# Meshing stiffness of spiral bevel gear based on finite element method

Stiffness excitation is one of the main excitation of gear meshing vibration. Determining the elastic deformation and meshing stiffness of gear teeth has always been an important problem in the study of gear dynamics.

In terms of gear stiffness calculation, scholars at home and abroad have done more research on the stiffness of cylindrical gears, and the stiffness calculation of cylindrical gears has been basically solved. Japanese scholar meizawa Qingyan has completed the stiffness calculation formula of bending and contact of involute cylindrical gears; Bu Zhonghong et al. Calculated the meshing stiffness and load distribution by using the linear programming method, and summarized the variation law of meshing stiffness in a meshing cycle; Shi Zhaoyao and others comprehensively considered the nonlinear factors such as time-varying meshing stiffness and error excitation in the gear meshing process, and studied the influence of meshing stiffness and machining error on vibration response under different working conditions. The research results have important theoretical and practical value for a complete understanding of complex gear dynamic performance and dynamic optimization design.

For spiral bevel gear, because its tooth surface is a complex curved surface, it is difficult to accurately calculate the time-varying meshing stiffness. It can be seen that there are few articles. Only Gosselin and others have given a method to calculate the stiffness of spiral bevel gear based on the finite strip method, but the literature only obtains the displacement curve along the tooth height and tooth length, and does not obtain the stiffness curve. Mennem et al. Used the finite element method to calculate the tooth contact flexibility under different loads, so as to obtain the time-varying stiffness.

(1) The construction method of time-varying meshing stiffness calculation model and meshing time-varying stiffness calculation method of spiral bevel gear based on finite element method are given, which lays a foundation for dynamic modeling and analysis of spiral bevel gear.

(2) Taking a pair of spiral bevel gears processed by denaturing method as an example, the calculation process of time-varying meshing stiffness is given, and its meshing stiffness curve is obtained.

(3) The variation of stiffness curve of spiral bevel gear under different loads is analyzed. The analysis results show that the change of load will have a great influence on the amplitude of stiffness curve. The increase of load increases the deformation of gear teeth, the contact area, the coincidence degree and the amplitude of stiffness curve. When calculating the stiffness curve, the influence of load on coincidence degree and contact position should be considered.

Based on the principle of loaded contact finite element analysis of spiral bevel gears, the calculation method of meshing stiffness of spiral bevel gears is studied, the finite element calculation and parameter processing method for calculating meshing stiffness are analyzed, and the normal contact force and comprehensive elastic deformation of a pair of five tooth spiral bevel gears are analyzed by using the commercial finite element software ABAQUS, The single tooth meshing stiffness and multi tooth comprehensive meshing stiffness are obtained, and the influence of load on the stiffness curve is studied, which lays a foundation for the dynamic analysis of spiral bevel gear.

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