Thermal errors caused by spindle rotation is a major factor that influences the precision stability of CNC machine tools. To determine an effective method for reducing thermal errors, a thermal experiment was carried out on the spindle of a vertical drilling center. The thermal deformation mechanism and thermal error variations of the spindle are presented. Based on the generation, convection, and conduction theory of heat, the thermal field model of a spindle system is derived. The relationship between the thermal field and the radial thermal error is established using a physically based method. Finally, the effect of the thermal error model proposed is verified by both a simulation and experiment. The results recorded on the two CNC machining centers indicate that the average fitting accuracy of the theoretical model is up to 94.1%, which validates the high accuracy and strong robustness of the presented model.

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