Abstract
Frictional finite-element solves of spur-gear tooth stress take tens of seconds. A ten-member Fourier neural operator (FNO) ensemble, trained on 270 of 432 quasi-static plane-strain solutions with Coulomb friction in the single-tooth contact zone, predicts the tooth stress field from normal approach, friction coefficient, elastic modulus, and contact position. On held-out trajectories, it reproduced finite-element labels to 1.0% relative L2 error (0.6% to 2.3% over six trajectory-grouped partitions) and to 1.9% on six trajectories with unseen contact positions and approaches. One prediction takes 76 ms on a CPU, 358 times faster than a solve. With a sharp, clamped root, refining every mesh length scale changed the labels by 5.6% (1.5-fold) and 7.4% (2-fold). A filleted root on a deformable rim reduced these changes to 1.9% and 2.4%; an ensemble trained likewise reproduced the labels to 0.9% and their peak root stress to 0.7%. Friction changed the field by 8.7% between μ = 0.04 and 0.12, a change the surrogate reproduced case by case. Under matched tuning budgets, the FNO outperformed U-Net and POD-DeepONet. The results describe agreement with the numerical models and, as the contact spans one to two grid pixels, concern tooth-body and root stress, not contact pressure.