The number of teeth of planetary transmission cannot be selected at will. Normal transmission can be carried out only when the basic constraints such as adjacency conditions, concentricity conditions and assembly conditions are met according to the characteristics of planetary transmission.
(1) Adjacency condition
The adjacency condition requires that two adjacent planetary gears do not collide with each other, which can be expressed by the following formula:
(2) Concentric condition
In order to ensure the correct meshing under the condition that the axes of the center wheel and the planet carrier coincide, the actual center distance of each meshing pair composed of the center wheel and the planet wheel must be equal, that is, the concentric condition, which can be expressed by the following formula:
(3) Assembly conditions
The assembly conditions require that n planetary gears can be evenly installed into the gear train and mesh correctly with the sun gear without dislocation, which can be expressed by the following formula:
Where: Z1, Z2, Z3 – number of teeth of sun gear, planetary gear and inner ring gear; NP – number of planetary gears; D12 – diameter of the top circle of planetary gear teeth; cos α 12、cos α 23 – actual meshing angle of sun gear and planetary gear, planetary gear and internal gear ring.