An assembly tolerance representation model based on spatial relations for generating assembly tolerance types

Abstract

The main advantage of polychromatic sets-based assembly tolerance representation model is that the number of feature types to be processed is larger. However, the number of recommended assembly tolerance types generated by the model is somewhat large for the same feature surfaces. Furthermore, the model cannot be directly applied to further assembly tolerance analysis and synthesis due to the fact that the information of degrees of freedom cannot be processed in polychromatic sets. To further reduce the number of recommended assembly tolerance types and to lay foundation for further assembly tolerance analysis and synthesis, a spatial relation layer is introduced into the polychromatic sets-based model and an assembly tolerance representation model based on spatial relations for generating assembly tolerance types is proposed. The proposed model is hierarchically organized and consists of part layer, assembly feature surface layer, spatial relation layer and assembly tolerance type layer. Each layer is defined with an adjacency matrix, respectively. By the mapping from spatial relations to assembly tolerance types, the number of recommended assembly tolerance types generated by the mapping from feature surfaces to assembly tolerance types is able to be further reduced. In addition, the information of degrees of freedom can be attached in the elements of adjacency matrices when recommended assembly tolerance types are generated by spatial relations so that the proposed model can be directly applied to further assembly tolerance analysis and synthesis. The effectiveness of the proposed model is demonstrated by an approach for generating assembly tolerance types and a practical example.

Keywords

Spatial relations tolerance representation model assembly tolerance types generation of tolerance types

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References

Wang Y. Semantic tolerance modeling with generalized intervals. ASME Trans J Mech Des 2008; 130: 081701(1–7).

Wang

. Interpretable interval constraint solvers in semantic tolerance analysis. Comput Aided Des Appl 2008; 5: 654–666.

Desrochers

Clement

. A dimensioning and tolerancing assistance model for CAD/CAM systems. Int J Adv Manuf Technol 1994; 9: 352–361.

Clement A, Riviere A, Serre P, et al. The TTRSs: 13 constraints for dimensioning and tolerancing. In: Proceedings of the 5th CIRP international seminar on computer-aided tolerancing, Toronto, Canada, 1997.

Prisco

Giorleo

. Overview of current CAT systems. Integr Comput Aided Eng 2002; 9: 373–387.

Liu

Gao

Cao

. An efficient approach to interpreting rigorous tolerance semantics for complicated tolerance specification. IEEE Trans Autom Sci Eng 2009; 6: 670–684.

Liu

Gao

. Hierarchical representation model and its realization of tolerance based on feature. Chin J Mech Eng 2003; 39: 1–7.

Zhang

Gao

. New reasoning algorithm for assembly tolerance specifications and corresponding tolerance zone types. Comput Aided Des 2011; 43: 1606–1628.

Zhang Y, Li Z, Xu L, et al. A new method for automatic synthesis of tolerance for complex assemblies based on polychromatic sets. Enterprise Information Systems 2011; 5(3): 337–358.

10.

Guilford

Turner

. Representational primitives for geometric tolerancing. Comput Aided Des 1993; 25: 577–586.

11.

Schulte

Weber

Stark

. Functional features for design in mechanical engineering. Comput Ind 1993; 23: 15–24.

12.

Requicha

AAG

. Solid modeling: a historical summary and contemporary assessment. IEEE Comput Graphics Appl 1982; 2: 9–24.

13.

Juster

. Modeling and representation of dimensions and tolerances: a survey. Comput Aided Des 1992; 24: 3–17.

14.

Roy

Liu

. Feature-based representational scheme of a solid modeler for providing dimensioning and tolerancing information. Rob Comput Integr Manuf 1988; 4: 333–345.

15.

Tsai

Cutkosky

. Representation and reasoning of geometric tolerances in design. Artif Intell Eng Des Anal Manuf 1997; 11: 325–341.

16.

Davidson

Shah

. Geometric tolerances: A new application for line geometry and screws. Proc IMechE, Part C: J Mechanical Engineering Science 2002; 216: 95–103.

17.

Ameta

Davidson

Shah

. Tolerance-maps applied to a point-line cluster of features. ASME Trans J Mech Des 2007; 129: 782–792.

18.

Zhang

Tang

. An integrated modeling method of unified tolerance representation for mechanical product. Int J Adv Manuf Technol 2010; 46: 217–226.

19.

Gossard

Zuffante

Sakuria

. Representing dimensions, tolerances, and features in MCAE systems. IEEE Comput Graphics Appl 1988; 8: 51–59.

20.

Anselmetti

. Generation of functional tolerancing based on positioning features. Comput Aided Des 2006; 38(8): 902–919.

21.

Peng

. Tolerance modeling and robust design for concurrent engineering. Proc IMechE, Part C: J Mechanical Engineering Science 2007; 221: 455–465.

22.

Turner

. Relative positioning of parts in assemblies using mathematical programming. Comput Aided Des 1990; 22: 394–400.

23.

Sodhi

Turner

. Relative positioning of variational part models for design analysis. Comput Aided Des 1994; 26: 366–378.

24.

ElMaraghy

. Geometric design tolerancing: theories, standards and applications, Berlin, Germany: Springer-Verlag, 1998.

25.

Serre P, Riviere A and Clement A. Dependence and independence of variations of a geometric object. In Proceedings of the 9th CIRP international seminar on computer-aided tolerancing, Tempe, AZ, USA, 2005.

26.

Dantan

Mathieu

Ballu

. Tolerance synthesis: quantifier notion and virtual boundary. Comput Aided Des 2005; 37: 231–240.

27.

Fleming

. Geometric relationships between toleranced features. Artif Intell 1998; 37: 403–412.

28.

Nigam

Turner

. Review of statistical approaches to tolerance analysis. Comput Aided Des 1995; 27: 6–15.

29.

Zhao

Pasupathy

TMK

Wilhelm

. Modeling and representation of geometric tolerances information in integrated measurement processes. Comput Ind 2006; 57: 319–330.

30.

Stefano

. Tolerance analysis and synthesis using the mean shift model. Proc IMechE, Part C: J Mechanical Engineering Science 2003; 217: 149–159.

31.

Khodaygan

Movahhedy

Foumani

. Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation. Mech Mach Theory 2011; 46: 558–573.

32.

Rao

. Fuzzy Analysis of Geometric Tolerances Using Interval Method. Proc IMechE, Part C: J Mechanical Engineering Science 2006; 220: 489–497.

33.

Cao

Mao

Ching

. A robust tolerance optimization method based on fuzzy quality loss. Proc IMechE, Part C: J Mechanical Engineering Science 2009; 223: 2647–2653.

34.

Hong

Chang

. A comprehensive review of tolerancing research. Int J Prod Res 2002; 40: 2425–2459.

35.

Salomons

Jonge Poerink

Haalboom

. A computer aided tolerancing tool I: tolerance specification. Comput Ind 1996; 31: 161–174.

36.

Salomons

Jonge Poerink

Haalboom

. A computer aided tolerancing tool II: tolerance analysis. Comput Ind 1996; 31: 175–186.

37.

Shah

Davison

. Computer modeling of geometric variations in mechanical parts and assemblies. ASME Transactions J Comput Inf Sci Eng 2003; 3: 54–63.

38.

Giordano M, Pairel E and Hernandez P. Complex mechanical structure tolerancing by means of hyper-graphs. In: Proceedings of the 9th CIRP international seminar on computer-aided tolerancing, Tempe, AZ, USA, 2005.

39.

Chase

Gao

Magleby

. Including geometric feature variation in tolerance analysis of mechanical assemblies. IEEE Trans 1996; 28: 795–807.

40.

Mejbri

Anselmetti

Mawussi

. Functional tolerancing of complex mechanisms: identification and specification of key parts. Comput Ind Eng 2005; 49: 241–265.

41.

Anselmetti

Chavanne

Yang

. Quick GPS: a new CAT system for single part tolerancing. Comput Aided Des 2010; 42: 768–780.

42.

Xiong

. A variational geometric constraints network for a tolerance types specification. Int Adv Manuf Technol 2004; 24: 214–222.

43.

Srinivasan

. A geometrical product specification language based on a classification of symmetry groups. Comput Aided Des 1999; 31: 659–668.

44.

Whitney

. Mechanical assemblies: their design, manufacture, and role in product development, New York, NY: Oxford University Press, 2004.

45.

Hu J. Study on theories and methods of geometric tolerance design based on variational geometric constraints network. PhD Dissertation, Zhejiang University, China, 2001.

46.

Mathew

Rao

CSP

. A novel method of using API to generate liaison relationships from an assembly. Int J Software Eng Appl 2010; 1: 167–175.

47.

Mathew

Rao

CSP

. A CAD system for extraction of mating features in an assembly. Assembly Autom 2010; 30: 142–146.

48.

ISO 1101:2004. Geometrical product specifications (GPS)—geometrical tolerancing—tolerances of form, orientation, location and run-out. International Organization for Standardization, Geneva, Switzerland.

49.

ISO 14405-1:2011. Geometrical product specifications (GPS)—dimensional tolerancing—Part 1: linear sizes. International Organization for Standardization, Geneva, Switzerland.

50.

ISO 14405-2:2011. Geometrical product specifications (GPS)—dimensional tolerancing—Part 2: dimensions other than linear sizes. International Organization for Standardization, Geneva, Switzerland.

51.

ASME Y14.5M. Dimensioning and tolerancing. New York, NY: American Society of Mechanical Engineers, 2009.