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Abstract

The tolerance analysis of assemblies, which is carried out during the design stage, is the basic tool to simulate the effects of the assigned tolerances on the required functionality, and then, to define the appropriate allocation of the tolerances. This tool has to be based on a mathematical model able to evaluate the effect that each single tolerance has on the whole assembly. There are some different models proposed in the literature to carry out the tolerance analysis of an assembly, but none of them is completely and univocally accepted. Some authors focus their attention on the solution of single problems found in these models or in their practical application in computer-aided tolerancing systems. None of them has done an objective and complete comparison among them, analysing the advantages and the weakness and furnishing a criterion for their choice and application. The present paper briefly introduces one of the main models for tolerance analysis, the variational model. The variational model is a family of schemes developed by different authors; the two most developed schemes are that involving rotational and translational parameters and that involving only translational parameters. These two models are briefly described herein and then compared to show their analogies and differences.

Keywords

tolerance analysis variational model functional requirements

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References

Lin

Thimm

Britton

G. A.

, ‘Alternative design specifications of prismatic parts for manufacturability’ Proc. IMechE, Part B: J. Engineering Manufacture 217 (4) (2003): 569–572 DOI: 10.1243/095440503321628242.

Asante

J. N.

, ‘A small displacement torsor model for tolerance analysis in a workpiece-fixture design’ Proc. IMechE, Part B: J. Engineering Manufacture 223 (8) (2009): 1005–1020 DOI: 10.1243/09544054JEM1337.

Chase

K. W.

Parkinson

A. R.

, ‘A survey of research in the application of tolerance analysis to the design of mechanical assemblies’ Res. Engng Des. 3 (1) (1991): 23–37.

Hong

Y. S.

Chang

T. C.

, ‘A comprehensive review of tolerancing research’ Int. J. Prod. Res. 40 (11) (2002): 2425–2459.

Shen

Ameta

Shah

J. J.

Davidson

J. K.

, ‘A comparative study of tolerance analysis methods’ J. Comput. Inform. Sci. Engng 5 (3) (2005): 247–256.

Turner

Gangoiti

A. B.

, ‘Tolerance analysis approaches in commercial software’ Concurr. Engng 1/2 (1991): 11–23.

Salomons

O. W.

van Houten

F. J. A. M.

Kals

H. J. J.

ElMaraghy

H. A.

, ‘Current status of CAT systems' In Geometric design tolerancing: Theories, standards and applications (London: Chapman and Hall 1998): pp. 438–452.

Prisco

Giorleo

, ‘Overview of current CAT systems’ Integrated Comput. Aided Engng 9 (4) (2002): 373–397.

ASME Standard Y14.5M-1994, Dimensioning and tolerancing (New York, New York: American Society of Mechanical Engineers 1994).

10.

ISO 8015:1985, Technical drawings - Fundamental tolerancing principle (Geneva, Switzerland: International Organization for Standardization 1985).

11.

Martino

P. M.

Gabriele

G. A.

, ‘Application of variational geometry to the analysis of mechanical tolerance’ Failure Prev. Reliab. 16 (1981): 19–27.

12.

Boyer

Stewart

N. F.

, ‘Modeling spaces for toleranced objects’ Int. J. Robot. Res. 10 (5) (1991): 570–582.

13.

Gupta

Turner

J. U.

, ‘Variational solid modelling for tolerance analysis’ IEEE Comput. Graph. Applic. Mag. 13 (1991): 64–74.

14.

Roy

, ‘Relative positioning of toleranced polyhedral parts in an assembly’ IIE Trans. 33 (4) (2001): 323–336.

15.

Berman

Y. O.

, Shape and position uncertainty in mechanical assembly (2005) PhD Thesis, Benin School of Engineering and Computer Science, The Hebrew University, Jerusalem.

16.

Creveling

C. M.

, Tolerance design (Reading, Massachusetts: Addison-Wesley 1997).

17.

Greenwood

W. H.

Chase

K. W.

, ‘Worst-case tolerance analysis with nonlinear problems’ Trans. ASMR: J. Eng. for Ind. 110 (3) (1998): 232–235.

18.

Luenberger

D. G.

, Linear and nonlinear programming (Reading, Massachusetts: Addison-Wesley 2003).

19.

Srinivasan

O'Connor

M. A.

ElMaraghy

H. A

, ‘Composing distribution function zones for statistical tolerance analysis' In Geometric design tolerancing: Theories, standards and applications (London: Chapman and Hall 1998): pp. 64–76.

20.

Whitney

D. E.

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

21.

Nigam

S. D.

Turner

J. U.

, ‘Review of statistical approaches to tolerance analysis’ Comput. Aided Des. 27 (1) (1995): 6–15.

22.

Nassef

A. O.

ElMaraghy

H. A.

Kimura

‘Probabilistic analysis of geometric tolerances' In

Computer aided tolerancing (London: Chapman and Hall 1996): pp. 187–203.

23.

Desrochers

Rivière

, ‘A matrix approach to the representation of tolerance zones and clearances’ Int. J. Adv. Mfg Technol. 13 (1991): 630–636.

24.

Chase

K. W.

Gao

Magleby

S. P.

Sorensen

C. D.

, ‘Including geometric feature variations in tolerance analysis of mechanical assemblies’ IIE Trans. 28 (10) (1996): 795–807.

25.

Gao

Chase

K. W.

Magleby

S. P.

, ‘Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments’ IIE Trans. 30 (1991): 367–377.