| Aspects of the structural reliability analysis of marine diesel engine shafting systems are refined. The cylinder-to-cylinder variability is statistically assessed for a typical medium speed diesel engine while the cycle-to-cycle variability is found to be negligible. A new model for the propeller load variability is introduced on the basis of recent experimental results. The level crossing problem is treated and the first excursion probability is derived, for the case that the stress on the shaft is a one frequency cyclostationary random process. A new method is introduced, where the cyclostationary process is replaced with an equivalent stationary random process, which is defined to have either (1) exactly the same upcrossing rate at a given threshold as the time-averaged upcrossing rate of the cyclostationary process, or (2) an envelope process with the same upcrossing rate as the envelope of the cyclostationary process. Both processes are assumed to have the same probability of upcrossing a specific threshold. The agreement between this approach, that results in an analytical expression, and the "exact" but computationally time-consuming "Markov approach" presented in earlier work is excellent. The level crossing problem is also treated for the case that the stress on the shaft is a two frequency cyclostationary random process. For one class of solutions, the two frequencies are assumed to be widely spaced. This method approximates the maxima of the process by the corresponding values of the envelope process. The discrete process of the maxima is assumed to be Markov. For the case where the two frequencies are of comparable magnitude, an equivalent stationary process approach to this two frequency case, similar to that developed for the one frequency problem, is presented. The range of frequencies for which each of these methods is valid is discussed. Finally, a simple design algorithm is proposed to allow the probabilistic method to be applied in shafting systems design. |
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