A Novel Curve for the Generation of the Non-circular Gear Tooth Profile

Abstract

This paper presents a novel curve generated by a point attached to an ellipse as it rolls without slipping along a datum line of rack cutter. A mathematical model of the non-circular gear profile has been developed based on the theory of gearing. The effect of an axial ratio l (the ratio of the lengths of the major and minor axes of the ellipse) and the position of the point KR, at which the novel curve starts to generate on the tooth shape and the undercut of the non-circular gear pair is also taken into consideration. A numerical program developed from the mathematical model has been proposed for the calculation and design of the non-circular gears (NCGs). Case studies are presented to show the steps of tooth shape design and to examine the geometrical profile of the NCGs in relation to design parameters of the rack cutter etc. From that, the axial ration l and position of the point KR on the generating ellipse ƩE can be selected for each specific case in order to design the appropriate profiles of the NCGs. On that basis, an experiment to determine the gear ratio of the NCGs pair based on the meshing between gears has manufactured.