The torque of the driving gear and the internal force acting on the gear are given. In order to show the force of the driving gear more clearly, the force of the driven gear is not given. Its magnitude is equal to that of the driving gear, and the direction is opposite to that of the driving gear. The dynamic meshing forces NPI (T) and NGI (T) acting on the driving gear and driven gear can be expressed as follows:
The viscous damping coefficient CI (T) of the gear system is time-varying. CI (T) can be expressed by time invariant damping ratio and gear time-varying meshing stiffness ki (T)
According to the formula, the friction force FPI (T) and FGI (T) of driving gear and driven gear can be expressed as follows:
The friction arm xpi (T) and NGI (T) of driving gear and driven gear can be expressed as follows:
To sum up, the governing equations of the dynamics of a 6-DOF nonlinear gear system can be expressed as follows:
