Nonlinear connection of multi stage gear transmission box coupling dynamic model

Bearing reaction force, meshing load of fixed shaft gear, driving torque of cutting motor and cutting roller load are considered as nonlinear connections. In addition, the gears of the planetary gear train are also non-linear connected, but because they have been written in the form of matrix, they can be easily coupled to the cutting transmission system, as shown in the formula.

In this paper, we only discuss the nonlinear connections which are difficult to be expressed in matrix form. They all exist in the form of self defined sub functions of MATLAB and are normally recorded as RI (Qi, Qi, t). The input variables are the generalized displacement vector, the generalized velocity vector and the time scalar of the substructure in turn. Taking the first and the third degree of freedom, the second and the fifth degree of freedom respectively adding nonlinear connections R1 and R2 as examples (assuming that the number of degrees of freedom of the system is 5), the matrix operation is described.

In the formula, the first and third degrees of freedom connected by R1, the second and fifth degrees of freedom connected by R2, and the number of degrees of freedom refer to the number after adding the rigid connection.