Efficient analysis of time-varying mesh stiffness of helical gear pair using neural networks and autoencoders

Abstract This study proposes a surrogate-based approach for estimating the Time-Varying Mesh Stiffness (TVMS) of gear pairs. TVMS is a significant source of parametric-induced vibrations in the gear transmission dynamic simulation. Traditionally, TVMS is estimated using computationally intensive finite-element-based methods like Loaded-Tooth Contact Analysis (LTCA). In a gear geometry dimensioning step, macro-geometry parameters such as module, pressure angle, and helix angle are varied within certain intervals to identify feasible gear designs. Then, LTCA calculates the TVMS for valid designs under the variation of Torque and micro-geometry parameters such as profile crowning. The TVMS response is discretized into 300 rolling positions to capture the nonlinear behavior of the gear meshing cycle. Two models are proposed: (1) ModelNN, a Fully Connected Neural Network (FCNN) that predicts TVMS of all rolling positions using the roll angle as input feature, and (2) ModelAE-NN, where an autoencoder reduces the 300-dimensional TVMS response to 5–20 low-dimensional features, which are then estimated using FCNN. Both models are validated on 200 unseen test samples, achieving R 2 (coefficient of determination) values over 0.99. However, ModelAE-NN is shown to be more robust, as dimensionality reduction reduces overfitting and enhances generalization. The models accelerate TVMS estimation by 24,000 times compared to LTCA. Global sensitivity analysis shows that torque is the dominant factor influencing the nonlinear gear mesh behavior. Overall, the study demonstrates the effectiveness of surrogate modeling in predicting TVMS.