Development of a Digital Model for Predicting the Variation in Bearing Preload and Dynamic Characteristics of a Milling Spindle under Thermal Effects

The spindle tool is an important module of the machine tool. Its dynamic characteristics directly affect the machining performance, but it could also be affected by thermal deformation and bearing preload. However, it is difficult to detect the change in the bearing preload through sensory instruments. Therefore, this study aimed to establish a digital thermal–mechanical model to investigate the thermal-induced effects on the spindle tool system. The technologies involved include the following: Run-in experiments of the milling spindle at different speeds, the establishment of the thermal–mechanical model, identification of the thermal parameters, and prediction of the thermal-induced preload of bearings in the spindle. The speed-dependent thermal parameters were identified from thermal analysis through comparisons with transient temperature history, which were further used to model the thermal effects on the bearing preload and dynamic compliance of the milling spindle under different operating speeds. Current results of thermal–mechanical analysis also indicate that the internal temperature of the bearing can reach 40 °C, and the thermal elongation of the spindle tool is about 27 µm. At the steady state temperature of 15,000 rpm, the bearing preload is reduced by 40%, which yields a decrease in the bearing rigidity by approximately 16%. This, in turn, increases the dynamic compliance of the spindle tool by 22%. Comparisons of the experimental measurements and modeling data show that the variation in bearing preload substantially affects the modal frequency and stiffness of the spindle. These findings demonstrated that the proposed digital spindle model accurately mirrors real spindle characteristics, offering a foundation for monitoring performance changes and refining design, especially in bearing configuration and cooling systems.