EIGENVALUES OF ROTATING MACHINERY (STABILITY, ROTORDYNAMICS, VIBRATION)

The current industry standard for linear eigenanalysis for vibration of rotating machinery is the transfer matrix method. This is true for both lateral and torsional vibration. Lateral vibration computer codes based on this method are subject to a variety of convergence problems including computing eigenvalues in random order, incomplete convergence on some, missing some altogether and a poor capability to compute many roots to try to ensure that none of importance are missed. A method of calculation is presented which overcomes these problems. A technique is derived by which transfer matrices are used to compute the coefficients of the system's characteristic polynomial. The eigenvalues are the roots of this polynomial. While overcoming convergence problems, the method also entails a tremendous increase in execution speed, making it well suited for small computers. The speed advantage is partly brought on by a new technique of condensation. This technique, also described here, is optimized automatically and easy to invoke.; Complete, experimental verifications of eigen-computer codes for lateral vibration are rare in the literature. As part of this work a verification has been done with a large scale test rig. Measurements were also made of tilt-pad bearing properties (also virtually nonexistent in the literature) and foundation transfer functions. Excellent agreement (7.5% error) was obtained between measured and computed natural frequencies of the running rotor. Another comparison is also shown for a large, single-stage industrial steam turbine.; For the case of torsional analysis the transfer matrix method has limited application due to modeling restrictions. A new method is presented which overcomes this shortcoming without resorting to a full matrix representation. The method computes the characteristic polynomial by using a single recursive equation. Single and multi-branch and open and closed-loop systems are all handled by the same equation. The new technique of condensation is also applicable here.; Together, these two methods permit the analysis of machines which can be represented by connections of lateral or torsional beam elements.; The eigenanalysis of a system which cannot be modeled in the above manner is also presented. The machine is a flywheel energy storage system subject to a subsynchronous whirling instability due to internal friction. The goal is to predict the stabilizing capacity of various system parameters. An experimental verification of the analysis with an unstable flywheel test rig is shown.