Thermal error compensation model for a motorized spindle with shaft core cooling based on exponential function

Thermal issues become more serious for high-speed and high-precision motorized spindle. Thermal error compensation is cost-effective and convenient to implement for this problem. To further improve the machining accuracy of the motorized spindle with shaft core cooling, this study aims to develop simple thermal error compensation model based on only the rotational speed of spindle and without any temperature data to predict the thermal error. In this study, a special measurement system was established to measure the axial thermal deformation of a motorized spindle with shaft core cooling at various speeds. A thermal error compensation model based on the exponential function was established using the experimental data. This model needs only two parameters—operating rotational speed and duration—of the motorized spindle to predict the thermal deformation and then can be easily and quickly executed without adding any extra hardware. The model is verified by comparing with experimental data at constant speeds of 4200 rpm and 7000 rpm as well as the stepped speed. The results show that the model has higher accuracy and better robustness. Under experimental conditions, when the motorized spindle operates at constant rotational speed, its accuracy increases by about 90% after compensation; when the motorized spindle operates at stepped rotational speed, the maximum thermal deformation of the motorized spindle is 29.95 μm before compensation and 2.01 μm after compensation, the accuracy of which increases by 93.2%.