A nonlinear approach based on the method of averaging has been developed to study unstable lateral vibrations of rotors in high-speed turbomachinery. The method makes use of an extended concept of bearing dynamic coefficients which are defined by applying small perturbations to the dynamic equilibrium positions. It has been applied to determine the stability threshold of flexible rotors supported on short and tilting-pad journal bearings respectively. Stability performance of systems supported on short journal bearings is improved by the presence of mass unbalance. However, for flexible rotors supported on tilting-pad journal bearings, increased unbalance can lead to lower rotordynamic stability margins. This has the significant implication that stability estimates from linear analysis are not always conservative. The present method provides a computationally more efficient way to better understand the nonlinear vibration behaviour of high-speed turbomachinery.

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