Load distribution model along the line of contact for involute external gears

Calculation methods of spur and helical gears for preliminary designs or standardization purposes available in technical literature use simple equations given by the linear theory of elasticity (Navier’s equation) and the Hertzian contact model to evaluate the bending and contact stresses, assuming the load to be uniformly distributed along the line of contact. However, these models are not in good agreement with experimental results because the changing meshing stiffness of the pair of teeth along the line of action produces a non-uniform load distribution, causing some load distribution factors to be required to compute bending and contact stresses. In this paper, a model of non-uniform load distribution along the line of contact, obtained from the minimum elastic potential energy criterion, is presented. This model combined with the equations of Navier and Hertz yields more realistic values of the bending and contact stresses. An approximate, accurate equation for the inverse unitary potential, allowing analytic calculations of the load per unit of length at any point of the line of contact and any position of the cycle of meshing, is also presented. The same equation, with a slight modification of the coefficients, is also valid for undercut teeth. Results have been validated by comparison with some studies carried out by the Finite Element Method.