currently being developed by Philippe Serré, based on the continuity of the work of André Clément and Alain Rivière, permits us to verify that the parametric tolerance of the dimensioning is complete and coherent, and give the compatibility relations (always in the case of a closed loop ) of the mechanism. We then show how this method enables the designer to determine the minimum gap necessary, knowing that in the majority of cases these are the gaps of the mechanism judiciously chosen to enable the relations of compatibility to be realized. The three chapters in this part are based on the general concept of dimension transfer, which has been the subject of numerous exchanges within the TRG Methods and tools The fourth part of this book presents some methodologies and associated computing tools, which constitute the first operational answers for 3D tolerancing. The method of CLIC tolerancing (dimensioning in location with the influence of contacts) presented in Chapter 9, was developed by Bernard Anselmetti. At the stage of detailed design, it allows the functional tolerancing of mechanisms

23 Issues in Tolerancing 11 completely defined and composed of rigid parts. The specifications are expressed directly with the ISO GPS standards in four main steps: synthesis of the requirements ensuring the mountability and functioning of the mechanism; qualitative synthesis of the functional specifications to be added to drawings in order to respect a given requirement; tolerance analysis by calculation of the resultant of part defects on the requirement studied; and finally quantitative synthesis of the tolerances with an objective function of minimum cost. Chapter 10 presents the MECAmaster tool developed by Paul Clozel. This tool, now connected to the CAO CATIA software, enables a kinematic simulation of any unconstrained 3D mechanical assembly from the definition of the product by surface or link. This simulation shows the influence that specific tolerances of the parts and assemblies have on the chosen functional conditions, and vice versa. Then, the definition for the different contacts, tolerance values, 3D position, 3D orientation and interfaces permits the evaluation of the chosen functional conditions. The conceptual basis of this tool relies on modeling the small displacement torsors of the mechanism. It is particularly interesting for determining the influence of each mechanism link at an early design step Manufacturing dimensioning and tolerancing The fifth part of this work focuses on the manufacturing stage of the product life cycle. The approaches to manufacturing simulation and transfer of functional tolerances to the manufacturing tolerances are traditionally 1D. The objective of the two chapters in this part are to show, on the one hand the necessity of envisaging the problem in 3D, and on the other, to show which models can be used to resolve the problem. Chapter 11, written by Stéphane Tichadou and Olivier Legoff, discusses the modeling of a machining process and the process plan by its representation in the form of a graph and a description of both the manufacturing and positioning geometric deviations. They use an approach based on the small displacement torsor. A simulation of the manufacturing process plan is then proposed to analyze whether this plan permits the functional tolerances of the components to be respected. Two approaches are proposed. The first is based on a formal calculation, which will be developed in the analysis and synthesis in Chapter 12. The second uses a CAM tool to measure the parts produced virtually with the simulated deviations.

24 12 Geometric Tolerancing of Products Chapter 12 draws on the essential parts of Frédéric Vignat s thesis, developed from the model of indeterminates (described in Chapter 6 for mechanisms) and extended to part manufacturing by François Villeneuve. From a synthesis of the two 1D approaches tested for the transfer to manufacturing tolerance, i.e. the Δl method and rational method, the 3D approach to manufacturing tolerance has been developed. This approach is based on the MMP (model of manufactured part), which permits an analysis of the functional tolerances and qualitative and quantitative synthesis of the manufacturing tolerances in the form of inequations or ISO standards. Contrary to the majority of approaches in the literature in this domain, an MMP approach allows, without ambiguity, the determination of surfaces and stages implicated in respect to a functional tolerance and the 3D mathematical expression of the transfer function. In addition, it presents the advantage of implementing a similar model to that used for the mechanisms presented in Chapter 6 of this book. This creates continuity in coherent modeling all along the product lifecycle in terms of deviations and tolerancing Uncertainties and metrology The sixth and last part of this book focuses on the concept of uncertainty. Uncertainty is inherent in any problem of tolerancing, either in the specification or in the measurement phase. Metrologists know that a result of measurement cannot be given without uncertainty, but few methods are available to integrate this knowledge. Moreover, very few works exist that enable us to predict the uncertainty generated by a set of functional specifications. Chapter 13 of this book provides a promising vision of these concepts applied to the field of three-dimensional metrology and to tolerancing. The work of Jean-Marc Linares and Jean-Michel Sprauel presents a new geometry modeling approach where the uncertain nature of the metrology and specification models is taken into account by using the notion of random vectors to describe the associated surfaces. The first and second central moments of these random vectors provide additional information on the geometry. This modeling takes the area of the surfaces and their form defects into account. The graphical representation of the second central moments allows us to implement the concept of a statistical limit envelope to the usual geometric elements: point, line and plane. The propagation of uncertainties by using variance/covariance matrices allows us to take the effect of the position and orientation of the estimated data into account to determine their uncertainty. 3D metrology is the main experimental field in this approach.

25 Issues in Tolerancing Research perspectives The contributions of the French community in the area of tolerancing are measurable by the interest and research they generate with foreign researchers. The following key results are subject of new studies: modeling of geometrical deviation by using small displacement torsor for design, manufacturing or measurement; modeling the nominal geometry by the technologically and topologically related surfaces; three-dimensional tolerance stack-up using domains and expression of the tolerances; and the measurement processes using the GeoSpelling model. These works, even if their applications contribute to meeting the expectations of industrials, do not meet all of the new challenges that the designing and manufacturing products face. Communication throughout the world, the overall vision of geometrical deviations all along the PLM, the control of uncertainties, the cost/tolerancing links, the virtual reality, and the identification of deviation parameters are the main objectives of future research. Tolerance communication remains a real difficulty and restrains product development. Exchanges across international boundaries and due to globalization have amplified the problem. The limits of the standardized graphical language and slow progress in the evolution of standards do not allow us to imagine there will be an answer in the short term. Although GeoSpelling offers a solution to the univocal expression of any type of specification, this language remains barely affordable to participants in the product life cycle. On the basis of new information technologies, new communication solutions have to be considered. Also, for a better control of geometrical deviations from the preliminary design, built-in methods have to be developed. They have to provide designers with ways to simply assess the robustness of their solutions. The tolerancing tools must coexist with those of geometrical modeling to assess the mechanism behaviors, as is done in the structural analysis domain for example. The 3D simulation of geometrical deviations in design, manufacturing, assembly and metrology requires complete and consistent models. Complete and consistent models meet the need for quality control all along the product life cycle and meet the rise of virtual reality requirements. The rise in virtual reality requirements is coming from globalization (the geographical dispersion of engineers). Modeling deviations and clearances with the small displacement torsor provides an interesting solution to study assemblies simulating manufacturing and metrology. However, current approaches remain deterministic and require a transfer from the standardized tolerances. On the basis of this model, work must be carried out that considers statistical analysis and synthesis approaches and other means of expressing tolerances. Parametric modeling of nominal geometry and deviations offers an alternative to the need for a complete and consistent model for the different

26 14 Geometric Tolerancing of Products engineering activities. Here again, the statistical simulation and tolerances expression must be processed to provide the solutions expected by industry. The identification of defect parameters on the means of production (manufacturing, assembly, etc.) is obviously linked to the development of simulation models. The progresses in measuring means on parts or in situ have to be exploited to develop new identification methods that are sophisticated enough for research or pragmatic and rapid for industry. Associating models and identifying parameters opens up a new branch of research on corrective actions on production means according to the defects. Metrology of geometrical deviations on the parts and on assemblies calls for unified treatment procedures and methods for the calculation of uncertainties. The current 3D measurement approaches provide, for a given specification, results that vary too much and are strongly dependent on the operators. As long as there are no reference methods and evaluation of uncertainties associated with tolerancing, it will be difficult to make good decisions on the quality of products and easily control the settings of the means of production. To help provide better control of geometric changes in a deformable structure, means of measuring must be better integrated into assembly units. Models and methods must be developed to determine where the measures need to be taken, where parts need to be supported, and where the linkages between parts need to be put. These industrial problems reveal scientific deadlocks in the field of uncertainties, which require us to completely rewrite the often implicit assumptions of the current models. Economic management of tolerances is also a fundamental aspect of future research. Tolerancing all the functional requirements to control functional aspects and production requirements to better control the means of production leads to a huge number of specifications that are incomprehensible to users and economically unacceptable to industry. In an integrated approach, it is necessary to prioritize characteristics, taking into account the risks and costs. Links must be established in a continuous manner between the functions and the customers feedback to optimize the tolerance allocations and to keep track of choices. These problems lead us to explore the scientific areas of optimization and, especially, multicriteria optimization. The following section introduces media that have supported discussions and exchanges within the TRG.

27 Issues in Tolerancing Media examples: centering and connecting rod-crank In this book, except when needed, most examples examined will be based on the example in Figure 1.3. This example has supported the debates conducted and ideas that have come up within the TRG. It is a centering that is intended to be placed in a modular fixture for machining work pieces. The top of the nozzle is considered as one of the three small supports contributing to the planed support of the work piece to be machined. The tapered portion of the axis allows the work piece to be centered by way of a conical hole. The axial mobility of the axis compensates for the dimensional variations of the hole in the casting. Two configurations are envisaged: a so-called free state, which is the state of centering before the setting the work piece; the other a so-called loaded state, that represents the system when it is in service and a work piece is clamped. The proposed detailed design defines three main parts called the axis, nozzle and body. Centering Workpiece Punctual supports free 2 Configurations loaded Workpiece clamped Axis Nozzle 4 vis CHC M4 Body Fixture Elements Clamping Module Figure 1.3. Centering in situ. A clamped work piece is inserted in a modular fixture The functional analysis of the fixture has generated some functional requirements for the centering. We list some requirements below for the loaded or free configuration: the system radially sets the work piece relative to the fixture; the system axially sets the work piece relative to the fixture; the positioning must be ensured despite the dimensional changes in the work piece;

28 16 Geometric Tolerancing of Products the tapered portion of the axis must go over the top of the nozzle; the useful pressure (or force) to move the axis has to remain lower than a given limit; the body should not interfere with the lower plate; in free configuration, the system must be easily accessible, and it must not hold up the positioning of the work piece. The proposed design also generates a number of assembly requirements that we outline here: fitting requirement body/nozzle, body/axis, body/support, axis/nozzle; proper functioning of the screw fastener; enough space must remain between the bottom of the body and the end of the axis for the compression spring. We can represent these requirements in the form of pseudo ISO tolerances (see Figure 1.4) A B E A Free configuration B M only 0 A B 0.04 A B 0.3 A B Configuration in charge ø0.15 A ± 0.02 A ø8 3 mini 3 mini 3 D ø8 0.3 D Figure 1.4. Pseudo ISO tolerances used to represent requirements A second classic example is used in several chapters in this book. It is a connecting rod-crank system, presented in Figure 1.5. This mechanism is composed of four parts: a cylinder block, a crankshaft, a connecting rod and a piston. Compared to the cylinder block, turning the crankshaft moves the connecting rod, which itself animates the piston with a movement of alternative translation.

29 Issues in Tolerancing 17 Figure 1.5. The connecting rod-crank mechanism studied To simplify the study and without losing its generality, the four parts of this mechanism have been modeled in a simplified way. For each part, a vector and a point are associated to the two cylinders and a bipoint establishes the connection between these two cylinders. As is indicated in Figure 1.6, each part is represented by three unit vectors and four setting specifications: a length and three angles Conclusion This book represents the first concrete step by the TRG members to share and debate in-depth the scientific problems of tolerancing in order to show and explain what is at stake for the scientific community. This book equally aims to present the successful results of this research to industrialists, whose problems are the driving force behind our work. The models, methods and tools presented in the following chapters constitute a country-wide synthesis of the principle results produced by the 10 laboratories involved in the TRG. The solutions proposed have been enriched by the exchanges and discussions of the group. Our greatest hope is that this book will help the work of new researchers in this domain and also awaken the curiosity of people from industry towards the implementation of new approaches.

30 18 Geometric Tolerancing of Products Distance: ACB C Angle: α C1 Angle: α C2 Angle: α C3 CYLINDER BLOCK Distance: EBF B Angle: α B1 Angle: α B2 Angle: α B3 CONNECTING ROD Distance: CVD Angle: α V1 Angle: α V 2 Angle: α V 3 CRANKSHAFT V PISTON Distance: GPH P Angle: α P1 Angle: α P2 Angle: α P3 Figure 1.6. Parameter set-up of the connecting rod-crank example

31 Issues in Tolerancing 19 This work is evidently not yet finished. Section 1.4 of this chapter offers a range of new research areas aimed at economic mastery of the geometric variations all along the product life cycle. The next objective of the TRG resides in the framework of a national research project in tolerancing and metrology, mobilizing different research groups all over the country to remove some of the scientific stumbling blocks identified and, at the same time, respond to the expectations of industry Bibliography [ISO 05] ISO/TS, Geometric Product Specification (GPS) General Concepts Part 1: Model for Geometrical Specification and Verification, ISO/TS , ISO, 2005.