The main difference between the three-dimensional dynamic model of the sun-planetary gear and that of the fixed-shaft gear drive is that the planetary gear has an associated motion with the motion of the planetary carrier.The three-dimensional dynamic model of the sun wheel and the first planetary wheel is shown in the figure.In the figure, Cs and C PI are the centroid positions of the sun and planetary wheels respectively; es and EPI are the eccentricities of the sun and planetary wheels respectively; and phis and phipi are the initial rotation angles of the sun and planetary wheels’centroid respectively.
A two-dimensional projection model of the three-dimensional dynamic model of the solar wheel and the first planetary wheel on the oxy plane is shown.In the figure, dashed line is the position of two gears at the initial moment, solid line is the position of two gears at any time, Oe is the centroid position of planetary carrier at any time, alphaspi is the engagement angle at any time, and gamma SPI is the relative position angle at any time.In the fixed coordinate system oxy, the vector coordinates of the planetary frame mass center Oc and the planetary wheel axis center Opi are:
Where I and j are the unit vectors in the fixed coordinate systems ox and oy.
