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Research Papers

Optimization of Fixture Layout Based on Error Amplification Factors

[+] Author and Article Information
Xiao-Jin Wan

Hubei Key Laboratory of Advanced Technology
of Automotive Components,
Wuhan University of Technology,
Wuhan 430070, China;
Hubei Collaborative Innovation Center for
Automotive Components Technology,
Wuhan University of Technology,
Wuhan 430070, China;
State Key Laboratory of Digital Manufacturing
Equipment and Technology of China,
Huazhong University of Science and Technology,
Wuhan 430074, China

Junqiang Yang, Hanjie Zhang, Zhi-Yong Feng, Zhigang Xu

Hubei Key Laboratory of Advanced Technology
of Automotive Components,
Wuhan University of Technology,
Wuhan 430070, China;
Hubei Collaborative Innovation Center for
Automotive Components Technology,
Wuhan University of Technology,
Wuhan 430070, China

1Corresponding author.

Manuscript received January 9, 2018; final manuscript received June 19, 2018; published online July 5, 2018. Assoc. Editor: Anurag Purwar.

J. Comput. Inf. Sci. Eng 18(4), 041007 (Jul 05, 2018) (12 pages) Paper No: JCISE-18-1016; doi: 10.1115/1.4040607 History: Received January 09, 2018; Revised June 19, 2018

Fixture locators are used to precisely locate and stably support a workpiece so that the desired position and orientation (pose) of the workpiece relative to the cutting tool can be maintained during machining or inspection process. It is believed that manufacturing errors of locators and locating datum surfaces are key factors for the pose error between the workpiece and the cutting tool. Optimizing the layout of locators is helpful to reduce the pose error so as to improve machining accuracy of the workpiece. In order to minimize the pose error, we introduced, for the first time, a singular value decomposition (SVD) technique for the location matrix to derive error amplification factors (EAF) in six degrees-of-freedom of the workpiece. The EAF principle defines the maximal singular value, the condition number, the product of all singular values and the manipulability as the maximal error amplification factor, the relative error amplification factor, the error ellipsoid volume and the location stability, respectively. The four defined indices taken as objective functions are optimized, by a nondominated sort genetic algorithm (NSGA-II), so that an optimal layout of locators is obtained due to the minimization of the pose error. Also, the feasibility of the proposed method was comprehensively validated by simulation and machining experiments.

FIGURES IN THIS ARTICLE
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Copyright © 2018 by ASME
Topics: Errors , Optimization
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Figures

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Fig. 1

A schematic of a generic workpiece-fixture system

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Fig. 3

Scheme of the layout of the fixture and machining feature

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Fig. 5

Relationship between error ellipsoid volume and error amplification factor

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Fig. 4

Stability with position change of the locator: (a) stability with first locator, (b) stability with second locator, (c) stability with third locator, (d) stability with fourth locator, (e) stability with fifth locator, and (f) stability with sixth locator

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Fig. 6

Relationship between error ellipsoid volume and stability

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Fig. 7

Relationship between error ellipsoid and relative error amplification factor

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Fig. 8

Relationship between stability and relative error amplification factor

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Fig. 9

Machining test experiment: (a) layout of locators, (b) machining operation, and (c) measurement operation

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