Computer Simulation of Helical Gears Generated by Rack-Type Cutters

Abstract

This paper studies the equations of rack cutters for generating involute gears with asymmetric teeth. The asymmetry means that different pressure angles are applied for the driving and coast sides. By applying the equations of the designed profile of the rack cutter, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of involute helical gear are given. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Furthermore, a computer simulation program is developed to generate the tooth profile of asymmetric involute gears and to illustrate the effect of tool geometry on the generated surfaces. A CAD/FEM procedure for finite element modeling of asymmetric gear teeth is presented. This simulation should be helpful in the design and manufacture of asymmetric gears.