Mesh Stiffness and Transmission Error of Spur and Helical Gears

In this study, the combined mesh stiffness characteristics of involute spur and helical gears and their transmission errors due to tooth deflections under load are evaluated. The bending and shear deflections on the contact line of a gear tooth are obtained by the finite element method (using isoparametric plate elements), and the contact deflections are obtained using Hertzian contact theory and the equation of Weber and Banaschek. With these deflections, under the assumption of mathematically exact geometry, the mesh stiffness and compliance of a tooth pair are found using the so called flexibility method. Then using the mesh contact ratio and load sharing ratio, the combined mesh stiffness characteristics of a gear pair and their transmission errors due to the tooth deflections along the line of action are evaluated.