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.

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Fig. 1

Illustration of the feature set and relation set

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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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

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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

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Fig. 7

Flowchart of the searching algorithm

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Fig. 8

The body structure of an aircraft

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Fig. 9

Detailed tolerance designs of the three cabins

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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)

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Fig. 11

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

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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)

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Fig. 13

Constraint directions between two parallel lines

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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)



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