# Vibration reduction of spiral bevel gear transmission based on additional damping ring

This paper makes a systematic analysis and Research on the vibration reduction of spiral bevel gear transmission based on additional damping ring. The main work and conclusions are as follows:

1) Parametric modeling and design of spiral bevel gear

The spherical involute profile equation of spiral bevel gear is deduced. Based on the meshing principle and machining principle of spiral bevel gear, the parametric accurate modeling method of spiral bevel gear based on CATIA software is studied, which lays a foundation for the simulation contact analysis of spiral bevel gear.

2) Analysis and Research on nonlinear dynamic characteristics of spiral bevel gear transmission

Using the self-developed parametric modeling software of spiral bevel gear, a pair of three-dimensional models of spiral bevel gear are established in CATIA, assembled and imported into ANSYS for finite element contact analysis, and the tooth comprehensive meshing stiffness of spiral bevel gear transmission is calculated. Using the lumped mass method, an 8-DOF nonlinear dynamic model of spiral bevel gear transmission considering tooth side clearance, transmission error and time-varying meshing stiffness is established, and the established vibration differential equation is dimensionless.

The natural characteristics of spiral bevel gear transmission are analyzed, including natural frequency and array diagram corresponding to each order frequency. The effects of the average meshing stiffness of spiral bevel gear and the support stiffness of driving and driven wheels on the natural frequency of the system are discussed. The results show that the support stiffness of the driven wheel of spiral bevel gear has a great influence on the low-order natural frequency of the gear system, and the average meshing stiffness and the support stiffness of the driving wheel have a great influence on the high-order natural frequency of the gear system.

The dynamic characteristics of spiral bevel gear transmission are analyzed, and the displacement and speed response and dynamic load characteristics of each degree of freedom are obtained. The effects of input speed, driven gear support stiffness and input torque on dynamic load coefficient are discussed. The results show that small support stiffness and large input torque can reduce the dynamic load coefficient of spiral bevel gear transmission.

3) Damping mechanism and contact analysis of gear damping ring

The advantages and application of damping technology are expounded; The structure of the existing damping ring is introduced, and the damping mechanism of the damping ring is discussed through a simple single degree of freedom vibration; Based on the relevant knowledge of mechanics, the contact analysis and calculation of closed damping ring and open damping ring are carried out, and the expression of contact pressure between them and gear groove is obtained respectively; The expression of contact stiffness between damping ring and gear is obtained by using contact theory.

4) Analysis and Research on dynamic characteristics of spiral bevel gear transmission system with damping ring

Using the lumped mass method, the 12 degree of freedom nonlinear dynamic model of spiral bevel gear transmission system with additional damping ring is established, and the vibration differential equation is listed and dimensionless. The natural characteristics of the spiral bevel gear transmission system with additional damping ring are studied, including the natural frequency and the corresponding array diagram of each order frequency. The effects of the average meshing stiffness of spiral bevel gear, the support stiffness of driving wheel and the radial support stiffness of damping ring on the natural frequency of the spiral bevel gear transmission system with additional damping ring are discussed. The results show that the average meshing stiffness of spiral bevel gear has a great influence on the 8th natural frequency; The support stiffness of driving wheel has a great influence on the 5th-7th natural frequency; The radial support stiffness of damping ring has a great influence on the 9th-11th natural frequency.

The dynamic response of spiral bevel gear transmission system with additional damping ring is studied. The dynamic response of gear system with additional damping ring and without additional damping ring is compared. It is found that the displacement and velocity response of each degree of freedom are significantly reduced after adding damping ring; The effects of structural parameters of closed damping ring and open damping ring on the dynamic response and dynamic load coefficient of the system are studied, which provides a certain theoretical basis for the rational design of damping ring structure.

5) Development of parametric design software and dynamic analysis software for spiral bevel gears

Using VB Net and CATIA, the structural design and parameter modeling software of spiral bevel gear pair is developed, and the program interface and examples are given; The dynamic analysis software of spiral bevel gear transmission is developed through MATLAB programming, including the dynamic analysis module of spiral bevel gear transmission and the dynamic analysis module of spiral bevel gear system with additional damping ring, and the program interface and examples are given.

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