Parametric Modeling of Geometric Errors for Machining Center Based on Legendre Polynomial

In order to predict the geometric errors of CNC machine tools, a geometric error modeling method based on Legendre polynomials is proposed. Firstly, the error data is developed with the Legendre polynomial basis function, and the linear regression coefficients are obtained by fitting the linear least squares method. The error polynomial about the Legendre polynomial basis function is obtained. Secondly, based on the relationship of variables, the polynomial model of the rotation term of the error axis is given. Thirdly, the Renishaw XL-80 laser interferometer was used to measure the geometric errors of two rotating axes of the VMC65m machine tool, and the C-axis was used as an example for parametric modeling. Finally, comparing it with the parametric modeling effect of the Chebyshev polynomial, the geometric error of the Legendre polynomial is parametrically modeled with higher accuracy and closer to the actual error of the machine tool. This paper provides a theoretical basis for machine tool error compensation.