# Numbering method of degrees of freedom for multi-stage gear transmission box coupling dynamic model

The generalized displacements of substructure dynamic equations are numbered in local coordinates, and the generalized displacements of each substructure will be renumbered in the global coordinates of the system after coupling. Therefore, it is necessary to clarify the two (local and global) numbering methods of degrees of freedom and their transformation relations. The number of substructures indicates the number of substructures in the coupling system, and 8 substructures can be numbered from 1 to 8 in any order; the number of nodes indicates the number of nodes contained in the substructure; the number of degrees of freedom of nodes indicates the number of degrees of freedom of any node in a substructure (the number of degrees of freedom of each node is equal).

It should be noted that the equality of the degrees of freedom of each node in the substructure is a condition artificially satisfied when the substructure is divided, which is for the convenience of programming. For example, the rocker box is regarded as two substructures when the degrees of freedom are numbered: box mode and box interface node. The box mode takes the first 60 orders, corresponding to 60 modal coordinates, so the box mode substructure can be regarded as one node, each node has 60 degrees of freedom, or as 60 nodes, each node has 1 degree of freedom. The product of the number of nodes and the number of degrees of freedom of the nodes is the total number of degrees of freedom of the substructure, and the total number of degrees of freedom of the eight substructures is 386.

The local number of degrees of freedom is represented by a three-dimensional vector

S is the number of substructures, n is the number of nodes, and D is the number of degrees of freedom. For example, the vector [3, 4, 5] t represents the fifth degree of freedom of the fourth node of the third substructure, that is, the fifth degree of freedom of the fixed axis gear 4. The global number of degrees of freedom is represented by a scalar. The method of converting the local number into the global number is as follows: according to the recorded information, all the degrees of freedom before the substructure s are accumulated, and the number of degrees of freedom of the local number in the substructure is added. For example, the global number converted from local number [3 4 5] t is 185. 