Investigation of Loading Distribution in Tooth Contact of Multi-Row Planetary Gears and Its Influence on Overall Economics of the Drive

Abstract

Multi-row planetary gears are widely used in engineering due to good technical and economic indicators: high load capacity with small dimensions and weight, small losses of frictional power, and large gear ratio in one stage. A significant disadvantage of these transmissions is the uneven load distribution in meshing of gearwheels, which is caused by inevitable manufacturing errors and deformations of their elements. However, the compliance of individual transmission elements (axes and bearings of the satellites, cheeks of the carrier) facilitates the equalization of the load both among satellites and their rows in the case of a multi-row design of the mechanism. In this connection, it is important to establish the degree of influence of the deformation of the planetary gear elements on the load distribution in meshing of gearwheels and on such an important technical and economic indicator as the ratio of the mass to the moment at the output shaft. The coefficient of uneven load distribution among satellites was determined by solving the system of equations for the compatibility of displacements, taking into account the deformation of jaws of the carrier, bearings and axes of the satellites. And the axis of the satellite in the places of its contact with jaws of the carrier and the bearing ring was considered as a beam on an elastic base, and the jaws of the carrier were made with grooves to reduce their rigidity. Thus, it was found that performance of compliant carrier jaws allows to reduce the coefficient of uneven load distribution among satellites by 8-11 %, which favorably affects the load capacity of the drive and its weight and overall dimensions. With a limited radial transmission size, it is advisable to perform a multi-row transmission. However, in this case, the deformation of the torsion of the sun gear leads to an uneven distribution of the load among the rows of satellites. To prevent this negative phenomenon, it is suggested to produce the carrier with different widths of bridges having dimensions chosen so that their deformation could correspond to deformation of the pinion torsion. Thus, the use of the proposed layouts of multi-row planetary gears with a rational choice of their parameters makes it possible to significantly reduce the uneven distribution of the load in gears and improve the technical and economic performance of the drive.