Stress-Strain State of Non-Involute Tooth of the Planetary Gearwheel

Abstract

Multisattelite planet transmissions are widely spread in the drive technique due to high loading ability and good mass and overall dimension features. The constructions of such transmissions envisage the presence of the sun pinion and the central wheel with internal teeth and rim thickness not less than three modules, which is set motionlessly in the casing of a planetary mechanism. As for transmissions developed at Kalashnikov Izhevsk State Technical University, a fixed central wheel is executed as a rim with non-involute teeth, that allows to decrease the radial size of the transmission on the thickness of the gearwheel rim. In addition, the enhanced compliance of teeth positively affects the load distribution in gearwheel meshing. However, they have lower bending resistance, than standard involute teeth, because the radius of curvature of the transitional curve of non-involute profile becomes close to zero. For determination of tooth bending stress in the place of its sealing-off in the rim of wheel, the element of the rim is presented as a beam on the elastic foundation, for which the equation of relation of power factors and deformations of bending and shearing is composed. The obtained differential equation of the stress-strain state was established by the analytical method of Euler. It ensues from the executed calculations, that stresses at the root of the non-involute tooth are substantially higher than stresses at the root of the involute tooth. In this connection it is expedient to apply wheels with non-involute teeth in comparatively low-loaded planetary transmissions rated for the long term service with the load-carrying capacity limited by the contact strength of gearwheel teeth.