A kinematic investigation of a spherical involute bevel-geared system

Abstract

This study gives an exact definition of the spherical involute curved face and the pitch azimuthal angle of a bevel-geared system. Using the coordinate-transformation method, it derives the kinematic relations between the operating pressure angles, pitch azimuthal angles, operating pitch cone angles, base cone angles, and pitch action angles. An exact spherical involute bevel gear illustrates that a spherical involute tooth profile can be modelled only if the operating pressure angle, operating pitch cone angle, number of teeth, and cone radius are given. The ratio of the angular speeds of the spherical involute bevel gear reveals that the comparison of a bevel gear with a cone friction wheel is similar to the situation in which a belt that is wound around a base cone becomes untied and is wound around the base cone of the other party. The findings confirm that even when the shaft angle changes, the ratio of angular speeds does not change. This study also exactly calculates the operating rate in an involute bevel gear in a theoretical manner. To review interchangeability, the study defines the angular pitch and the crown number of teeth and shows that the proposed spherical involute bevel gear possesses interchangeability. To verify the contact phenomenon of the spherical involute bevel gear, a computer-graphic verification is conducted on three models to see whether gear interference occurs when two gears are operating while going in gear with each other.