Influence of profile modifications on meshing stiffness, load sharing, and trasnsmission error of involute spur gears

The meshing stiffness, load sharing ratio, and quasi-static transmission error of spur gear pairs are related to each other and are dependent on tooth geometry. In addition, profile modifications influence the contact conditions, because modified profile points may only contact under load conditions and owing to load-induced elastic deflections. However, this is not the case under no-load conditions, wherein a gap would exist between the teeth owing to the contact of other tooth pairs at unmodified points. In this paper, the contact conditions of modified teeth under load have been studied, and the influence of the amount, length, and shape of the profile modification on the load sharing and transmission error has been described. A simple, analytic formulation of all these relations is provided, based on a previously developed approximate equation for the meshing stiffness, which provides accurate results. The simplicity of the obtained equations facilitates the study of the influence of the profile modification on the load sharing and transmission error, and the required profile modification for predesigned functions of load sharing ratio or quasi-static transmission error was also obtained.