An ease-off flank modification method for high contact ratio spiral bevel gears with modified curvature motion

Abstract

In order to solve the problem of the design and fabrication of high contact ratio spiral bevel gears with seventh-order transmission error (TE), an ease-off flank modification method is proposed based on the modified curvature motion method. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, the pinion target tooth surface is obtained by modifying the pinion auxiliary tooth surface along the meshing line with a predesigned modification curve, and the pinion auxiliary tooth surface is obtained with the predesigned seventh-order transmission error through using the gear as a virtual cutter. Thirdly, a new method called modified curvature motion (MCM) method is proposed to improve the adjustability of spiral bevel gear by modifying parts of machine-tool settings in the process of gear manufacturing. Finally, an optimization model solved by using the improved NSGA-II algorithm is proposed to solve the adjustments of pinion machining settings, and we carry out TCA and LTCA to verify the feasibility of the tooth modification method. The results keep in line with the preconditions that transmission error is seventh-order curve and the contact path is located in the middle of the tooth surface. The proposed flank modification methodology can serve as a basis for developing a general technique of flank modification for spiral bevel gears.