Straightness and flatness tolerance evaluation: an optimization approach

This paper presents an optimization approach that could be used to calculate exact values of straightness and flatness errors as defined by the ANSI Y14.5M standards on geometric dimensioning and tolerancing. The straightness and flatness error evaluation problems are formulated as nonlinear optimization problems with linear objective function and nonlinear constraints. Because of the special structure of the problem, a linear search method is developed that reduces the nonlinear problem to a linear programming problem with only two constraints. Examples are presented to compare the optimization approach with the least-squares method and some exact methods. The results show that the optimization procedures presented in this paper provide exact values of straightness and flatness errors and are superior to the existing methods in terms of computation time.