Test function.

To determine the optimal design parameters of spur gear under a specific condition, based on the basic theories of gear dynamics theory, gear meshing principle, tooth contact analysis and load tooth contact analysis, a six-degree-of-freedom vibration analysis model of spur gear pair is established, and a gravitational search-simulated annealing hybrid algorithm (GSA-SA) is used to optimize the gear addendum modification coefficient and profile modification parameters. The vibration response of the spur gear pair is evaluated through the optimization objective function established by the combination of the G1 method and variation coefficient method. The study shows that the optimized design parameters effectively reduce the level of the vibration, which proves the effectiveness of the optimization method, and the simultaneous optimization of the addendum modification coefficient and profile modification parameters of the gear has a better result than only optimizing the addendum modification coefficient or profile modification parameters. This method can be used for gear transmission system vibration optimization design in the automotive industry and shipbuilding.