Numerical Modelling of the Crack Propagation Path at Gear Tooth Root

A numerical model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. The Coffin-Manson relationship is used to determine the number of stress cycles N_i required for the fatigue crack initiation, where it is assumed that the initial crack is located at the point of the largest stresses in a gear tooth root. The simply Paris equation is then used for the further simulation of the fatigue crack growth, where required material parameters have been determined previously by the appropriate test specimens. The functional relationship between the stress intensity factor and crack length K = f(a), which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is obtained numerically. The total number of stress cycles N for the final failure to occur is then a sum N = N_i + N_p. Although some influences were not taken into account in the computational simulations, the presented model seems to be very suitable for determination of service life of gears because numerical procedures used here are much faster and cheaper if compared with the experimental testing.