A Generalised Mathematical Model of Involute Gears Generated by Rack Type Cutters

Abstract

In this study, a mathematical model of involute beveloid gears is developed based on the vector expression of the cutting tool. Coordinate transformations, differential geometry and gear theory were applied to obtain the fabricated surfaces. In addition, the ranges of the helical design parameter are also examined. Depending on the angular displacement of the contact point on the line of action of the rack gear mechanism, a generalized expression is proposed to determine the boundary point between the involute profile and the tip circle. Numerical examples were prepared to investigate the effect of design parameters on the manufactured gear geometry. For the accuracy and validity of the presented model, a comparison was made with a beveloid gear model in the literature. In addition, the undercut and the zero top land formations were investigated in various sections of spur and helical beveloid gears.