Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

In this paper, a three-dimensional model for the estimation of the deflections, load sharing attributes, and contact conditions will be presented for pairs of meshing teeth in a spur gear transmission. A nonlinear iterative approach based on a semi-analytical formulation for the deformation of the teeth under load will be employed to accurately determine the point of application of the load, its intensity, and the number of contacting pairs without a priori assumptions. At the end of this iterative cycle the obtained deflected shapes are then employed to compute the pressure distributions through a contact mechanics model with non-Hertzian features and a technique capable of obtaining correct results even at the free edges of the finite length contacting bodies. This approach is then applied to a test case with excellent agreement with its finite element counterpart. Finally, several results are shown to highlight the influence on the quasi-static behavior of spur gears of different kinds and amounts of flank and face-width profile modifications.