A Simulation of the Stress Intensity Factors K_I and K_II Variation in the Hertzian Stresses Field of Gear Teeth

Abstract

The most outstanding parameter that governs the fatigue crack growth under tensile stresses field is the stress intensity factor, mode I, KI. This is a sufficient parameter to describe the whole stress field at the crack tip. An accurate stress intensity factor KI evolution was worked out taking into account the position of the crack centre depth, and also, the residual stresses that act on the surface of the tooth, tensions that are linearly decreasing with the depth in the contact zone. On the other hand, the parameter that governs the crack fatigue growth in the case of compression stresses field is the stress intensity factor mode II, KII. This paper also presents the KII variation along pitch line with respect to the Hertzian contact stresses, the residual stresses and the crack centre depth of an initial crack in the sub-surface of the pinion tooth, having different inclination angle α. As result of this study, some particular factors favorable to the propagation of the fatigue cracks towards the surface of the gear tooth were identified. The availability of a master curve for a particular material relating fatigue crack growth rate and range of stress intensity factor enables a designer to predict growth rates for any cracked body, and it is not limited to situations similar to those pertaining to the cracked stressed specimen used to generate the original data.