SUBSYNCHRONOUS VIBRATION PROBLEM AND SOLUTION IN MULTISTAGE CENTRIFUGAL COMPRESSOR by Paul E. Allaire. Carroll G. (Chet) Stroh. Ronald D.

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1 SUBSYNCHRONOUS VBRATON PROBLEM AND SOLUTON N MULTSTAGE CENTRFUGAL COMPRESSOR by Paul E. Allaire Professor Mehanial and Aerospae Engineering Department University of Virginia Charlottesville, Virginia Carroll G. (Chet) Stroh Mehanial Consultant Engineering Servies Division E.. dupont de Nemours and Company, norporated Neark, Delaare Ronald D. Flak Professor John A. Kour Jr. and Lloyd E. Barrett Assoiate Professor Mehanial and Aerospae Engineering Department University of Virginia Charlottesville, Virginia Paul E. Allaire is Professor of Mehanial Engineering at the University of Virginia. He reeived his B.E. and M.E. degrees from Yale, in Mehanial Engineering. After to years in the Peae Corps, teahing at the Teleommuniations nstitute in Addis Ababa, Ethiopia, he earned his Ph. D. in Mehanial Engineering at Northestern University. He is the founder of the Rotating Mahinery and Controls (ROMAC) ndustrial Researh Program at the University, hih no has over 5 orporate members. n addition to riting one textbook on finite elements and editing three books, Dr. Allaire has presented over 8papers at tehnial onferenes and injournals. lloyd E. Barrett is an Assoiate Professor of Mehanial Engineering at the University of Virginia. He reeived an M. S. degree in 1975 and a Ph. D. degree in 1978, both from the University of Virginia. He has orked in the areas of turbomahine vibration and lubriation for 16 years. Speial areas of interest inlude bearing design and optimiation to redue rotor vibrations and the effets of strutures and foundations on turbomahinery vibration. He has ritten over 4 papers in these areas and has been a onsultant to industry on a ide variety of turbomahine vibration problems. 65 Dr. Barrett is urrently the Diretor of the Rotating Mahinery and Controls ndustrial Researh Program at the University of Virginia. R. D. Flak reeived his B.S.M. E., M.S.M.E. and Ph.D. degrees from Purdue University, in 197, 1973, and 1975, respetively. He as an Analytial Design Engineer for Pratt & Whitney Airraft for to years, and is urrently a Professor of Mehanial and Aerospae Engineering at the University of Virginia. Dr. Flak peiforms researh in experimental fluid film bearings and internal turbomahinery flos and is ative in several professional soieties, inluding ASME, ASLE, and ASEE. John A. Kour, Jr., is a Researh Engineer at the Amoo Corportation Researh Center in Naperville, llinois. n this apaity, he onduts applied researh in the areas of mahinery vibration analysis, rotor bearing system dynamis and omputational fluids. He also ats as a onsultant to the refineries, hemial plants and prodution failities of the Amoo subsidiaries, both domesti and foreign. 1 Mr. Kour has B. S.M.E. andm.s.m.e. degrees from the University of Virginia and an MBA from Tulane

2 66 PROCEEDNGS OF THE SXTEENTH TURBOMACHNERY SYMPOSUM University. He is urrently finishing requirements for a Ph.D., from the University of Virginia. The dissertation researh involves a finite element analysis of three dimensinal visous fluid flo in bounded regions. He has o-authored papers on hydrostati bearing analysis, oil seal/rotor interations, and numerial methods for aurately evaluating dynami oefftients for hydrodynami bearings. He is a member of ASME. Carroll G. (Chet) Stroh is a Consultant ith E.. du Pont de Nemours and Company, norporated. He is assigned to the Mehanial Engineering Consultants of the Engineering Servie Division. His onsulting servie involves turbomahinery and reiproating ompressor analysis, repair, and speifation. He has 13 years ith Du Pont, during hih he spent five years in a regional engineering offie at Beaumont, Texas, onsulting on turbomahinery problems for Du Pont plants along the Gulf Coast, three years in turbomahinery rotordynamis researh at the Experimental Station in Wilmington, Delaare, and five years at his present position in Neark, Delaare. Prior to joining Du Pont, Mr. Stroh orked four years for the Westinghouse rge Steam Turbine Division in Lester, Pennsylvania, here he as involved ith the design of rotors and blades. He earned a B.S. degree, M.S. degree, and did three years of post graduate ork in Mehanial Engineering at the University of Pennsylvania. He also has a B.A. degree in Mathamatis from Lebanon Valley Colege. He is a member of Tau Beta Pi. ABSTRACT The investigation of a subsynhronous vibration problem enountered in a six stage entrifugal ompressor is disussed. At a running speed of approximately 9 rpm, a subsynhronous vibration (at 42 rpm) of nearly to times the synhronous vibration level as enountered. A systemati program as undertaken to identify the problem and orret it. A detailed analysis of the floating ring annular oil seals, balane piston labyrinth seals and impeller aerodynami ross oupling as onduted. The oil seals ere identified as the primary ause of the subsynhronous vibration due to lok up, and a modified seal design inorporating irumferential grooves as developed. This radially redued the seal ross oupled stiffness. Further, a modified bearing design as investigated to inrease the rotor logarithmi derement. Changes ere implemented in the ompressor ith the result of no subsynhronous vibrations for the operating onditions of the ompressor thus far. NTRODUCTON High speed multistage ompressors are often subjet to unanted vibrations. Partiularly undesirable are subsynhronous vibrations, hih may inrease suddenly, or over a long period of time. Often the subsynhronous vibration is larger than the synhronous omponent and may limit mahine safe running speeds. n addition, ompressors have failed as a result of subsynhronous vibrations. t is best to remove these vibrations, if possible. Often the ause of the subsynhronous vibration is not ell understood at the onset of the problem [1]. Several possible auses have been identified in reent years: 1) fixed pad bearings, 2) annular oil seals, 3) balane piston labyrinth seals, and 4) impeller aerodynami effets. n many ases, to or more of these are present. A systemati rotordynamis analysis as undertaken to identify and orret the problem in a partiular ompressor. The ompressor (Figure 1) as a six stage entrifugal ompressor ith an average shaft diameter of approximately 6.25 in, bearing span of 67.8 in, rotor eight of 16 lb, and design speed of 96 rpm. The ompressor rotor and the key omponents are illustrated in Figure 2. Figure 1. Geometry of Six-Stage Centrifugal Compressor. SHAFT??? ll ' '. g, ltm m l) ::a :: ;J;J ::tl ll ) : l) R/liiiiiiRllllli\Ff E A B O A M E T E R D=159mm (S.251n) ;: : ANNULAR OL SEAL ANNULAR OL SE AL TLTNG PAD TLTNG PAD A SEARNG SPAN --- SEARNG 1 =1.77m (67.61n) NG Figure 2. Shaft Parameters and Geometry for Six-Stage Compressor. The rotor as supported on five-pad tilting pad bearings ith load-on-pad orientation. The bearing learane as 3. mils (radial) and the bearings had a preload of.5. The length to diameter ratio as.45. The bearing stiffness and damping oeffiients at 9 rpm [2] are given in Table 1. t is ell knon that tilting pad bearings ill not ause subsynhronous vibrations by themselves but may or may not have the damping required to suppress other auses of instability [3]. Table 1. Tiliting Pad Bearing Properties at 9 RMP. Kxx (lb/in) K yy (lb/in) Cxx (lb-se/in) 979 yy (lb-se/in) 1134 e/ch.235 Load (lb) 89 At a running speed of approximately 9 rpm, a large subsynronous vibration (at 42 rpm) of nearly to times the synhronous vibration level as enountered [ 4]. The vibration pattern is shon in Figure 3 at a ontinuous running speed of 921 rpm. The subsynhronous vibration persisted at modest levels hen operating belo 92 rpm, but ould suddenly spike hen operating at or above this speed, requiring im-

3 SUBSYNCHRONOUS VBRATON PROBLEM AND SOLUTON N MULTSTAGE CENTRFUGAL COMPRESSOR 67 mediate operational hanges. Servie as limited to belo 92 rpm for fear of larger vibration spikes at higher speeds. Figure 4 that the rotor is running above the first ritial speed but just belo the seond, third and fourth. There as some orry that softening the bearings to improve mahine stability might loer the seond or third ritial speed too near the operating speed of 96 rpm. The measured rotor response at one of the bearings for probe horiontal and probe vertial is shon in Figure 5. The predited vertial ritial speed of 34 rpm (from Figure 4) is about nine perent belo the measured values of 37 and 38 rpm. 3 a: " e "' <t if 2 1 Subsynhronous Vibration At 42 RPM Synhronous Vibration At 921 RPM Figure 3. Vibration Pattern at 921 RPM. With the plant running, it as not onsidered eonomially feasible to shut the ompressor don for investigation of possible fixes. Thus a rotordynamis analysis as performed to determine the problem and its solution. The ompressor shaft and impellers, bearings, floating annular oil seals, balane piston labyrinth seals, and impeller aerodynamis ere inluded in the omputer model. A logarithmi derement as evaluated for possible mehanisms ausing the subsynhronous vibration, on a relative basis. On this basis, the oil seals ere identified as the primary ause. The seals ere modified to redue exitation, and the bearings ere also modified to inrease the rotor damping properties. After installation, the ompressor had no subsynhronous vibration up to the operating pressures attained so far.-these levels are not quite up to the peak pressures possible ith this ompressor. UNDAMPED CRTCAL SPEEDS The rotor as modelled using standard transfer matrix methods. Undamped ritial speeds ere obtained and are shon in Figure 4. Four ritial speeds are shon on the figure. The horiontal and vertial tilting pad bearing stiffnesses are shon on the rital speed map as ell. t an be seen from "' ;: X E e- a. rt)..j <( () j::: a: () a. ::;; <( :::> N N2 --N3 - - N = -- 1 L- lll _u -- LLUUU.1 1 STFFNESS (lbf/in x t o6) Figure 4. Undamped Critial Speed Map. ::>, :J?" 2 a.. ". <t g. 1 E 1 > SPEED x 13 (RPM) Figure 5. Measured First Critial Speed. OL SEAL ANALYSS A summary of the oil seal analysis by Allaire, Kour, and Stroh [4] follos. The oil seal in this ompressor has a seal ring around the shaft, as shon in Figure 6. The seal ring minimies the leakage of the proess gas into the atmosphere. HGH PRESSURE SHAFT (a) Seal Ring Geometry SURE f STATONARY COMPONENT RNG l.r1 A<T J E3 s t r 11 t t tjlld SSURE (b) Pressure Fores Ating On Seal Ring Figure 6. Seal Ring Geometry and Pressure Fores. LOW PRESSURE The ring is a nonrotating omponent normally designed to float (move radially) ith the shaft to prevent unbalaned fores in the seal ring annulus. To seal, suh seal rings must have a ontat fae (Figure 6b), hih inhibits this floating motion. High pressure, also sho\vn in Figure 6b, reates a normal fore ating on the ontat fae. This is related to the frition fore

4 68 PROCEEDNGS OF THE SXTEENTH TURBOMACHNERY SYMPOSUM ating along the ontat fae by the oeffiient of frition times the normal fore. f the frition fore is large enough, the ring ill not move radially. The oil film beteen the shaft and loked-up seal ring then ats as a fixed plain journal bearing. A plain journal bearing produes ross oupled stiffness terms, Ky, and K, y, hih an ause rotor instability [3]. Ordinarily, the axial pressure drop aross the seal suppresses any possible avitation in the oil film for the seal. t may be onsidered as a nonavitating plain journal bearing hih further inreases the destabling effets. To papers by Kirk, et al. [5, 6], disuss the properties of loked-up oil seal rings. These orks are extended by Kirk's 1986 paper [7] hih inludes plots of seal ring stiffness and damping oeffiients vs eentriity for short seals. The ross oupled stiffness oeffient of the seal ring an gro by over a fator of ten in magnitude, ith inreasing lokup eentriity. Kirk also shos some results for ompressor modifiations to the oil seals, but does not give details of the modifiations. Several other authors disuss oil seal effets on ompressors. Doyle [8] and Wahel [9] presented papers at orkshops. A paper by Emerik [1] desribes a seal lokup problem aused by ear of a taper on one of the seal omponents. A redesigned seal removed the subsynhronous vibration problem from the multistage ompressor. n that ase, the seal ring as redesigned to be better balaned, thus reduing the frition fores tending to lok the ring against the stationary seal omponent. A different effet of seal ring lokup as reported by Cerinske, Nelson, and Salamone [11]. n this ase, synhronous vibrations ere the problem. A rotordynami analysis indiated that seal ring lokup may have arried most or all of the shaft load. Beause the seals are loser together than the bearings, a signifiant shift in ritial speeds an be enountered. Elimination of radial looseness under the bearings ensured that the bearings arried the load and suessful running as reported. Allaire, et al. [ 4], presented a quasi-stati method for estimating the lokup eentriity of the seal ring. The steps are: At ero shaft speed, the shaft rests in the bottom of the bearings and the oil seal ring rests on the shaft. The geometry for the ompressor seal is illustrated in Figure 7. /" / y -.,; Searing -- Pod Cirle... ',,/ ' \ \ y i = - 3. mils y r = mils prevent further motion of the seal ring (lokup). The geometry for this seal is presented in Figure 8. f the ring loks, up it stays at the same postion in spae y Searing -----, Pod Cirle ' \ -2.i9 mils Seal Ring X nner Radius Figure 8. Bearing and Seal Ring Clearane Cirle Plots at Lokup Speed (611 RPM). f the seal ring is loked up, ontinuing inreases in shaft speed provide bearing fores hih lift the shaft upard. This produes an oil seal ring eentriity of the shaft ithin the oil seal ring (Figure 9). Generally, inreasing the eentriity auses higher oil seal ring ross oupled stiffness oeffiients. y Bearing , ; Pad Cirle ' ' \ -.85 mils.lrt-:...-: mils Seal Ring nner Radius (Position At Lok-up 611 RPM Shon) X Figure 9. Bearing and Seal Ring Clearane Cirle Plots at nstability Threshold Speed (9, RPM). Figure 7. Bearing and Seal Ring Clearane Cirle Plots at Zero Speed. As the shaft speed inreases, the oil film fore lifts the seal ring so that the fore must exatly equal the ring eight (if dynami fores are small). The radial frition fore on the ring ontat fae inreases ith speed as pressure builds. The point of interest is hether the frition fore beomes large enough to Dynami fores due to unbalane are alays present on shafts and generally inrease ith speed. f the dynami fores are large enough, a loked-up seal ring may break free and move ith the shaft. This possibility must be explored to determine if the oil seal ring ill stay loked-up. These steps an be investigated for a given seal design. A lokup speed equation as developed in [ 4] as N lok = Nd ( f.l s;: A ) 'll 1 (1)

5 SUBSYNCHRONOUS VBRATON PROBLEM AND SOLUTON N MULTSTAGE CENTRFUGAL COMPRESSOR 69 The exat lokup speed is not very important. What is important is the likelihood of seal ring lokup belo runing speed. f it is likely to lok up ell belo running speed, then a stability analysis inluding the seal ross oupled effet, should be ompleted. f lokup is unlikely due to good seal ring balaning, then there ill be no ross oupled stiffness terms and the seal is not going to ause subsynhronous vibration. The reported seal ring analysis [4] indiated that the seal ring ould be loked up at 611 rpm, hih as far belo the shaft running speed. Numerial values for the seal stiffness and damping oeffiients at 98 rpm are given in Table 2. The method used to alulate the seal dynami oeffiients is a finite element approah [12] hih inludes the effets of an axial pressure drop and turbulene. The axial pressure drop effets produe prinipal stiffness terms hih may be important in the rotordynamis analysis. Table 2. Summary of Seal Properties at 9,8 RPM ith Attitude Angle -135" and Eentriity.5 Seal Design Existing To Groove (1A) Three Groove (1B) To Groove Large Clearane (1C) Load Flo Rate (lbf) (gavmin) Kxx Stiffness (lbfi'in) Damping (lbf-sedin) K,y Kyx Kyy, C,y Cy, Cyy The ross oupled stiffness values are 19,3 lb/in. The alulated value of the oil leakage through the seal, 13.5 gal/min, as rather lose to the average measured leakage, approximately 12 gal/min. This as one indiation that a good model of the oil film as used. Some information an be gained by omparing stiffness and damping numbers for the bearings and seals. n nearly all ompressors, the bearings and oil seals are in lose proximity. Prinipal stiffness terms of the original bearings, K,. and K yy are on the order of 1,, lb/in. The orresponding prinipal stiffness terms of the seals are only about 1, lb/in, so the bearing stiffnesses dominate. Conversely, the tilting pad bearings have no ross oupling stiffness terms, K y x and Kx, so here the oil seal terms dominate. The ross oupled stiffuess terms ause subsynhronous vibration, so the seals are very important. Also, the bearing prinipal damping terms, C,. and C yy, are muh larger than the oil seal terms so the bearing damping terms dominate. This led to modifying the bearings to improve overall system damping properties after the seals ere improved. CAUSE OF NSTABLTY nitially, the ause of the subsynhronous vibration as unlear. Suspeted omponents ere the oil seals, the balane piston labyrinth seals, and aerodynami ross oupling at the ompressor impellers. A systemati rotordynamis stability analysis as arried out to determine the ause. The objetive as to evaluate the sensitivity of the ompressor to eah possible ause. This involved alulating the logarithmi derement of the least stable eigenvalue for a series of analyses. The largest destabiliing hange ould indiate the primary ause. First, a baseline run as made ith the free-free shaft. The log derement of., as it should be, is given in Table 3. The hirl speed of the least stable mode as 37 rpm. Next, the tilting pad bearings ere added and the log derement improved to.19. The balane piston labyrinth seal ross oupling stiffness as alulated as 19,8 lb/in [13]. t as added to the model and the log derement dropped to.14. Removing the balane piston and adding the loked up oil seal dynami oeffiients gave a log derement of.9. Thus, the oil seal redued the stability by.1, hile the balane piston only redued it by.5. Table 3. Sensitivity of Current Design to Different Destabiliing Mehanisms at 9 RPM. Shaft Only (.5X 1 6 lb/in Supports) Shaft, Bearings Shaft, Bearings, Balane Piston (19.8 Klb/in) Shaft, Bearings, Seals Shaft, Bearings, Seals, Balane Piston Shaft, Bearings, Seals, Balane Piston, Aerodynami Cross Coupling at Wheels (1 Klb/in) Logarithmi Derement Whirl Speed 8 (pm) The analysis as ontinued to inlude shaft, bearings, oil seals and balane piston. The log derement as.6, or very lose to ero. One should reall that the onset of the subsynhronous vibration, shon in Figure 3, must our at a log derement value of ero. Finally, aerodynami ross oupling as added at the ompressor impellers. At the time the analysis as done, industrial experiene indiated that a value of about 2, lb/in per heel of ross oupling ould be representative. n this ase, a value of 2, lb/in as hosen for eah of the four entral impellers and 1, lb/in taken for the end impellers. The resulting log derement as -.6 for a derease of.66 over the previous ase. Again, this hange as less than the oil seals. t as judged that the oil seal as the major ause of the subsynhronous vibration. The alulated hirl speed, indiated in Table 3, as 378 rpm. This ompares fairly ell ith the observed ritial speed of 42 rpm. The alulated hirl speed is lo by 1 perent. Currently, there are several methods for better evaluation of the ompressor labyrinth seal effets, hih seem to be primarily responsible for impeller aerodynami ross oupling. That partiular possible ause of instability did not turn out to be the major ause for this problem so no further efforts ere made to better model them. One partiularly enouraging feature of the analysis as that the stability analysis yielded a logarithmi derement very lose to ero hen all possible auses ere inluded. This implies that the theoretial model reated for this problem as a very aurate one. Component modelling for the shaft, bearings, oil seals and balane piston as obtained from the basi equations of engineering, rather than empirial field data. A fe years ago, the omputer modelling and solution of subsynhronous vibration problems in ompressors as muh more empirial in nature.

6 7 PROCEEDNGS OF THE SXTEENTH TURBOMACHNERY SYMPOSUM OL SEAL MODFCATONS To possible objetives ould be onsidered in modifying the seals. They ere: Redue seal ross oupling hile maintaining present leakage rate. Ensure that the seal ring moves ith the seal. nitially, it as deided to investigate the first option. Design options ith irumferential grooves ut in the seal are shon in Figure 1 (a) and (b). A pressure j balaning arangement for the three groove seal is also given in Figure 1 (). L L = Land Length t L G = Groove Length DG = Groove Depth log derement at 98 rpm as alulated as.12 (stable). This value, given the inauraies of omputer modelling, as good, but judged not to be as large as desired. The seond objetive of ensuring that the seal ring moves ith the seal as not pursued, beause the first modifiation appeared to be suffiient to remove the subsynhronous vibration. Also, the first modifiation introdued the least number of seal hanges. From a leakage point of vie, the seal performed ell, so there as no desire for major hanges. BEARNG MODFCATONS The tilting pad bearings used in this ompressor ere modified to further improve stability. To parameters ere hosen for modifiation: the bearing preload, m, and learane b. These are related to the bearing ground in pad learane of CP by the equation (2) (a) To Groove Design =t> Qj (b) Three Groove Design Note that all values of learane in this paper are radial rather than diametral values. The original bearings had a pad learane of CP 6 mils = and a preload of m =.5. First, the pad learane as held onstant and the preload varied. The original seal dynami oeffiients at 9 rpm ere employed here. The results are depited in Figure 11. A derease in the bearing preload gives a signifiant inrease in the system log derement. Seond, the bearing learane as held onstant and the preload varied. This produed an even larger improvement in stability, as seen in Figure 11. () Balane Ring Fae Design Figure 1. Geometry for Cirumferential Groove and Balaning Seal Modifiations. Cutting irumferential grooves in the seal land region redues the ross oupled stiffness. Generally, the ross oupled stiffness is proportional to the length, ubed. ntroduing to grooves, as indiated in Figure 1 (a), redues the length by a fator of 3, but triples the number of lands, so the net redution in ross oupled stiffness is a fator of 9. n a similar fashion, the three groove design of Figure lob yields a redution fator of 16. The alulated values of loked up seal ring stiffness and damping are given in Table 1. A larger learane ase also redued the ross oupled stiffness but the oil leakage rate nearly doubled. This as onsidered unaeptable. Modifying the seals to improve the pressure balaning, and thus redue the frition fore ating on the seal ontat fae, as also onsidered. This ould not affet the ross oupled stiffness diretly, but ould ensure that the seal ring ould not lok up at a large eentriity. The dynami fores ating on the seal ring ould move it toard the entered position. Thus, the very large ross oupled stiffness hih ours at high eentriity ould be avoided. This design feature as not adopted due to ear onsiderations. The three groove seal design as adopted for the seal modifiations. With all of the other omponents kept the same, the 1-.4 :::!! a:.2 Cl...J. ' f Cb=.3 ln. L/=.45. a=.5 '\. 5 pad-load on pad '\ original seals, 9rpm " " C p =.6 in,l/=.45, a=.5 5 pad-load on pad original seals, 9rpm Baseline, Cb=.3 in P =.6 in, m =.5, a=.5 5 pad-load on pad, original seals ::::-. 9rpm -.2L- J _J _J BEARNG PRELOAD Figure 11. Log Derement vs Bearing Preload for Original Seals for Constant Values of Cb and C P at 9 RPM. This type of study as repeated for the rotor ith the three groove seal design and at 98 rpm. Figure 12 depits the results. Again, holding the bearing learane onstant and varying the preload produed the largest inrease in log derement. Also, the balane piston as removed for one set of runs, to determine hether the redution of ross oupled stiffness ould greatly inrease the log derement. As seen in Figure 12, the improvement is marginal. Finally, the optimum bearing design as hosen to have a preload fator of.1 and the bearing learane varied. The results, inluding the three groove seals and a running speed of 98 rpm, are presented in Figure 13. The bearing design modifiation as fixed at a bearing learane of 3.5 mils (radial) and a preload fator of.1. The final stiffness and damping oeffiients at 98 rpm are given in Table 4. Note, the pre-

7 SUBSYNCHRONOUS VBRATON PROBLEM AND SOLUTON N MULTSTAGE CENTRFUGAL COMPRESSOR ,... :::;: a:.2 (!)..J. -.2 ' ' ' " " " ', Cb =.3 in, LD =.45, a =.5, 5 pad-load on pad, 3 groove seal, 98rpm.4 C p =.6 in, L/=.45, Q =.5, 5 pad-load on pad, 3 groove seal, 96rpm, ' (No Balane piston, C b =.3 n, LD=.45, a =o.s, 5 pad-load on pad, 3 groove seal, 98rpm BEARNG PRELOAD Figure 12. Log Derement vs Bearing Preload for Three-Groove Seals for Constant Values of Cb and C P at 98 RPM. Table 4. Dynami Coeffiients for Modified Bearing at 98 RPM.,... :::;:.4 a:.2 (!)..J 2 Kxx = 21614lb/in K yy = lb/in Cxx = 789 lb-se/in C YY = 1184 lb-se/in 3 Groove Seals Reommended m=.1, a =.5, Bearing Cb=3.5 mils, 5 pad-load on pad, L/ =.45 Bearing: m =.1, a=.5, 5 pad-load on pad, L/=.45, 98rpm 4 6 b (mils) Figure 13. Log Derement vs Radial Bearing Seals for m. 1 at 98 RPM. third mode is at 9193 rpm, hih is in the operating speed range. Hoever, it too has large predited motion in the bearing loations, and thus ill be damped out. t is not a matter for onern. The next mode is at 13,15 rpm, ell above the running speed range ::l: () <(...J a. en. N ::::i <( ::l: a: STATON NUMBER Figure 14. Mode Shapes for First Four Damped Eigenvalues. UNBALANCE RESPONSE N MODFED ROTOR Unbalane response has not been a problem ith this ompressor. Again, hoever, it as desired to verify that no ne problems ere introdued ith the design modifiations. Unbalane response alulations ere arried out for the modified rotor. The first unbalane ase as hosen to simulate a typial unbalane in the rotor enter. This ould exite both the first mode at 3563 and the third mode at 9193 rpm. To.5 o-in unbalanes ere plaed in the enter impellers, and to similar unbalanes ere plaed in the to outer impellers at 18 degrees out of phase ith the first to. The response vs speed at several loations is given in Figure 15. There is a first ritial speed peak at the midspan, ith another very broad peak at the bearings at the third ritial speed. t is easily seen that there are no strong vibration peaks in the running speed range of 9, to 1, rpm. dieted log derement is no about.5, as ompared to the value of.12, ith just the modified seals. This is a major improvement. CRTCAL SPEEDS AND MODE SHAPES N MODFED ROTOR t is important \\oith any rotordynamis redesign that the hanges introdued to remove one problem do not introdue other problems. One should reall from the ritial speed map in Figure 4 that the ompressor operated at just belo the seond and third ritial speeds. There as some onern that reduing the bearing stiffness, as done by the above bearing modifiation, ould possibly drop one of these ritial speeds into the operating speed range. This as investigated by looking at the mode shapes for the modified rotor. The alulated damped mode shapes for the modified rotor running at 98 rpm are shon in Figure 14. All ere overdamped. The first mode is at 3563 rpm and is a standard first shaft bending mode. The seond mode is at 5465 rpm and represents a onial mode, ith large predited amplitudes at the bearings. Bearing damping ill damp this mode out. The i X UJ :::>,... :J a. ::l: <( 1. LNE S T ATON NUMBER DESCRPTON UNBALANCE STA TON NUMBER Tilt pad brg Mid-disk Tilt pad brg NFORMATON AMOUNT (o-ln) o. PHASE (degree) o.o FREQUENCY (RPM x 1) Figure 15. Unbalane Response for Compressor- nterior Distributed Unbalane (Case 1).

8 72 PROCEEDNGS OF THE SXTEENTH TURBOMACHNERY SYMPOSUM Another unbalane ase as hosen to exite the seond mode at 5465 rpm and the fourth mode at 13,159 rpm. To unbalanes of.5 o-in ere plaed 18 degrees out of phase at the to impellers nearest the bearings. The unbalane response is shon in Figure 16. There is no peak near 5465 rpm indiating that the seond mode is very ell damped. There is a large peak at 13, rpm, ell above running speed. The rotor modifiations do not appear to have reated any vibration problems, due to turbulene. LNE STATON DESCRPTON Till pad brg 24. Mid-disk 39 Tilt pad brg in Figure 17 (a). t started at 46 rpm, then dropped to 18 rpm, and finally disappeared. This ourred over a period of hours. The vibration spetrum after the lo frequeny as gone is shon in Figure 17 (b). Kirk observed a similar vibrational behavior on a ompressor test stand. He attributes the lo frequeny vibrations to an unstable motion of the seal ring [14]. The lo frequeny did not reappear. Perhaps the ause as a rubbing omponent hih ore in during startup. The ompressor as finally run up to 9621 rpm and the vibration spetra reorded (Figure 18). There as no subsynhronous vibration present. The objetive of the redesign as to remove the subyshronous vibration so it has been suessful to date ui e 9621 rpm STATON AMOUNT (o-ln) PHASE (degree) :::> 1-.J D. ::E < Figure 16. Unbalane Response for Out of Phase Unbalane Distribution (Case 2). VBRATONS AFTER NSTALLATON OF MODFCATONS During plant dontime, the modifiations to the oil seals and bearings ere made and installed. The plant as restarted and vibration data ere reorded. The initial startup data taken at 86 rpm are shon in Figure 17. There as a synhronous vibration omponent at 86 rpm as expeted, plus a very lo frequeny omponent, as indiated ui E Very Lo Frequeny 861 Orpm 1 :;)... ::; Q. ::::; 12, < -.. U) e: :;) 1. FREQUENCY (rpm) a) nitial Vibration Spetrum 861rpm...J Q..AJ ::::; 3 12, < FREQUENCY (rpm) b) Vibration Spetrum After a Fe Hours Figure 17. Vibration Spetrum just after Startup Folloing Modified Seals and Bearings at 86 RPM. FREQUENCY (rpm) 12, Figure 18. Final Spetrum Folloing Modifiation of Seals and Bearings. NOMENCLATURE A b p m n Nd N lok pd J..l.s Unbalaned Seal Ring Area Bearing Clearane Pad Clearane Bearing Preload Pressure Poer La Shaft Speed at Design Lok Up Speed for Seal Ring Seal Pressure Drop at Design Coeffiient of Stati Frition REFERENCES 1. Stroh, C. G., "Rotordynami Stability-A Simplified Approah," Proeedings of 14th Turbomahinery Symposium, Turbomahinery Laboratories, Department of Mehanial Engineering, Texas A&M University, College Station, Texas, pp. 3-1 (1985) Niholas, J. C., Gunter, E. J., and Allaire, P. E., "Stiffness and Damping Coeffiients for the Five-Pad Tilting Pad Bearing," Transations of the Amerian Soiety of Lubriation Engineers," 22 (2), pp (April 1979). Allaire, P. E., and Flak, R. D., "Design ofjournal bearings for Rotating Mahinery," Proeedings of loth Turbomahinery Symposium, Turbomahinery Laboratories, Department of Mehanial Engineering, Texas A&M University, College Station, Texas, pp (1981). Allaire, P. E., Kour, J. A., and Stroh, C. G., "Oil Seal Effets and Subsynhronous Vibrations in High Speed Compressors," Presented at nstability in Rotating Mahin-

9 SUBSYNCHRONOUS VBRATON PROBLEM AND SOLUTON N MULTSTAGE CENTRFUGAL COMPRESSOR 73 ery Sysposium, Bently Nevada, Carson City, Nevada, June 1985, NASA CP 249 (1986). 5. Kirk, R. G., and Miller, W. H., "The nfluene of High Pressure Oil Seals on Turbo-Rotor Stability," ASLE Transations, 22 (1), pp Ganuary 1979). 6. Kirk, R. G., and Niholas, J. C., "Analysis of High Pressure Oil Seals for Optimum Turboompressor Dynami Performane," Vibrations in Rotating Mahinery Seond nternational Conferene, nstitution of Mehanial Engineers, Cambridge, pp (September 198). 7. Kirk, R. G., "Oil Seal Dynamis: Considerations for Analysis of Centrifugal Compressors," Proeedings of 15th Turbomahinery Symposium, Turbomahinery Laboratory, Department of Mehanial Engineering, Texas A&M University, College Station, Texas, pp (1986). 8. Doyle, H. E., "Field Experienes With Rotor Dynami nstability in High-Performane Turbomahinery," Rotordynami nstability Problems in High-Performane Turbomahinery Conferene, Texas A&M University, pp (198). 9. Wahel, J. C., "Rotordynami nstability Field Problems," Rotordynami nstability Problems in High-Performane Turbomahinery Conferene, Texas A&M University, pp (1982). 1. Emerik, M. F., "Vibration and Destabiliing Effets of Floating Ring Seals in Compressors," Proeedings of Rotordynami nstability Problems in High-Performane Turbomahinery Conferene, Texas A&M University, pp (198). ll. Cerinske, T. J., Nelson, W. E., and Salamone, D. J., "Effets of High Pressure Oil Seals on the Rotordynami Response of a Centrifugal Compressor," Proeedings of 15th Turbomahinery Symposium, Turbomahinery Laboratory, Department of Mehanial Engineering, Texas A&M University, College Station, Texas, pp (1986). 12. Shmaus, R. H., "Stati and Dynami Properties of Finite Length Turbulent Annular Flo Seals," M. S. Thesis, University of Virginia (1981). 13. latsubo, T. Motooka, N., and Kaai, R. "Flo ndued Fore of Labyrinth Seal," Proeeding ofrotordynami nstability Problems in High Performane Turbomahinery Conferene, Texas A&M University, pp (1982). 14. Kirk, G. R., and Simpson, M., "Full Load Shop Testing of 18, HP Gas Turbine Centrifugal Compressor for Off shore Platform Servie: Evaluation of Rotordynamis Performane," Proeedings of an nstability in Rotating Mahinery Symposium, sponsored by Bently Rotordynamis Researh Corporation, (1985), NASA CP 249 (1986).

10 74 PROCEEDNGS OF THE SXTEENTH TURBOMACHNERY SYMPOSUM