Optimization and Stochastic Modeling Applied to Propulsion Shafting Alignment

Abstract

Two aspects of propulsion shaft alignment analysis are discussed: a) finding an optimized solution by minimizing the deviation between bearing loads, and b) determining the acceptability of the optimized solution (or any alignment solution) by calculating the probability of acceptable bearing loads that result from a simulated series of random bearing offset events. The optimizing method is straight forward: the bearing loads are calculated using a· series of bearing offsets which are independently allowed to vary within a range of predetermined displacements. The acceptability of the alignment solution is judged against desired bearing load criteria. Several types of internal and external causes of bearing elevation effects are recognized, and the combination of the effects are presented as shaft alignment conditions. By distributing the nominal offset solutions about their most likely values, a simulation can be performed which reveals the probability of an acceptable solution when using the same acceptability criteria used in the optimizing calculations. A triangle distribution is shown in a subroutine and can be employed in an algorithm designed to randomly distribute the bearing offsets. Methods are described and examples are presented which show the application of shaft alignment optimization and probability analysis to produce alignment solutions which meet example criteria.