The figure shows the dynamic model of spiral bevel gear transmission system under elastic support. Establish a rectangular coordinate system, the coordinate origin is the intersection of the axes of two spiral bevel gears, and the x-axis and y-axis are the axes of pinion and big gear respectively. The dynamic model is established based on the concentrated parameter method. The concentrated mass and concentrated moment of inertia are used to simulate the two spiral bevel gears, the massless rigid body is used to simulate the shaft, and the spring and damper are used to simulate the elastically supported bearing. In this way, an 8-DOF spiral bevel gear transmission system can be obtained, including the coupling vibration of the axial vibration, bending vibration and torsional vibration of the two gears along the x-axis, Y-axis and z-axis.
The generalized displacement column vector of spiral bevel gear transmission is:
Where Xi, Yi and Zi (I = 1,2) are the transverse vibration displacement of spiral bevel gear axis along X axis, Y axis and Z axis respectively; θ I (I = 1,2) torsional vibration angle of main driven gear around x-axis and y-axis respectively.