Dynamic Models of Spur and Planetary Gear Drives

For involute spur gear drive and planetary gear drive, the yaw-torsion coupling non-linear dynamic model including the dynamic changes of gear meshing plane force system and meshing force direction was established.

(1) For involute spur fixed-shaft gear drive, firstly, considering the uneven load distribution in the direction of tooth width, the meshing plane force system between gear pairs is analyzed, which is equivalent to the meshing force and the offset load moment perpendicular to the meshing plane. Then, the centroid position vector of each gear is analyzed, and the center distance variation caused by geometric eccentricity, center distance deviation and transverse displacement is considered.The dynamic changes of meshing force action direction are analyzed by changing tooth surface and meshing state. Finally, considering the gyroscopic effect caused by the change of space orientation of rotating shaft, the yaw-torsion coupling non-linear dynamic model is established by Lagrange method.

(2) For Involute Spur Planetary Gear drive, firstly, for external engagement pair composed of sun gear planetary gear and internal engagement pair composed of ring gear respectively, the centroid position vector of each gear is analyzed, the center distance change and tooth surface and engagement state change caused by geometric eccentricity and transverse displacement are considered, and the dynamic change of engagement force action direction is analyzed; secondly, the dynamic change of engagement force direction is considered.The nonlinear dynamic model of yaw-torsion coupling is established by Lagrange method for gyroscopic effect caused by the change of spatial orientation of rotation axis.

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