For the fixed shaft gear drive, the design parameters of each gear pair are different, the period of meshing stiffness is also different, and the superposition effect of periodic vibration is not obvious. In the same stage of planetary gear transmission, there may be phase difference between the meshing pairs, that is, when the teeth of one planetary gear just enter the meshing, the teeth of other planetary gears have already entered or have not entered the meshing, and the phase exists leading or lagging. The theory of phase difference design points out that there is phase difference in planetary gear drive when the following conditions are met simultaneously:
Where, ZS is the number of sun gear teeth, zγ is the number of ring gear teeth, and I is an integer.
There are three kinds of phase difference relations for each meshing pair in planetary gear drive, respectively:
(1) The phase difference relationship between the outer meshing pairs of the sun wheel and each planet wheel;
(2) The phase difference relationship between the ring gear and the inner meshing pair of each planetary gear;
(3) For each planetary gear, there is a phase difference relationship between the outer meshing pair of the planetary gear and the sun gear and the inner meshing pair of the planetary gear and the ring gear.
Firstly, the dynamic backlash caused by the change of center distance is derived. Secondly, the influence of the change of speed, phase difference and the meshing state of tooth surface and tooth back on the meshing stiffness is analyzed, and the dynamic meshing stiffness is calculated by analytic method. Finally, the dynamic backlash is combined with the dynamic tooth side A nonlinear dynamic mesh model is proposed for clearance and dynamic mesh stiffness.