Vibration reduction of flexible rotors
A novel method of flexible-rotor vibration control, using an active contactless angular electromagnetic actuator is presented. A theoretical comparison of radial and angular damping is performed. Three different performance indices are defined and used to determine controller optimum damping/location data for different shaft systems. The controller settings are determined for two main cases: i) such that only one damping value is allowed throughout the entire shaft speed range (passive or fixed-gain active control), ii) the damping value is controlled as a function of rotor speed (adaptive control). The parameter optimisation, made possible by the creation of a simple but efficient numerical technique employed in conjunction with the transfer matrix method, is restricted to considering a speed range covering the first three rigid-bearing critical speeds for a uniform shaft supported by a variety of bearings. However, the approach is sufficiently general to allow the study of any required speed range. It is shown that for both the radial and angular dampers when mounted at the bearings, there is a definite support stiffness value above which the angular damper is the more efficient, but below which the opposite is true. When the conditions for 'fixed-points' are satisfied, then a simple on-off control strategy can be used effectively employing either type of controller. Angular damping is shown also to be an effective means of suppressing 'oil-whirl' type instability. The theoretical work is supported by experimental investigations on a laboratory rig which is representative of a general flexible rotor system. An electromagnetic controller is mounted at one bearing and the reduction of shaft unbalance response and bearing forces recorded for various conditions. Significant reductions in system synchronous response are observed at running speeds close to the first critical speed when electromagnetic stiffness and/or damping is employed. When electromagnetic damping is introduced, non-synchronous vibration components, resulting from shaft asymmetries, are also eliminated. The combined theoretical and experimental studies show angular control to be a viable alternative means of reducing flexible rotor vibrations.