Active vibration control of an elastic rotor by using its deformation as controlled variable

Abstract

An elastic gyroscopic rotor system is modelled using the finite element method. The rotor is supported with two piezoelectric actuators which allow a dynamic manipulation of the rotational axis. The piezos are modelled as displacement actuators causing a base excitation. It is known from the literature that actively reducing the displacements of the rotor in the self-centring area leads to increasing bearing forces. We propose an approach which theoretically allows the use of the rotor displacements for active control without significantly increasing the bearing forces, even in the self-centring area. We use the relative displacements of the rotor for control which are proportional to the deformation of the rotor. The relative displacements are the difference between the absolute displacements, which describe the rotor centre, and a virtual active rotor axis which is a linear interpolation of the theoretically load-free actuator displacements of the piezos. A combination of integral force feedback and the least-mean-squares algorithm is chosen for control which takes full advantage of complex time signals. The analytic optimum of this control shows resonances which match with the resonances of the unsupported rotor if only the bearing forces are minimized. We refer to them as force-free resonances. While minimizing the absolute displacements in addition to the bearing forces only eliminates the first resonance, minimizing the relative displacements in addition eliminates all resonances. Using an additional weighting of the controller part prevents the force-free resonances and eliminates the difference between using the absolute and relative displacements. This is confirmed by experiments on the test-rig. However, there is no additional resonance when using the absolute displacement in addition to the bearing forces. Using the relative displacements allow for a higher reduction of the bearing forces caused by unbalance excitation in comparison to the absolute displacements when no weighting of the controller output is used. The test-rig results also show that it is not possible to eliminate the first conventional resonance peak which comprise forward and backward whirl vibrations by only controlling the bearing forces in the first bearing plane. The additional consideration of the absolute or relative displacements is able to eliminate these resonances with just a low increase of the bearing forces after the second resonance.