An algorithm for form error evaluation — using the theory of discrete and linear Chebyshev approximation

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

“…Detail review for solving the two problems can be found in [1,6,7] and [5,8], respectively. For the former problem, a number of methods have been presented for resolving the problem P1 (or P2), such as linear approximation method [9,10], and computational geometry-based method [1,7], etc. For the later problem, as summarized in our previous works [5,8], assessment of the spatial straightness error is a difficult task in form error evaluation because its mathematical model cannot be linearized [3,11].…”

An immune evolutionary algorithm for sphericity error evaluation

“…Some efforts have been devoted to evaluating the sphericity error. Using discrete Chebyshev approximations, Danish [1] calculated the minimum zone solution for sphericity error; Kanada [2] computed the minimum zone sphericity using iterative least squares and the downhill simplex search methods; Fan and Lee [3] proposed an approach with minimum potential energy analogy to the minimum zone solution of spherical form error. And the problem of finding the minimum zone sphericity error is transformed into that of finding the minimum elastic potential energy of the corresponding mechanical system.…”

A Probabilistic View of Problems in Form Error Estimation

“…Thus, the sampling strategy (location and number of points) and sample data analysis are critical issues in the context of inspection using discrete sample points. Murthy and Abdin (1980) and Shunmugam (1986Shunmugam ( , 1987aShunmugam ( , 1987bShunmugam ( , 1990Shunmugam ( , 1991 have already demonstrated that estimates of W obtained from the least squares method do not agree with the definition of form errors.…”

“…The curve fitting approach uses L, ; -norm estimation, e.g., Caskey et al (1991Caskey et al ( , 1992, Dhanish andShunmugam (1991), andHopp (1993). Using computational geometry, planar feature boundaries are determined from the convex hull and supporting lines, while circular features require application of Voronoi diagrams, e.g., Etesami and Qiao (1989), Traband et al (1989) and Roy and Zhang (1992).…”