Geometric tolerancing of products

Geometric Tolerancing of Products


Geometric Tolerancing
of Products

Edited by
François Villeneuve
Luc Mathieu


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,
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ISTE Ltd
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© ISTE Ltd 2010
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 1988.
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 978-1-84821-118-6
1. Tolerance (Engineering) 2. Geometry, Descriptive. I. Villeneuve, Francois, 1960- II. Mathieu, Luc,
1954TS172.G467 2010
620'.0045--dc22
2010003707
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-118-6
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.


Table of Contents

PART I. GEOMETRIC TOLERANCING ISSUES. . . . . . . . . . . . . . . . . . . . .

1

Chapter 1. Current and Future Issues in Tolerancing: the GD&T
French Research Group (TRG) Contribution. . . . . . . . . . . . . . . . . . .
Luc MATHIEU and François VILLENEUVE

3

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Presentation of the Tolerancing Resarch Group: objectives and
function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Synthesis of the approach and contributions of the group . . . .
1.3.1. Languages for geometric specification . . . . . . . . . . . . .
1.3.2. Dimension chains in 3D . . . . . . . . . . . . . . . . . . . . . .
1.3.3. Methods and tools . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.4. Manufacturing dimensioning and tolerancing . . . . . . . . .
1.3.5. Uncertainties and metrology . . . . . . . . . . . . . . . . . . .
1.4. Research perspectives . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Media examples: “centering” and “connecting rod-crank” . . . .
1.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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15
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19

PART II. GEOMETRIC TOLERANCING LANGUAGES . . . . . . . . . . . . . . . .

21

Chapter 2. Language of Tolerancing: GeoSpelling . . . . . . . . . . . . . . .
Alex BALLU, Jean-Yves DANTAN and Luc MATHIEU

23

2.1. Introduction . . . . . . . . . . . . . . . .
2.2. Concept of the GeoSpelling language
2.3. Geometric features . . . . . . . . . . .
2.3.1. Ideal features . . . . . . . . . . . .
2.3.2. Non-ideal features . . . . . . . . .
2.3.3. Limited features . . . . . . . . . . .

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vi

Geometric Tolerancing of Products

2.4. Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1. Intrinsic characteristic . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2. Situation characteristic . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3. Situation characteristic between ideal features . . . . . . . . . .
2.4.4. Situation characteristic between limited and ideal features . .
2.4.5. Situation characteristic between non-ideal and ideal features .
2.4.6. Situation characteristic between non-ideal features . . . . . . .
2.5. Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1. Operations to identify the geometric features . . . . . . . . . .
2.5.2. Evaluation operation . . . . . . . . . . . . . . . . . . . . . . . . .
2.6. Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7. Specifications on assemblies – quantifiers . . . . . . . . . . . . . .
2.8. Applications to part specification . . . . . . . . . . . . . . . . . . . .
2.9. Applications to product specifications . . . . . . . . . . . . . . . . .
2.10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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51
52

Chapter 3. Product Model for Tolerancing . . . . . . . . . . . . . . . . . . . .

Denis TEISSANDIER and Jérôme DUFAURE

55

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Objectives and stakes . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1. Cover the design cycle of the product . . . . . . . . . . . . .
3.2.2. Propose an environment of collaborative work . . . . . . .
3.2.3. Ensure the traceability of geometric specifications . . . . .
3.3. Proposal for a product model . . . . . . . . . . . . . . . . . . . .
3.3.1. History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2. General description of the IPPOP product model . . . . . .
3.3.3. Basic entities definition of the product model . . . . . . . .
3.3.4. Description of the connection links between basic entities
3.3.5. Description of the decomposition and aggregation of
basic entities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6. Correspondence between tolerancing data and product
model data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Benefits of the IPPOP product model . . . . . . . . . . . . . . .
3.4.1. Description of the transfer principle . . . . . . . . . . . . . .
3.4.2. Formalization of the geometric condition transfer activity .
3.4.3. Traceability of specifications . . . . . . . . . . . . . . . . . .
3.5. Application on the centering device . . . . . . . . . . . . . . . .
3.5.1. Description of the case studied . . . . . . . . . . . . . . . . .
3.5.2. Functional analysis of the centering device. . . . . . . . . .
3.5.3. Transfer in preliminary design (stage 1) . . . . . . . . . . .
3.5.4. Transfers in embodiment design (stages 2 and 3) . . . . . .

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Table of Contents

3.5.5. Transfer in detailed design (stage 4) . .
3.5.6. Traceability of specifications of axis 3
3.6. Conclusion . . . . . . . . . . . . . . . . . . .
3.7. Bibliography . . . . . . . . . . . . . . . . . .

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84

Chapter 4. Representation of Mechanical Assemblies and Specifications
by Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Alex BALLU, Luc MATHIEU and Olivier LEGOFF

87

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Components and joints . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1. Components, surfaces and datum features . . . . . . . . . . . . .
4.2.2. Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3. Models of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4. Models of contacts . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. The requirements, technical conditions and specifications . . . . . .
4.3.1. The requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2. Technical conditions . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3. The specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Manufacturing set-ups . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5. Displacements between situation features and associated loops . . .
4.5.1. Relative displacements . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2. The loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3. Loops with or without a coordinate system on the components .
4.6. The key elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1. The key deviations, surfaces, joints and components . . . . . . .
4.6.2. The loops and key sub-graphs . . . . . . . . . . . . . . . . . . . .
4.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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107
107
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109
110

Chapter 5. Correspondence between Data Handled by the Graphs
and Data Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Denis TEISSANDIER and Jérôme DUFAURE

111

5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Correspondence between tolerancing graphs and the product data
5.2.1. Kinematic graphs . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2. Graph of the elementary joints . . . . . . . . . . . . . . . . . . .
5.2.3. Closings of influential loops and traceability of specifications
5.3. Correspondence between manufacturing set-ups and the data
product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1. Manufacturing graph of body 1. . . . . . . . . . . . . . . . . . .
5.3.2. Manufacturing set-up 10 of the body . . . . . . . . . . . . . . .
5.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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vii

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118
118
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121

viii

Geometric Tolerancing of Products

PART III. 3D TOLERANCE STACK-UP. . . . . . . . . . . . . . . . . . . . . . . . .

123

Chapter 6. Writing the 3D Chain of Dimensions (Tolerance Stack-Up)
in Symbolic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pierre BOURDET, François THIÉBAUT and Grégory CID

125

6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. A reminder of the establishment of the unidirectional chain of
dimensions by the Δl method . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1. Definition and properties . . . . . . . . . . . . . . . . . . . . . .
6.2.2. The Δl model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3. A reminder of the Δl method . . . . . . . . . . . . . . . . . . . .
6.3. Establishment in writing of a chain of dimensions in 3D by the
method of indeterminates in the case of a rigid body . . . . . . . . . . .
6.3.1. General points . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2. Model of the indeterminates . . . . . . . . . . . . . . . . . . . .
6.3.3. Laws of geometric behavior of a mechanism with gaps and
defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.4. An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Consideration of the contact between parts in the mechanisms . .
6.4.1. General theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2. Calculation of the distance between a point and a surface . . .

6.4.3. Utilization of the distance function expressed in the symbolic
calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Mechanisms composed of flexible parts, joints without gap (or
imposed contact) and imposed effort . . . . . . . . . . . . . . . . . . . .
6.5.1. General theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2. Utilization of a coordinate system on the parts . . . . . . . . .
6.5.3. Modeling of form defects and deformations . . . . . . . . . . .
6.5.4. Integration of flexibility of the parts . . . . . . . . . . . . . . . .
6.5.5. The principle of writing an equation(s) for a mechanism
composed of a single flexible part . . . . . . . . . . . . . . . . . . . . .
6.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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148

Chapter 7. Tolerance Analysis and Synthesis, Method of Domains . . . . .
Max GIORDANO, Eric PAIREL and Serge SAMPER

151

7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. Deviation torsor and joint torsor . . . . . . . . . . . . . . . .
7.2.1. Cartesian frame linked to a surface . . . . . . . . . . . .
7.2.2. Deviation torsor . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3. Relative deviation torsor and absolute deviation torsor
7.2.4. Joint torsor, kinematic torsor and clearance torsor . . .

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152
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Table of Contents

7.3. Equations of loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1. Mechanism without clearance or deviation . . . . . . . . . . . .
7.3.2. Taking into account the clearances and deviations . . . . . . .
7.4. Deviation and clearance domains . . . . . . . . . . . . . . . . . . . .

7.4.1. Deviation domain . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.2. Clearance domain . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5. Representation and properties of the domains . . . . . . . . . . . .
7.5.1. Change of Cartesian frame . . . . . . . . . . . . . . . . . . . . .
7.5.2. Symmetry with regard to the origin . . . . . . . . . . . . . . . .
7.5.3. Representation by polytopes . . . . . . . . . . . . . . . . . . . .
7.5.4. Stacking of tolerances and sum of Minkowski . . . . . . . . . .
7.5.5. Resulting clearance domain . . . . . . . . . . . . . . . . . . . . .
7.5.6. Zone corresponding to a domain . . . . . . . . . . . . . . . . . .
7.5.7. Cases of axisymmetric systems . . . . . . . . . . . . . . . . . . .
7.6. Application to the analysis of simple chains . . . . . . . . . . . . .
7.6.1. Condition of assembly for one loop . . . . . . . . . . . . . . . .
7.6.2. Application to a chain of dimension taking angular defects
into account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.3. Application to a connecting rod-crank system . . . . . . . . . .
7.6.4. Application to the synthesis of tolerances . . . . . . . . . . . .
7.6.5. Condition of assembly, virtual state and domain . . . . . . . .
7.7. Case of assemblies with parallel joints . . . . . . . . . . . . . . . . .
7.7.1. Notion of residual clearance domain and inaccuracy domain .
7.7.2. Condition of assembly for joints in parallel . . . . . . . . . . .
7.8. Taking elastic displacements into account . . . . . . . . . . . . . . .
7.8.1. Elastic deviation and joint torsor definition . . . . . . . . . . .
7.8.2. Elastic deviation torsors . . . . . . . . . . . . . . . . . . . . . . .
7.8.3. Elastic joint torsors . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8.4. Use rate and elastic domains . . . . . . . . . . . . . . . . . . . .
7.8.5. Elastic clearance domain . . . . . . . . . . . . . . . . . . . . . .
7.8.6. Elastic deviation domains . . . . . . . . . . . . . . . . . . . . . .
7.8.7. Elastic domain duality . . . . . . . . . . . . . . . . . . . . . . . .
7.8.8. Application to a simple assembly . . . . . . . . . . . . . . . . .
7.8.9. Assembly without clearances . . . . . . . . . . . . . . . . . . . .

7.8.10. Assembly with clearances in joints . . . . . . . . . . . . . . . .
7.9. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.10. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

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180

Chapter 8. Parametric Specification of Mechanisms . . . . . . . . . . . . . .
Philippe SERRÉ, Alain RIVIÈRE and André CLÉMENT

183

8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

183


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8.2. Problem of the parametric specification of complete and consistent
dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1. Model of dimensioning . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3. Analysis of the coherence and completeness of dimensioning .
8.3. Generation of parametric tolerancing by the differential variation
of the specification of dimensioning . . . . . . . . . . . . . . . . . . . . . .
8.3.1. Generation of implicit equations of a parametric tolerancing . .

8.3.2. Case study (continuation) . . . . . . . . . . . . . . . . . . . . . . .
8.3.3. Analysis and resolution of compatibility relations . . . . . . . .
8.4. Problem of the specification transfer . . . . . . . . . . . . . . . . . . .
8.5. Expression of parametric tolerancing. . . . . . . . . . . . . . . . . . .
8.5.1. Relation between the variation intervals of specification
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.2. Interchangeability and “clearance effect” . . . . . . . . . . . . . .
8.6. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.1. Representation of parts. . . . . . . . . . . . . . . . . . . . . . . . .
8.6.2. Assembly representation. . . . . . . . . . . . . . . . . . . . . . . .
8.6.3. Generation of the equation system associated with the
mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.4. Generation of compatibility relations . . . . . . . . . . . . . . . .
8.6.5. “Clearance effect” calculation . . . . . . . . . . . . . . . . . . . .
8.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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204
205

PART IV. METHODS AND TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207

Chapter 9. CLIC: A Method for Geometrical Specification of
Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bernard ANSELMETTI

209

9.1. Introduction . . . . . . . . . . . . . . . . . . . .
9.2. Input of a tolerancing problem . . . . . . . .
9.2.1. Definition of nominal model . . . . . . .
9.2.2. External requirements . . . . . . . . . . .
9.3. Part positioning . . . . . . . . . . . . . . . . .
9.3.1. Setting up of parts . . . . . . . . . . . . .
9.3.2. Positioning tables . . . . . . . . . . . . . .
9.3.3. Selection of positioning surfaces . . . . .
9.3.4. Virtual part assembly. . . . . . . . . . . .
9.4. Tolerancing of positioning surfaces . . . . .
9.4.1. Generation of positioning requirements .
9.4.2. Generation of positioning tolerancing . .

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217

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218


Table of Contents

9.5. Generation of functional requirements . . . . . . .
9.5.1. Generation of proximity requirements . . . .
9.6. Specification synthesis . . . . . . . . . . . . . . . .
9.6.1. Principle . . . . . . . . . . . . . . . . . . . . . .
9.6.2. Simple requirement . . . . . . . . . . . . . . . .
9.6.3. Decomposition of complex requirements . . .
9.6.4. Tolerancing of the support . . . . . . . . . . .
9.7. Tolerance chain result . . . . . . . . . . . . . . . . .
9.7.1. Analysis lines method . . . . . . . . . . . . . .
9.7.2. Application . . . . . . . . . . . . . . . . . . . .
9.7.3. Statistical result . . . . . . . . . . . . . . . . . .
9.7.4. Representation in Excel ranges . . . . . . . . .
9.8. Tolerance synthesis . . . . . . . . . . . . . . . . . .
9.8.1. Variation of nominal models . . . . . . . . . .
9.8.2. Quality optimization . . . . . . . . . . . . . . .
9.8.3. Effective method for maximizing tolerances .
9.9. Conclusion . . . . . . . . . . . . . . . . . . . . . . .
9.10. Bibliography . . . . . . . . . . . . . . . . . . . . .

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238

Chapter 10. MECAmaster: a Tool for Assembly Simulation from Early
Design, Industrial Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Paul CLOZEL and Pierre-Alain RANCE

241

10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2. General principle, 3D tolerance calculation . . . . . . . . . . . . .
10.2.1. Kinematic definition of the contact. . . . . . . . . . . . . . . .
10.2.2. Calculation principle . . . . . . . . . . . . . . . . . . . . . . . .
10.2.3. “3D chains of dimension” results . . . . . . . . . . . . . . . . .
10.2.4. Tolerance definition . . . . . . . . . . . . . . . . . . . . . . . .
10.3. Application to assembly calculation . . . . . . . . . . . . . . . . .
10.3.1. Preamble: definition of surfaces playing a part in the model .
10.3.2. Model definition . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.3. Hyperstatism calculation and analysis . . . . . . . . . . . . . .
10.3.4. Possible assembly configurations. . . . . . . . . . . . . . . . .

10.3.5. Quantification of functional conditions, choice of system
architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4. From model to parts tolerancing . . . . . . . . . . . . . . . . . . . .
10.4.1. Choice of reference system . . . . . . . . . . . . . . . . . . . .
10.4.2. Connections graph . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.3. Identification of specifications: example . . . . . . . . . . . .
10.4.4. Identification of numerical values: example . . . . . . . . . .
10.5. Statistical tolerancing . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6. Industrial examples . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xii

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10.6.1. Aeronautic industry: structure . . . . . . . . . . . . . . . . . . .
10.6.2. Automotive industry: body structure assembly . . . . . . . . .
10.6.3. Automotive industry: mechanical assembly – engine group .
10.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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272

PART V. MANUFACTURING TOLERANCING . . . . . . . . . . . . . . . . . . . . .

275

Chapter 11. Geometric Manufacturing Simulation . . . . . . . . . . . . . . .
Stéphane TICHADOU and Olivier LEGOFF

277

11.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2. Modeling of manufacturing set-up . . . . . . . . . . . . . . . . . .
11.2.1. Analysis of a set-up . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.2. Modeling of a set-up . . . . . . . . . . . . . . . . . . . . . . . .
11.2.3. Chart of a set-up . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.4. Representation of a process plan . . . . . . . . . . . . . . . . .
11.3. Approaches to geometric manufacturing simulation . . . . . . . .
11.3.1. Formal approach to geometric manufacturing simulation . .
11.3.2. Geometric manufacturing simulation with the CAM system
11.3.3. Comparison of approaches. . . . . . . . . . . . . . . . . . . . .
11.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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277
279
279
281
283
286
288
288
292
301
303
303

Chapter 12. 3D Analysis and Synthesis of Manufacturing Tolerances . . .
Frédéric VIGNAT and François VILLENEUVE

305

12.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2. Manufacturing transfer, analysis and synthesis in 1D . . . . .
12.3. 3D manufacturing simulation model (MMP) . . . . . . . . . .
12.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2. The MMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4. From the manufacturing process to the MMP . . . . . . . . . .
12.4.1. Determination of the positioning deviation . . . . . . . . .
12.4.2. Determination of machining deviations . . . . . . . . . . .
12.5. 3D analysis of the functional tolerances . . . . . . . . . . . . .
12.5.1. Definition of the virtual gauge and assembly properties .
12.5.2. Numerical analysis method in the worst case scenario . .
12.6. 3D synthesis of manufacturing tolerances . . . . . . . . . . . .
12.6.1. Functional tolerance transfer by splitting the inequation
GapGP≥0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6.2. Determination of the surfaces concerned . . . . . . . . . .
12.6.3. Proposition of a group of manufacturing tolerances . . . .

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330
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Table of Contents

xiii

12.6.4. Verification of the validity of tolerances and values chosen . . . .
12.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

335
338
339

PART VI. UNCERTAINTIES AND METROLOGY . . . . . . . . . . . . . . . . . . . .

341

Chapter 13. Uncertainties in Tolerance Analysis and Specification
Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jean-Marc LINARES and Jean Michel SPRAUEL

343

13.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.2. Proposal for a statistical model of real surfaces . . . . . . . . . . . .
13.2.1. Nominal model and vector modeling . . . . . . . . . . . . . . .
13.2.2. Limits and impacts on tolerance analysis and metrology . . . .
13.2.3. Definition: signature . . . . . . . . . . . . . . . . . . . . . . . . .
13.2.4. Proposal for a limited model and modeling by random vector.
13.3. Applications in metrology . . . . . . . . . . . . . . . . . . . . . . . .
13.3.1. Independent variables and common components . . . . . . . .
13.3.2. Application on a 2D line . . . . . . . . . . . . . . . . . . . . . . .
13.3.3. Extension to ordinary surfaces . . . . . . . . . . . . . . . . . . .
13.3.4. 2D point/line distance . . . . . . . . . . . . . . . . . . . . . . . .
13.3.5. Extension to three fundamental distances . . . . . . . . . . . . .
13.3.6. Effect of the planning process of measurement . . . . . . . . .
13.4. Application to tolerance analysis . . . . . . . . . . . . . . . . . . . .
13.4.1. Review of the principle of modeling . . . . . . . . . . . . . . . .
13.4.2. Effect of the reference surface extent . . . . . . . . . . . . . . .

13.4.3. Effect of surface spacing . . . . . . . . . . . . . . . . . . . . . . .
13.4.4. Effect of shape defect on reference surfaces . . . . . . . . . . .
13.4.5. Effect of the choice of a reference system. . . . . . . . . . . . .
13.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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370
371
371
373
373
374

List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

375

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

377

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PART I

Geometric Tolerancing Issues


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.


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 2001.
1.2. 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.


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 2009.
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 1.5.
1.3. 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):


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:


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


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.
1.3.1. 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 JeanYves 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 17450-1 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


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 4.
1.3.2. 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

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.
1.3.3. 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


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.
1.3.4. 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.


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.
1.3.5. 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.


Issues in Tolerancing

13

1.4. 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


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.