• The highlights of the study focus on the following aspects: • An analytical expression for the frictional torque across a single oscillation cycle was subsequently developed, utilizing simulation data and prior experimental measurements by partitioning the oscillation interval, thereby facilitating a quantitative characterization of the frictional process for one complete cycle. • A hybrid-driven model for the oscillating frictional torque of spherical bearings under fretting conditions—integrating simulation, prior data, and analytical methods—quantifies the adhesion-to-slip process and describes the torque evolution within a single cycle, while its structure is robust against variations in frequency, load, and coating. Spherical bearings are widely used in the field of dampers, and their oscillating friction characteristics are a key factor affecting the damper's attitude adjustment capability. This study proposes a modeling approach for single-cycle friction torque in spherical bearings under oscillating conditions, driven by a hybrid integration of simulation, prior data, and analytical models, to advance the understanding of frictional behavior during oscillatory motion. First, the stress distribution of the bearing's inner ring was simulated using ANSYS software to obtain the maximum contact stress and path stress required for the analytical model. Then, a first-order differential equation for friction torque was established based on spherical micro-elements, and the oscillating friction torque was mathematically modeled by dividing the swing angle range using prior data. Compared to existing qualitative descriptions of oscillating friction torque under fretting conditions, this hybrid-driven torque model achieves a quantitative description of the friction process. Finally, oscillating friction experiments were conducted on three types of bearings—graphite-embedded copper bearings, TiAlN-coated graphite-embedded copper bearings, and graphite bearings—under different swing speeds and radial loads. The results verified the accuracy and generalization capability of the proposed oscillating friction torque model.
Liang et al. (Sun,) studied this question.