Investigation of the stress-strain state of a satellite axle-carrier joint in a planetary gear

Determining the deformation of mating elements of internal and external planetary gears and studying their stress-strain state is of great importance. Deformability of the elements of the planetary gear affects its stiffness and load capacity; therefore, to optimize these properties, it is necessary to investigate the stress-strain state of a satellite axle-carrier joint and establish its influence on the load distribution in the contact area and on the axle flexibility. A method for determining the deformation of a satellite axle mating with a planetary carrier and the load distribution in the contact area is developed. The method is based on the solution of the differential equation of a curved axle on an elastic foundation and the finite element analysis of the stress-strain state of mating parts. The displacement of the satellite axle at the bearing location point depends on the axle flexibility and deformation of mating parts in the contact area where the axle is embedded in the carrier. The former displacement component is determined by the methods of the strength of materials using Mohr's integrals, the latter is determined from the solution of the differential equation of a curved axle on an elastic foundation whose stiffness is found experimentally. A computer model of mating parts is constructed and their stress-strain state is studied by the finite element method implemented in the Solid Works software. The obtained results are in good agreement. Equations for determining the deformation of the satellite axle and the mating carrier are deduced, the influence of the flexibility of these parts on the load distribution in the contact area is established, and the finite element analysis of the stress-strain state of the gear elements is performed. The study showed that the satellite axle displacement caused by the deformation of the mating parts in the contact area exceeds the bending deflection of this axle. This should be taken into account when determining load distribution factors in meshes and computing the rigidity and strength of gears.

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