Modeling and dynamics analyzing of a torsional-bending-pendular face-gear drive system considering multi-state engagements

A face-gear drive system has been extensively used in important transmission devices with strict requirements for size and weight such as helicopter reducer and so on. Its dynamic characteristics directly affect the stability and reliability of the equipment. A piecewise torsional-bending-pendular nonlinear dynamics model of the face-gear drive system is established to study its nonlinear dynamics and dynamic characteristics. The multi-state engagements including drive-side teeth engaging, teeth disengagement, back-side teeth engaging, and alternate engaging between single-teeth pair and double-teeth pairs caused by the couple of the backlash and the contact ratio being greater than 1.0 is considered. The change of the dynamic engaging force and load distribution ratio for the system is analyzed by numerical results under three different states engagement. The effects of the load coefficient, meshing frequency and the comprehensive transmission error on the dynamic characteristics and nonlinear dynamics of the system are studied based on three different Poincare mappings defined by bifurcation diagrams, top Lyapunov exponent diagrams, phase portraits and variation curve of the dynamic engaging force. Results show that the complex phenomena such as teeth disengagement, drive-side and back-side impact occur with alternating meshing of the single and double pair teeth via the change of studied parameters. The research is helpful for the optimization of the face-gear drives.