Geometric Tolerancing of Products

François Villeneuve, University of Grenoble, France.Luc Mathieu, University Paris-Sud 11, France.

• PART I. GEOMETRIC TOLERANCING ISSUES 1 Chapter 1. Current and Future Issues in Tolerancing: the GD&T French Research Group (TRG) Contribution 3Luc MATHIEU and François VILLENEUVE1.1. Introduction 31.2. Presentation of the Tolerancing Resarch Group: objectives and function 41.3. Synthesis of the approach and contributions of the group 51.4. Research perspectives 131.5. Media examples: “centering” and “connecting rod-crank”151.6. Conclusion 171.7. Bibliography 19PART II. GEOMETRIC TOLERANCING LANGUAGES 21Chapter 2. Language of Tolerancing: GeoSpelling 23Alex BALLU, Jean-Yves DANTAN and Luc MATHIEU2.1. Introduction 232.2. Concept of the GeoSpelling language 242.3. Geometric features 262.4. Characteristic 292.5. Operations 382.6. Conditions 432.7. Specifications on assemblies – quantifiers 442.8. Applications to part specification 452.9. Applications to product specifications 482.10. Conclusion 512.11. Bibliography 52Chapter 3. Product Model for Tolerancing 55Denis TEISSANDIER and Jérôme DUFAURE3.1. Introduction 553.2. Objectives and stakes 563.3. Proposal for a product model 583.4. Benefits of the IPPOP product model 683.5. Application on the centering device 733.6. Conclusion 843.7. Bibliography 84Chapter 4. Representation of Mechanical Assemblies and Specifications by Graphs 87Alex BALLU, Luc MATHIEU and Olivier LEGOFF4.1. Introduction 874.2. Components and joints 894.3. The requirements, technical conditions and specifications 974.4. Manufacturing set-ups 1004.5. Displacements between situation features and associated loops1034.6. The key elements 1074.7. Conclusion 1094.8. Bibliography 110Chapter 5. Correspondence between Data Handled by the Graphs and Data Product 111Denis TEISSANDIER and Jérôme DUFAURE5.1. Introduction 1115.2. Correspondence between tolerancing graphs and the product data 1125.3. Correspondence between manufacturing set-ups and the data product 1185.4. Conclusion 121PART III. 3D TOLERANCE STACK-UP 123Chapter 6. Writing the 3D Chain of Dimensions (Tolerance Stack-Up) in Symbolic Expressions 125Pierre BOURDET, François THIÉBAUT and Grégory CID6.1. Introduction 1256.2. A reminder of the establishment of the unidirectional chain of dimensions by the ∆l method 1266.3. Establishment in writing of a chain of dimensions in 3D by the method of indeterminates in the case of a rigid body 1356.4. Consideration of the contact between parts in the mechanisms 1426.5. Mechanisms composed of flexible parts, joints without gap (or imposed contact) and imposed effort 1446.6. Conclusion 1476.7. Bibliography 148Chapter 7. Tolerance Analysis and Synthesis, Method of Domains 151Max GIORDANO, Eric PAIREL and Serge SAMPER7.1. Introduction 1517.2. Deviation torsor and joint torsor 1527.3. Equations of loops 1557.4. Deviation and clearance domains 1587.5. Representation and properties of the domains 1627.6. Application to the analysis of simple chains 1687.7. Case of assemblies with parallel joints 1737.8. Taking elastic displacements into account 1767.9. Conclusion 1807.10. Bibliography 180Chapter 8. Parametric Specification of Mechanisms 183Philippe SERRÉ, Alain RIVIÈRE and André CLÉMENT8.1. Introduction 1838.2. Problem of the parametric specification of complete and consistent dimensioning 1848.3. Generation of parametric tolerancing by the differential variation of the specification of dimensioning 1888.4. Problem of the specification transfer 1928.5. Expression of parametric tolerancing 1938.6. Case study 1988.7. Conclusion 2048.8. Bibliography 205PART IV. METHODS AND TOOLS 207Chapter 9. CLIC: A Method for Geometrical Specification of Products 209Bernard ANSELMETTI9.1. Introduction 2099.2. Input of a tolerancing problem 2109.3. Part positioning 2129.4. Tolerancing of positioning surfaces 2179.5. Generation of functional requirements 2219.6. Specification synthesis 2229.7. Tolerance chain result 2279.8. Tolerance synthesis 2349.9. Conclusion 2389.10. Bibliography 238Chapter 10. MECAmaster: a Tool for Assembly Simulation from Early Design, Industrial Approach 241Paul CLOZEL and Pierre-Alain RANCE10.1. Introduction 24110.2. General principle, 3D tolerance calculation 24210.3. Application to assembly calculation 24510.4. From model to parts tolerancing 26310.5. Statistical tolerancing 26810.6. Industrial examples 26910.7. Conclusion 27110.8. Bibliography 272PART V. MANUFACTURING TOLERANCING 275Chapter 11. Geometric Manufacturing Simulation 277Stéphane TICHADOU and Olivier LEGOFF11.1. Introduction 27711.2. Modeling of manufacturing set-up 27911.3. Approaches to geometric manufacturing simulation 28811.4. Conclusion 30311.5. Bibliography 303Chapter 12. 3D Analysis and Synthesis of Manufacturing Tolerances 305Frédéric VIGNAT and François VILLENEUVE12.1. Introduction 30512.2. Manufacturing transfer, analysis and synthesis in 1D 30612.3. 3D manufacturing simulation model (MMP) 31412.4. From the manufacturing process to the MMP 31712.5. 3D analysis of the functional tolerances 32312.6. 3D synthesis of manufacturing tolerances 32912.7. Conclusion 33812.8. Bibliography 339PART VI. UNCERTAINTIES AND METROLOGY 341Chapter 13. Uncertainties in Tolerance Analysis and Specification Checking 343Jean-Marc LINARES and Jean Michel SPRAUEL13.1. Introduction 34313.2. Proposal for a statistical model of real surfaces 34313.3. Applications in metrology 35413.4. Application to tolerance analysis 36713.5. Conclusion 37313.6. Bibliography 374List of Authors 375Index 377