0
Research Papers: Design for Manufacture and the Life Cycle

Searching Multibranch Propagation Paths of Assembly Variation Based on Geometric Tolerances and Assembly Constraints

[+] Author and Article Information
Zhiqiang Zhang

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District,
Beijing 100081, China
e-mail: ericzhangbit@163.com

Jianhua Liu

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District,
Beijing 100081, China
e-mail: jeffliu@bit.edu.cn

Xiaoyu Ding

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District,
Beijing 100081, China
e-mail: xiaoyu.ding@bit.edu.cn

Ke Jiang

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District,
Beijing 100081, China
e-mail: jiangke73@126.com

Qiangwei Bao

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District,
Beijing 100081, China
e-mail: fory123@163.com

1Corresponding author.

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 2, 2016; final manuscript received February 14, 2017; published online March 20, 2017. Assoc. Editor: Rikard Söderberg.

J. Mech. Des 139(5), 051701 (Mar 20, 2017) (13 pages) Paper No: MD-16-1732; doi: 10.1115/1.4036135 History: Received November 02, 2016; Revised February 14, 2017

Assembly variation should be predicted accurately in the design process of a product to ensure the performance of the assembled parts. One important issue in predicting assembly variation is to search propagation paths along which variation accumulates. In this paper, a new searching algorithm of multibranch propagation paths of assembly variation for rigid body assemblies is proposed. First, the concepts of feature set and relation set are proposed to express the information of geometric tolerances and assembly constraints among features. Second, the actual constraint directions of a reference relation considering the precedence level are obtained. Third, the search of multibranch propagation paths is conducted by intersecting the actual constraint directions of different reference relations. Finally, the accuracy and efficiency of the proposed method are validated by comparing with the commercial computer-aided tolerancing (CAT) software package, 3DCS, for predicting assembly variation of the body structure of an aircraft. The outcomes of the paper can treat geometric tolerances, which overcome the drawback of traditional dimension-chain-based methods in predicting assembly variation. It is expected that a synthetic use of the proposed method and the dimension-chain-based methods can provide a computationally efficient substitute for the classical Monte Carlo simulation in predicting assembly variation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chen, H. , Jin, S. , Li, Z. M. , and Lai, X. M. , 2014, “ A Comprehensive Study of Three Dimensional Tolerance Analysis Methods,” Comput. Aided Des., 53, pp. 1–13. [CrossRef]
Bo, C. W. , Yang, Z. H. , Wang, L. B. , and Chen, H. Q. , 2013, “ A Comparison of Tolerance Analysis Models for Assembly,” Int. J. Adv. Manuf. Technol., 68(1–4), pp. 739–754. [CrossRef]
Hong, Y. S. , and Chang, T. C. , 2002, “ A Comprehensive Review of Tolerancing Research,” Int. J. Prod. Res., 40(11), pp. 2425–2459. [CrossRef]
Islam, M. N. , 2009, “ A Dimensioning and Tolerancing Methodology for Concurrent Engineering Applications I: Problem Representation,” Int. J. Adv. Manuf. Technol., 42(9), pp. 922–939. [CrossRef]
Prisco, U. , and Giorleo, G. , 2002, “ Overview of Current CAT Systems,” Integr. Comput Aided Eng., 9(4), pp. 373–387.
Islam, M. N. , 2004, “ Functional Dimensioning and Tolerancing Software for Concurrent Engineering Applications,” Comput. Ind., 54(2), pp. 169–190. [CrossRef]
Franciosa, P. , Gerbino, S. , and Patalano, S. , 2010, “ Variational Modeling and Assembly Constraints in Tolerance Analysis of Rigid Part Assemblies: Planar and Cylindrical Features,” Int. J. Adv. Manuf. Technol., 49(1–4), pp. 239–251. [CrossRef]
Sarigecili, M. I. , Roy, U. , and Rachuri, S. , 2014, “ Interpreting the Semantics of GD&T Specifications of a Product for Tolerance Analysis,” Comput. Aided Des., 47, pp. 72–84. [CrossRef]
Guo, C. Y. , Liu, J. H. , and Jiang, K. , 2016, “ Efficient Statistical Analysis of Geometric Tolerances Using Unified Error Distribution and an Analytical Variation Model,” Int. J. Adv. Manuf. Technol., 84(1–4), pp. 347–360.
Requicha, A. A. G. , 1983, “ Toward a Theory of Geometric Tolerancing,” Int. J. Robot. Res., 2(4), pp. 45–60. [CrossRef]
Jayaraman, R. , and Srinivasan, V. , 1989, “ Geometric Tolerancing: I. Virtual Boundary Requirements,” IBM. J. Res. Dev., 33(2), pp. 90–104. [CrossRef]
Wirtz, A. , 1993, “ Vectorial Tolerancing: a Basic Element for Quality Control,” 3rd CIRP Conference on Computer Aided Tolerancing, Cachan, France, Apr., pp. 115–128.
Clement, A. , and Bourdet, P. , 1988, “ A Study of Optimal-Criteria Identification Based on the Small-Displacement Screw Model,” CIRP Ann. Manuf. Technol., 37(1), pp. 503–506. [CrossRef]
Clement, A. , Riviere, A. , and Serre, P. , 1996, “ A Declarative Information Model for Functional Requirements,” Computer-Aided Tolerancing, K. Fumihiko , ed., Springer, The Netherlands, pp. 3–16.
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. [CrossRef]
Singh, G. , Ameta, G. , Davidson, J. K. , and Shah, J. J. , 2013, “ Tolerance Analysis and Allocation for Design of a Self-Aligning Coupling Assembly Using Tolerance-Maps,” ASME J. Mech. Des., 135(3), p. 031005. [CrossRef]
Wang, H. Y. , Pramanik, N. , Roy, U. , Sudarsan, R. , Sriram, R. D. , and Lyons, K. W. , 2006, “ A Scheme for Mapping Tolerance Specifications to Generalized Deviation Space for Use in Tolerance Synthesis and Analysis,” IEEE Trans. Autom. Sci. Eng., 3(1), pp. 81–91. [CrossRef]
Turner, J. U. , Subramaniam, S. , and Gupta, S. , 1992, “ Constraint Representation and Reduction in Assembly Modeling and Analysis,” IEEE Trans. Rob. Autom., 8(6), pp. 741–750. [CrossRef]
Adams, J. D. , and Whitney, D. E. , 2001, “ Application of Screw Theory to Constraint Analysis of Mechanical Assemblies Joined by Features,” ASME J. Mech. Des., 123(1), pp. 26–32. [CrossRef]
Ohwovoriole, M. , and Roth, B. , 1981, “ An Extension of Screw Theory,” ASME J. Mech. Des., 103(4), pp. 725–735. [CrossRef]
Wang, N. , and Ozsoy, T. M. , 1993, “ Automatic Generation of Tolerance Chains from Mating Relations Represented in Assembly Models,” ASME J. Mech. Des., 115(4), pp. 757–761. [CrossRef]
Rikard, S. , and Hans, J. , 1999, “ Tolerance Chain Detection by Geometrical Constraint Based Coupling Analysis,” J. Eng. Design., 10(1), pp. 5–24. [CrossRef]
Wang, H. , Ning, R. X. , and Yan, Y. , 2006, “ Simulated Toleranced CAD Geometrical Model and Automatic Generation of 3D Dimension Chains,” Int. J. Adv. Manuf. Technol., 29(9–10), pp. 1019–1025. [CrossRef]
Li, J. G. , Yao, Y. X. , and Wang, P. , 2014, “ Assembly Accuracy Prediction Based on CAD Model,” Int. J. Adv. Manuf. Technol., 75(5–8), pp. 825–832. [CrossRef]
Xue, J. B. , and Ji, P. , 2002, “ Identifying Tolerance Chains With a Surface-Chain Model in Tolerance Charting,” J. Mater. Process. Technol., 123(1), pp. 93–99. [CrossRef]
Hu, J. , Xiong, G. L. , and Wu, Z. , 2004, “ A Variational Geometric Constraints Network for a Tolerance Types Specification,” Int. J. Adv. Manuf. Technol., 24(3–4), pp. 214–222.
Gao, Z. B. , Wang, Z. X. , Wu, Z. J. , and Cao, Y. L. , 2015, “ Study on Generation of 3D Assembly Dimension Chain,” Proc. CIRP, 27, pp. 163–168.
Tsai, J. C. , and Kuo, C. H. , 2012, “ A Novel Statistical Tolerance Analysis Method for Assembled Parts,” Int. J. Prod. Res., 50(12), pp. 3498–3513. [CrossRef]
Singh, P. K. , Jain, P. K. , and Jain, S. C. , 2009, “ Important Issues in Tolerance Design of Mechanical Assemblies. Part 1: Tolerance Analysis,” Proc. Inst. Mech. Eng. B, 223(10), pp. 1225–1247. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Illustration of the feature set and relation set

Grahic Jump Location
Fig. 2

Geometrical design of a simple assembly of two parts: (a) detailed design of two parts and (b) Functional requirement of the assembly

Grahic Jump Location
Fig. 3

Local coordinate systems for different MGDEs: (a) point, (b) line, and (c) plane

Grahic Jump Location
Fig. 4

Schematic of the process of obtaining the constraint directions of one reference relation

Grahic Jump Location
Fig. 5

Illustration of the searching process of the propagation path of variation determined by translation constraints: (a) step 1, (b) step 2, (c) step 3, and (d) propagation path

Grahic Jump Location
Fig. 6

Illustration of the searching process of propagation paths of variation determined by rotation constraints: (a) step 1, (b) step 2, (c) step 3, (d) step 4, and (e) propagation paths

Grahic Jump Location
Fig. 7

Flowchart of the searching algorithm

Grahic Jump Location
Fig. 8

The body structure of an aircraft

Grahic Jump Location
Fig. 9

Detailed tolerance designs of the three cabins

Grahic Jump Location
Fig. 10

Propagation path determined by translation constraints for the body structure of an aircraft (features on the propagation path are shown in dark color)

Grahic Jump Location
Fig. 11

A typical simulation result in 3DCS (8192 simulation runs)

Grahic Jump Location
Fig. 12

The obtained variation range of the relative angle under different simulation numbers (two horizontal dashed lines are the results obtained using the method proposed in the current study)

Grahic Jump Location
Fig. 13

Constraint directions between two parallel lines

Grahic Jump Location
Fig. 14

Analysis of the actual constraint directions when only a fraction of the possible constraint directions are redundant: (a) Δi,k = 1, αi,k = 2, βi,k = 2, (b) Δi,k = 2, αi,k = 3, βi,k = 2, (c) Δi,k = 1, αi,k = 2, βi,k = 1, (d) Δi,k = 1, αi,k = 3, βi,k = 1, ti,k,1 × di,1 ≠ (0,0,0), and (e) Δi,k = 1, αi,k = 3, βi,k = 1, ti,k,1 × di,1 = (0,0,0)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In