Tooth Surface Generation and Geometric Properties of Straight Noncircular Bevel Gears

Abstract

A general mathematical model is established to describe the geometries and geometric characteristics of tooth surfaces of straight noncircular bevel gears. One of the direction angles of the normal vector of the tooth surfaces is taken as a function of the angular position of its origin, called the direction angle function (DAF). The normal vector and DAF are introduced to characterize this model. The normal vector including its direction angles and modulus is solved first and then the corresponding tooth surfaces and their geometric properties, such as major curvatures and slide coefficients, could be generated and calculated directly, logically and systematically by using this model and defining various DAFs. This method is applicable to many types of straight noncircular bevel gears with different tooth surfaces including tooth surfaces cut by the crown rack cutter or others. In addition, by using this method, it is relatively easy to realize the desired geometrical and mechanical properties into the design.