Optimization and prediction for gear microgeometry modification considering fabrication errors

Transmission error (TE) in multistage gear transmission is the main excitation source of gear mesh noise. Gear microgeometry modification can effectively reduce TE, while the determination of the modification amount is a challenge. The stochastic fabrication errors of modification dimensions lead to uncertain results. To anticipate and evaluate this uncertainty during the design stage, a convolution optimization method is proposed that takes both the nominal modification values and the probable deviations of fabrication errors into consideration. To best simulate the distribution of deviations of fabricated dimensions, a multi-dimensional skew-normal Gaussian kernel is studied. By calculating the convolution of the Gaussian kernel and TE levels of candidate modification range, one obtains a prediction that is closer to the reality than simply treating the nominal values as design variables. To verify the effectiveness of this method, a case study of vehicle's transmission is conducted. Monte Carlo stochastic simulation and experimental bench test are performed. Compared with the single-point nominal value optimization, the average level of peak-peak TE and vibration acceleration is reduced. The quality of products is increased for large-scale production. It provides new ideas for both gear microgeometry modification and other industries that need to estimate the uncertain influence of fabrication errors and predict the massive manufacturing results.