关键词: 高线速, 直齿圆柱齿轮, 齿面网格离散, 有限元仿真, 滑移能

Abstract:  Finite element, as a common gear mesh simulation analysis method, is widely used in the study of gear dynamics performance. When the gear tooth surface is discretized by finite element grids, the grid size has a great influence on the correctness of the gear mesh finite element simulation results. In the gear meshing process, the contact between the gear teeth belongs to the contact between the two surfaces. The basic idea of surface finite element discretization is to use a finite number of grids to simulate a continuous smooth surface body, and to achieve the same discretization accuracy.The smaller the radius of curvature of the surface, the smaller the grid size is required. In addition, high linear speed spur gears have a high rotational speed, and the mesh of the tooth surface finite element has large centrifugal strength, which leads to impact vibration between meshes when the tooth surface finite element model is involved in meshing.The model has some error regarding the actual tooth surface contact. Therefore, in order to establish an accurate tooth contact finite element model, the key problem is to find an optimal multiplicative relationship between the tooth face finite element grid size and the tooth face radius of curvature at different rotational speeds. To solve the precise discretization problem of the finite element mesh of a high-speed spur gear tooth surface, this paper presents a method for selecting the tooth surface grid size. This method can adapt to the variation of the tooth surface sliding speed and the curvature radius during tooth meshing. Formulas of the curvature radius, tangential velocity, relative slip velocity and loads at any meshing point on the tooth profile are acquired according to the geometric and velocity vector relations to the main and slave gear tooth profile in the meshing process. Taking the transmission gear in an aero-engine under research as an example, the approximate range of parameters such as radius of curvature, tangential velocity, relative slip velocity, and loads on the high-speed gear tooth surface of the aero-engine is obtained through calculation. Based on this range, several sets of cylindrical roller surface contact finite element models are established with suitable curvature radius, different rotational speeds, contact surface grid size, and constant relative slip velocity and loads. The sliding energy generated by the contact of the two cylindrical rollers is used to simulate the sliding energy generated by the tooth contact. Finally, under the condition that the error between the simulation value and the theoretical value of the sliding energy is less than 10%, the optimal relationship between the tooth surface grid size and the tooth surface curvature radius at different tooth surface tangential speeds is obtained through analysis. The research results show that, when the maximum tooth surface tangential velocity is 0-25 m/s, the tooth surface grid size should be one fortieth of the minimum curvature radius of the tooth surface; when the maximum tooth surface tangential velocity is 25-40 m/s, the tooth surface grid size should be one seventieth of the minimum curvature radius of the tooth surface; when the maximum tooth surface tangential velocity is 40-55 m/s, the tooth surface grid size should be one hundred and tenth of the minimum curvature radius of the tooth surface. The simulation results of the finite element model obtained by using the above-mentioned tooth surface finite element grid discretization method have an error of less than 10% of the theoretical value.