Flow-Induced Vibration of Rotating Shafts
Chapter 4 deals with flow-induced vibration of rotors and in particular with the most important case, known as 'steam whirl', often appearing in large steam turbines. Stability criteria, Thomas Stability Criterion and Torque-Deflection Number are applied
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Flow-Induced Vibration of Rotating Shafts
Abstract Chapter 4 deals with flow-induced vibration of rotors and in particular with the most important case, known as ’steam whirl’, often appearing in large steam turbines. Stability criteria, Thomas Stability Criterion and Torque-Deflection Number are applied and compared. Vibration of rotors in fluid annuli occurs due to dynamic interaction of cylinders with the surrounding fluid in parallel or cross-flow. The integrated effect of pressure and dynamic fluid forces generated results to imbalance. Application of Hurwitz-Routh determinants is used for checking stability conditions. Self-excited vibration of a rotating hollow shaft partially filled with viscous liquid occurs within a certain range of rotating speed. Approximate solutions of the equations of motion for the non-dimensional time-dependent radial and circumferential velocity of a small internal liquid element yield non-dimensional liquid forces and, furthermore, stability limits for the rotor. The marginal condition under which the system becomes absolutely stable is investigated.
4.1 The Steam Whirl Problem In the 1940s, two non-condensing turbines built by General Electric Company, designed very differently from the previous ones, and having very flexible rotors, experienced violent whirl at high loads [1]. This whirl could not be corrected by balancing and appeared at high loads only. To cure the trouble, the machines were modified with completely new rotors or pad bearings or both. It was later recognised that forces due to steam flow contributed to this instability. Alford [2] reported that modification to the steam path largely eliminated the problem. There is conflicting information of these two cases. We know, however, that an empirical stability criterion resulted from an investigation related to these two unstable turbines, the Torque Deflection Number (TDN). Later, in 1956, Thomas [3] reported similar problems with AEG turbines, and the efforts to study this
A. D. Dimarogonas et al., Analytical Methods in Rotor Dynamics, Mechanisms and Machine Science 9, DOI: 10.1007/978-94-007-5905-3_4, Ó Springer Science+Business Media Dordrecht 2013
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4 Flow-Induced Vibration
phenomenon both analytically and experimentally. Thomas indicated some of the sources of the excitation, and developed a stability criterion based on a combination of analytical results and experimental calibration. He concluded that the excitation originated from the steam flow through the packing clearances, and the stabilizing effect came from damping forces. He also reported that the problem was corrected mainly by decreasing the span and thus raising the critical speed, and sometimes by bearing changes. Thomas and Alford agreed that the vibration occurred at frequencies equal to the critical speed of the rotor. Alford, however, stated that variation of the whirl speed in jet engines was associated with a wide range of parameters, depending on the amplitude and the test conditions. In the late 1960s the problem arose again, a
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