# Construction of mathematical model of multi-stage gear transmission system

According to the stiffness characteristics, there is a certain difference between the multi-stage gear transmission and the general gear transmission. The main purpose of installing radial meshing multi-stage gear transmission between load and actuator is to transfer power and realize movement, so the influence of elasticity and backlash must be considered. The mathematical model is established by considering the influence of elasticity and backlash.

In the model, IL is the load inertia, IM is the inertia of the rotor and wave generator of the executive motor. The rotation angle of the motor is calculated according to φ m (T) = φ m (T) / IH.

When the backlash is 2jt, the following equations can be used to express the equations.

It is considered that the backlash is a nonlinear function. In the multi-stage gear transmission system, the system from the motor to the load is equivalent to a link with two elastic elements, which is the motion transfer of the concentrated mass separated by the gap. In the model, I I is the inertia converted from im to the output shaft, and φ I (T) and Ti are the input torque and angle converted to the output end.

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