Observer-based critical response estimation in rotating machinery

Critical response estimation attempts to determine the synchronous forced response (displacement) of a rotor at critical points which cannot be measured directly. This type of critical response prediction capability, if accurate and reliable, has broad potential use in the rotating machinery industry. Many machines have close clearance points on their shafts, such as seals, which can easily be damaged by excess vibration. Accurate estimates of the actual level of vibration at these points could usefully assist machine operators in troubleshooting and in protecting the equipment from expensive damage. This type of response information can be used both to generate less conservative alarm limits and, if magnetic bearings are available, to directly guide the bearing controllers in restricting the rotor motion at these critical points.; It is assumed that the disturbance forces acting upon the rotor are predominantly synchronous (e. g., mass unbalance.) The design of the estimator also accounts for the fact that most industrial rotating machinery operates at a single, constant speed over long periods of time, eliminating the benefits of variable speed response measurements. The unmeasurable response estimate is constructed using the response from the measurable sensor locations and from an estimator gain matrix derived from a model of the transmissibilites of the rotor system. A fundamental performance bound is established based on the single-speed set of measurements by bounding the response to the unmeasurable component of the disturbance force. Acknowledging that some model uncertainty will always exist, a robust performance analysis is performed using structured singular value (μ) analysis techniques. Assuming some reasonable levels of uncertainty for the model parameters (natural frequencies, modal dampings, mode shapes, bearing stiffnesses and dampings) the results of the estimator construction and analysis establish feasibility of the proposed estimation. The unmeasurable response estimation errors consistently lie below 0.001 inches for the representative examples examined. Structured singular value techniques are used again to construct critical response estimators which are intended to yield superior robust performance results. Two reference rotor models that are representative of industrially sized machines are used to demonstrate and evaluate the estimation.; To improve estimator performance, it is proposed that an on-line identification of the rotor system can be conducted. This rotor identification is facilitated by the use of magnetic bearings. The force excitation and response measurement environment provided by the magnetic bearings permits system identification implementation in the industrial environment rather than just in the laboratory. Currently available rotordynamics modeling and system identification techniques which are able to substantially reduce the amount of Uncertainty and error in a rotor model are presented and reviewed in anticipation of future research and actual implementation. An extension of these methods is proposed which allows better use of a priori rotordynamic models to construct an internally matched model from measured data. This approach permits model extrapolation to the critical locations where no experimental data is available.