Establishment of equivalent dynamic model of Spur Planetary Gear

The model of gear transmission system is the expression of system mechanics and mathematics, and is the basis of gear dynamics analysis. A good model can accurately simulate the actual system, and can simplify the problem and reduce the amount of calculation to a certain extent. For the single-stage planetary gear transmission system studied, the dynamic model of the system is established by the centralized parameter method, and the variables in the model have nothing to do with the spatial position.

Each component contains three degrees of freedom, which are translation degrees of freedom in vertical and horizontal directions and rotational degrees of freedom about their own axis. Considering the complexity of the translational torsional dynamic model established in this paper, before analyzing its dynamic characteristics, it is necessary to make relevant reasonable simplification and assumptions on the structure of the system

(1) The mass of each component in the system is concentrated at one point of the mass center; the meshing motion between the teeth is simplified as the relative motion between two mass blocks connected by spring and damping in the direction of the meshing line; the radial and circumferential supports of the component are equivalent to the elastic spring and damping of tension and compression and torsion respectively, and the spring and damping are regarded as the elastic elements without mass.

(2) The gears studied in this paper are all involute standard spur gears, ignoring the axial force, each component vibrates in the plane perpendicular to the axis, and ignores the friction between the components.

(3) The quality and machining accuracy of each planetary gear are the same, which are evenly distributed on the planet carrier, and the support stiffness of each planetary gear is the same.