Critical stress and load conditions for bending calculations of involute spur and helical gears

In this paper, a non-uniform model of load distribution along the line of contact of spur and helical gears, obtained from the minimum elastic potential criterion, has been used, combined with the equations of the linear elasticity, to evaluate the fatigue tooth-root stress. The critical value of the stress and the critical load conditions have been obtained and a complete analysis of the tooth bending strength has been carried out. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic equation, a complete study of the location and the value of the tooth-root bending stress has been carried out. From this study, a recommendation for the calculation of the bending load capacity of spur and helical gears is proposed.