Method of Geometric Design of Non-Circular Gear Wheels of a Planetary Rotary Hydraulic Machine

Abstract

Until now, planetary rotary hydraulic machines with floating planetary gears were rarely produced and remained poorly studied. One of the main problems was the lack of a simple and affordable method for geometric design of non-circular gear rims. Previously, we proposed a fairly simple engineering method for designing non-circular wheels of planetary hydraulic machines, but in some problems, its application gives a small error. The paper discusses a refined method for profiling non-circular gear rims of volumetric planetary rotary hydraulic machines. The proposed method begins with the choice of the geometric parameters of the round-link planetary mechanism - the prototype of the designed hydraulic machine. Next, the number of waves of the sun gears and the form of the cyclic function characterizing the paths of the planetary gear center in the coordinates associated with the sun gear and the epicycle are selected. The preliminary calculation of the angle of rotation of the planetary gear and the polar coordinates of its center on the path relative to the given sun gear in the variety of the planetary gear positions is performed at the next stage. In this case, the positions of the planetary gear relative to one of the sun gears correspond to its rolling along the calculated centroid of this gear at a constant angular velocity of the imaginary carrier. Next, the difference between the obtained angles of rotation of the planetary gear is calculated in the coordinates associated with the imaginary carrier. This difference is halved and distributed as a correction between the rotation angles of the planetary gear relative to the sun gear and the epicycle. In conclusion, the profile of the rim of each non-circular sun gear is obtained graphically as an envelope of the family of profile curves of the planetary gear in a variety of its positions. The refined design technique, almost without complicating the process of profiling the wheels of planetary hydraulic machines, eliminates the previously obtained error and provides an accurate solution to the problem.