2D nonlinear and non-Hertzian gear teeth deflection model for static transmission error calculation

Aim of this paper is to establish a bi-dimensional approach under quasi-static conditions to model the deflection and the load sharing characteristics as well as the contact conditions between engaging teeth in a spur gear transmission. A semi-analytical model is used to obtain tooth deformations and its stiffness, which is employed in an iterative nonlinear scheme to obtain the actual location of the point of application of the load and its intensity between the different teeth pairs. Next a numerical non-Hertzian contact mechanics model is used to obtain surface displacements and pressure distributions accounting for curvature variations and possible tip contacts once equilibrium is established. Several results are shown in terms of static transmission error, load sharing and contact pressures distributions along the roll angle of the gears with and without different kinds and amounts of profile modifications.