The most fundamental, and perhaps most important, task in the tolerance analysis of assemblies is to test whether or not the components with tolerances are actually able to fit together (called assembleability). Another important task of tolerance analysis is to check how the tolerances affect the quality or functionality of a product when they are assembled together. This paper presents the way the tolerance analyses are implemented by an assembly model, called the GapSpace model. The model can not only capture the necessary and sufficient conditions for assembleability analysis, but also transfers the functionality into the modeling variables (gaps). The assembleability analyses based on the GapSpace model for nominal components and those with worst case or statistical tolerances are introduced through an example. The problems of testing the quality of assemblies and calculating sensitivities are solved quickly and precisely using the model. The GapSpace model is more suitable for certain GD&T tolerancing methods than for parametric plus/minus tolerancing.

Issue Section:
Technical Papers
Keywords:
tolerance analysis, mechanical engineering computing, assembling, production engineering computing, Assembleability Analysis, GapSpace Model, Mechanical Assembly, Tolerancing, GD&T
Topics:
Manufacturing, Dimensions, Fittings
1.
ANSI, Y14.5M-1994, Dimensioning and Tolerancing, ASME, New York.
2.
Lee
,
W. J.
, and
Woo
,
T. C.
, May
1999
, “
Tolerances: Their Analysis and Synthesis
,”
J. Eng. Ind.
,
112
, pp.
113
–
121
.
3.
Altschul, R. E., and Scholz, F. W., 1993, “Statistical Tolerancing: A Case Study,” CIRP 3th, pp. 199–205, ASME.
4.
Cagan, J., Vogel, C. M., and Weingart, L. R., 2001, “Understanding Perceptual Gaps in Integrated Product Development Teams,” 13th International Conference on Design Theory and Methodology, ASME.
5.
Bjorke, O̸., 1989, Computer Aided Tolerancing, ASME Press, New York, NY.
6.
Chase, K. W., Gao J., and Magleby S. P., 1997, “Tolerance Analysis of 3- and 3-D mechanical Assemblies with Small Kinematic Adjustments,” Advanced Tolerancing Techniques, John Wiley.
7.
Gao, J., Chase, K. W., and Magleby, S. P., 1995, “Comparison of Assembly Tolerance Analysis by the Direct Linearization and Modified Monte Carlo Simulation Methods,” Procedure of the ASME Design Engineering Tech. Conf.
8.
Mantripragada
,
R.
, and
Whitney
,
D. E.
,
1998
, “
The Datum Flow Chain: A Systematic Approach to Assembly Design and Modeling
,”
Res. Eng. Des.
,
10
, pp.
150
–
165
.
9.
Whitney, D. E., Shukla, G., and Praun, S. V., 2001, “A Design Procedure Applicable to Different Classes of Assemblies, Proceedings of DETC,” ASME Design Engineering. Technical Conference, CIE-21304, PA, USA.
10.
Narahari, Y., etc., 1998, “Design for Tolerance of Electro-Mechanical Assemblies: An Integrated Approach,” Technical Report, NIST.
11.
Turner, J. U., 1987, “Tolerances in Computer-Aided Geometric Design,” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York.
12.
Clement, A., Valade, C., and Riviere, A., 1996, “The TTRSs: 13 Oriented Constraints for Dimensioning, Tolerancing and Inspection,” Advanced Mathematical Tools in Metrology III, Berlin, pp. 24–41
13.
Ballot, E., and Bourdet, P., “Geometrical Behavior Laws for Computer Aided Tolerancing,” Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing, Tokyo, Japan, pp. 143–154, 1995.
14.
Ballot, E., and Bourdet, P., “A computational Method for the Consequences of Geometric Errors in Mechanisms,” Proceedings of the 5th CIRP Seminar on Computer Aided Tolerancing, Toronto, Canada, pp. 137–148, 1997.
15.
Mullins, S. H., 1995, “Constraint Management in Mechanical Assembly Modeling,” Ph.D. Thesis, Purdue University.
16.
Mullins
,
S. H.
, and
Anderson
,
D. C.
,
1998
, “
Automatic Identification of Geometric Constraints in Mechanical Assemblies
,”
Comput.-Aided Des.
,
30
(
9
), pp.
715
–
726
.
17.
Kriegel, Jon M. “Exact Constraint Design.” In ASME International ME Congress and Exhibition (Winter Annual Meeting) Paper 94-WA/DE-18, November 1994.
18.
Adams
,
J. D.
, and
Whitney
,
D. E.
,
2001
, “
Application of Screw Theory to Constraint Analysis of Mechanical Assemblies joined by Features
,”
J. Mech. Des.
,
123
, pp.
26
–
32
.
19.
Morse, E. P., 1999, “Models, Representations, and Analyses of Toleranced one-dimensional Assemblies,” Ph.D. Thesis, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY.
20.
Morse, E. P., “Introduction to GapSpace,” in review, ASME J. Mech. Des.
21.
Zou, Z. H., and Morse, E. P., 2001, “Statistical Tolerance Analysis Using GapSpace,” 7th CIRP Seminar, ENS de Cachan, pp. 313–322, France.
22.
Zou, Z. H., 2002, “Tolerance Analysis for Multidimensional Mechanical Assemblies,” Ph.D. dissertation, University of North Carolina at Charlotte, NC.
23.
Zou, Z. H., and Morse, E. P., “A Gap-based Approach to Capture the Fits Conditions for Mechanical Assembly,” Comput.-Aided Des. (submitted to review)
24.
Solomons, Otto, 1994, “Computer Support in The Design of Mechanical Products,” Ph.D. thesis, University Twente, Netherlands.
25.
Spotts, M. F., 1983, “Dimensioning and Tolerancing for Quantity Production,” Prentice-Hall.
26.
Chase, K. W., and Parkinson, A. R., 1991, “A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies,” ADCATS Reports No. 91-1, Brigham Young University, Provo, Utah 84602.
27.
Parkinson
,
D. B.
,
1982
, “
The Application of Reliability Methods to Tolerancing
,”
ASME J. Mech. Des.
,
104
, pp.
612
–
618
.
28.
http://adcats.et.byu.edu/WWW/ADCATS
29.
Neumann, A., 1995, “Geometric Dimensioning and Tolerancing Workbook,” distributed by ASME.
30.
Kandikjan
,
L.
,
Shah
,
J. J.
, and
Davidson
,
J. K.
,
2001
, “
A Mechanism for Validating Dimensioning and Tolerancing Schemes in CAD Systems
,”
Comput.-Aided Des.
,
33
, pp.
721
–
737
.
Copyright © 2003
 by ASME
You do not currently have access to this content.