Modeling and analysis of thermal-vibration coupling of turntable bearing-torque motor

This article focuses on the thermal-vibration behaviors of permanent magnet synchronous torque motor systems during machine tool cutting. To study thermal-mechanical dynamic interaction, it establishes a dynamic model and a thermal resistance network model. For the dynamic model, Hertz contact theory analyzes angular contact bearing vibration displacements to derive elastic restoring forces and stiffness matrices; the slicing method obtains turntable bearing roller loads, yielding vibration displacement-related nonlinear restoring force and stiffness. For thermal analysis, the Palmgren formula calculates rotating angular contact bearing heat generation; turntable bearing’s sliding, rolling, and viscous friction losses are evaluated. For motor heating, Bertotti’s theory splits stator iron loss into hysteresis, eddy current, and supplementary losses; Joule’s law computes stator copper loss, considering rotor permanent magnet eddy current loss. Temperature-displacement bidirectional coupling is achieved via the closed-loop iterative method. Experiments verify the method’s correctness and effectiveness (temperature comparison points’ maximum relative errors: 9.7986 and 6.3207%; Pearson correlation coefficients r of vibration responses at three speeds: 0.9317, 0.9216, 0.9208; p ≪ 0.05). Parameter analysis shows rotational speed, bearing preload, and turntable bearing roller number significantly affect system heat generation and response. Rotational speed has the most prominent impact (a 10 rpm increase leads to >30% amplitude growth and more than doubled temperature rise). Moreover, the spindle system’s thermal-mechanical dynamic interaction is non-negligible.