A MATHEMATICAL-MODEL FOR THE TOOTH GEOMETRY OF HYPOID GEARS

Abstract

A mathematical model of the circular-cut hypoid gear set has been developed herein to represent the tooth surface geometry of hypoid gears. It can be applied to simulate the tooth profiles manufactured by the Duplex Method, Helical Duplex Method, and Formate Method. By applying the computer graphics and the proposed mathematical model, the profile of the hypoid gear and the precision coordinates of any tooth surface point can be obtained. The coordinates of the tooth surface can be considered as the standard for checking the profile precision of the actual products. The proposed mathematical model of the hypoid gear can also be applied to the computer numerical controlled (CNC) machining, tooth contact analysis (TCA), and finite element stress analysis.