A fracture mechanics model of gear flanks fatigue

A new model for determination of the fatigue pitting resistance of gear flanks is presented in this paper. An equivalent model of two cylinders, with diameters equal to the appropriate curvature radii of gear flanks at any point on the engagement line, is used to study the process of fatigue crack initiation and crack propagation in the contact area. The stress field in the contact area and dependence of the stress intensity factor on the crack length are determined by the finite element method. On the basis of numerical results and with consideration of some particular material parameters, the service life of gear flanks can then be determined as the sum of the number of stress cycles required for crack initiation and the number of stress cycles required for a crack to propagate from the initial to the critical crack length. In this model the theory of dislocation motions on persistent slip is used to describe the process of crack initiation. The crack growth is described using the short crack growth theory, in which the microstructure of a material plays an important role. The model presented is used for determination of the service life of a real spur gear pair which has been also experimentally tested. The comparison of the numerical and experimental results is in a good agreement. lt can be concluded that the model presented is appropriate for calculation of the pitting resistance of gear flanks. However, the model could be still further improved by some additional theoretical, numerical and above all, experimental research.