Abstract

From the beginning, engineers have focused on the special case of determinism in the design process, and an enormous methodology has been developed to support this approach. Today, however, customers are demanding greater reliability and are imposing greater penalties for failure. In order to achieve higher reliability, and in order to assess the risk of failure, probabilistic approaches will almost certainly have to be employed. While designers have always used probability in their work, it has usually been done with risk represented in a single factor of safety. This paper focuses on the application of probability theory to the design of multi-degree of freedom systems that are subjected to a number of discreet excitation frequencies. Problems of this nature are often encountered in rotating machines where the excitation frequencies are multiples of the speed of rotation. In a previous paper (Pigott, 1996), only variability in the system natural frequencies was considered, and the probability of exceeding a certain vibratory stress was determined. It was shown that, at the reliability levels of interest, it is necessary to consider multiple mode contributions to the total vibratory stress. In this paper, the previous approach is extended to include variability in the magnitude of the excitation force, system damping, and system fatigue strength leading to the determination of a total probability of failure due to high cycle fatigue. The results of applying the deterministic analysis, the first level of probabilistic analysis (Pigott, 1996) and the full probabilistic analysis are presented for a sample system. The benefits from using the probabilistic approach for component design are also discussed.

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