A unified approach for circularity and spatial straightness evaluation using semi-definite programming

International Journal of Machine Tools and Manufacture

Volumn 47, Issue 10, 2007, Pages 1646-1650

  Ding, Ye ^a   Zhu, LiMin ^a   Ding, Han ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Circularity evaluation; Computational metrology; Interior point method; Minimum zone criterion (MZC); Semi definite programming (SDP); Spatial straightness evaluation

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; COMPUTER SOFTWARE; NUMERICAL METHODS; OPTIMIZATION; PROBLEM SOLVING;

CIRCULARITY EVALUATION; COMPUTATIONAL METROLOGY; INTERIOR POINT METHODS; MINIMUM ZONE CRITERION (MZC); SEMI DEFINITE PROGRAMMING (SDP); SPATIAL STRAIGHTNESS EVALUATION;

PRODUCTION ENGINEERING;

EID: 34047267480     PISSN: 08906955     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmachtools.2006.12.001     Document Type: Article

References (24)

1. Zhu L.M., Ding H., and Xiong Y.L. A steepest descent algorithm for circularity evaluation. CAD Computer Aided Design 35 3 (2003) 255-265
2. Wang M., Cheraghi S.H., and Masud A.S.M. Circularity error evaluation theory and algorithm. Precision Engineering 23 3 (1999) 164-176
3. Zhang Q., Fan K.C., and Li Z. Evaluation method for spatial straightness errors based on minimum zone condition. Precision Engineering 23 4 (1999) 264-272
4. Wen X., and Song A. An improved genetic algorithm for planar and spatial straightness error evaluation. International Journal of Machine Tools and Manufacture 43 11 (2003) 1157-1162
5. Zhu L., Ding Y., and Ding H. Algorithm for spatial straightness evaluation using theories of linear complex chebyshev approximation and semi-infinite linear programming. Journal of Manufacturing Science and Engineering, Transactions of the ASME 128 1 (2006) 167-174
6. Wen X., Xia Q., and Zhao Y. An effective genetic algorithm for circularity error unified evaluation. International Journal of Machine Tools and Manufacture 46 14 (2006) 1770-1777
7. Huang J., and Lehtihet E.A. Contribution to the minimax evaluation of circularity error. International Journal of Production Research 39 16 (2001) 3813-3826
8. Zhu L.M., Ding H., and Xiong Y.L. Distance function based algorithm for spatial straightness evaluation. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 217 7 (2003) 931-940
9. Dhanish P.B., and Shunmugam M.S. Algorithm for form error evaluation. Using the theory of discrete and linear Chebyshev approximation. Computer Methods in Applied Mechanics and Engineering 92 3 (1991) 309-324
10. Xiong Y.L. Computer aided measurement of profile error of complex surfaces and curves. Theory and algorithm. International Journal of Machine Tools and Manufacture 30 3 (1990) 339-357
11. Liu J., and Wang X.M. Saddle Point Programming and Geometric Error Evaluation (1996), Dalian University of Technology Press, Dalian
12. Chen M.C., Tsai D.M., and Tseng H.Y. A stochastic optimization approach for roundness measurements. Pattern Recognition Letters 20 7 (1999) 707-719
13. Lu P., and Lu J.S. A calculating method of circle error using genetic algorithms. Trans Nanjing University of Aeronautics Astronautics 31 4 (1999) 393-397
14. Weber T., Motavalli S., Fallahi B., and Cheraghi S.H. A unified approach to form error evaluation. Precision Engineering 26 3 (2002) 269-278
15. Vandenberghe L., and Boyd S. Semidefinite programming. SIAM Review 38 1 (1996) 49-95
16. Nesterov Y., and Nemirovskii A. Interior Point Polynomial Algorithms in Convex Programming (1994), Philadelphia, SIAM
17. Gahinet P., Nemirovski A., Laub A.J., and Chilali M. Manual of LMI Control Toolbox (1995), The MathWorks Inc
18. Lofberg J. Yalmip: A Matlab Toolbox for Rapid Prototyping of Optimization Problems, ETH Zurich (2004), Switzerland, Automatic Control Laboratory
19. Zhu L., Xiong Z., Ding H., and Xiong Y. A distance function based approach for localization and profile error evaluation of complex surface. Journal of Manufacturing Science and Engineering, Transactions of the ASME 126 3 (2004) 542-554
20. Coleman T., Branch M.A., and Grace A. Optimization Toolbox for Use with MATLAB (2006), The MathWorks Inc
21. Samuel G.L., and Shunmugam M.S. Evaluation of circularity from coordinate and form data using computational geometric techniques. Precision Engineering 24 3 (2000) 251-263
22. Huang S.T., Fan K.C., and Wu J.H. New minimum zone method for evaluating straightness errors. Precision Engineering 15 3 (1993) 158-164
23. Carr K., and Ferreira P. Verification of form tolerances Part II: cylindricity and straightness of a median line. Precision Engineering 17 2 (1995) 144-156
24. Huang J. Exact minimum zone solution for three-dimensional straightness evaluation problems. Precision Engineering 23 3 (1999) 204-208