Fast tooth deflection calculation method and its validation

Abstract

AbstractFor the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed.An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor.A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed.