Synchronous Response Estimation in Rotating Machinery

Synchronous response estimation attempts to determine the forced response (displacement) of a rotor at critical points which cannot be measured directly. This type of prediction, 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. The response estimate is constructed using the measurable response in conjunction with an estimator gain matrix derived from a model of the transmissibilities 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 developed 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. Two reference rotor models that are representative of industrially sized machines are used to demonstrate and evaluate the estimation. The unmeasurable response estimation errors consistently lie below 25 μm for the examples examined.