Probabilistic Analysis of the Reliability and Fatigue Life of Machine Parts by Fatigue Failure

The problem of calculating the reliability and fatigue life of machine parts by the fatigue failure under random changes in the actual and limit stresses is considered. According to the corrected theory of the linear summation of damage, a transcendental equation has been obtained that relates the number of cycles until failure to the random loading parameters and the ultimate strength. From this equation, the ultimate strength threshold is determined, which corresponds to the destructive number of cycles over the service lifetime. The fatigue reliability equals the probability of exceedance of this value by the ultimate strength. Analytical dependences have been obtained for determination of the probabilistic characteristics of the fatigue life under a simultaneous random change in the normal and tangential stresses.