The Influence of Stiffness of the Planet Shafts and Bearings on Load Distribution among the Planets in a Planetary Gear

This paper proposes a method for determining the mesh load factor for a multi-satellite planetary gear with self-adjusting elements in the presence of manufacturing errors. The problem is solved taking into account the stiffness of the rolling bearings, deformation of the two-point shafts and the adjacent elements. Multi-satellite planetary gears have been widely used in mechanical engineering due to their high technical and economic indicators. However, the non-uniform load distribution in the meshed gears that is caused by manufacturing errors diminishes the effect of the multiple planets. Therefore, it is important to improve loading capacity indicators of the planetary gear mechanism. The major index of the planetary gear bearing capacity is the non-uniformity of load distribution among the planets. It depends on the deformation of such elements as bearing and shaft, hence the problem of determining the influence of stiffness of these elements on the mesh load factor. For the determination of load distribution laws in the zones where the planet shaft is in contact with the carrier surface and the bearing ring, the shaft is considered as an axle on elastic foot. A system of two differential equations is solved where the integration constants are determined taking into account shaft bending at intermediate sections. The obtained linear load in the adjacent areas, and the stiffness of the shaft and rolling bearing are included in the system of displacement compatibility equations, from which the forces in the meshed planets are calculated. The study results for planetary gears with 5 to 7 planets have shown that loading capacity of a seven-satellite gear with manufacturing errors exceeds that of a five- and six-satellite assembly approximately by 20–30%, and with no errors by 40% and 17% respectively. The deformability of the planet shafts and bearings has a significant impact on load distribution among the planets. The reduction of the mesh load factor reaches 30% or more, which increases the loading capacity of the mechanism.

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