Transmission error prediction of spur gear and parameter optimization of tooth profile modification considering micro-contact of the tooth surface

This study, which is based on Blending ensemble learning and a differential evolution algorithm, achieved the prediction of gear transmission error while considering micro-contact and the optimization of tooth profile modification. First, the micro-topography of the modified tooth surface was generated based on the conjugate gradient method. A modified spur gear model with a rough tooth surface was constructed, and its meshing process was simulated to obtain the static transmission error and calculate the peak-to-peak value. Second, on the basis of finite element modeling and simulation methods, the peak-to-peak values of the gear transmission error under different modification parameter conditions were obtained, and a dataset of 50 groups was constructed and divided into a training set and a test set. Eight single surrogate models were selected, and on the basis of the Blending ensemble learning strategy, base learners and meta-learners were optimized to construct a prediction model for the peak-to-peak value of the gear static transmission error. The differential evolution algorithm was employed to optimize modification parameters, minimizing the peak-to-peak value of static transmission error, with finite element simulation verifying the reliability of the optimization results. Research findings indicate that utilizing RF, SVR, GBM, and RBF as base learners and RBF as a meta-learner in the Blending ensemble learning model yields the highest prediction accuracy, achieving a Mean Absolute Percentage Error (MAPE) of 14.183%. This represents an average decrease in prediction error of 2.75% compared to single models. Furthermore, the peak-to-peak value of static transmission error for the gear with optimized modification parameters was 3.69 μm, a reduction of 23.19% compared to gears with randomly generated modification parameters, thereby validating the accuracy and reliability of the proposed method.