Weibull Stress/Strength Method to Random Vibration by Considering the Cumulative Damage

The paper presents a methodology to determine the reliability of a mechanical element directly from the accumulated vibration damage. To make damage representative, the time, geometry, load and resonance effects were all incorporated into the analysis through a simulation. And since vibration is a variant stress, then the element’s reliability was determined by using a common shape parameter of the Weibull stress and Weibull strength distributions. The formulas to estimate the stress Weibull parameters from the vibration stress values, and the formulas to determine the strength Weibull parameters by considering the material fatigue factor and the vibration testing profile are both given. Then the common Weibull shape parameter and the accumulated damage were used to determine the element reliability. From the application, the element’s reliability occurred in the first row, and the expected reliability of 97% occurred in the seventh row of the accumulated damage table. Also, the reliability index of each accumulated damage row is provided.