Wear-Induced Nonlinear Dynamic Response of a Face Gear Pair Considering Tooth-Surface Update and Phase-Dependent Backlash

To evaluate the influence of tooth surface wear on face gear dynamics, this study proposes a coupled wear–dynamics modeling method. A phase-dependent backlash model is developed to preserve the meshing-phase modulation induced by nonuniform wear along the meshing path. The wear-updated tooth surface is used to update the time-varying mesh stiffness, loaded transmission error, and backlash. These quantities are then incorporated into a nonlinear dynamic model. For the single-sided working-flank wear considered here, separate drive- and back-side thresholds are defined in an LTE-referenced coordinate. Experimental measurements are used to assess the contact trace and calibrate the effective wear coefficients. The wear-profile comparison uses the calibration dataset and is interpreted as a post-calibration assessment. The dominant low-speed torque-spectrum peak is consistent with the mesh frequency calculated from shaft speed and tooth count; this kinematic check does not independently validate the dynamic model. The nonlinear dynamic responses are evaluated for a prescribed severe-wear state constructed numerically to give a maximum pinion wear depth comparable to the experimental value. The results show that nonuniform wear changes not only the mean backlash level but also the backlash boundary over the meshing phase. Across the 25-point b0 = 50:2.5:110 μm comparison at W=1.19 and four tested initial conditions, the phase-dependent model gives displacement RMS values of 47.60–166.50 μm and peak dynamic mesh forces of 7.46–20.42 kN, compared with 39.03–44.11 μm and 3.23–5.74 kN, respectively, for the three scalar models. The 2000-period calculations identify period-3 and period-1 responses at the two representative conditions, with initial-condition dependence at the latter.