Probabilistic HCF Life Estimation of a Mechanical Component

Abstract

Goodman Diagram method or similar methods are used to estimate safety of a mechanical structure under high cycle fatigue loading for any combination of alternating and mean stresses. Magnitude of the factor of safety (FS) indicates margin from nominal design capable of desired performance. The value of larger than one of FS is desired to account for uncertainty and variability in loads and material properties. This FS based on stress does not provide any direct knowledge about the life of the mechanical structure. A FS based on life can be derived and used in conjunction with Goodman concept. This method yields an estimate of FS based on life (FN) for a given stress based FS for any combination of alternating and mean stresses. A procedure is described in this paper that helps in estimating reliability of a mechanical structure. Reliability depends on the magnitude of stresses and material properties. Usually variability in load and in material properties can be quantified by a statistical distribution. Methods of probabilistic theories can be used to determine the influence of these variations on the reliability. The procedure utilizes established methods and theories to yield practical evaluation of reliability. First, the modified Goodman equation of factor of safety is combined with the life equation proposed by Jo Dean Morrow (Dowling, 1999). This provides a relationship between calculated factor of safeties based on stress and life. Finally, the developed equations are utilized in a probabilistic approach that incorporates statistical distribution of uncertainties. This procedure yields reliability assessment of a mechanical structure to perform an expected task.