# Meshing stiffness analysis of variable hyperbolic arc gear based on finite element method

In the process of gear meshing, the periodic changes of the number of meshing teeth and meshing position lead to the periodic changes of gear meshing stiffness, which leads to gear vibration and noise. In order to determine the meshing stiffness of gear, it is necessary to accurately calculate the comprehensive elastic deformation and normal contact force of the tooth surface in the meshing area at each moment, which has always been an important problem in the study of gear dynamics.

In the aspect of gear stiffness calculation, scholars at home and abroad have done a lot of research. Wang Longbao analyzed the calculation formula of gear meshing stiffness and determined the influencing factors and regularity of spur gear meshing stiffness; Li Yapeng and others put forward an improved Ishikawa formula based on the analytical Ishikawa formula, and obtained a new calculation method of gear time-varying meshing stiffness; Bu Zhonghong and others used linear programming The meshing stiffness of involute cylindrical gear is calculated by the finite element method, and the change rule of meshing stiffness in one meshing cycle is obtained; Tang Jinyuan et al. 23-24 studied the meshing stiffness calculation method of spiral bevel gear by using the finite element method, and obtained the single tooth meshing stiffness and multi tooth comprehensive meshing stiffness. However, it is difficult to deduce and determine the meshing stiffness of a new type of variable hyperbolic arc gear whose tooth surface is a hyperboloid with constant curvature.

Based on the finite element analysis of load contact of variable hyperbolic arc gear, the finite element calculation method of meshing stiffness of variable hyperbolic arc gear is studied. The principle of parameter selection in the process of finite element calculation is analyzed, and the comprehensive elastic deformation and maximum normal contact force of a pair of variable hyperbolic arc gear pair in the meshing area are analyzed by using the finite element software ABAQUS, and the single tooth meshing stiffness and double tooth meshing stiffness are obtained. Finally, the influence of different loads on the meshing stiffness curve is studied, and the influence law of load on the meshing stiffness of variable hyperbolic arc gear is obtained, which lays the foundation for the dynamic analysis of variable hyperbolic arc gear. 