Dynamic model of helical gear transmission system

The dynamic equation of helical gear system shown in the following formula is established by finite element method:

Where m is the mass matrix; X is the generalized coordinate; C is the damping matrix, including rotor gyro moment; K is the stiffness matrix; F is the external load vector.

The dynamic model of 12 DOF parallel shafting helical gear rotor system is established according to the dynamic equation. As shown in the figure, it is composed of large and small gears, primary parallel shafting and bearings. The system can be divided into shaft segment element, helical gear meshing element and bearing element. In order to consider the shear deformation of shaft segment element, the improved Euler Bernoulli beam is used as the theoretical model of shaft segment element. The detailed element model and matrix form can be referred to. Shaft 1 is composed of 7 shaft segments and 8 nodes, Shaft 2 consists of 10 shaft segments and 11 nodes in total. The mean value of meshing stiffness of helical gear K12 = 5.98 × 108n / M is substituted into the system dynamic model to the undamped natural frequency of the coupling system.

Scroll to Top