Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces

In the spiral bevel and hypoid gear manufacturing industry, master gear sets are usually developed from initial machine settings obtained from computer software or instruction sheets. These initial machine settings are then modified until a satisfactory bearing pattern is obtained, a process called bearing pattern development. Once a satisfactory bearing pattern is obtained, manufacturing errors and heat treatment distorsions can be accounted for by proportionally changing the machine settings according to the results of a V-H test in which the pinion vertical and horizontal positions are modified until the bearing pattern is acceptable. Once a satisfactory combination of master pinion and gear is obtained, their actual tooth surfaces usually do not correspond to those of the initial theoretical model, and the theoretical pinion and gear surface definitions are unknown. This paper presents a computer algorithm used to identify the machine settings producing a theoretical tooth surface closest to that of a measured surface, what the authors call Surface Match, in order to effectively simulate the kinematical behavior of real gear teeth. The approach is applicable to both 1st and 2nd order surface errors, including profile deviation, for any cutting process. However, given the availability of experimental data for the Fixed Setting™, Formate™ and Helixform™ cutting processes, the examples presented in the paper are related to these cutting processes.