due to self-excitations

Transcription

1 SOLUTO OF SUBSYCHROOUS VBRATO PROBLMS RADAL FLOW HGHSPD TURBS by Heilm D. Sandstede ngineering Manager Klaus Reishl Mehanis ngineer Martin L. Leonhard Mehanis Manager Atlas Copo Applied Compressor Tehnique (ACT) Cologne, West Germany Heiko D. Sandstede is ngineering Manager of the Department for Contrat ngineering and Design in Atlas Copo nergas GmbH in Cologne, Germany, a division of Atlas Copo Applied Compressor Tehnique (ACT). He is responsible for the order related design of ompressors and turbines, and joined Atlas Copo in Before he worked for eight years the design of turbine and srew ompressors. Dr. Sandstede graduated as a Mehanial ngineer from the Tehnial University of Hannover, Germany, where he also reeived his Dr.ng. He is a member ofvd. Klaus Reishl graduated in Mehanial ngineering (Dipl.ng.) at RWTH Aahen. From 1976 to 1984, he was involved solving vibration problems in rotating and reiproating mahinery at Linde AG. He gained pratial experiene in a wide range of turbomahinery. Sine 1984, he has been working in the Mehanial Development department of Atlas Copo nergas GmbH, Cologne, a division of Atlas Copo Applied Compressor Tehnique (ACT) investigating rotordynami and bearing design. He is a member ofvd. Martin L. Leonhard graduated in Mehanial ngineering (Dipl.ng.) from Karlsruhe University. He did researh in high speed frition journal bearings at the Mehanial Design nstitute and earned his dotoral degree in Mehanial ngineering at Karlsruhe University. Sine 1984, Dr. Leonhard has worked at Atlas Copo nergas GmbH, Cologne, West Germany, a division of Atlas Copo Applied Compressor Tehnique (ACT), first as a manager of the development design for turbines, and, sine 1986, as Manager of the Mehanial Development Department. He is member ofvd. ABSTRACT xperiene, theoretial and pratial, investigations are presented on two radial flow highspeed turbines, whih showed unaeptable high subsynhronous vibrations during operation onsite. The first example deals with a twostage integrally geared turbine for energy reovery, ith generator brake installed in a hemial plant. Measurements and alulations ruled out that the subsynhronous vibrations were aused by the bearings. Measurements of pressure at the inlet and outlet of both stages and in the interstage pipe hinted at an aousti exitation in the annular spae between impeller and adjustable nozzle ring. The aousti exitation and resulting subsynhronous vibrations ould be redued by installing a few fixed nozzles, thus interrupting the vaneless spae to the extent that safe operation of the gear turbine is possible adhering to the relevant guidelines. The seond example is a ompressorloaded turbine with bilaterally overhung radial impellers employed in an air separation plant. onreproduible, subsynhronous vibrations ourred, due to variations of manufaturing toleranes of bearing geometry, labyrinth seals and gap geometries representing the main auses. The results of parameter studies in the bearing and sealing zones showed that the damping effet of the bearings an be eliminated by the influene of the labyrinths. Thus, the rotor beomes unstable. The rotor was stabilized by the installation of swirl brakes and antiswirl sleeves. After that, subsynhronous vibrations eased to exist resulting in stable and safe operation. TRODUCTO Although, today, rotordynami design of turbomahines has beome standard, direted in partiular at optimizing the damping effet of journal sleeve bearings, subsynhronous vibrations are experiened in prodution turbomahines. Sometimes, these vibrations lead to unaeptable high and flutuating vibration levels, so that it is imperative to searh for assoiate reasons and introdue appropriate ation for orretion. Subsynhronous vibrations for example are, due to selfexitations instability aused by bearings aerodynami swirl exitation destabilizing foes in seals external elastiity internal frition due to foredexitations seal rubs 19

2 2 PROCDGS OF TH SVTTH TURBO MACHRY SYMPOSUM raked shafts dynami fores oming from the proess gas or from the gears The subsynhronous vibrations experiened in two different turbomahines, one integrally geared turbine and one boosterturbine, were represented and analyzed. the mass flow and the pressure drop in the turbine near op. timum for prodution. positions of labyrinth seals GAR TURB The integrally geared turbine (Figure 1) expands natural gas in two stages. Figure 2. Compressor Turbine. Figure 1. Gear Thrbine. The design onditions of this gearturbine are maximum power 2.5 MW (3,4 hp) bull gear speed 18 rpm ( 3 Hz) first stage pinion speed 27 rpm ( 45 Hz) seond stage pinion speed rpm ( 366 Hz) inlet pressure 23.4 bar ( 34 psia) outlet pressure 5.1 bar ( 74 psia) inlet temperature 42 2 K ( 3 OF) outlet temperature 374 K ( 215 OF) The pinion shafts of eah stage have an overhung radial impeller and are supported in tilting pad journal bearings with five pads. One of the two lobed bearings of the bull gear shaft is a ombined journal thrust bearing with fixed thrust sliding faes. The thrust fores are transferred from the pinion shafts to the bull gear by thrust ollars. The power of the turbine is ontrolled by adjustable inlet nozzles on both stages. COMPRSSOR TURB The ompressorloaded turbines are used in air separation plants. The ompressor is driven diretly by the turbine. The speed is automatially adjusted aording to the power balane between the turbine and the ompressor and adapts itself to power hanges. The ross setion of the ompressor turbine (Figure 2) shows the turbine at the left hand side. The proess gas streams through the turbine impeller from outside to inside and leaves the impeller in axial diretion. The turbine is fully admitted. The adjustable nozzles are loated around the impeller and ontrol The ompressor is arranged on the right hand side of the ross setion. The ompressor impeller is overhung, too. The gas flows from inside to outside. The bearing housing with the sliding bearings, the seals and the thrust load balaning system, are loated between the turbine and ompressor. The seals onsist of labyrinths with arbon bushes. On the turbine side, buffer gas is fed in, the pressure of whih is a little higher than that on the bak side of the turbine impeller. n the diretion of the bearing, there is an intermediate pressure hamber, via whih the leakage gas is vented with a pressure of about 6. bar (85 psia). The sliding bearing area has atmospheri pressure. On the ompressor side, there is a balane piston, by means of whih the thrust load onto the thrust bearing an be redued. The balane piston is pressurized on one side, with the ompressor inlet pressure and on the other side with the turbine outlet pressure. The sliding bearings are oil lubriated. The loaded thrust bearing is loated at the turbine side. The thrust bearings are tapered land fixed geometry bearings, whereas the journal bearings are tilting pad bearings with five pads. The oil is fed to the sliding faes via an annular hannel and bores in the bearing bush. The oil is throttled at the outlet so that the bearing is flooded. Typial design onditions of the ompressor loaded turbine for the given frame size are power up to 12 kw ( 1,6 hp) speed up to 34 1min ( 57 Hz) impeller diameter about 19mm ( 7, 5 inh) for the turbine inlet pressure about 55 bar 8 psia) outlet pressure about 6bar 85 psia) inlet temperature about 285K 54 OF) outlet temperature about 175K 145 OF) for the ompressor inlet pressure about36bar 52 psia) outlet pressure about 55 bar 8 psia) With other frame sizes other operating ranges are obtained.

3 SOLUTO OF SUBSYCHROOUS VBRATO PROBLMS RADAL FLOW HGHSPD TURBS 21 LATRAL VBRATO AALYSS AD HGH SPD ROTOR DSG For highspeed rotors, an extensive lateral vibration analysis is arried out in most ases. For modelling of the rotor and bearing systems arefully tested omputer programs are in use. Substitute System of the.rotor and Dynami Bearing Coeffiients For the substitute system, the rotor is divided into shaft setions with a onstant ross setion [1]. Further masses and their mass moments of inertia an be added. Bearing fores, other additional fores, stiffness, damping and fored exiting fores an at at the end of eah setion. At the journal bearing positions, the properties of the sliding bearings are linearly approximated with the stiffnes and damping oeffiients [2]. Additional external elastiity, damping and masses an be added in the bearing positions, whih are modelled as omplex substitute oeffiients for the whole bearing. The substitute systems ofboth rotors, with the overhung masses of the impellers, the journal bearing and the assumed unbalane positions are shown in Figures 3 and 4. 5!:. 4 '== 2 f, 1 1;z; 1 :: r = :=_, +1 5f v 11 f o _j. LL L o ọ..o... M,m j lo' L isotropi bearing stiffness 6 Figure 5. Critial Speed Map of Pinion Shaft (seond stage); Stiffness Range Aording to Tables 1 and 3. added kg( lib 1 L_._.J u B u u B 671 mm (1743 in J Figure 3. Substitute System of Pinion Shaft of Gear Thrbine (seond stage). added [kg] (lbl 62\mm in Figure 4. Substitute System of Compressor Thrbine Rotor. Critial Speed Map The ritial speed map allows a quik overview on the position of the ritial speeds in relation to the rotational speed (Figures 5 and 6). This map shows the natural frequenies as a funtion of a \\ide range of the isotropi bearing stiffuess without damping influene. The bearing stiffuesses are influened, for example, by manufaturing toleranes or different operating onditions. With this map it an easily be shown how this stiffness hange influenes the ritial speeds. The pinion shaft of the gearturbine operates between the first and seond ritial speed (Figure 5), whih is typial for pinions ' F l. #, LL v isotropi bearing stiffness 8 v = WT'A ""ii:pn;; 14 3 rd: "tmlnl 2nd: n( n 1st: n 1 n 1 14 M m 1 1!> ktbfin 1 6 Figure 6. Critial Speed Map of Compressor Thrbine Rotor; Stiffness Range Aording to 'lhble 2. with one overhung wheel. The rotor of the ompressor turbine runs between the seond and third ritial speeds, beause with a stiff symmetri rotor, the first and seond natural modes are lose together (Figure 6). System Damping and atural Frequenies The natural modes of the totally oupled rotorbearing system are alulated with the unisotropi and antimetri bearing stiffnesses and dampings, so that generally one natural mode is split in two eigenvalues whih are omposed of the natural frequenies and the system dampings. The logarithmi derement 8 also often used an be alulated from the system damping D* as follows 8 = 2'11' D* Positive values mean stable onditions. The natural frequenies of the gear turbine pinion are shown in Figure 7 and the related system damping values in Figure 8. As the dynami oeffiients of the tilting pad bearing are alulated for idealized onditions, the rotorbearing system has no stability limit. The damping reserve at operating speed is high enough for these idealized preassumptions. For the r()tor of the ompressorturbine the natural frequenies (Figure 9) are only slightly different, beause the influene

4 22 PROCDGS OF TH SVTTH TURBO MACHRY SYMPOSUM 5 r,., 4.., so 4 m.z m.1 modem 9 >. u :::J CT.t ;;;.. z ro v 1.2 mode rotational speed n 1 3 rpm l Figure 7. atural Frequenies of Pinion Shaft (seond stage). e 3 u '.2.. > 2 u CT z ro rotational speed n 13 rpm l Figure 9. atural Frequenies of Compressor Turbine Rotor. 4.. oo * D ro 1.& > , * 2 :n. ro.& ;:, 1 n op. 1 rotational speed n 1 3 rpm l Figure 8. System Damping of Pinion Shaft (seond stage). ill.l ill,2 modem rotational speed n 1 3 rpml Figure 1 System Damping of Compressor itrbine Rotor. 4 of mass moments of inertia and anisotropy of the low loaded bearings is very small. The damping of the first two natural modes is relatively high while that of the third natural mode is very small (Figure 1). nfluene of Bearing Clearane and Preload Fator Parameters whih are essentially influening the dynami oeffiients of tilting pad journal bearings are bearing learane

5 SOLUTO OF SUBSYCHROOUS VBRATO PROBLMS RADAL FLOW HGHSPD TURBS 23 and preload fator. t is neessary to vary these parameters for optimizing the bearings and for estimating the influene of hanges due to manufaturing toleranes or operating onditions. For the pinion shaft of the gear turbine, the hange of bearing learane has only a small influene. The system damping of the first natural mode is redued a little with inreased bearing learane. On the other hand, the system damping inreases remarkably by reduing the preload fator (Table 1). pivot point of a tilting pad has only a limited stiffuess sometimes similar to bearing stiffuess. Additional elastiities are also possible around the bearing pedestal. The external elastiity influenes the overall stiffuess and also the overall damping of the bearing struture. The system damping of all three natural modes of the ompressor turbine is remarkably redued by inreasing external elastiity that means dereasing of the external stiffness (Table 4). Table 1. nfluene of Bearing Clearane and Preload Fator on igenvalues of Pinion Shaft. Table 3. nfluene of Additional Stati Loads on the igenvalues of Pinion Shaft. bearing preload natural freque n y n e [pm system learane fator dampi n g D * = 1i ( 2 n ) 6D m, 1, 2 ][. 1 [%o] ne o * ne o * ne o * bearing po11er load 1,1 1,2 n. 1 [%) ne o * ne o * ne o* , , , , , For the rotor of the ompressor turbine, the system damping of the first three natural modes inreases with dereasing bearing learane and with dereasing preload fator (Table 2). nfluene of an Additional Stati Load The stati bearing loads of the pinion shafts vary during operation by ontrolling the power of the gear turbine. During no load mehanial tests (sometimes also arried out without the impellers), even the weight of the pinion shaft itself an dominate. For all these operating onditions, a stable running behavior has to be guaranteed. For the pinion shaft supported in tilting pad bearings, the system damping of the first natural mode dereases strongly with inreasing additional stati load (Table 3). nfluene of xternal lastiity The external elastiity being in series to the bearing lubriant film an often not be avoided by the design. For example, the Sealing nfluene The sealing influene on the rotor vibration an be easily explained. With a small defletion of the rotor in the sealing area, a pressure fore omponent perpendiular to the defletion omes about. This effet is amplified by gas flowing through the seal, with a veloity omponent in the diretion of the rotor rotation. The sealing influene an be explained mathematially by an antimetrial stiffness matrix whih onsists of ross oupling oeffiients. To alulate the ross oupling oeffiients of the labyrinth seals, a simplified model was made espeially for the swirl veloity, in aordane to Benkert and Wahter [3]. With this omputer program, the ross oupling oeffiients were alulated for eah of the 11 sealing parts of the ompressor turbine (Figure 2), depending on the geometry and gas parameters and on the assumed swirl veloity (Table 5). The influene on the rotor system damping was dependent on the value of the oeffiient and also on the related amplitude of the natural mode. The redution of the system damping due to the influene of eah labyrinth seal is also shown in Table 5. The labyrinth seals loated near the over plates of the impeller shrouds (Figure 2, positions 1 and 11) and near the balane piston (positions 8 to 1) influene the system damping the most. Table 2. nfluene of Bearing Clearane and Preload Fator on igenvalues of Compressor Thrbine Rotor. bearing preload natural frequeny n e [pm] j system dampin g o* = tit 1 2 n 1 learane fator 6 m, 1 2, 1 :rr,2 m, 1 m.2 [%o] ne o* n e o* ne o* ne o* ne o* ne o* , , ,17

6 24 PROCDGS OF TH SVTTH TURBO MACHRY SYMPOSUM Table 4. nfluene of xternal lastiity on igenvalues of Compressor Thrbine Rotor. external natural frequeny n, [pm system damping o *" i = 6(2 1t) stiffness Mm l 1 2 n 1 li 1 2 ml 1 ]( 2 (klbfinl ne o * n e o * ne o (97) (285) ( 171 ) When operating the gear turbine at part load, high subsynhronous vibration levels ourred in the shaft vibration spetra of both turbine stages (Figure 11). The vibrations led to shutdown of the turbine unit in some ases. With inreasing load, the subsynhronous vibrations were redued. The frequeny spetra measured in the ourse of the testing at the manufaturer did not demonstrate suh instabilities. To find out what aused the vibrations, different test runs were made onsite. The following observations were made: The subsynhronous vibrations are always present at ertain part load operations and strongly depend on the nozzle position. The subsynhronous frequenies of the vibrations of both rotors were between 3 to 4 perent of the synhronous onstant running speeds. Depending on the load the thermodynami and aerodynami onditions inside the turbines hange, i.e., preso * ne o * ne o * ne o * Table 5. Cross Coupling Stiffness Coeffiients of Labyrinth Seals and the nfluene 1i System Damping of the Compressor Thrbine Rotor. seal ross oupling oeffiient redution of system position C xy damping [ M m 1 [ klbfin l flo t o o o.o o.o VBRATO XPRC WTH GAR TURB e. '. : C) :.:: ;;: r: e r:rn L'V: o...:.. o A )\ )\..._ first seond ::J: D... rn A frequtny [Hz stage ::J:_ C>.. J stage soo. Figure 11. Vibration Spetra of First and Seond Stage Pinion. Shaft of Gear Turbine. sure, temperature, flow diretion and veloity. The disturbing frequenies were dominating, when the pressure ratio aross the nozzles was low and the irumferential omponent of the absolute flow veloity was high. The situations was ompliated by the fat that the frequenies observed at the rotors were lose to the first natural lateral bending frequeny and therefore the rotors showed an inreased sensitivity due to exiting frequenies of this value. An alteration suffiient to ome away from the exitation range would have required a ompletely new design of the rotors. The earlier tests to improve the damping behavior of the bear ings by hanging preload fator and learane ratio also showed no positive results to ensure stable performane. To determine the exiting mehanism, not observed so far, pressure pulsation measurements were arried o_ut. Frequeny analyses of the pressure pulsations were made at different loations, namely at the entry and exit of both stages, at the bak of the wheels and in the gap between stator (nozzles) and wheel. The measurements showed a relation between shaft vibrations and dynami pressure hanges at the entry and bak of the wheel, and thus, demonstrated an aerodynami exitation effet. The existene of pressure pulsations in the annular spae between nozzles and turbine wheel ould be made evident. The nozzle position and aerodynami and thermodynami onditions in the annular spae were dependent on eah other in all ases. The adjustable nozzle ring and the hange of geometrial dimensions of the annular spae between nozzles and turbine wheel are shown in Figure 12. With losed nozzles the ross se

7 ... i SOLUTO OF SUBSYCHROOUS VBRATO PROBLMS RADAL FLOW HGHSPD TURBS 25 1% open position.. minimal annular spae losed position maximal annular spae ''. ;2 A typial vibration spetrum of a ompressorturbine is shown in Figure 13. The speed of the rotor is rpm. The synhron. A fr U" U" rn rn vertial! W turbine :! Figure 12. Change of Annular Spae between ozzles and Turbine Wheel with ozzle Position.... ro C Vl 1, h ō r ī z _ o _ n _ t a,1,w:: : _ : t u :r b : i : n_e 8 f +1 &.f+j 6 ' \ 4" U" 4 6 oi t 1 2 f..l.f++t ff'equen y [ 1 3 pm J Figure 13. Vibration Spetrum of Compressor Turbine. tion of the annular spae and its equivalent peripheral length is maximal. \Vhen the nozzles are opened, the ross setion and the peripheral length derease until there is only a small gap between nozzles and turbine wheel. The veloity of sound "a" depending on the gas onditions in the annular spae, relates to the equivalent peripheral length 1e q and results in a frequeny f = a [ 4 l., q ] whih orrespon?s to the measured exitation frequeny of the subsynhronous vibrations. The relation shown refers to a.v4resonane of a standing wave, in a pipe open at one end, and losed at the other. f the aousti resonane really existed in the annular spae, it ould be eliminated bv hanging the peripheral length of the annular spae. Theref(>r, thre of the 27 nozzles were fixed n a 1 perent open position, distributed evenly around the Cirumferene. Consequently, the peripheral length was divided in the omplete part load operation range. The efllieny loss reated by the uneven flow entering the wheel at part load was small and aeptable. Mter the modifiation with fixed nozzles, the frequeny spetra showed almost no subsynhronous vibration. A stable operation within the vibration speifiation was possible. Up to now, it ould not be larified for ertain if the pulsations in kind of a "standing wave" were exlusively involved or if other effets ontributed to the exitation proess. Additional measurements will reveal if there is a loally fixed pressure maximum or minimum in the annular spae, or if there are rotating pressure pulsations. Sine the measurements are not yet ompleted, the omplex interrelations annot be ompletely interpreted now. VBRATO XPRC WTH COMPRSSOR TURB n ompressor loaded turbines, subsynhronous vibrations were observed at full load in some ases. During the test runs in the test bed of the manufaturer, however, the mahines operated at part load without any problems. Troubles onneted \Vith subsynhronous vibration was on the one hand dependent on the operation onditions suh as load, speed, seal g s pressure, oil supply, and on the other hand, dependent on aidental satter in tolerane bands suh as balaning status, geometry of bearings, bearing learane, learane in labyrinth seals a?" d gaps and learanes adjusted during assembly. The frequenies of the subsynhronous vibrations were between about 2 and 65 perent of the speed. Vibrations before Modifiations ous vibrations of 6 mils (15 f.lln) are the main part of the total vibrations. The subsvnhronous vibrations our at 166 rpm and have a peaktop ak level of 14 to 21 mils (3. 5 to 5 Jlm). The synhronous vibration is limited to a narrow frequeny band, whereas the subsynhronous vibration an be observed in a broader band. n another ompressor turbine, the subsynhronous vibration was higher than the synhronous vibration (Figure 14). The level of subsynhronous vibration is osillating, the synhronous and ultraharmoni vibrations, however, are onstant. For this turbine, the vibration behavior during oastdown is shown in a asade plot (Figure 15). The frequeny of the subsynhronous vibration depends only very slightly on speed, while the amplitude of subsynhronous vibration hanges remarkably with speed. At that stage of the investigation, the rotordynamis were heked several times with various parameters, i.e., preload fators and learane ratio of the journal tilting pad bearings. Other influenes suh as piping fores, stiffness, alignment toleranes, and oil were disussed and investigated. Uneven oil distribution and flows inside the bearing, reating uneven temperatures and temperature inreases were supposed, b1t ould be ruled out by alulations. Detailed measurements of temperatures and pressures inside the bearing and of the oil flows onfirmed the alulated results V> 1 :.::: 8 :':'. 6 ;;: 4 tu C V> 2. u ""r <rn. '< r )\..... :: '' 1.1" r rn..., ro.jl. vertial C turbine 8' t ""rr:. A ho ri zon tal 8' t Ll"o r:::rr:... C turbine!..), frequeny [ 1 3 pm J Figure 14. Vibration Spetrum with High Subsynhronous Vibrations of Compressor Turbine.

8 26 PROCDGS OF TH SVTTH TURBO MACHRY SYMPOSUM frequeny khz 1 synhronous vibration 2 mils Figure 15. Casade Plot of Vibrations During Coast Down of Compressor Turbine. The hange of only a single parameter in a realisti range was not suffiient to alulate an instability of the rotor in theory. Vibration after Modifiations The theoretial parameter studies showed that the only important destabilizing effets are the ross oupling oeffiients of the labyrinth seals and the external elastiity of the journal bearings. When both effets are onsidered together, negative damping, i.e., instability is alulated for the seond eigenvalue (Figure 16). Damping values for the other natural frequenies are all in the high positive stable range. The main influene of the destabilizing effets is also in the labyrinth seals as is demonstrated in Figure 16...!!! e Q. Q. V :;:::. ;:...r:. ) f f l:cid l e vertial C turbine ' & 11 +_:_:::._:_:.:::.:. + :::::.:_:::...::.::.:.::_1 f+1 [!i & e,..,... rn horizontal C turbine vertial W turbine horizontal \J turbine frequeny [ 1 3 pm 1 Figure 16. ffet of xternal nfluenes on System Damping of Compressor Thrbine Rotor. Based on the knowledge gained from the investigations and literature [4], [5] a atalogue of ation was arranged. Swirl brakes at the gap over plate loated at the turbine wheel shroud aording to Figure 17. The 24 grooves loated at the irumferene shall interrupt the rotating gas flow in the gap and produe a flow with a low irumferential omponent admitted to the labyrinths. Swirl brakes at the over plate loated at the turbine wheel rear. Grooves ut into the over plate shall redue the rotational flow of the gas in the gap. Swirl brakes at the gap over plate loated at the ompressor impeller shroud redue the rotational flow between the impeller and housing and at the entry to the labyrinth. The braking of the swirls is obtained by grooves similar to those shown in Figure 17. Admission of gas to the balane piston in an ounterrotational diretion by bores drilled tangentially into the labyrinth seal ring of the piston (Figure 18). Seal gas supply into the labyrinth ring of the turbine side shaft seals via tangential bores similar to those in Figure 18. Mounting of the bearing into the asing with a very tight fit to obtain a higher external stiffness of the bearings. The positive fit was produed by mahining the outer diameter of the bearing housing aording to the atual bore diameter of the asing. Figure 17. Gap Cover with Swirl Brakes. e.!: a> s = &e... & e : e r....., "" m '8& l Figure 18. Labyrinth Ring with Tangential Gas Supply Bores. Unfortunately, all ations had to be arried out in parallel beause of prodution reasons, so the individual effets of eah ation ould not be affirmed by field measurements. The tight fit of the bearing in the asing proved to be bad beause of the speial temperature onditions in the turbine. n spite of a learane ratio of 26 during assembly, the bearing failed after about 2 hr of operating time, due to shrinking of the asing by low temperature, thus reduing the learane. Sub

9 SOLUTO OF SUBSYCHROOUS VBRATO PROBLMS RADAL FLOW HGHSPD TURBS 27 synhronous vibrations did not appear during this time. The bearing damage learly showed inferior learanes at operating onditions. Therefore, the same bearing was used again whih had run already in the mahine for several months with subsynhronous vibrations. The vibration spetra after the next start are shown in Figure 19. The vibration level is far below the allowable limit. Remarkable subsynhronous vibration amplitudes do not our anymore. 3 The subsynhronous vibration problems were desribed and analyzed as observed at two different turbine installations, a twostage turbine with gear box and a singlestage ompressor loaded turbine. Vibrations in the gear turbine were aused by an aousti resonane in the annular spae between nozzles and turbine wheel. The aousti phenomenon has not been mentioned before in literature as an exitation fore of subsynhronous vibration in turbomahines. The available measurements and data are not suffiient to bak a theoretial approah. Therefore, further investigations and measurements will be neessary for final larifiation. The aousti resonane in the gear turbine ould be avoided by dividing the annular spae. Subsynhronous vibrations were redued to an aeptable level. The subsynhronous vibrations in the ompressor turbine were aused by a ombined effet of destabilizing influenes. The main influene ame from the labyrinth seals in ombination with an external elastiity in the bearing. By installing modified gap over plates and seal rings into the ompressorturbine to interrupt the rotational flow in the seals, the subsynhronous vibration was eliminated. The theories and omputer odes available now enable manufaturers to find the auses for subsynhronous vibration and to work out measures to avoid the vibrations in future designs. * C) 1 2 [ 1 ltl "C 1 stable unstable with labyrinth seal ross oupling with external bearing elastiity and labyrinth seal ross ouplin 2 3 to. rotational speed n 1 3 rpm Figure 19. Vibration Spetra of Compressor Turbine after Modifiation. SUMMARY AD COCLUSO RFRCS 1. Han, D. C. and Meyer, A., "Computer Program for Calulating Self and Unbalanexited Lateral Vibrations of Frition Bearing Supported Rotors," in German, Researh Paper o. 139, Forshungsvereinigung, Antriebstehnik; FrankfurtM (1983). 2. Han, D. C., "xtended Computer Program for Calulating Stati and Dynami Parameters of Frition Bearings with High Speed and with Misalignement," in German. Researh Report o. 299, ForshungsvereinigungVerbrennungskraftmashinen, FrankfurtM (1981). 3. Benkert, H., and Wahter, T., "Flow ndued Spring Coeffiients of Labyrinth Seals for Appliations in Rotor dynamis", ASA CP 2133, Rotordynami nstability Problems in HighPerformane Turbomahinery, pp , Proeedings of a Workshop held at Texas A&M University (May 198). 4. Jenny, R., and Wyssmann, H. R., "Lateral Vibration Redution in High Pressure Centrifugal Compressors," Proeedings of the inth Turbomahinery Symposium, Turbomahinery Laboratories, Department of Mehanial ngineering, Texas A&M University, College Station, Texas (198). 5. Kirk, R. G., "Labyrinth Seal Analysis for Centrifugal Compressor Design Theory and Pratie," Proeedings F TOMnternational Conferene on Rotordynamis, Tokyo, Japan, pp (September 1986) ACKOWLDGMT Thanks are due to Mr. Frederik W. Braun from Union Car bide Corporation, Linde Division, Tonawanda, ew York, for disussions, suggestions and support reeived in solving the vibration problems.

10 28 PROCDGS OF TH SVTTH TURBO MACHRY SYMPOSUM