| It is of great importance to study the vibration of rotary machinery because it has impact on the life-span, reliability, noise and economy of machine directly. During the rotating parts design, the dynamics characteristics should be addressed carefully. It is crucial to keep the vibration on any monitoring point not exceeding safe and acceptable levels while running up, shutting down or running at operating speeds. As consequences of exceeding safe and acceptable levels, failures could be caused by excessive wear on bearing, blade(s) on the rotor in contact with stationary housing. These failures would result a disaster situation. Besides, a violent vibration of rotor brings an adverse impact to the supporting structure.The rotor's flexibility, mass distributions and its supports' flexibility associating with its maximum operating spin speed will essentially determine whether or not residual rotor unbalance can produce forced vibration resonance. That is, these factors determine if the rotor has the one or more natural frequency modes below the operating speed. If so, then the machine must pass through the critical speeds where the residual mass unbalances act as synchronous harmonic forces to excite the one or more natural frequencies the rotor speed traverses when the machine accelerates to operating speed and when coasting down. Mode shapes at critical speeds, as called resonant modes, are also determined by the same properties as rotor and bearing supporting stiffness and dumping etc. Because of demands for compact high-performance turbo generator machines, many modern turbo machineries are designed to operate above one or more critical speeds.In general speaking, a flexible rotor supported by rigid bearings often lacks some vibratory motion at the bearing supports, because they provides essential buffering and damping to keep vibration magnitude at resonance conditions within acceptable levels. But, the opposite case is also far more common in rotor dynamic, that is to say the potential for rotor dynamic deflection significantly contributes to the lateral vibration characteristics. The rotor bending increases with rotor spin speed and with bearing-to-rotor stiffness ratio.For the vast majority of rotating machines, shaft bow (hog and sag) is negligible for practical reasons. On driving machines as turbo-generators in power generation plants or machines with long spacer shaft the bent shaft may be considered. The shafting of1000MW rotor system is so long that the shafting's bend could not be ignored. This work also studied the influence of bent shafting on the vibration responses. A bent shaft could be caused during shipping or installation. The bend in shaft also could be caused in normal operating conditions by such factors as:thermal distortion due to fast load changes, cooling or heating of the rotor, rubbing, the frictional heat produced at the site of rubbing, and change of shaft stiffness, etc. The force response caused by the bend is similar to that caused by conventional mass unbalance, which is a function of square of speed, though there is a slight difference in amplitude and phase angle. A bent shaft can either generate high vibration or create a lot of stress on other components during operation, subsequently catastrophic failure will result. Hence, it is therefore important to be able to recognize such a fault.When turbine generator is operating, temperature of the overall shafting is non-uniform, which is caused by such fault as machine windings etc. Non-uniform thermal (stress) distribution along the shaft will lead such material properties as stiffness, and damping etc at different area to be changed. Then the critical speeds, natural frequencies of the shaft will be shifted up or down. Obviously, temperature variations can significantly influence the dynamic characteristic of the rotor. However, the relationship among temperature and the mass and stiffness matrices of the rotor is nonlinear and complex so it has rarely scientific studied in recently.Stability is a major consideration in the operating and designing of rotor bearing systems. Many unstable vibrations arise because of the effects of the bearing parameters and internal damping. Otherwise, the non-symmetry in the stiffness matrix of journal bearing can make rotor become unstable, particular when the rotors are supported by fluid film bearing. Rotors have the internal damping, which often are expected that damping reduces the amplitude of any vibration. But in fact, damping in a flexible shaft can cause instability when the rotor's spinning speed exceeds at least one of critical speed of the rotors. Viscous damping in the rotor tends to separate the real parts (eigenvalues roots) associated with each resonance frequency, making one more positive and the other more negative. At a sufficiently high rotor spinning speed, internal damping in the rotor causes instability by driving at least one of the roots into the positive real part in roots locus.The rotor with deflection due to out-of-balance and other force has different vibration behaviors. And centrifuge force produced by deflection acts on the rotor and gives rise to hoop and radial stress. On the other hand, the lateral and torsional vibration also cause bending and shear stresses. In turn, these stresses can affect the dynamic behavior of the rotor. During normal operation, however, shear stress on rotor has been somehow become forgotten, though it is the main source of potential catastrophic failure under abnormal operation. Therefore, designers have to study the torsional vibration of turbo machinery for safety. In general, exciting forces are estimated to determine the torques of the each section along the shafting at first. Then related stresses on each rotor are calculated. Subsequently, the calculated stresses are compared to the admissible stress of the shaft material to evaluate the probability of fatigue failure.Comparing with typical lateral vibration modes, torsional vibration modes are usually quite lightly damped. With very little damping, excitation of a torsional mode can lead to serious rotor failure without warning. Because torsional modes are often uncoupled from lateral modes, so that the torsional modes can be continuously undergoing at large amplitude forced resonance without outward signs of distress or the machine exhibiting any readily monitored. It can lead to the shaft suddenly broken from an initiated crack as a consequence of vibration-caused material fatigue-without warning.In recent years, due to its advantages of high efficiency, energy saving and environment protection,1000MW USC (Ultra Supercritical) units have been developed rapidly. Despite of the fact that machining quality of rotor, assembly precision and the maintenance quality of power plant have been improved, rotor vibration of1000MW USC is still a main fault on such unit due to its complex rotor structure, the larger number of bearings, long shaft, and lower shaft support stiffness.The1000MW USC is a large, heavy machine. It consists fives individual rotors linked by coupling as rigidly with total shaft length of54.652m and total weight of the rotor about300tonnes. So it is necessary to investigate the dynamic behavior vibration of the rotor's shafting. In this thesis, finite element method (FEM) is used to analyze dynamic characteristic of the rotor. Several decades, with the increasing in computing power, the FEM has become the de factor standard method for the static and dynamics analysis rotor bearing system. Shafting is the most common (model) used to analysis in rotor dynamic. So FEM is used in this thesisBased on the full-size1000MW USC rotors system modeling and analysis, this work focuses on studying in the following areas:Firstly, dynamic characteristics of the1000MW USC turbine generator shafting vibration are analyzed. The main features of the rotor vibration such as natural frequency, mode shape, critical speed, respectively for both lateral and torsional vibration are determined.The unbalance responses of the rotor in two cases isotropic and anisotropic bearing systems and the response due to bend shaft are analyzed. The results show that in case the rotor supported by isotropic bearing, only forward modes are excited and orbits are circular at all nodes along the shaft. Whereas in case of the rotor supported by anisotropic bearings, or bent shaft both forward and backward modes are excited and the orbits are elliptical-not circular. The rotor vibration behavior excited by out-of-balance is almost indistinguishable from excited by a bent shaft. In fact, the slight differences can be described as:if the vibration whirl is caused by bent shaft, the whirl can be removed by balancing the rotor at only one speed, and if the rotor rotational speed changes, the whirl will arise againIn case of torsional vibration, torque response of torsional vibration when electric fault is considered. The results show that, torque at the coupling between the LP B and the GEN rotors is the largest and it is the where may be more dangerous than the other locations.Secondly, sensitivity analysis on vibration behavior of the rotor under thermal effect is one major subjects of this work. Both lateral and torsional vibrations, the sensitivities under thermal effect are analyzed in actual operation condition in temperature range of20-570?at first. The influence of temperature-dependent material properties was considered primarily with respect temperature variation. The temperature increasing leads the material properties changed, then critical speeds changed. For lateral vibration, the results show that the modes that associate with the HP and the LP modes are more sensitivity than the others. For torsional vibration, the sensitivity under thermal effects is small, maximum value is about4%. On the other hand, this work also considers the combination influence of temperature, rotary inertia and gyroscopic effect and rotor speed on shafting vibration.In addition, for lateral vibration, the sensitivities of the critical speeds are analyzed by changing bearing stiffness. The results show that the bearing-support stiffness increase leads to natural frequencies increase gradually but not linear. The first order is much more sensitive than the others. When stiffness of bearing is large enough, the natural frequencies almost do not change. Then this stiffness quantity could be considered as the upper limited to frequencies. For torsional vibration, the sensitivities of natural frequencies are analyzed by changing some mechanical parameters. With changing the stiffness and inertia of the rotor, their influences to the characteristics of the torsional vibration are obtained. The frequency can be modulated by changing the sectional structure of the shafting to avoid torsional vibration resonant. In another word, for a real turbine generator, the tuning would be realized conveniently by changing structural parameters in such place as joints, linking shafts, or by changing the diameter of certain area. The results are also shown that torsional frequency and mode shape is much more sensitive to mechanical parameter than to thermal effect.Thirdly, the instability due to cross-coupled stiffness of fluid film bearings and instability due to the effect of internal damping are the major subjects in this work. In hydrodynamic bearing, there is an oil film existent in a small clearance between the rotating and the static elements. The rotor creates a hydrodynamic pressure distribution within the oil film, which supports the unbalance force and weight of the rotor. The results show that hydrodynamic bearing can cause rotor instability, because of the non-symmetry bearing stiffness matrix. Damping is often supposed that reducing the amplitude of any vibration. But analysis rotor instability in case internal damping in the flexible shaft of1000MW rotor show that it can cause instability when rotor spinning speed exceeds at least one critical speed.Finally, in this work, full-size shaft is modeled and rotor stresses are computed by using ANSYS. From that the dangerous area of the rotor can be found. The results show that the displacement of both lateral and torsional vibration are very small, therefore, dynamic stresses in the shaft are low during normal operation. Dynamic torsional stresses are more at the fillet regions and the slope of the mode shape larger and almost concentrate at the coupling regions of the rotor associate with torsional modes. Where are usually less stiff in comparison to the main body sections of the rotor. Thus, if the problem occurs, the couplings are often broken at first. |
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