As shown in the figure is the translation torsion coupling dynamic model of the spur gear transmission system established in this paper. Considering that each component contains three degrees of freedom, and the relative motion relationship between the components is relatively complex, in order to facilitate the establishment of the dynamic model and the subsequent solution, the following system coordinate system is established, and the position on the diagram is defined as the initial reference position, and oxy is taken as the initial reference position As an absolute reference coordinate system, the origin o is located at the rotation center of the planetary carrier, and this coordinate system is fixed; oxryr, oxcyc and oxsys are the dynamic coordinate systems on the inner gear ring, planetary carrier and sun gear respectively, and the origin o is located at the rotation center of the planetary carrier, and the X of the three coordinate systems is X The axis passes through the theoretical center of the first planetary gear, and is fixedly connected with the planetary carrier, and rotates at the same speed with the planetary carrier at its theoretical speed; the coordinate system onxnyn is the coordinate system which is fixed with the planetary carrier and rotates with the planetary carrier at constant speed. The origin on is located at the theoretical center of the nth planetary gear, and the two coordinate axes are connected with the coordinate system oxcyc on the planetary carrier
The two axes of are parallel. The choice of coordinate system does not change the physical characteristics of planetary gear transmission system, only affects the degree of difficulty in the analysis process.
In the picture:
KIX, KiY — the radial support stiffness of the ith member (I = s, C, R, 1, 2, 3,…, N;)
CiX, ciy — represents the radial support damping of the ith member;
KJT represents the stiffness of the jth member (J = s, C, R;)
Cjt — represents the damping of slewing support of planetary gear;
CSPN — the meshing damping between the nth planetary gear and the sun gear;
Crpn — the meshing damping between the nth planetary gear and the inner ring gear;
UI — represents the torsional line displacement of the ith member, UI = RI θ I, IR is the radius of the base circle of each gear; for the planetary carrier, it is the radius of the central distribution circle of the planetary gear, and θ I is the angular displacement of each member, and it is specified that the counter clockwise direction is positive.