Issue 30

F. Curà et alii, Frattura ed Integrità Strutturale, 30 (2014) 446-453; DOI: 10.3221/IGF-ESIS.30.54 447 As a matter of fact, if a crack occurs in thin rim gears near the tooth root, it may propagate along the tooth thickness direction by cutting the entire tooth, or the crack may propagate along the radial direction by destroying the whole gear, see Fig. 1 (respectively a and b ). a) b) Figure 1 : Possible failure modes in a thin rim gear: a) safe fail, b) catastrophic fail. The first failure mode is the desired one (Fig. 1a), as it may allow the airplane to land safely, while the second one may bring to the projection of big parts of the gear with consequent catastrophic damages to the whole transmission. This work is focused on the analysis of crack propagation path on thin rim gears and, in particular, the effect of both rim thickness and initial crack orientations has been investigated. Some researchers studied the effects of the rim thickness on the stress entity, but only a few have carried out an analysis of fatigue crack growth. Among works available in literature about gears crack propagation paths, the most relevant are those carried on by Lewicki et al. [1 - 5] where both experimental and numerical investigations have been presented. These papers consider gears without web and the experimental investigation has been focused on the effect of rim thickness [1]; the corresponding numerical investigation (performed with 2D FEM models) was referred to the effect of some geometrical parameters, to the initial crack location ant to the load application point. Experimental tests were carried out also by Glodez et al. [6], but this research was focused on the effects of different load distributions along the tooth width on the growth of fatigue cracks. Kramberger et al. [7] proposed a model to predict the bending fatigue life of cylindrical gears with thin rim, including the two stages of initiation and propagation of cracks. The study of the propagation phase involved the determination of the trajectory of the crack propagation, which could be through the root of the tooth or the crown of the wheel and the useful life remaining until the final collapse. Flasker et al. [8] investigated the effect of the contact area on the crack propagation direction and evaluated the residual life of the wheel with a crack along the tooth root for different loading conditions, both experimentally and numerically. Kato et al. [9] developed a method to simulate the growth of a fatigue crack in carburized tooth by considering the effect of residual stresses, but by neglecting the crack initiation period. The effect of the crack closure on the propagation was investigated by Ural et al. [10] and Guagliano et al. [11]. The results of their analysis showed that the effect of the crack closure could be significant when the applied load is lower and the crack propagation phase represents a significant portion of the wheel life. Studies in three dimensions are required in case of not uniform load distributions or when the crack does not growth uniformly along the tooth width. One example is the analysis carried out by Pehan et al. [12]. Other simulations about cracks growth in three dimensions were carried out by Lewicki, [3] which study allowed to obtain the following conclusions: initial cracks in the connection to the bottom of the tooth produce higher stress intensity factors (and thus the crack growth rate increases) than those in the tooth root area. Kramberger at al. [13] investigated the effect of different web positions on the crack propagation path in thin rim gears. In this work a numerical analysis about crack propagation in thin rim gears has been carried on; in particular the effect of some geometrical parameters, the initial crack position and shape has been investigated. Numerical models have been developed by means of the Extended FEM (XFEM) technique, realizing 3D models. XFEM 3D is a relatively new technique consisting in enriching traditional finite element with more complex shape functions; in this way it is possible to propagate cracks also between mesh nodes and to have mesh independent results [14]. Aim of this work is to predict the crack propagation path orientation, by knowing geometrical gear parameters and initial crack position, in order to avoid catastrophic failures and to give to designers a high confident design criterion. In particular, the effect of rim thickness and the 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 results found in the literature [1].