Thông tin tài liệu
//INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 585 ± [584±604/21] 29.10.2001 4:06PM done. Rotor mass unbalance from dissymmetry, nonhomogeneous material, distortion, and eccentricity can be corrected so that the rotor can run with- out exerting undue forces on the bearing housings. In balancing procedures only the synchronous vibrations (vibration in which the frequency is the same as the rotor rotating speed) are considered. In a real rotor system the amount and location of unbalances cannot always be found. The only way to detect them is with the study of rotor vibration. Through careful operation, the amount and the phase angle of vibration amplitude can be precisely recorded by electronic equipment. The relation between vibration amplitude and its generating force for an uncoupled mass station is " Ft " Fe i!t 17-1 " Yt " Ae i!tÀ 17-2 " A " F=K 1 À ! ! n 2 i2 ! ! n 17-3 tan À1 2 ! ! n 1 À ! ! n 2 17-4 where: " Ytvibration amplitude " F generating force " A amplification factor phase lag between force and amplitude From Equation (17-4), one will find that the phase lag is a function of the relative rotating speed !=! n and the damping factor . (See Figure 17-1.) The force direction is not the same as the maximum amplitude. Thus, for max- imum benefit, the correction weight must be applied opposite to the force direction. Balancing 585 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 586 ± [584±604/21] 29.10.2001 4:06PM Figure 17-1. Typical phase lag between force and vibration amplitude chart. Figure 17-2. Distribution of unbalance in a rotor. 586 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 587 ± [584±604/21] 29.10.2001 4:06PM The existence of unbalance in a rotor system may be in continuous form or discrete form, as shown in Figure 17-2. Ascertaining an exact distribution is an extremely difficult, if not impossible, task by today's techniques. For a perfectly balanced rotor, not only should the center of gravity be located at the axis of rotation, but also the inertial axis should coincide with the axis of rotation shown in Figure 17-3. This condition is almost impos- sible to achieve. Balancing may be defined as a procedure for adjusting the mass distribution of a rotor so that the once-per-revolution vibration motion of the journals or forces on the bearings is reduced or controlled. Balancing functions can be separated into two major areas: (1) determining the amount and location of the unbalance and (2) installing a mass or masses equal to Figure 17-3. Balanced rotor. Balancing 587 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 588 ± [584±604/21] 29.10.2001 4:06PM the unbalance to counteract its effects or removing the mass of the unbal- ance exactly at its location. Static techniques to determine unbalance can be performed by setting a rotor on a set of frictionless supports; the heavy point of the rotor will have a tendency to roll down. Noting the location of this point, the resultant unbalance force can be found, and the rotor can be statically balanced. Static balancing makes the center of gravity of the rotor approach the centerline of two end supports. Dynamic balancing can be achieved by rotating the rotor either on its own supports or on an external stand. Unbalance can be detected by studying rotor vibration with various types of probes or sensors. Balancing is then achieved by placing correction weights in various planes that are perpen- dicular to the rotor axis. The weights reduce both the unbalanced forces and unbalanced moments. Placing the correction weights in as many planes as possible minimizes the bending moments along the shaft introduced by the original unbalance and/or the balance correction weights. Flexible rotors are designed to operate at speeds above those correspond- ing to their first natural frequencies of transverse vibrations. The phase relation of the maximum amplitude of vibration experiences a significant shift as the rotor operates above a different critical speed. Hence, the unbalance in a flexible rotor cannot simply be considered in terms of a force and moment when the response of the vibration system is in-line (or in- phase) with the generating force (the unbalance). Consequently, the two-plane dynamic balancing usually applied to a rigid rotor is inadequate to assure the rotor is balanced in its flexible mode. The best balance technique for high-speed flexible rotors is to balance them not in low-speed machines, but at their rated speed. This is not always possible in the shop; therefore, it is often done in the field. New facilities are being built that can run a rotor in an evacuated chamber at running speeds in a shop. Figure 17-4 shows the evacuation chamber, and Figure 17-5 shows the control room. High-speed balancing should be considered for one or more of the follow- ing reasons: 1. The actual field rotor operates with characteristic mode shapes sig- nificantly different than those that occur during a standard produc- tion balance. 2. Flexible rotor balancing must be performed with the rotor whirl configuration approximating the mode in question. The operating speed(s) is in the vicinity of a major flexible mode resonance (damped critical speed). As these two speeds approach one another, a tighter 588 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 589 ± [584±604/21] 29.10.2001 4:06PM Figure 17-4. Evacuation chamber for a high-speed balancing rig. (Courtesy of Transamerica Delaval, Inc.) Figure 17-5. Control room for high-speed balancing rig. (Courtesy of Transamerica Delaval, Inc.) FPO FPO Balancing 589 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 590 ± [584±604/21] 29.10.2001 4:06PM balance tolerance will be required. Those designs that have a low rotor-bearing stiffness ratio or bearings in the vicinity of mode nodal points are of special concern. 3. The predicted rotor response of an anticipated unbalance distribution is significant. This type of analysis may indicate a sensitive rotor which should be balanced at rated speed. It will also indicate which components need to be carefully balanced prior to assembly. 4. The available balance planes are far removed from locations of expected unbalance and are thus relatively ineffective at the operating speed. The rule of balancing is to compensate in the planes of unbal- ance when possible. A low-speed balance using inappropriate planes has an adverse effect on the high-speed operation of the rotor. In many cases, implementation of an incremental low-speed balance as the rotor is assembled will provide an adequate balance, since com- pensations are being made in the planes of unbalance. This is particu- larly effective with designs incorporating solid-rotor construction. 5. A very low-production balance tolerance is needed to meet rigorous vibration specifications. Vibration levels below those associated with a standard production-balanced rotor are often best obtained with a multiple-plane balance at the operating speed(s). 6. The rotors on other similar designs have experienced field vibration problems. Even a well-designed and constructed rotor may experience excessive vibrations from improper or ineffective balancing. This situation can often occur when the rotor has had multiple rebalances over a long service period and thus contains unknown balance dis- tributions. A rotor originally balanced at high speed should not be rebalanced at low speed. A wealth of technical literature concerning balancing has been published. Various phases of a variety of balancing procedures have been discussed in these papers. Jackson and Bently discuss in detail the orbital techniques. Bishop and Gladwell, as well as Lindsey, discuss the modal method of balan- cing. Thearle, Legrow, and Goodman discuss early forms of influence coeffi- cient balancing. The author, Tessarzik, and Badgley have presented improved forms of the influence coefficient method that provide for the balancing of flexible rotors over a wide speed range and multiple-bending critical speeds. Practical applications of the influence coefficient method to multiplane, multispeed balancing are presented by Badgley and the author. The separate problem of choosing balancing planes is discussed at some length by Den Hartog, Kellenberger, and Miwa for the (N 2)-plane method, and by Bishop and Parkinson in the N-plane method. 590 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 591 ± [584±604/21] 29.10.2001 4:06PM Balancing Procedures There are three basic rotor balancing procedures: (1) orbital balancing, (2) modal balancing, and (3) multiplane balancing. These methods are sub- ject to certain conditions that determine their effectiveness. Orbital Balancing This procedure is based on the observation of the orbital movement of the shaft centerline. Three signal pickups are employed, of which two probes measure the vibration amplitudes of the rotor in two mutually perpendicular directions. These two signals trace the orbit of the shaft centerline. The third probe is used to register the once-per-revolution reference point and is called the keyphazor. A schematic arrangement of these probes is shown in Figure 17-6. The three signals are fed into an oscilloscope as vertical-, horizontal-, and external-intensity marker input. The keyphazor appears as a bright spot on the screen. In cases where the orbit obtained is completely circular, the maximum amplitude of vibration occurs in the direction of the keyphazor. To estimate the magnitude of the correction mass, a trial-and-error process is initiated. With the rotor perfectly balanced, the orbit finally shrinks to a Figure 17-6. Typical arrangement for orbit. Balancing 591 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 592 ± [584±604/21] 29.10.2001 4:06PM point. In the event of an elliptic orbit, a simple geometric construction allows for the establishment of the phase location of the unbalance (force). Through the keyphazor spot, a perpendicular is dropped on the major axis of the ellipse to intersect its circumcircle as shown in Figure 17-7. This intersecting point defines the desired phase angle. Correction mass is found as described earlier. It is important to note that for speeds above the first critical, the keyphazor will appear opposite the heavy point. In the orbital method, the damping is not taken into account. Therefore, in reality, this method is effective only for very lightly damped systems. Further, as no distinction is made between the deflected mass and the centrifugal unbalance due to its rotation, the balance weights are mean- ingful only at a particular speed. The optimum balancing plane considered is the plane containing the center of gravity of the rotor system or, alternately, any convenient plane that allows for the orbit to be shrunk to a spot. Modal Balancing Modal balancing is based on the fact that a flexible rotor may be balanced by eliminating the effect of the unbalance distribution in a mode-by-mode sequence. Typical principal modes of a symmetric, uniform shaft are shown Figure 17-7. Typical probe positions and the phase angle in an elliptic orbit. 592 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 593 ± [584±604/21] 29.10.2001 4:06PM in Figure 17-8. The deflections of a rotor at any speed may be represented by the sum of various modal deflections multiplied by constants dependent on speed " Yx;! I r1 " B r ! r x17-5 where " Y(x, !) represents the amplitude of transverse vibrations, as a function of the distance along the shaft at a rotational speed !. " B r (!) and r (x) express, respectively, the complex coefficient at rotating speed ! and the r th principal mode. Thus, a rotor, which has been balanced at all critical speeds, is also balanced at any other speed. For end-bearing rotors, the recommended procedure is: (1) balance the shaft as a rigid body, (2) balance for each critical speed in the operating range, and (3) balance out the remaining noncritical modes as far as possible at the running speed. Balance planes picked are the ones wherein the maximum amplitudes of vibration occur. Modal balancing is one of the proven methods for flexible rotor balan- cing. Modal balancing has also been applied to problems of dissimilar lateral stiffness, hysteretic whirl, and to complex shaft-bearing problems. In many discussions on modal balancing fluid-film damping is not included. In other Figure 17-8. Typical principal modes for a symmetric and uniform shaft. Balancing 593 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 17.3D ± 594 ± [584±604/21] 29.10.2001 4:06PM instances rolling-element bearing effects are neglected. In such cases, the practical usefulness of the modal method is not fully defined. Several problems hinder the application of the modal technique to more complex systems. To use the technique, calculated information is required on the mode shapes and natural frequencies of the system to be balanced. The accuracy of the computed results depends on the capabilities of the computer program used and on the input data (dimension, coefficients, system model effectiveness) used in the calculations. In turbomachinery where system damping is significant, as with fluid-film bearings, problems arise. The mode shapes and resonant frequencies of heavily damped systems often bear little resemblance to undamped mode shapes and frequencies. The reliance of modal balancing on predicted modes and frequencies is at least an inconvenience and, without proper response programs, can be a significant disadvantage. At present, no general-purpose modal balancing computer programs exist that are comparable in nature to the programs developed for the influence coefficient (multiplane) method. Such a program would require calculated modal amplitudes and phase angles, and that the measured amplitudes and phase angles of the rotor bearing system be balanced. The program would then be run for each separate rotor whirl mode, including the full- speed residual balance correction. At present, no general analysis suitable for programming exists. Multiplane Balancing (Influence Coefficient Method) Modal balancing came into being to alleviate the problems of the supercritical rotor unbalance of the steam turbine-generator industry. It combined the then available techniques for calculating response amplitudes for the various rotor vibrational modes with the available instruments for measuring actual installed vibration levels. In recent years, more systems have been designed for supercritical operation. Newer types of sensors and instruments are becoming available, making it feasible to obtain precision in amplitude and phase measurement. Minicomputers for operation on the shop floor or in balancing pits, and time-sharing terminals for in-the-field access to large computers, are now commonly available. The newest multi- plane balancing techniques owe their success to advancement in these areas. The influence coefficient method is simple to apply, and data are now easily obtainable. Consider a rotor with n discs. The method of influence coefficients provides the means for measuring the compliance characteristics of the rotor. 594 Gas Turbine Engineering Handbook [...]... Amplitude and Phase-In-Plane 1 2 3 4 5 Final Vibration Amplitude and Phase Before Balancing In-Plane 1 2 2 4 5 Phase //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 17.3D ± 6 02 ± [584±604 /21 ] 29 .10 .20 01 4:06PM 6 02 Gas Turbine Engineering Handbook Data Sheet B Trial Weight Plane _ Radius Angle Amplitude Vibration Amplitude and Phase In-Plane Phase 1 2 3 4 5 Data Sheet C Options 1 2 If the same weight as the... under which the coupling works //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 611 ± [605±633 /29 ] 29 .10 .20 01 4:06PM Couplings and Alignment 611 Figure 18-5 Recommended limits of misalignment vs operating speed (Reference 3) //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 6 12 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 6 12 Gas Turbine Engineering Handbook Oil-Filled Couplings Very few high-performance couplings... Equipment, Proceedings of the 25 th Turbomachinery Symposium, Texas A&M University,'' p 25 3, 1996 Tessarzik, J.M., Badgley, R.H., and Anderson, W.J., ``Flexible Rotor Balancing by the Exact-Point Speed Influence Coefficient Method,'' Transactions //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 17.3D ± 604 ± [584±604 /21 ] 29 .10 .20 01 4:06PM 604 Gas Turbine Engineering Handbook ASME, Inst of Engineering for Industry,... //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 620 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 620 Gas Turbine Engineering Handbook justification to review, with the latest techniques, the nature of the rotating system to be coupled Couplings, whether gear or disc-type, should not be simply picked from a catalog Some installations are very old, and some have been revised in other ways in the field Unfortunately, such engineering. .. couplings are as follows: 605 //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 606 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 606 Gas Turbine Engineering Handbook Figure 18-1 Flexible coupling operating spectrum 1 2 3 4 Centrifugal force Varies in importance, depending on the system speed Steady transmitted torque Smooth nonfluctuating torque in electric motors, turbines, and a variety of smooth torque-absorbing... vacuum-degassed alloy steel, forged with a radial-grain orientation, and has a contoured profile machined on high-precision equipment The contoured profile is shown in Figure 18-8 The diaphragm undergoes axial deflection The forces acting on the disc that are generating the stresses //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 616 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 616 Gas Turbine Engineering Handbook. .. nitriding has been used to correct or minimize small errors of tooth geometry caused by the shaping or hobbing processes //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 614 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 614 Gas Turbine Engineering Handbook Table 18 -2 Types of Typical Gear Coupling Failures Standard or Sealed Lube Wear Fretting corrosion Worm tracking Cold flow Lube separation Continuous Lube... low Moderate Low Moderate Low Moderate High High High Moderate Moderate High Low *This table is intended as a rough guide only Gear //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 608 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 608 Gas Turbine Engineering Handbook Gear couplings, disc couplings, and diaphragm-type couplings are best suited for this type of service Table 18-1 shows some of the major characteristics... around pieces of metal or rubber even when they fail, and they can work longer in corrosive conditions than many other couplings //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 18.3D ± 610 ± [605±633 /29 ] 29 .10 .20 01 4:06PM 610 Gas Turbine Engineering Handbook A major disadvantage in gear couplings is the misalignment problem Tooth-sliding velocity is directly proportional to the tooth-mesh misalignment... radius NS1 2 NS1 _ Radius at which balancing weights will be placed If NS1 2, give the locating radius in each plane (This is not applicable if NS1 1.) Plane No 1 2 3 4 5 Radius 3 4 5 6 If balancing is to be done to the initial run-out, then NS2 1 If balancing is to be done to zero amplitude, NS2 2 NS2 _ If add-on weights will be used, NS3 1 If holes will be drilled, NS3 2 NS3 . Phase Vibration Amplitude and Phase In-Plane 1 2 3 4 5 6 02 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 17.3D ± 603 ± [584±604 /21 ] 29 .10 .20 01 4:06PM Bibliography Badgley,. the phase angle in an elliptic orbit. 5 92 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 17.3D ± 593 ± [584±604 /21 ] 29 .10 .20 01 4:06PM in Figure 17-8. The deflections. (N 2) -plane method, and by Bishop and Parkinson in the N-plane method. 590 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 17.3D ± 591 ± [584±604 /21 ] 29 .10 .20 01
Ngày đăng: 13/08/2014, 09:20
Xem thêm: Gas Turbine Engineering Handbook 2 Episode 13 ppt
