Analytical modelling of transient thermal characteristics of precision machine tools and real-time active thermal control method

Thermal error is one of the primary factors affecting the machining accuracy of precision machining tools. Therefore, it is important to study the transient thermal characteristics of machine tools and the thermal-error control strategies. Thus far, a transient analytical modelling method for characterising the thermal characteristics of machine tools was proposed and an active error control strategy was provided. First, temperature-field modelling was conducted using an analytical method based on the Fourier series method and partial differential equations of heat conduction. Second, using the derived temperature field, the thermal deformation field was calculated based on finite element theory. Subsequently, the continuous real-time effect of the thermal power per unit heat source on the temperature and deformation fields of precision machine tools was studied. The proposed analytical modelling method not only predicts the machine tool heat deformation based on the working conditions of the heat source, but also matches the thermal control source power with the demand of the machine tool heat deformation. The optimal real-time power of the thermal control source is dynamically iterated and matched, such that the thermal deformation caused by the heat and thermal control sources can be balanced in real time at the displacement control point. Finally, the volumetric thermal error was actively controlled by adjusting the temperature field of the machine tool.

The simulated and experimental results indicate that the transient analytical model can accurately predict the real-time thermal characteristics of the machine tool and that the real-time active thermal control method can effectively reduce volumetric thermal errors. Using active thermal control, the squareness error in the YZ-plane was reduced by approximately 45%, the spindle thermal elongation was reduced from 23 μm to 7 μm, and the volumetric thermal error in the X, Y, and Z directions were reduced by approximately 16, 14, and 17 μm, respectively.