Parametric Modeling of Geometric Errors for CNC Machine Tools Based on Chebyshev Polynomial

Abstract

In order to establish the mathematical model of rotary axes geometric error of machine tool quickly and accurately, a parameterized modeling method based on Chebyshev polynomial is proposed in this paper. First, the rotation angle of the rotation axis of the machine tool is converted into a Chebyshev variable, and then the Chebyshev variable is substituted into Chebyshev polynomials of different orders. Second, The corresponding coefficients are obtained by multiple linear regression based on Chebyshev basis function values and Chebyshev variables. Finally, the transformation relationship between the rotation angle of the rotation axis and the Chebyshev variable is substituted into the mathematical model of the basic geometric error term. Compared to other methods, the modeling process is simple and easy to program. This paper takes the two rotary axes of VMC65m as an example to obtain the geometric error distribution of the working space of the machine tool, which provides a theoretical basis for the design and error compensation of the machine tool.