Abstract
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.
Issue Section:
Technical Papers
1.
Zhang
, Q.
, Fan
, K. C.
, and Li
, Z.
, 1999, “Evaluation Method for Spatial Straightness Errors Based on Minimum Zone Condition
,” Precis. Eng.
0141-6359, 23
, pp. 264
–272
.2.
Liu
, J.
, and Wang
, X. M.
, 1996, Saddle Point Programming and Geometric Error Evaluation
, Dalian University of Technology Press
.3.
Dhanish
, P. B.
, and Shunmugam
, M. S.
, 1991, “An Algorithm for Form Error Evaluation-Using the Theory of Discrete and Linear Chebyshev Approximation
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 92
, pp. 309
–324
.4.
Xiong
, Y. L.
, 1991, “Computer Aided Measurement of Profile Error of Complex Surfaces and Curves: Theory and Algorithm
,” Int. J. Mach. Tools Manuf.
0890-6955, 30
, pp. 339
–357
.5.
Huang
, S. T.
, Fan
, K. C.
, and John
, H. W.
, 1993, “A New Minimum Zone Method for Evaluating Straightness Errors
,” Precis. Eng.
0141-6359, 15
, pp. 158
–165
.6.
Chen
, C. K.
, and Wu
, S. C.
, 1999, “A Method for Measuring and Separating Cylindrical and Spindle Errors in Machine Tool Rotational Parts
,” Meas. Sci. Technol.
0957-0233, 10
, pp. 76
–83
.7.
Wen
, X. L.
, and Song
, A. G.
, 2003, “An Improved Genetic Algorithm for Planar and Spatial Straightness Error Evaluation
,” Int. J. Mach. Tools Manuf.
0890-6955, 43
(11
), pp. 1157
–1162
.8.
Agarwal
, P. K.
, Aronov
, B.
, and Sharir
, M.
, 1999, “Line Transversals of Balls and Smallest Enclosing Cylinders in Three Dimensions
,” Discrete Comput. Geom.
0179-5376, 21
, pp. 373
–388
.9.
Huang
, J. P.
, 1999, “An Exact Minimum Zone Solution for Three-Dimensional Straightness Evaluation Problems
,” Precis. Eng.
0141-6359, 23
, pp. 204
–208
.10.
Carr
, K.
, and Ferreira
, P.
, 1995, “Verification of Form Tolerances, Part II: Cylindricity and Straightness of a Median Line
,” Precis. Eng.
0141-6359, 17
, pp. 144
–156
.11.
Zhu
, X. Y.
, Ding
, H.
, and Wang
, M. Y.
, 2004, “Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm
,” ASME J. Manuf. Sci. Eng.
1087-1357, 126
(3
), pp. 535
–541
.12.
Ellacott
, S.
, and Williams
, J.
, 1976, “Linear Chebyshev Approximation in the Complex Plane Using Lawson’s Algorithm
,” Math. Comput.
0025-5718, 30
, pp. 35
–44
.13.
Burnside
, D.
, and Parks
, T. W.
, 1995, “Optimal Design of FIR Filters with the Complex Chebyshev Error Criteria
,” IEEE Trans. Signal Process.
1053-587X, 43
(3
), pp. 605
–616
.14.
Zhu
, L. M.
, Ding
, H.
, and Xiong
, Y. L.
, 2003, “Distance Function Based Algorithm for Spatial Straightness Evaluation
,” Proc. Inst. Mech. Eng., Part B
0954-4054, 217
, pp. 931
–939
.15.
Zhu
, L. M.
, Xiong
, Z. H.
, Ding
, H.
, and Xiong
, Y. L.
, 2004, “A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface
,” ASME J. Manuf. Sci. Eng.
1087-1357, 126
(3
), pp. 542
–554
.16.
Streit
, R. L.
, and Nuttall
, A. H.
, 1982, “A General Chebyshev Complex Function Approximation Procedure and an Application to Beam Forming
,” J. Acoust. Soc. Am.
0001-4966, 71
(1
), pp. 181
–190
.17.
Tang
, P. T.P.
, 1988, “A Fast Algorithm for Linear Complex Chebyshev Approximations
,” Math. Comput.
0025-5718, 51
(3
), pp. 721
–739
.18.
Glashoff
, K.
, and Roleff
, K.
, 1981, “A New Method for Chebyshev Approximation of Complex-Valued Function
,” Math. Comput.
0025-5718, 36
, pp. 233
–239
.19.
Anderson
, E. J.
, and Nash
, P.
, 1987, Linear Programming in Infinite-Dimensional Spaces
, Wiley
, New York.20.
Zhu
, X. Y.
, Ding
, H.
, and Tso
, S. K.
, 2004, “A Pseudodistance Function and its Applications
,” IEEE Trans. Rob. Autom.
1042-296X, 20
(2
), pp. 344
–352
.Copyright © 2006
by American Society of Mechanical Engineers
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