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Geometric Tolerance Analysis

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Geometric Tolerances

Abstract

This chapter focuses on five main literature models of geometric tolerance analysis – vector loop, variational, matrix, Jacobian, and torsor – and makes a comparison between them in order to highlight the advantages and the weaknesses of each, with the goal of providing a criterion for selecting the most suitable one, depending on the application. The comparison is done at two levels: the first is qualitative and is based on the analysis of the models according to a set of descriptors derived from what is available in the literature; the second is quantitative and is based on a case study which is solved by means of the five models. Finally, in addition to providing comparative insight into the five tolerance analysis models, some guidelines are provided as well, related to the development of a novel approach which is aimed at overcoming some of the limitations of those models.

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References

  • ASME Y14.5M (1994) Dimensioning and tolerancing. American Society of Mechanical Engineering, New York

    Google Scholar 

  • Ballot E, Bourdet P (1995) Geometrical behaviour laws for computer aided tolerancing. In: Proceedings of the 4th CIRP seminar on computer aided tolerancing, University of Tokyo, April 1995

    Google Scholar 

  • Ballot E, Bourdet P (1997) A computational method for the consequences of geometric errors in mechanisms. In: Proceedings of the 5th CIRP seminar on computer aided tolerancing, Toronto, 27–29 April 1997

    Google Scholar 

  • Berman YO (2005) Shape and position uncertainty in mechanical assembly. PhD thesis, The Hebrew University, Jerusalem

    Google Scholar 

  • Boyer M, Stewart NF (1991) Modeling spaces for toleranced objects. Int J Robot Res 10:470–582

    Article  Google Scholar 

  • Chase KW (1999) Multi-dimensional tolerance analysis (automated method). In: Drake PJR (ed) Dimensioning and tolerancing handbook. McGraw-Hill, New York

    Google Scholar 

  • Chase KW, Gao J, Magleby SP (1995) General 2-D tolerance analysis of mechanical assemblies with small kinematic adjustments. J Des Manuf 5:263–274

    Google Scholar 

  • Chase KW, Gao J, Magleby SP et al (1996) Including geometric feature variations in tolerance analysis of mechanical assemblies. IIE Trans 28:795–807

    Google Scholar 

  • Chase KW, Gao J, Magleby SP (1997) Tolerance analysis of 2- and 3D mechanical assemblies with small kinematic adjustments. In: Zhang HC (ed) Advanced tolerancing techniques. Wiley, New York

    Google Scholar 

  • Clément A, Rivière A, Temmerman M (1994) Cotation tridimensionelle des systèmes mécaniques, théorie & pratique. Cachan, France

    Google Scholar 

  • Clément A, Riviére A, Serré P et al (1998) The TTRSs: 13 constraints for dimensioning and tolerancing. In: ElMaraghy HA (ed) Geometric design tolerancing: theories, standards and applications. Chapman & Hall, London

    Google Scholar 

  • Delchambre A (1996) CAD method for industrial assembly. Concurrent design of product, equipment and control systems. Wiley, New York

    Google Scholar 

  • Desrochers A, Rivière A (1997) A matrix approach to the representation of tolerance zones and clearances. Int J Adv Manuf Technol 13:630–636

    Article  Google Scholar 

  • Desrochers A, Ghie W, Laperrière L (2003) Application of a unified Jacobian-torsor model for tolerance analysis. J Comput Inf Sci Eng 3:2–14

    Article  Google Scholar 

  • Faerber PJ (1999) Tolerance analysis of assemblies using kinematically derived sensitivities. ADCATS report no. 99-3. http://adcats.et.byu.edu/reportsandpublications.php

    Google Scholar 

  • Gao J, Chase KW, Magleby SP (1998) Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments. IIE Trans 30:367–377

    Google Scholar 

  • Gupta S, Turner JU (1993) Variational solid modelling for tolerance analysis. IEEE Comput Graph Appl 13:64–74

    Article  Google Scholar 

  • Hong YS, Chang TC (2002) A comprehensive review of tolerancing research. Int J Prod Res 40:2425–2459

    Article  MATH  Google Scholar 

  • ISO 8015 (1985) Fundamental tolerancing principle. International Organization for Standardization, Geneva

    Google Scholar 

  • Laperrière L, Lafond P (1999) Modelling tolerances and dispersions of mechanical assemblies using virtual joints. In: Proceedings of ASME design engineering technical conferences, September 12–15, Las Vegas, Nevada, USA

    Google Scholar 

  • Laperrière L, Kabore T (2001) Monte Carlo simulation of tolerance synthesis equations. Int J Prod Res 39:2395–2406

    Article  Google Scholar 

  • Laperriére L, Ghie W, Desrochers A (2002) Statistical and deterministic tolerance analysis and synthesis using a unified Jacobian-torsor model. CIRP Ann 51:417–420

    Article  Google Scholar 

  • Legoff O, Villeneuve F, Bourdet P (1999) Geometrical tolerancing in process planning: a tridimensional approach. Proc Inst Mech Eng Part B 213:635–640

    Article  Google Scholar 

  • Li B, Roy U (2001) Relative positioning of toleranced polyhedral parts in an assembly. IIE Trans 33:323–336

    Google Scholar 

  • Marziale M, Polini W (2009a) Clearance joint modeling for tolerance analysis. In: Proceedings of the 11th CIRP international conference on CAT, Annecy, France, March 26–27

    Google Scholar 

  • Marziale M, Polini W (2009b) A review of two models for tolerance analysis: vector loop and matrix. Int J Adv Manuf Technol 43:1106–1123

    Article  Google Scholar 

  • Nigam SD, Turner JU (1995) Review of statistical approaches to tolerance analysis. Comput Aided Des 27:6–15

    Article  MATH  Google Scholar 

  • Prisco U, Giorleo G (2002) Overview of current CAT systems. Integr Comput Aided Eng 9:373–397

    Google Scholar 

  • Salomons OW, Haalboom FJ, Jonge Poerink HJ et al (1996) A computer aided tolerancing tool II: Tolerance analysis. Comput Ind 31:175–186

    Article  Google Scholar 

  • Shen Z, Ameta G, Shah JJ et al (2004) A comparative study of tolerance analysis methods. J Comput Inf Sci Eng 5(3):247–256

    Article  Google Scholar 

  • Teissandier D, Couétard Y, Gérard A (1999) A computer aided tolerancing model: proportioned assembly clearance volume. Comput Aided Des 31:805–817

    Article  MATH  Google Scholar 

  • Villeneuve F, Legoff O, Landon Y (2001) Tolerancing for manufacturing: a three-dimensional model. Int J Prod Res 39:1625–1648

    Article  MATH  Google Scholar 

  • Whitney DE (2004) Mechanical assemblies. Their design, manufacture and role in production development. Oxford University Press, New York

    Google Scholar 

  • Whitney DE, Mantripragada R, Adams JD et al (1999) Toward a theory for design of kinematically constrained mechanical assemblies. Int J Robot Res 18:1235–1248

    Article  Google Scholar 

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Polini, W. (2011). Geometric Tolerance Analysis. In: Colosimo, B., Senin, N. (eds) Geometric Tolerances. Springer, London. https://doi.org/10.1007/978-1-84996-311-4_2

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  • DOI: https://doi.org/10.1007/978-1-84996-311-4_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-310-7

  • Online ISBN: 978-1-84996-311-4

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