Boundary load distribution of simultaneously meshed gear teeth pairs

The load distribution of simultaneously meshed gear teeth pairs has a significant influence in determining the relevant stress for the working capacity calculation of cylindrical gear pairs with respect to surface and volume strength. According to conventional calculation procedures, the influence of the boundary-ideally uniform load distribution, when all simultaneously meshed teeth pairs are equally engaged in the load transfer, on the teeth flanks stress state is taken into account by approximate expressions for contact ratio factor Z_ε . In addition, this factor is not defined, no assumptions were given on the basis of which approximate expressions were determined, and no procedure for determining these expressions was disclosed. This paper defines a factor on the basis of which an analysis of the boundary-ideally uniform load distribution can be carried out. By observing the contact lines in the meshing area, when one and two or two and three meshed gear teeth pairs are alternating during the meshing period, a set of analytical expressions is developed to describe the boundary-ideally uniform load distribution of simultaneously meshed gear teeth pairs. Based on the developed analytical expressions, the limiting values of the gear teeth flank stresses can be determined more precisely and the degree of accuracy of the approximate expressions for the contact ratio factor which are given in conventional calculation procedures can be tested. The analysis carried out in this paper can be used for more accurate considerations of all cylindrical gear pairs occurrences which depend on load distribution, such as: load capacity, mesh stiffness, vibration, noise, energy efficiency, etc.