Nonlinear Dynamics of Double-Helical Gear Transmission Under Multi-Source Excitations with TEHL and Wear Coupling

A bidirectional tribo-dynamic coupled model for a double-helical gear transmission is established by integrating tooth surface wear, thermal elastohydrodynamic lubrication (TEHL), eccentricity error, tooth profile error, and temperature-induced deformation. The time-varying mesh stiffness and meshing impact excitation is also calculated. The proposed model distinguishes itself from previous works through the bidirectional coupling between the dynamic model and the TEHL/wear sub-models, which allows tribological evolution (wear accumulation and thermal expansion) to feed back into the vibration response—a feature absent in previous studies. Using this model, the influence of multi-source excitations on vibration characteristics is investigated, and the distributions of film thickness, pressure, temperature rise, and friction coefficient in the contact zone are obtained. The results show that eccentricity error affects vibration displacement more strongly than velocity (ratio ≈ 2:1), whereas wear influences velocity more than displacement (after 3 × 106 cycles, velocity increases by 50% vs. 8.1% for displacement); temperature rise significantly increases vibration velocity while slightly decreasing displacement. The TEHL sub-model predicts that the minimum film thickness and maximum pressure occur near the pitch point, with a temperature rise of approximately 35 K, and the friction coefficient exhibits a U-shaped distribution that shifts upward with accumulated wear. Vibration response is partially validated using vibration acceleration measurements on an FZG test rig under multiple operating conditions; the model shows consistent trends with experiments (errors < 20%), though direct validation of the tribological sub-models remains for future work.