# Calculation of meshing stiffness and meshing damping of straight bevel gear

If you want to solve the dynamic equation of straight bevel gear pair, you need to get the values of various parameters in the equation, including the values of gear meshing stiffness and gear meshing damping; At present, it is difficult to accurately solve the gear meshing damping. In addition, compared with the gear meshing stiffness, the gear meshing damping has little impact on the system performance. Many gear researchers ignore the impact of meshing damping on the dynamic characteristics of gears. Therefore, R. kasuba calculation formula is used to solve the straight bevel gear meshing damping in this paper.

Let the number of teeth of the straight bevel gear pair participating in the transmission at a certain time be n, and the deformation of the teeth of the driving gear and the driven gear in the transmission process be respectively δ 1I and δ 2I, the gear meshing force is fi, from which the gear meshing stiffness K can be obtained as follows:

In the transmission process of straight bevel gear pair, the position of tooth transmission and the number of teeth entering the meshing state at the same time change periodically with time, resulting in the time-varying comprehensive meshing stiffness of teeth. However, the meshing stiffness of straight bevel gear changes little with time, and there is no sudden change in the change process. Therefore, the vibration equation of straight bevel gear system can be solved by referring to the method of solving linear differential equation.

In the meshing process of straight bevel gear, the comprehensive meshing stiffness of straight bevel gear is formed by the comprehensive action of the meshing stiffness between each pair of meshing teeth. The deformation, stiffness and coincidence of teeth will have different degrees of influence on the comprehensive meshing stiffness of straight bevel gear.

The meshing damping of straight bevel gear can be solved according to the existing theoretical formula:

Where, ζ G is the gear meshing damping ratio coefficient, which is obtained by R. kasuba and K.L. Wang through calculation and test analysis ζ The value of G is 0.03 ~ 0.17. I1 and I2 are the moment of inertia of planetary and half shaft gears respectively, and R1 and R2 are the indexing circle radius of planetary and half shaft gears respectively.

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