LOW FREQUENCY BUCKETS FOR INDUSTRIAL STEAM TURBINES by

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1 LOW FREQUENCY BUCKETS FOR INDUSTRIAL STEAM TURBINES by Firm L. Weaver Engineering Consultant Sun City Center, Florida Firm L. Weaver graduated from Roanoke Coll ege, in Salem, Virginia, with a B.S. degree in Mathematis in He reeived B.S. and M.S. degrees in Eletrial Engineering from Massahusetts Institute of Tehnology in He is a liensed professional engineer in both Massahusetts and New Jersey. Mr. Weaver was employed for twentynine years by General Eletri Company before joining Delaval Turbine, In. in I967. With General Eletri, his experiene overed all funtions of steam turbine researh, design and testing for all types of turbine appliations, inluding entral station generator drives, variable speed industrial turbines, Marine and Navy fossil fuel propulsion turbine-generator sets, and Navy nulear main propulsion and turbine-generator sets. He was Manager of Engineering for Delaval Turbine, In. for nine years. In this position, he was responsible for both development and prodution engineering for entrifugal pumps, entrifugal ompressors, steam turbines and gears for industrial, utility, Navy and Marine appliations. Sine April, I977, he has been a onsultant on turbomahinery appliation and operation, speializing in vibration problems and failure of parts. Mr. Weaver is a member of the Amerian Soiety of Mehanial Engineers, the Soiety of Naval Engineers and the Soiety of Naval Arhitets and Marine Engineers. He has published various tehnial papers on subjets suh as turbine buket vibration, turbine effiieny and reliability, overspeed ontrol devies, entrifugal pump performane, rotor vibration, and engineering design tehniques. ABSTRACT Buket failures have been known to our on the later stages of industrial type steam turbines after prolonged operational life of as muh as five or six years. All of these failures are harateristially fatigue in nature. It is the purpose of this paper to disuss the reasons for these failures as related to the operating load and speed of the turbine and to the design of the bukets. Buket banding an be used to minimize the possibility of failure. INTRODUCTION Buket failures have been known to our in the later stages of industrial type turbines after prolonged operational life of as muh as five years or more. All of these failures are harateristially fatigue in nature. It is typial of these appliations that both load and speed may vary over the life of the equipment. It is the purpose of this paper to onsider the speial ase in whih the buket is tall and its first natural frequeny is relatively low. This buket may have its first natural frequeny exited by a stimulus having a frequeny equal to some low multiple of turbine running speed. The various soures of this low frequeny stimulus are disussed, and the effets of turbine speed and loading on buket life are onsidered. A relationship is shown in whih the shroud band an be used to redue the vibratory response of the banded group of bukets and iinprove their life. NOZZLE PASSING FREQUENCY Nonuniform buket loading around the 360 ar that the buket travels is the soure of vibratory stimulus on the buket. One obvious soure of nonuniform loading is the stationary nozzles that diret the steam flow to the buket. These nozzles, being of finite thikness, ause perturbations in the steam flow pattern at a frequeny orresponding to the number of nozzles per 360 times the operating speed. This stimulus is ommonly alled the nozzle passing frequeny stimulus. Sine this stimulus is not sinusoidal in nature, it ontains omponents not only at the nozzle passing frequeny, but also at higher multiples of that frequeny. These stimuli have frequenies that are generally 50 times running speed or more. These higher frequeny stimuli, although important in turbine design pratie, are not being onsidered in the text of this artile. LOW FREQUENCY STIMULUS NONUNIFORM BUCKET LOADING The same nozzles that were disussed above are also a soure of nonuniform buket loading that generates low frequeny stimulus to the bukets. In the. manufature of the stationary blading, or diaphragm, there is always some variation in stationary, or nozzle, blade spaing, and therefore some variation in nozzle area per unit of irumferential distane around the diaphragm. These variations in area per unit of irumferene are usually at a maximum at eah side of the horizontal joint of the diaphragm, or asing. Therefore, it is not unommon to find that the diaphragm is a signifiant soure of "two per revolution" (2 Per-Rev) stimulus, due to the variations in nozzle area at the horizontal joint. Sine the area variations are not sinusoidal in nature, it an be found that most diaphragms are soures not only of 2 Per-Rev stimuli, but also of all the lower Per-Rev multiples, suh as 1 X, 2 x, 3 x, 4 X, 5 X, et. Most of the time, the majority of these stimulus omponents are relatively small, being less than one or two perent of the normal driving fore on the buket. Their size is, of ourse, diretly dependent on the auray of manufature of the stationary bladed parts. Another soure of low frequeny stimulus is found in the exhaust onfiguration of steam turbines. The exhaust asing ats to ontrol the diretion of steam flow and to turn it perpendiular to the axis of the turbine. This ation results in a nonuniform exhaust pressure around the 360 irumferene of the last stage. This nonuniform loading generally produes primarily a 2 Per-Rev stimulus, but it also may produe other signifiant low multiple stimuli. The exhaust area distribution also is not always onsistent 15

2 16 PROCEEDINGS OF THE TWELFTH TURBOMACHINERY SYMPOSIUM with that needed for uniform loading of the buket. It is ommon pratie to strengthen and support large ondensing exhaust asings with stay braing and stiffening ribs. All of these features are potential soures of nonuniform lo ding on the 360 irumferene of the stages of bukets that are subjet to these variations. This not only inludes the last stage bukets, but it also may inlude the next to last stage and other rows of bukets that are involved in industrial type turbine double flow ondensing exhaust designs. Obviously, none of the fators disussed above are of a purely sinusoidal nature. Therefore, it an be expeted that they will generate stimuli at all the lower Per-Rev multiples. There are no extensive data on the size of these stimuli, but buket failures that have been assoiated with them indiate that they an be of the order of magnitude of 5% to 15% of the normal driving fore on the buket. The same types of physial features that are desribed for the turbine exhaust may also be found in other areas of the turbine, suh as at extration openings or other disontinuous features in the design of the turbine asing and other internal stationary parts. The low frequeny stimuli will ause vibratory stresses in the buket that are small as long as the buket does not operate on or near its natural frequeny. The buket vibratory stress, off resonane, will be in approximately diret proportion to the low frequeny stimulating fore. For example, a stimulus that is 5% of the normal driving fore will produe a vibratory stress that is equal to approximately 5% of the normal steady state steam bending stress, provided that the buket is not on resonane. From the above disussion it an be seen that low frequeny stimuli will be prevalent throughout the turbine to a larger or smaller degree, depending on the physial onstrution of the stationary parts in the steam path of the turbine. However, the effet of these stimuli on buket stresses will be small as long as the bukets are not on resonane. LOW FREQUENCY STIMULUS ROTOR VIBRATION A soure of low frequeny stimulus to the buket is found in the vibratory spetrum of the turbine rotor. It is well known that the vibration signature of the turbine rotor always shows some vibration at several of the lower multiples of running speed. Figure 1 shows one suh typial low frequeny vibration spetrum. Cl :::0!: A. IE 2N 4N The available vibration standards [1] are usually interpreted only in terms of running speed. That is, the mahinery overall vibration in mils, or veloity in inhes per seond, is judged to be adequate or not based on omparison to a standard limit that is determined at the turbine operating speed. There are today no speifi rules for determining vibration limits for the vibration at multiples of running speed. For example, API Standard 612 for Speial Purpose Steam Turbines for Refinery Servies has the following shaft vibration limit: Unfiltered double amplitude = 1.25 inluding runout (mils) J'i2,000 V --qm;- The speifiation also requires that, at slow roll, the shaft runout should not exeed one-fifth the above value or 0.25 mils, whihever is less. This ould be interpreted to say that a turbine operating at any speed of 12,000 rpm or less ould have journals out of round by 0.25 mils. This out-of-round ould be in any shape of two, three or more lobes to stimulate the turbine at 2 X, 3 X, 4 X, et. The rotor vibration is a omplex funtion depending on the rotor and bearing designs, as well as the runout of the journals and the rotor unbalane. Although the journal runout is not a diret measure of the resultant rotor vibration, it is some indiation of the probable level of vibration at the various multiples of running speed. When there is a geared drive, the vibration signature of the gear and the driven equipment may also show up on the turbine rotor vibration signature. Figure 2 shows an example of a bearing ap reading taken on a turbine that drives a ompressor through a step up gear. The step up gear ratio was suh that the 3 X ompressor vibration ourred at 4.87 X turbine speed. That is, the 5 X turbine vibration nearly oinided with the 3 X ompressor vibration to make this a major omponent of the vibration spetrum of the turbine. The vibration level was inhes per seond at 547 Hz on the turbine bearing ap. This is a relatively low veloity. Casing veloities of 0.15 to 0.20 inhes per seond are generally onsidered as aeptable levels of vibration. However, this turbine had experiened buket failures that were attributed to exitation of the buket first tangential frequeny by 5 Per-Rev stimulus from the turbine. BLADING RESPONSE TO ROTOR VIBRATION It has been stated earlier that buket failures have been thought to have been aused by stimuli of the order of 5% to 15% of the normal driving fore on the buket. This would orrespond to about 100 psi to 300 psi off-resonant vibratory stress in a buket having 2000 psi steady state bending stress. There are so many variations in buket design that it is impossible to generalize to over all bukets. However, for a 10 inh long by 2 inh wide uniform buket, having a ross setion area of 1.11 square inhes and a setion modulus of ubi inhes, the rotor vibration neessary to produe 100 psi alternating stress at the base of the buket is found to be as follows: a= (1) FREQUENCY Figure 1. Typial Low Frequeny Vibration Spetrum. where a = peak to peak rotor vibration, mils N = frequeny, Hz This equation has been used to alulate the information in

3 LOW FREQUENCY BUCKETS FOR INDUSTRIAL STEAM TURBINES 17 Table 1, whih shows the peak to peak vibration amplitude and the veloity required to produe 100 psi alternating stress in the 10 inh long uniform buket for various foring frequenies. Therefore, if the ' 10 inh long buket were operated at 6000 rpm (100 Hz), it ould be expeted to have fatigue failures if the buket resonane were exited by any of the rotor vibrations in Table 1. Table 1. Rotor Vibration Neessary to Produe 100 psi Alternating Stress in a 10 Inh Buket. >!:: <..> 0 > txturbine lxcomp. 4xT 3XC SXT FREgUENCY AMPLITUDE! EL!!,IU P-P 100 Hz, 1.38 MILS.44 IN /sec 3XT &xt os However, there will be few 10 inh long straight bukets operating at 6000 rpm. Instead, they will most likely be tapered. A buket has a relatively large taper when the ross setion area at the buket tip is equal to only half the area at the buket root. For a buket having this amount of taper, the rotor vibration required to produe a given stress at the root will be approximately three times the amount required for a straight buket of the same length. The rotor vibration amplitude required to produe a given fored vibration stress in the buket will vary approximately diretly with the buket width and inversely with the square of the buket length. So, longer or narrower bukets will be easier to exite with rotor vibration, and shorter and wider bukets will be more diffiult. Today's vibration instrumentation gives an indiation of the rotor vibration, but does not give a diret measurement omparable to the values disussed above. The asing or bearing ap measurement obviously does not give rotor vibration. The so-alled "shaft reading" instrumentation really measures the differene between the bearing braket vibration and the shaft vibration. Both of these measurements are taken near the ends of the rotor, while the rotor vibration alulated by Equation 1 and shown in Table 1 is the rotor vibration at the buketed stage. The rotor vibration at the buketed stage will, in most ases, be substantially larger than the vibration at the bearings. The vibration levels in Table 1 are not diretly omparable to usual vibration readings, but they are indiative that it is possible that buket failure an be aused by levels of rotor vibration not onsidered objetionable by urrent vibration standards. STIMULUS RELATIVE IMPORTANCE The low frequeny stimulus has little or no effet on the majority of bukets in the usual industrial steam turbine. The reason for this is that most bukets have a first (or lowest) natural frequeny that is well above the low frequeny stimulus that we have been disussing. For example, the first natural frequeny (first tangential) of a typial straight, uniform setion buket that is inhes wide and 4 inhes tall will be about 1, 000 Hz. It would require a 10 Per-Rev stimulus to exite this frequeny buket for a turbine operating at 6, 000 rpm. While it FREQUENCY Figure 2. Turbine Bearing Cap Vibration Veloity Showing Exitation from Gear Driven Com pressor. is not impossible for this stimulus to exist, it is highly unlikely that it will be of suffiient magnitude to ause failure of the buket. There have been a few isolated ases in whih buket failure of these smaller, high frequeny bukets has been attributed to rotor vibration. In these ases, the rotor was vibrating at higher frequenies, orresponding to a stimulus from the driven equipment that was usually geared to the turbine. The problem of low frequeny buket stimulus beomes more ritial as the buket beomes taller and its first tangential frequeny beomes lower. There is no absolute limit of inreased first tangential frequeny beyond whih you an onlude that there is no probability of a problem. There is experiene of buket failures due to operation with the buket first tangential natural frequeny stimulated by multiples of running speed from 2 X to 7 X. There seem to be few, if any, failures due to this ause when the buket natural frequeny is above 7 X running speed. Also, there have been no reent failures at 1 X, beause all manufaturers suessfully design to avoid operation with the buket natural frequeny on running speed. For industrial drive turbines the buket frequenyspeed relation shown in Figure 3 is somewhat typial for the last stage ondensing buket. The relationship of Per-Rev stimulus and buket failure as presented above is a great oversimplifiation of this problem. Obviously, a buket operating with very low steady state steam bending stress will be more likely to operate suessfully on any given Per-Rev stimulus than a buket with very high steam bending stresses. TURBINE SPEED RANGE Figure 3 shows an example of a relationship of the buket first tangential frequeny to the lower multiples of running speed. In this example, the buket first tangential frequeny an be exited by either 4 X or 5 X running speed within the normal operating speed range of the turbine. You an see that a minor inrease in buket natural frequeny will not eliminate the problem of potential resonant exitation. As long as the operating speed range remains as shown, raising the buket frequeny by some moderate amount will only tend to shift the exitation soures to 5 X and 6 X or some other higher multiple of the running speed. To hange the buket design to inrease its frequeny will usually redue the risk of failure. The higher frequeny buket will be stronger and stiffer than the lower frequeny buket, and therefore better able to withstand any given vibratory

4 .. 18 PROCEEDINGS OF THE TWELFTH TURBOMACHINERY SYMPOSIUM SPEED, RPM Figure 3. Buket Resonant Frequeny and Per-Rev Stimulus Versus Turbine Speed. stimulus. Also, it is likely that the stimulus at a higher Per-Rev resonane will be smaller than at the lower Per-Rev unless there is some speifi identified soure of the higher Per-Rev stimulus, suh as the number of asing internal stay-bars per 360, or signifiant rotor vibration response at the orret frequeny. If the operating speed range in Figure 3 were broadened a small amount, it ould be possible for any one of three Per-Rev stimuli to exite the buket natural frequeny, provided that the appropriate speed were run. Usually, this possibility is ompliated by the fats that the buket natural frequeny is not preisely known and that the natural frequeny is a range of values, due to manufaturing toleranes, rather than a single speifi number. So, taking these fators into aount, it is not unusual for a broad operating range of speed to have the possibility of two or three different low Per-Rev stimuli that ould exite the buket somewhere within the speed range. EFFECT OF OPERATING SPEED ON VIBRATION STRESSES The relative vibration magnitude for a simple spring mass system that is exited by a vibratory fore is given by Equation 2. A= where A = magnifiation fator or relative vibration N = frequeny of exiting fore, whih is proportional to turbine operating speed, Hz Ne = natural frequeny of the system, or buket natural frequeny, Hz 8 = logarithmi derement damping of the system, per unit 11' = From Equation 2 it is seen that the vibration amplitude, A, 1 (2) and, therefore, the buket vibratory stress amplitude are primarily ontrolled by damping, 8, when the system is operating on or near resonane (N = Ne) Measurements that have been made indiate that the logarithmi damping for banded turbine bukets is probably between 1.0% and 4.0% [2]. A value of 2.0% (or 0.020) was seleted as representative, and Equation 2 was solved for "A" for various ratios of NINe. This information is plotted in Figure 4, whih illustrates the major effet of turbine operating speed on buket vibratory stress. From Figure 4 it an be seen that, if the turbine were operating only 1% off the buket resonane (that is, NINe= 0. 99), the vibratory stress would be only approximately a third of what it would be if the turbine were operating at a speed that plaed the buket exatly on resonane (NINe= 1.00). This indiates that, for a turbine operating at about 6000 rpm, it is possible that a 60 rpm hange in speed ould hange the vibratory stress in a low frequeny buket by a fator of as muh as three to one. This is the most likely explanation for the experiene of those industrial turbines that have operated suessfully for several years, but then have had repeated buket failures after a relatively small hange in normal operating onditions that inluded a small hange in speed z u a: L z u - 50 z CJ:I 40 :E > a: N/N Figure 4. Buket Relative Vibratory Stress for 2% Damping Versus the Ratio of Turbine Speed to Buket Resonant Speed.

5 LOW FREQUENCY BUCKETS FOR INDUSTRIAL STEAM TURBINES 19 BUCKET LOADING So far, the disussion has been on buket natural frequenies and potential exiting frequenies. An equally signifiant fator is the normal steady state buket bending stress due to the average tangential driving fore on the bukets. In general, the amount of the stimuli disussed above will be in approximately diret relation to the buket bending stress. That is, if the same buket were applied in two different turbines, and the normal buket loading, and therefore the buket bending stress, were double in one turbine what it was in the other turbine, it would be expeted that, with all else equal, the higher loaded buket would have signifiantly higher vibratory stimulus, approahing double that of the lower loaded buket. Steady state buket bending stresses are low. Praties vary within the industry, but usual experiene is that bukets are designed to have steady state bending stresses less than about 3000 psi. Operating experiene indiates that the turbine an be expeted to run suessfully with the buket first tangential natural frequeny exited by 4 Per-Rev and higher multiples of running speed, if the normal buket bending stress due to the average driving fore on the buket does not exeed approximately 1, 000 psi. Even suh a low design stress does not assure safe operation, sine there has been at least one failure from buket resonane with these lightly loaded bukets. BUCKET LIFE When operating on or through a harmful resonant range, a buket inurs fatigue damage. This damage is umulative in nature and may, in time, result in the failure of the buket. The length of time that it takes for failure to our is dependent on the vibratory stress that exists at any operating speed and the length of time the turbine operates at that partiular speed. Therefore, for any given design of turbine having a buket that an operate on harmful resonane, the operating time of the turbine for failure may vary from only a few hours to a few years, or perhaps never, depending on the speeds at whih the turbine is operated. For example, let us assume that the overall design is suh that the buket, when operating exatly on resonane, will have a vibratory stress just equal to the fatigue strength of the material. Conventional engineering would indiate that, under these onditions, the buket life would be about 10 million yles. It does not take very long to operate for this number of yles, even with a so alled "low frequeny" buket. The usual range of natural frequenies for the "low frequeny" buket is about 100 Hz to 500 Hz. Using these natural frequenies, it an be seen that it will take only about 6 to 28 hours of operation to fail these bukets, provided that they are operated preisely at resonane with a vibratory stress equal to the fatigue strength of the material. These same bukets may have a vibratory stress of only 10% of the fatigue strength when operating slightly off resonane. At this stress level, the blading an operate indefinitely without measurable fatigue effet. Therefore, the total operating time to failure for these bukets depends on how long it takes in the normal operating yle of the turbine, perhaps hanging from season to season, to aumulate the 6 to 28 hours total life at or very near to resonant operating speed. The major fator in turbine buket life is the operating speed at whih the turbine is run. Relatively small variations in speed an result in large hanges in vibratory stress as the buket moves into and out of resonane. There are also other turbine operating variables, suh as hanges in turbine load and steam onditions, that may ause hanges in the buket operating vibratory stress. The effet of these fators is generally small, ompared to the effet of hanges in speed. Corrosive steam environment an also be a fator ating to redue the fatigue strength of the material. The short time effet of a wet steam atmosphere is to redue the buket fatigue strength to about half of what it would have been in air, or in superheated steam. If there are orrosive elements in the wet steam, they will tend to ause a ontinuing deterioration of the material fatigue strength with time, suh that it may affet the long time life of the bukets. There may be pitting of the buket surfae with time. Pits inrease the stress onentration fator in the blading and therefore inrease the effetive vibratory stress. In these ases, when blades have raked, it is typial to find that the rak started at a orrosion pit. The effet of orrosive elements in the steam environment is not normally evaluated unless evidene of stress orrosion or orrosion fatigue is deteted by metallurgial examination of the frature surfae of the failed buket. BUCKET BANDING EFFECT ON VIBRATORY STRESS Buket banding on low frequeny bukets generally has been of the nature that it had little effet on either the natural frequeny of the buket or the resonant response of the bukets to some stimulus at low multiples of running speed. That is, the number of bukets banded together under a single band has been so few that the banded group responded essentially like a single buket would at its first tangential natural frequeny. This will no longer be true if the bukets are banded in large groups [3]. For example, if it is assumed that the buket first tangential natural frequeny is equal to C times the rotating speed of the rotor, and that there are P buket pithes in the 360 ar of the wheel, then it is apparent that the total vibratory energy input to a banded group of bukets will be zero when the number of bukets per banded group is equal to PIC, or to 2PIC, or to 3PIC, or to any multiple of the ratio of PIC. By solving for the average energy input to a banded group of bukets, it an be shown that the relative energy input, or stimulus per buket, when there are B number of bukets per banded group, is as shown in Figure 5. It is obvious that in no ase an B be greater than P, sine this represents a single band 360 around the wheel. From inspetion of Figure 5, it is apparent that if the number of bukets per band, B, is seleted on the basis of the smallest Per-Rev, C, that is likely to be enountered in the operating speed range, this number of bukets per band will also be very effetive in reduing the relative stimulus of the other higher multiples of running speed that may be in the operating range., :::> :::> IE, 20 = BC p Figure 5. Relative Buket Stimulus for Various Numbers of Bukets Per Band.

6 20 PROCEEDINGS OF THE TWELFTH TURBOMACHINERY SYMPOSIUM Table 2 shows the effetive vibratory response of a banded group of bukets, relative to a single buket response, for various Per-Rev resonanes and for various amounts of ontinuous band ar. For example, if a buket operating on 4 Per Rev is ontinuously banded in 60 ars, it will have only 39% of the vibratory stress that it would have had as a free standing buket. Table 2. Relative Buket Stimulus for Various Per-Rev Exitations and Various Lengths of Band. RELATIVE STIMULUS 1 PERCENT PER BAND ARC REV REFERENCES 1. Mithell, J. S., Mahinery Analysis and Monitoring, Penn Well Books, Tulsa, Oklahoma (1981). 2. Gotoda, H. and Nakasu, K., "An Analysis on Resonant Stress of Turbine Blade," Tehnial Report of Kawasaki Heavy Industries, Ltd., Kobe, Japan (1975). 3. Ortolano, R. J., La Rosa, J. A., and Welh, W. P., "Long Ar Shrouding-A Reliability Improvement for Untuned Steam Turbine Blading," Engineering for Power, Trans. ASME, 103, pp (1981) Zero Zero Zero 20 Zero THERMAL EFFECTS Changes in temperature in the turbine stage an be expeted to ause transient stresses in the banded group. The band is thinner than either the turbine buket or wheel and will therefore respond to a temperature hange at a faster rate. This will ause bending stresses in both the band and the bukets. The longer the band is, the higher these stresses will be. The stage temperature hanges are primarily assoiated with load hanges on the turbine. How muh this may be depends on individual turbine design. However, in the superheated steam region of the turbine, a 30% hange in load will ause approximately 50 F hange in stage temperature. The temperature hange for the same load hange will tend to be less in the saturated steam setions of the turbine. There are very small temperature hanges in the ondensing exhaust under normal operating onditions. However, there may be a temperature hange as large as 200 F on start-up when going from prolonged operation at no load to a loaded ondition. These thermal onsiderations indiate that the band should not be made any longer than is neessary to give safe operation of the bukets. SUMMARY Stimuli at low multiples of running speed exist throughout the turbine. These stimuli have aused failure of bukets operating on resonane with the buket first tangential natural frequeny. Stimuli may ome from rotor vibration, as well as from the steam path of the turbine. Buket failure and length of life are largely dependent on operating speeds. Banding an be used to redue or eliminate the risk of buket failure due to low multiple stimuli. However, the length of band should be as short as possible to redue stimuli aused by thermal stresses.