Thermal error regression modeling of the real-time deformation coefficient of the moving shaft of a gantry milling machine

This paper describes a novel modeling method for determining the thermal deformation coefficient of the moving shaft of a machine tool. Firstly, the relation between the thermal deformation coefficient and the thermal expansion coefficient is expounded, revealing that the coefficient of thermal deformation is an important factor affecting the precision of moving shaft feed systems. Then, thermal errors and current boundary and machining conditions are measured using sensors to obtain the first set of parameters for a thermal prediction model. The dynamic characteristics of the positioning and straightness thermal errors of the moving axis of a machine tool are analyzed under different feed speeds and mounting modes of the moving shaft and bearing. Finally, the theoretical model is derived from experimental data, and the axial and radial thermal deformation coefficients at different time and positions are obtained. The expressions for the axial and radial thermal deformation of the moving shaft are modified according to theoretical considerations, and the thermal positioning and straightness error models are established and experimentally verified. This modeling method can be easily extended to other machine tools to determine thermal deformation coefficients that are robust and self-correcting.