Kinematic properties of planar and spherical logarithmic spirals: Applications to the synthesis of involute tooth profiles

Abstract

The design of the contact profiles of spur gears with involute teeth is well developed, with industry standards that set values for pressure angle and ratios for virtually all dimensions. This is not the case for bevel gears, where involute teeth, although known for several years, haven’t been adopted by industry. As a result, no standards for involute bevel gears are available. In the case of hypoid gears, owing their name to the pitch surfaces, the definition of involute surfaces is still to be seen. This state of affairs motivated the authors to look for alternative means of synthesizing the contact profiles of interest. Reported in this paper is the application of the Camus Theorem to the synthesis of the contact profiles of spur (planar)- and bevel (spherical)-gear teeth. It is shown that, upon using the planar or, correspondingly, the spherical logarithmic spiral as auxiliary centrode, the contact profiles of spur and bevel gears with involute teeth can be obtained within a unified framework.