Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming

[+] Author and Article Information
LiMin Zhu1

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, P. R. Chinazhulm@sjtu.edu.cn

Ye Ding, Han Ding

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, P. R. China


To whom correspondence should be addressed.

J. Manuf. Sci. Eng 128(1), 167-174 (Jun 09, 2005) (8 pages) doi:10.1115/1.2120777 History: Received January 09, 2005; Revised June 09, 2005

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Minimum circumscribed cylinder

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Figure 2

Deviation from a measurement point to the reference line

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Figure 3

Computational times of the algorithm for different sample size problems



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