Computerized Generation of Nonstandard and Asymmetric Involute Spur Gears Based on Rack Cutter Parametric Tracing

Abstract

In the field of gear design, to apply any form of analysis (such as FEA, dynamic, and stress analyses), a delicate and accurate representation of the gear geometry is essential. It is the foundation for any design modification attempts, and any approximation of the tooth profile must be avoided. In the literature, many approximations were held to the involute tooth geometry, particularly in the filet region, where it was simply represented by a straight line or circular arc instead of a true trochoidal arc from a generation process. This approach might lead to inaccurate bending stress results, as it fails to detect the impact of the undercut or the profile correction process. Other common approximations have been widely observed in the literature, such as utilizing an asymmetric cutter to simultaneously generate the two sides of the asymmetric gear. Moreover, the graphical rack-cutter generation technique was widely used to generate involute gears. This technique, although shown to be accurate in generating a 2D standard tooth, is time-consuming as it necessitates the use of source code, a programming language, a graphic processor for displaying computer graphs, a post-graphic processor for eliminating unrelated lines, and a post-process for exporting the tooth geometry to CAD software. This research presents an alternative direct computerized generation method that is shown to be accurate, generate both 2D and 3D gears, and be significantly more time-efficient. Moreover, a novel technique to generate a fully asymmetric nonstandard tooth (pressure angle, trochoidal fillet, and shifting factor) is proposed using two half-cutters.