Legendre polynomials based parametric modeling of geometric errors for machining center

To predict the geometric error of machining center quickly and accurately, a parametric modeling method was proposed based on Legendre polynomials. The error of machining center was modeled with the multi-body system theory. The Legendre polynomials basis functions were constructed to expand the error data. The linear regression coefficients were obtained with least square method to get the fitting polynomial of error. The polynomial model of error term on displacement of moving axis was obtained from the relationship of variables. The XL-80 Renishaw laser interferometer was used to measure the positioning error of machining center's linear axis and the Y axis was taken as an example for parametric modeling. The parametric model of machine tool obtained by Legendre polynomials could fit the error data very well, which had smaller residual error and higher accuracy. The fifth-order model had higher fitting accuracy and could be applied to error compensation.