One-dimensional model for axial thermal error in a micro high-speed spindle

This article proposes a robust and accurate axial thermal error model for a micro high-speed spindle. With measured temperatures, an inverse method is applied to obtain the heat source and temperature field in the spindle for demonstrating that there exists a uniform temperature distribution along the axial direction within the motor range. Hence, a simple one-dimensional heat transfer model is established to acquire the temperature and resulting thermal errors using only one measured temperature on housing surface. Jumped displacement when the spindle starts and stops and the nonlinear deformation on the bearings are satisfactorily treated in the model. The results show that the estimated thermal errors agree with the measured data for both constant and various speeds. In addition, the results reveal that spindle speed significantly affects the maximum thermal error. A short processing time is an advantage of the proposed method. The model promises effective integration in machine tools for compensating thermal errors.