Study on an approach for decoupling and separating the thermal positioning errors of machining center linear axes

CNC machining center linear axis thermal positioning errors, seen as the synthetic consequences of geometric and thermal errors, respectively generated due to the manufacturing and assembling inaccuracies and the asymmetric thermal deformation of the machining center structure, are significantly affected by varying position of the cutting point and shifting state of temperature field. Hence, developing a practical approach to reduce or even to eliminate thermal positioning errors is crucial. This paper proposes an approach to decouple and separate machining center linear axis thermal positioning errors, based on which a highly accurate prediction model of the thermal positioning error is formulated. A sensitivity analysis-based thermal critical point optimization method is presented where grey theory is borrowed to characterize the mapping between thermal positioning error and varying temperature fields, according to which the highly related temperature sensors are derived. The thermal positioning errors are then decoupled and separated into geometric and thermal errors by adopting multiple regression algorithm and linear fitting approach, respectively. Accordingly, the comprehensive thermal positioning error prediction model is constrcuted, based on which the compensation approach is also proposed. Next, the corresponding compensation module is developed within the SIEMENS 840D CNC system to realize the online compensation strategy, providing the engineering applications. Experimental validations are performed on a commercial machining center, where the thermal positioning errors of the Z-axis are measured with the help of a laser interferometer testing kit and a thermal inspection instrument. The data comparisons indicate that the maximum thermal positioning errors of the Z-axis in the cold and warm state are respectively decreased for 87.09%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} and 49.87%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}after activating the compensation module, which also suggests that the proposed approach is adequate and accurate to decouple and separate the thermal positioning errors.