Vibration due to non-circularity of a rotating ring having discrete radial supports - With application to thin-walled rotor/magnetic bearing systems

This paper investigates the vibration arising in a thin-walled cylindrical rotor subject to small non-circularity and coupled to discrete space-fixed radial bearing supports. A Fourier series description of rotor non-circularity is incorporated within a mathematical model for vibration of a rotating annulus. This model predicts the multi-harmonic excitation of the rotor wall due to bearing interactions. For each non-circularity harmonic there is a set of distinct critical speeds at which resonance can potentially arise due to flexural mode excitation within the rotor wall. It is shown that whether each potential resonance occurs depends on the multiplicity and symmetry of the bearing supports. Also, a sufficient number of evenly spaced identical supports will eliminate low order resonances. The considered problem is pertinent to the design and operation of thin-walled rotors with active magnetic bearing (AMB) supports, for which small clearances exist between the rotor and bearing and so vibration excitation must be limited to avoid contacts. With this motivation, the mathematical model is further developed for the case of a distributed array of electromagnetic actuators controlled by feedback of measured rotor wall displacements. A case study involving an experimental system with short cylindrical rotor and a single radial AMB support is presented. The results show that flexural mode resonance is largely avoided for the considered design topology. Moreover, numerical predictions based on measured non-circularity show good agreement with measurements of rotor wall vibration, thereby confirming the validity and utility of the theoretical model.