Study on the thermally induced spindle angular errors of a five-axis CNC machine tool

Thermally induced spindle angular errors of a machine tool are important factors that affect the machining accuracy of parts. It is critical to develop models with good generalization abilities to control these angular thermal errors. However, the current studies mainly focus on the modeling of linear thermal errors, and an angular thermal error model applicable to different working conditions has rarely been investigated. Furthermore, the formation mechanism of the angular thermal error remains to be studied. In this study, an analytical modeling method was proposed by analyzing the formation and propagation chain of the spindle angular thermal errors of a five-axis computer numerical control (CNC) machine tool. The effects of the machine tool structure and position were considered in the modeling process. The angular thermal error equations were obtained by analyzing the spatial thermoelastic deformation states. An analytical model of the spindle angular thermal error was established based on the geometric relation between thermal deformations. The model parameters were identified using the trust region least squares method. The results showed that the proposed analytical model exhibited good generalization ability in predicting spindle pitch angular thermal errors under different working conditions with variable spindle rotational speeds, spindle positions, and environmental temperatures in different seasons. The average mean absolute error (MAE), root mean square error (RMSE) and R2 in twelve different experiments were 4.7 μrad, 5.6 μrad and 0.95, respectively. This study provides an effective method for revealing the formation mechanism and controlling the spindle angular thermal errors of a CNC machine tool.