Investigation about crack propagation paths in thin rim gears

Crack propagation in gears is a problem related not only to the life of the components, but also to the concept of failsafe design. Fail safe design means to design a component in order that, if a failure occurs, this may cause a safe failure. This aspect is very important above all in aerospace industry. As a matter of fact, in aerospace application, the need of reducing weight brings to produce gears with very thick rim and web. Considering thin rim gears, when a crack is nucleated near the tooth root, it may propagate through the tooth (causing the loss of the entire tooth or a portion of it) or the propagation may follow a path across the wheel diameter (causing the projection of big parts of the gear that may break the gearbox and may cause serious damage to the aircraft). The first failure mode is define as failsafe failure and the second one as catastrophic failure and of course has to be avoided. Designers need to have robust design criteria in order to predict crack propagation paths and to avoid catastrophic failures. In literature, few works are present concerning this topic, in particular related to the effect of geometrical parameters that may affect the crack propagation. In this work a numerical analysis about crack propagation in gears with respect to the backup ratio (ratio between tooth height and rim thickness), initial crack position and shape has been done by means of the Extended FEM (XFEM) technique, realizing 3D models. XFEM 3D is a relatively new technique consisting in enriching traditional finite elements with more complex shape functions; in this way it is possible to propagate crack also between mesh nodes and to have mesh independent results. Aim of this paper is to highlight the crack propagation path in order to give to designers an high confident design criterion, related to the gear geometry. In particular, the effect of both rim thickness and orientation of the initial crack have been considered in order to enrich the literature knowledge. Numerical results obtained in this work have been compared with those found in the literature, showing a very good correlation.