Geometric calculation of non-circular gear segments of the planetary mechanism in rotary hydraulic machines

Abstract

The article discusses the improvement of the methods of geometric design of positive-displacement hydraulic machines with floating satellites. At the first stage, based on standard methods, an “average” round-link planetary mechanism, having the number of teeth as in the designed hydraulic machine, is calculated. At the second stage, the same-type cyclic functions characterizing the paths of the center of the satellite in the coordinates associated with each of the central gearwheels are specified. At the third stage, the coordinate arrays of the satellite in a variety of its positions are calculated. The angular position of the satellite relative to one of the profiled gearwheels (for example, the sun gearwheel) provides equidistance of the centroid of this gearwheel to the path of the center of the satellite. The angular position of the satellite relative to the other profiled wheel is determined by its running around the first wheel. At the final stage of the design, the satellite is constructed in a variety of positions, and the profile of the corresponding non-circular gear rim is obtained as an envelope of the family of satellite curves-profiles.