Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis

Abstract

The main defects of misaligned helical gear drives with parallel axes are: edge contact, noise, and not favorable conditions of bearing contact. One of the greatest concern of manufacturing of helical gear drives (with parallel axes) is the edge contact of tooth surfaces that is caused by misalignment. At present, attempts to avoid edge contact are based on providing chamfers of the tooth surfaces of the gears that may be obtained by modification of the profile of the cutting hobs. The zones of tooth surfaces with chamfers and zones with conventional screw involute surfaces are not connected smoothly, in many cases the magnitude of required chamfers is not determined analytically, and the edge contact is not avoided. The finishing process of helical gears with chamfers is a complicated one. The existing design has to be complemented with TCA (tooth contact analysis). These are the reasons why a new topology of modified helical gear tooth surfaces with involute and crowned zones is proposed. An involute zone is provided in the central area of gear tooth surfaces that will allow line contact if misalignment does not occur. Zones at the top, bottom, front, and back sides of tooth surfaces are crowned and allows localization of the bearing contact when misalignments occur. Crowned zones with smooth connections to the involute zone are obtained as the result of profile and longitudinal crowning. The function of transmission errors is provided at each cycle of meshing as the sum of three branches. Two branches of a parabolic function at the extremes of the cycle of meshing are in tangency with the middle branch of zero transmission errors. The generation of gear tooth surfaces is accomplished by a grinding worm. This has required the solution of two problems, (i) determination of the worm thread surface that is conjugated to the theoretical pinion tooth surface, and (ii) generation by the grinding worm of a crowned pinion tooth surface. Simulation of meshing of misaligned gear drives is accomplished by application of TCA program developed by the authors. The formation of the bearing contact is analyzed considering more than one cycle of meshing. Existence of areas of severe contact stresses is avoided. The developed approach is illustrated with numerical examples.