Numerical modelling of crack growth in a gear tooth root

Abstract

A computational model for determination of crack growth in a gear tooth root is presented. Two loading conditions are taken into account: (i) normal pulsating force acting at the highest point of the single tooth contact and (ii) the moving load along the tooth flank. In numerical analysis it is assumed that the crack is initiated at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for a further simulation of the fatigue crack growth. The functional relationship between the the stress intensity factor and crack length K = f(a), which is needed for determining the required number of loading cycles N for a crack propagation from the initial to the critical length, is obtained using a displacement correlation method in the framework of the FEM-method considering the effect of crack closure. The model is used for determining fatigue crack growth in a real gear made from case carburised and ground steel 14CiNiMo13-4, where the required material parameters were determined previously by appropriate test specimens. The results of the numerical analysis show that the prediction of crack propagation live and crack path in a gear tooth root are significantly different for both loading conditions considered. © 2011 Journal of Mechanical Engineering.