Scatter assessment of rotating system vibrations due to uncertain residual unbalances and bearing properties

Abstract

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the eight-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration responses is the inherently random nature of residual unbalances as well as stiffness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based on Taylor series expansion in most of the analyzed cases fail to approximate the rotor-shaft response statistics.