Nonlinear dynamic model of coupling of involute spur gear drive

According to the method used in establishing dynamic model, the dynamic model of gear transmission system can be divided into centralized parameter model and finite element model.Among them, the centralized parameter model has high calculation efficiency and is widely used in the research of dynamic characteristics of gear transmission system.

The test shows that the transverse vibration caused by the deformation of the drive shaft and bearing needs to be considered in order to establish an accurate centralized parameter model.Many scholars at home and abroad assume that the meshing force of gears distributes uniformly along the tooth width direction, simplify the gear movement into two-dimensional plane motion including transverse and torsional degrees of freedom, and establish the transverse-torsional coupling non-linear dynamic model of involute spur gear drive system on this basis.

At the same time, the meshing force of gears in most models always follows the direction of theoretical meshing line, ignoring the influence of center distance change and meshing state change of tooth surface (working tooth surface) and back (non-working tooth surface) on the direction of meshing force.With the development of gear drive system toward high speed and heavy load, the vibration of gear drive system is aggravated, and the change of center distance during gear drive process is also increased. Due to the existence of tooth side clearance, the engagement state of tooth surface and tooth back may alternate.At the same time, the vibration form of gear transmission system is more complex, including not only transverse and torsional vibration but also swing vibration.

For involute spur fixed-shaft gear drive and planetary gear drive respectively, a yaw-torsion coupling non-linear dynamic model was established by Lagrange method. In the model, the influence of center distance change on the direction of engagement force caused by geometric eccentricity, center distance deviation and transverse displacement of the gear was considered, and the influence of meshing state change on the direction of engagement force was also considered.The unbalanced inertia force caused by geometric eccentricity, the gyroscopic moment caused by the change of spatial orientation of the rotating shaft and the unbalanced load moment caused by the uneven load distribution along the tooth width direction are considered.