Nonlinear dynamic model of yaw-torsion coupling was established for involute spur fixed-shaft gear drive and planetary gear drive respectively, and a non-linear dynamic engagement model was put forward. Vibration characteristics test and model verification were carried out for two-stage fixed-shaft gear drive and single-stage planetary gear drive respectively. Single-stage gear drive was analyzed based on yaw-torsion coupling non-linear dynamic model.Dynamic and non-linear dynamic characteristics of stage gear drive system under steady-state and no-load conditions; for single-stage gear drive system, the influence of profile modification parameters on static and dynamic characteristics is analyzed, and the optimal design of profile modification is carried out; for tracked vehicle gear drive system, the dynamic characteristics of gear drive system under gears are systematically analyzed and established.An optimization model considering the dynamic characteristics of each gear is developed and the optimization design is carried out.The main research results and conclusions are as follows:

(1) For involute spur fixed-shaft gear drive and planetary gear drive respectively, a non-linear dynamic model of yaw-torsion coupling including dynamic changes of gear meshing plane force system and direction of meshing force is established by Lagrange method. The influence of center distance change on direction of meshing force caused by geometric eccentricity, center distance deviation and transverse displacement of gear is considered in the model.The influence of meshing state changes of tooth surface and back on the direction of meshing force is considered. The unbalanced inertia force caused by geometric eccentricity, the gyroscopic moment caused by the change of space orientation of rotating shaft and the unbalanced load moment caused by uneven load distribution in the direction of tooth width are considered.

(2) For involute spur fixed-shaft gear drive and planetary gear drive respectively, a non-linear dynamic engagement model including dynamic backlash and dynamic engagement stiffness is proposed, which can be applied to profile modification gear. In the model, the influence of center distance change on backlash is considered, and profile modification, speed change, center distance change, tooth surface and back engagement state change are also considered.Effect on meshing stiffness.The non-linear dynamic engagement model realizes feedback calculation of the non-linear dynamic model coupled with the yaw-torsion of gear drive and can be used to analyze the coupling effect between dynamic changes of engagement parameters and vibration response during gear drive.

(3) Vibration characteristic test research and model validation were carried out for two-stage fixed-shaft gear drive test device and single-stage planetary gear drive test device respectively.The numerical simulation results and test results of gear drive system under several steady-state conditions are compared and analyzed.The results show that the simulation results are in agreement with the test results and the errors are within acceptable range, which verifies the correctness of the proposed nonlinear dynamic model and the nonlinear dynamic engagement model for the yaw-torsion coupling of involute spur gear drive.