Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects

•Mesh stiffness equations including hertzian effects for spur gears are presented.•Approximate equations for the mesh stiffness and the load sharing ratio are provided.•Critical stresses and load conditions for bending and pitting are obtained.•Results from a model regardless contact deflections are compared.•Validation by Finite Element Analysis is performed.

In this paper, the meshing stiffness of spur gear pairs, considering both global tooth deflections and local contact deflections, is evaluated at any point of the path of contact and approximated by an analytical, simple function. With this function, the load sharing ratio is calculated and compared with previous results obtained from the hypothesis of minimum elastic potential energy (MEPE model), considering the tooth deflections, but neglecting the hertzian deflections. Critical bending and contact stresses from both models are also compared both for standard and high contact ratio spur gears.