Vibration Control of Rotating Machines Using Actuated Bearing Seatings (2011)

This thesis addresses the problem of controlling the vibration of rotating machines using active bearing seatings. Contributions have been in seven areas: test rig development, rotating machinery modelling, developing appropriate control laws, updating method for piezoelectric actuators, determining specifications for the actuators from FE models, modal correlation methods (with and without frequency weighting) and modal expansion. A rotating machine test rig has been designed and constructed. In this rig, an active bearing seating has been designed to accommodate two actuators, located orthogonally and exerting control forces at each of two bearings. The rig is a versatile unit- the first one of its kind in the UK having a rotor whose bearings are supported on active seatings. Determining the requirements for force, stroke and bandwidth of the actuators for bearing seatings begins with an accurate numerical model of the system. A displacement-based FE model incorporating the active bearing seating has been developed and applied for predicting the dynamic behaviour of a rotating machine. Both steady-state responses and transient responses (run-up / run-down) are considered. The model has been validated experimentally by performing an experimental modal analysis of the test rig. A third area is in the development of suitable control laws. The same numerical model developed for assessing the actuator specifications has been employed to develop the control strategy. A control algorithm has been developed for vibration suppression. In this, the core ideas of classical optimal control are adopted (namely trading-off control effort against tracking performance). The "Simplex" (Nelder- Mead) method has been applied. The optimisation study is carried out for collocated actuation and sensing and for the general case, non-collocated control. Synchronous vibration is minimized in a root mean squares sense. Numerical simulations have shown that the proposed optimal closed-loop control strategy is very effective in reducing the amplitude of the forced vibration under different operating conditions. This controller is easy to implement in practical applications. A complete experimental and computational characterisation has been carried out on the piezoelectric actuators. An experimental arrangement has been established to measure two frequency- response functions. From these the complete dynamic properties of the piezoelectric stack actuators can be determined. Based on the measurements and the basic equations of the actuator, a computational model written in MA TLAB has been developed by which the parameters can be extracted. The experiment is simple to do with standard vibration-laboratory equipment and is very effective in characterising the actuator. The tests have been performed on four nominally-identical actuators and different parameters are obtained in each case. Obtaining accurate values for these parameters is an essential step towards having a reliable model for the complete closed-loop system. A set of novel modal correlation measures for generally-damped systems has been developed. In each case, a dimensionless (n x n) modal-matching array is produced whose entries indicate which pairs of modes from the first system best correlate with any particular pair of modes from the second system. This modal-matching array exhibits 2nd -order behaviour with respect to any scalar measure of that discrepancy. The work was motivated originally by the application of developing Campbell diagrams for rotating machines as continuous curves - rather than simply plotting large set of discrete points. There are several possible motivations for the proposed procedures. The most important is probably the model updating application where a vital first step is to ensure that modes have been correctly paired. The methods have been illustrated in two examples and comparisons with the established Modal Assurance Criterion methods show the new method in a good light. Two frequency dependent operations for generally-damped systems are presented in this thesis. The first operation involves developing a new frequency dependent modal expansion while the second operation generalises a previously-proposed modal correlation approach for these systems such that particular frequencies are targeted. The two suggested methods are illustrated using numerical examples.