Research on dimensionality reduction method of a high-dimensional nonlinear gear dynamics model and its dynamic characteristic analysis

With the development of gear dynamics towards refinement and systematization, various nonlinear factors are introduced, which leads to the contradiction between computational efficiency and requirements. It is necessary to find a method that can reduce the number of degrees of freedom to improve computational efficiency. Therefore, this paper proposes a proper orthogonal decomposition (POD) dimension reduction method for high-dimensional gear system nonlinear dynamic model, which can improve solution accuracy and efficiency. Firstly, the coupled nonlinear dynamic model of power split helical gear transmission system is established, and the rigid body displacement is eliminated by modal rigid body displacement method. Then, the system nonlinear response is equivalent to the superposition of static displacement, quasi-static displacement, linear small perturbation and nonlinear correction. The analytical expressions of the former two and POD dimension reduction model of the latter two are derived, and the system POD dimension reduction model is obtained. The POD model is further compared with the calculation results of full-freedom accurate model, and the influence of dimension on the efficiency and accuracy of the model is analyzed. Finally, the influence of main system parameters on system nonlinear dynamic characteristics is analyzed. The results show that the results of POD dimension reduction model are in good agreement with those of accurate model. The accuracy of POD model in strong nonlinear state is not as good as that in linear state, but it still meets the requirements. This method provides a solution to improve computational efficiency of high-dimensional gear system dynamic model.