Prediction of thermal errors in a motorized spindle in CNC machine tools by applying loads based on heat flux

Abstract

The thermal errors of a motorized spindle are seen as a source of significant errors in computer numerical control (CNC) machine tools, and motion errors, geometrical errors, among others, that are consequences of the thermal errors in the spindle. A predictive model of the thermal errors of a motorized spindle is proposed using a loading method based on heat flux. At first, a finite element model for the steady-state and transient thermal-structure coupling analysis of a motorized spindle is established, in which the loading method based on heat flux is adopted to assign the total amount of heat to the ball, an inner race, and an outer race of angular-contact ball bearing proportionally. The response values of sample points are obtained by simulation, and then a response surface model for the prediction of the steady-state elongation of the spindle thermal deformation under the influences of four factors including rotational speed of a bearing, coolant temperature, ambient temperature, and preload is constructed. The simulation and experimental results indicate that predictive error of the steady-state elongation of the spindle thermal deformation is only 3.81 μm, and the thermal equilibrium time in the transient thermal-structure coupling analysis is almost same to the experimental result. The response surface model can predict steady-state errors arising from the changes in working conditions and corresponding changes of the spindle.