# Solution of dynamic equation and analysis of dynamic characteristics of spiral bevel gear transmission

The dynamic characteristics of spiral bevel gear transmission system are studied. The main contents are as follows:

(1) Using the self-developed spiral bevel gear parametric modeling software, a pair of three-dimensional models of spiral bevel gears are established in CATIA, assembled and imported into ANSYS for finite element analysis, and the tooth comprehensive meshing stiffness of spiral bevel gear transmission system is calculated.

(2) The 8-DOF nonlinear dynamic model of spiral bevel gear is established by using the concentrated mass method. The tooth side clearance, time-varying meshing stiffness and transmission error of gear pair are comprehensively considered in the model. The model is a multi degree of freedom bending torsion axis coupling vibration model. By introducing the relative vibration displacement along the meshing line, the 8-DOF nonlinear dynamic model is reduced to 7-DOF nonlinear dynamic model, and the differential equation and dimensionless unified differential equation of the 7-DOF nonlinear dynamic model are derived.

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

(4) The non dimensional unified differential equation of spiral bevel gear is solved by Runge Kutta method. The dynamic response characteristics of spiral bevel gear transmission, including time-domain response and dynamic load characteristics of each degree of freedom, are studied and analyzed. The effects of input speed, driven gear support stiffness and input torque on dynamic load coefficient are discussed, The results show that smaller support stiffness and larger input torque can reduce the dynamic load coefficient of spiral bevel gear transmission.

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