An Improved Self-Born Weighted Least Square Method for Cylindricity Error Evaluation

Abstract

In order to improve the stability of the evaluation results and the gross error resistance of the algorithm in view of the widespread gross errors in geometric error evaluation, an improved self-born weighted least square method (ISWLS) is proposed in this paper. First, the nonlinear cylindrical axial model is linearized to establish the error equation of the observed values. We use the conditional equations of the independent observations found as valid information to derive the weights of the observations. The weights of the observations are subjected to least-square iteration to calculate the error values and equation parameters. Meanwhile, the ordinal numbers of the independent sets of equations in the observed equations are updated several times. By updating the ordinal number information of the conditional equations, the influence of gross error data on the solution of the equations is minimized. Through a series of experiments, the algorithm is proved to have a strong resistance to gross differences, and operation time is shorter. According to the evaluation results of cylindricity error, the uncertainty of cylindricity error was calculated by the Guide to the expression of uncertainty in measurement method (GUM)and the Monte Carlo method (MCM). Experiments show that the uncertainty results of the MCM method can verify the results assessed by the GUM method, which proves that the results of the ISWLS method are effective and robust.