Synchronous whirl mode maps for rotor vibration with stator interaction across clearance annuli in multiple planes

For rotating machines having rotor-stator structures with non-linear stiffness characteristics or finite clearances between rotor and stator parts, there can be a multiplicity of possible vibration behaviours for any given operating speed. When the dynamic characteristics of the machine structure possess rotational symmetry, possible vibration modes arising due to unbalance can be calculated exactly from the frequency response of the structure. This study extends current theory by considering systems for which rotor-stator contact interaction may occur in multiple transverse planes. Damping and friction effects arising from contact mechanics are also accounted for. The model equations can be used to compute a complete set of vibration solutions involving circular whirl and thereby establish parametric regions where a low amplitude whirl can transgress to a high amplitude one with rotor-stator contact in one or more planes. Experimentally identified whirl modes for a flexible rotor system interacting with two clearance bearings show a good correlation with the theoretical predictions and thus indicate the suitability of the approach as a tool for prediction and design. The results are pertinent to the design of magnetic bearing and auxiliary bearing systems but are also relevant to a wide range of machines where rotor vibration may exceed clearance limits or boundaries of linearity.