Functional tolerancing must ensure the assembly and the functioning of a mechanism. This paper compares two methods of tolerance analysis of a mechanical system: the method of “analysis lines” and the method of “polytopes.” The first method needs a discretization of the ending functional surface according to various analysis lines placed on the outer-bound of the face and oriented along the normal of the surface. The second method uses polytopes. The polytopes are defined from the acceptable limits of the geometric deviations of parts and possible displacements between two parts. Minkowski sums and intersections polytopes are then carried out to take into account all geometric variations of a mechanism.
Issue Section:
Research Papers
References
1.
Salomons
, O. W.
, Haalboom
, F. J.
, Jonge Poerink
, H. J.
, van Slooten
, F.
, Van Houten
, F. J. A. M.
, and Kals
, H. J. J.
, 1996
, “A Computer Aided Tolerancing Tool I: Tolerancing Specification
,” Comput. Ind.
, 31
(2
), pp. 161
–174
.10.1016/0166-3615(96)00046-22.
Salomons
, O. W.
, Haalboom
, F. J.
, Jonge Poerink
, H. J.
, van Slooten
, F.
, Van Houten
, F. J. A. M.
, and Kals
, H. J. J.
, 1996
, “A Computer Aided Tolerancing Tool II: Tolerancing Analysis
,” Comput. Ind.
, 31
(2
), pp. 175
–186
.10.1016/0166-3615(96)00047-43.
Chase
, K. W.
, 1999
, “Tolerance Allocation Methods for Designers
,” ADCATS Report No. 99-6.4.
Islam
, M. N.
, 2004
, “Functional Dimensioning and Tolerancing Software for Concurrent Engineering Applications
,” Comput. Ind.
, 54
(2
), pp. 169
–190
.10.1016/j.compind.2003.09.0065.
Anselmetti
, B.
, 2006
, “Generation of Functional Tolerancing Based on Positioning Features
,” Comput. Aided Des.
, 38
(8
), pp. 902
–919
.10.1016/j.cad.2006.05.0056.
Johannesson
, H.
, and Sodderberg
, R.
, 2000
, “Structure and Matrix Models for Tolerance Analysis From Configuration to Detail Design
,” Res. Eng. Des.
, 12
(2
), pp. 112
–125
.10.1007/s0016300500277.
Ballot
, E.
, and Bourdet
, P.
, 1995
, “Geometrical Behavior Laws for Computer Aided Tolerancing
,” Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing
, Tokyo
, Japan
, Apr. 5–6, pp. 143
–153
.8.
Mehdi-Souzani
, C.
, and Anselmetti
, B.
, 2008
, “Integration of Automatic Functional Tolerancing Into the Design Process
,” Proceedings of IDMME—Virtual Concept
, Beijing
, China
, CDRom IDMME.9.
Nigam
, S. D.
, and Turner
, J. U.
, 1995
, “Review of Statistical Approaches to Tolerance Analysis
,” Comput. Aided Des.
, 27
(1
), pp. 6
–15
.10.1016/0010-4485(95)90748-510.
Shan
, A.
, and Roth
, R. N.
, 2003
, “Genetic Algorithms in Statistical Tolerancing
,” J. Math. Comput. Model.
, 38
(11–13
), pp. 1427
–1436
.10.1016/S0895-7177(03)90146-411.
Kuo
, C. H.
, and Tsai
, J. C.
, 2010
, “An Analytical Computation Method for Statistical Tolerance Analysis of Assemblies With Truncated Normal Mean Shift
,” Int. J. Prod. Res.
, 49
(7
), pp. 1937
–1955
.10.1080/0020754100363963412.
Skowronski
, V. J.
, and Turner
, J. U.
, 1997
, “Using Monte Carlo Variance Reduction in Statistical Tolerance Synthesis
,” Comput. Aided Des.
, 29
(1
), pp. 63
–69
.10.1016/S0010-4485(96)00050-413.
Lin
, C.
, Huang
, W.
, Jeng
, M.
, and Doong
, J. L.
, 1997
, “Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation
,” J. Mater. Process. Technol.
, 70
(1
), pp. 9
–16
.10.1016/S0924-0136(97)00034-414.
Shah
, J. J.
, Ameta
, G.
, Shen
, Z.
, and Davidson
, J. K.
, 2007
, “Navigating the Tolerance Analysis Maze
,” Comput. Aided Des. Appl.
, 4
(5
), pp. 705
–718
10.1080/16864360.2007.10738504.15.
Giordano
, M.
, Pairel
, E.
, and Samper
, S.
, 1999
, “Mathematical Representation of Tolerance Zones
,” Proceedings of the 6th CIRP Seminar on Computer Aided Tolerancing
, University of Twente
, Enschede, The Netherlands
, Mar. 22–24, pp. 177
–186
.16.
Davidson
, J. K.
, Mujezinovic
, A.
, and Shah
, J. J.
, 2002
, “A New Mathematical Model for Geometric Tolerances as Applied to Round Faces
,” ASME J. Mech. Des.
, 124
(4
), pp. 609
–622
.10.1115/1.149736217.
Roy
, U.
, and Li
, B.
, 1999
, “Representation and Interpretation of Geometric Tolerances for Polyhedral Objects. II: Size, Orientation and Position Tolerances
,” Comput. Aided Des.
, 31
(4
), pp. 273
–285
.10.1016/S0010-4485(99)00028-718.
Pierre
, L.
, Teissandier
, D.
, and Nadeau
, J. P.
, 2009
, “Integration of Thermomechanical Strains Into Tolerancing Analysis
,” Int. J. Interact. Des. Manuf.
, 3
(4
), pp. 247
–263
.10.1007/s12008-009-0058-819.
Pierre
, L.
, Teissandier
, D.
, and Nadeau
, J. P.
, 2014
, “Variational Tolerancing Analysis Taking Thermomechanical Strains Into Account: Application to a High Pressure Turbine
,” Mech. Mach. Theory
, 74
, pp. 82
–101
.10.1016/j.mechmachtheory.2013.11.01420.
Clozel
, P.
, and Rance
, P. A.
, 2010
, “MECAmaster: a Tool for Assembly Simulation From Early Design, Industrial Approach
,” Geometric Tolerancing of Products
, Wiley
, New York
, pp. 241
–273
10.1002/9781118587027.ch10.21.
cetol.6, “
Reduce Assembly Variation with Tolerance Analysis Software
,” http://www.sigmetrix.com/22.
23.
Falgarone
, H.
, and Chevassus
, N.
, 2004
, “An Innovative Design Method and Tool for Structural and Functional Analysis
,” Proceedings of 14th CIRP Design Seminar
, Cairo
, Egypt
.24.
Loof
, J.
, Hermansson
, T.
, and Sodderberg
, R.
, 2005
, “An Efficient Solution to the Discrete Least Cost Tolerance Allocation Problem With General Loss Functions
,” Model for Computer Aided Tolerancing in Design and Manufacturing
, Springer
, Dordrecht, The Netherlands
, pp. 115
–124
.25.
Kurlarni
, S. V.
, and Garg
, T. K.
, 1987
, “Allocation of Tolerances to the Components of an Assembly for Minimum Cost
,” Int. J. Mech. Eng.
, 67
(6
), pp. 126
–129
.26.
Anselmetti
, B.
, 2010
, “Part Optimization and Tolerances Synthesis
,” Int. J. Adv. Manuf. Technol.
, 48
(9–12
), pp. 1221
–1237
.10.1007/s00170-009-2355-627.
Khanafer
, M.
, Desrochers
, A.
, and Laperrière
, L.
, 2007
, “Tolerancing Assistance Methodology in a Product Life Cycle Perspective
,” Proceedings of 18th IASTED International Conference: Modeling and Simulation
, Anaheim, CA
, May 30–June 1, pp. 514
–520
.28.
Benichou
, S.
, and Anselmetti
, B.
, 2011
, “Thermal Dilatation in Functional Tolerancing
,” Mech. Mach. Theory
, 46
(11
), pp. 1575
–1587
.10.1016/j.mechmachtheory.2011.06.00929.
Fleming
, A.
, 1988
, “Geometric Relationships Between Toleranced Features
,” Artif. Intell.
, 37
(1–3
), pp. 403
–412
.10.1016/0004-3702(88)90062-830.
ISO 1101:2013,
2013
, Geometrical Product Specifications (GPS), Geometrical Tolerancing, Tolerances of Form, Orientation, Location and Run-Out, ISO, Geneva, Switzerland.
31.
Fleming
, A. D.
, 1987
, “Analysis of Uncertainties and Geometric Tolerances in Assemblies of Parts
,” Ph.D. thesis, University of Edinburgh, Edinburgh, Scotland.32.
Srinivasan
, V.
, 1993
, “Role of Sweeps in Tolerancing Semantics
,” Manufacturing Review
, 6
(4
), pp. 275
–281
.33.
Giordano
, M.
, and Duret
, D.
, 1993
, “Clearance Space and Deviation Space
,” Proceedings of the 3rd CIRP Seminar on Computer Aided Tolerancing
, ENS Cachan
, France
, Apr., pp. 179
–196
.34.
Teissandier
, D.
, and Delos
, V.
, 1999
, “Operations on Polytopes: Application to Tolerance Analysis
,” Proceedings of the 6th CIRP Seminar on Computer Aided Tolerancing
, University of Twente
, Enschede, The Netherlands
, Mar. 22–24, pp. 425
–433
.35.
Wu
, Y.
, Shah
, J. J.
, and Davidson
, J. K.
, 2003
, “Improvements to Algorithms for Computing the Minkowski Sum of 3-Polytopes
,” Comput. Aided Des.
, 35
(13
), pp. 1181
–1192
.10.1016/S0010-4485(03)00023-X36.
Teissandier
, D.
, and Delos
, V.
, 2011
, “Algorithm to Calculate the Minkowski Sums of 3-Polytopes Based on Normal Fans
,” Comput. Aided Des.
, 43
(12
), pp. 1567
–1576
.10.1016/j.cad.2011.06.01637.
Anselmetti
, B.
, Chavanne
, R.
, Yang
, J.-Y.
, and Anwer
, N.
, 2010
, “quick gps: A New CAT System for Single-Part Tolerancing
,” Comput. Aided Des.
, 42
(9
), pp. 768
–780
.10.1016/j.cad.2010.04.00638.
Chavanne
, R.
, 2011
, “Contribution au Tolérancement Fonctionnel 3D des Mécanismes Complexes: Synthèse des Spécifications et Analyse de Tolerances
,” Ph.D. thesis, Cachan, France.Copyright © 2015 by ASME
You do not currently have access to this content.
