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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. [ABSTRACT FROM AUTHOR]

Bearing preload significantly affects the running performance of a shaft-bearing system including the fatigue life, wear, and stiffness. Due to the mounting error, the bearing rings are often angularly misaligned. The effects of the combined bearing preload and angular misalignment on the fatigue life of ball bearings and a shaft-bearing system are analyzed in this paper. The contact force distribution of angular contact ball bearings in the shaft-bearing system is investigated based on the system model. The system model includes the bearing model, and the shaft model is verified by comparing with the manufacturer's manual and the results from other theoretical models, with the difference between the results from the present bearing model and manufacturer manual within 3%. The global optimization method is used to replace the Newton–Raphson algorithm to solve the ball elements' displacements and friction coefficients, which improves the computation efficiency of the system model. The fatigue life of each bearing is evaluated with the consideration of the two preload methods and two angular misalignment cases. The fatigue life results show that the system life at the optimal angular misalignment is more than 1.5 times that without angular misalignment at the low preload value, and this ratio decreases as the preload value increases. The optimal angular misalignment of both the shaft-bearing system and the misaligned bearing is not always consistent, which depends on the preload value and bearing life. Both the constant-displacement preload and constant-force preload do not cause a significant difference in the highest system life. The different misaligned bearings can lead to different highest system lives as the preload value is low. [ABSTRACT FROM AUTHOR]