Gas Turbine Casing Response to Blade Vibrations: Analytical and Experimental results

Transcription

1 Gas Tubine Casing Response to Blade Vibations: Analytical and Expeimental esults Gaeth L. Fobes, Robet B. Randall School of Mechanical and Manufactuing Engineeing, Univesity of New South Wales, PO Box 6359, UNSW Sydney, NSW, 1466, Austalia Abstact The non-intusive measuement of blade condition within a gas tubine would be a significant aid in the maintenance and continued opeation of these engines. Online condition monitoing of the blade health by non-contact measuement methods is obviously the ambition of most techniques, with a numbe of methods poposed, investigated and employed fo such measuement. The cuent dominant method uses poximity pobes to measue blade aival time fo subsequent pocessing. It has been ecently poposed howeve, that measuement of the tubine casing vibation esponse could povide a means of blade condition monitoing. The casing vibation is believed to be excited pe-dominantly by (i) the moving pessue wavefom aound each blade thoughout its motion and (ii) the moments applied by the stationay stato blades. Any changes to the pessue pofile aound the otating blades, due to thei vibation, will theefoe in tun affect these excitation foces. Pevious wok has intoduced an analytical model of a gas tubine casing, and simulated pessue signal associated with the otating blades. The model has been extended in this pape to moe closely epesent a commecial gas tubine with expeimental veification being pesented fo vaious aspects of the analytical modelling pocedue. Keywods: Gas tubines, foced esponse, casing vibations, oto blade vibations. Intoduction The intenal components of gas tubines opeate unde the exteme conditions of high stess and tempeatues. The main woking sufaces inside a tubine engine encounteing these conditions ae the multiple oto and stato blade ows. It is of no supise that analysis of the stess and heat tansfe ability of these components has continually been subject to eseach and development to impove engine design and opeating life. Measuement and modelling of blade vibations has developed fo two main applications, detemination of stess levels induced by the blades dynamic motion and to quantify blade condition. Analytical [1] and moe ecently computational [2] models have been developed to detemine foced blade motion and stesses taking into account effects such as; wake passing, blade tip votices as well as stuctual and aeodynamic loadings on blades. The cuent dominant blade vibation measuement method, in the aeo-industy [3, 4], duing the engine development phase, is blade tip timing (BTT). BTT is achieved though poximity pobe measuements obtaining the aival time of blades at diffeent points aound the casing peiphey. BTT methods ae cuently able to satisfactoily measue asynchonous, non-intege multiples of shaft speed, and blade vibations due to otating stall, flutte and compesso suge, but equie two tansduces, pefoating the casing, fo each blade ow. Howeve, no single method is able to fully chaacteise the vibation paametes of blades in sevice [5]. An altenative method has been poposed fo non-intusive measuements of blade vibations by means of extenal acceleomete measuements on the casing of a gas tubine [6-8]. Investigation into the esponse of a tubine casing unde the influence of opeating pessue

2 conditions was fist undetaken in [9], with the coelation between measued intenal pessue signals and casing vibation measuements shown. Futhe investigations by the same autho have been conducted into the use of unsteady wall pessue signals fo blade fault identification in [10] with the extension to CFD simulation of blade faults in [11, 12]. The peceding woks have dealt solely with the deteministic peiodic foced vibations. It is thought this is diven by the fact that it is these peiodic foces that usually ae the most destuctive foces within an engine and can cause lage deflections and blade stesses. It is howeve well undestood that the opeating conditions inside a gas tubine ae highly tubulent, due to a wide vaiety of influences including but not limited to; ingested tubulence, tubulent bounday laye flow, wake inteaction, evesed flow and tip votex flow. Measuements of the casing wall pessue and vibation signal have been taken fom a simplified expeimental tubine test ig and ae pesented within this pape. An analytical simulation of the intenal pessue signal is also compaed to the expeimental measuements. Although the aim of this study is to highlight the ability to obtain blade vibation infomation fom casing vibations, a compaison between the measued and analytic signal is pimaily done on the pessue signal. Both wall pessue and casing vibation signals should contain the same essential infomation, which will be discussed futhe in late sections, howeve in this case the measuement and intepetation of the pessue signal is less complex than the casing vibation esponse measuements. Convesely in pactice, the ease of making pessue measuements is much less than fo acceleomete measuements, since pessue tansduces equie pefoation of the casing and opeate in a much hashe envionment. Futhemoe, the analysis and esults within this pape deal pedominantly with the effects of the andom fluctuations on the mean peiodic flow, and it is shown that afte sepaation of the dominant peiodic components that the stochastic potion of the pessue and casing measuements contains key infomation on blade vibations. Pessue Geneation Flow ove the oto and stato blade aeofoils in a tubine causes high and low pessue foces to act ove the blade sufaces. These high and low pessue pofiles then inteact as the pessue distibutions aound the oto blades otate aound, causing fluctuating pessues on the casing suface, as well as inteacting with the stationay pessue pofiles aound the stato blades. Shown schematically in Fig. 1 is the fist hamonic of the pessue pofile aound a set of oto blades. It can be seen that the pessue on the suface of the casing will theefoe vay hamonically with the ate at which blades pass that point, i.e. the blade passing fequency, BPF. Blade foced esponse It has been stated at the beginning of this section that the pessue pofiles aound both the stato and oto blades will cause a fluctuating pessue on the suface of the casing due to blade passing fequency. Additionally as the oto blades otate aound the engine they will in tun also be influenced by the vaying pessue pofile and wakes fom the tailing edges of leading stato ows, schematically shown in Fig. 2. The fluctuating foces on the oto blades will now cause them to vibate due to the fluctuating pessue, which is diven at the ate which the oto blades pass though this changing pessue field, i.e. stato passing fequency, SPF.

3 u 3 p Fig. 1 Coss sectional schematic of tubine casing, blades and pessue pofiles. The dashed lines epesent blade motion. Note: only 6 blades shown The pessue acting on oto blades downsteam of a stato blade ow has been shown to have, in geneal, a damped impulse shape [13] (obviously this vaies widely and is dependent on the specific tubine). Tubo-machiney flow conditions ae howeve inheently tubulent, with backgound tubulence intensity levels often epoted to be appox. 3-4%, and tubulence within the wake egion often five times geate than the backgound tubulence [14, 15]. It is also noted that the fequency content of tubulence within a gas tubine will be somewhat band-limited; howeve in the context of this wok the tubulence was assumed to be completely boadband. The foces acting on the oto blades ae theefoe modelled as a aised cosine with a peiod of half the stato blade passing fequency, efe to Fig. 3, and modulated by andom fluctuations due to tubulence. The Fouie seies expansion of the foce on the th blade can be expessed as: f t F0 bt 1 i cos A i spf t (1) i0 2 s 1 s 1 ound 2 (2) b b whee Ai ae the Fouie coefficients, spf is the stato passing fequency, bt is the unifomly distibuted andom vaiable with a zeo mean and a deviation of 7.5%, with s the numbe of stato blades and b the numbe of oto blades. The oto blades ae modelled as a simple oscillato, i.e. a single degee of feedom sping mass dampe system being an adequate model fo blades with well sepaated modes [16]. Only the solution fo the stochastic potion of both the blade motion and pessue foce will be obtained in this study fo bevity; this is also the potion of the signal that contains the most useful infomation. Deivation of the solution fo the deteministic potion can howeve be found in [6]. The solution fo the motion of the th blade can theefoe be shown to be: X f H f F f (3) whee capitalization efes to the Fouie tansfom of the coesponding time signal H f is the tansfe function of the th blade being: and

4 A being the gain facto fo the th blade. H f 2 2 nb A 2 j 2 nb (4) Fig. 2 Wake inteaction between stato (1) and oto (2) blade ows (a) T/4 3T/4 T (b) T/4 3T/4 T Fig. 3 blade focing function, puely deteministic (a), with andom fluctuations (b) Pessue on casing suface The pessue geneated on the casing suface will be affected by the motion of the blade. This will now cause the pessue aound the oto blades to vay due to the blade motion, with the blade pessue pofile following the blade motion as it vibates about its equilibium position. The pessue fom the th blade is once again modelled as a aised cosine with half a peiod of one oto blade spacing, with the Fouie expansion given as: i0 ji t x t P A. P. e (5) i Note that Eqn. (5) is a otating sinusoidal pessue with the phase modulated by the blade motion x t.

5 Expeimental Setup and Measuement The test ig consists of a 19 flat blade oto aangement diven by an electic moto which is cuently capable of unning at speeds up to 2500pm. A tooidal ing in font of the bladed aangement, supplied with high pessue ai, povides six jets which act like tailing edge flow fom upsteam stato blade ows exciting the oto blades at multiples of shaft speed. A micophone and acceleomete ae located in the vetical plane above the blade on the casing. Measuements wee taken with a shaft otational speed of 2000 pm, and analyze sampling ate of khz of which the useful fequency ange is 25.6 khz. 2 1 Fig. 4 Expeimental test ig. (1) Ai jets located on a tooidal ing which is supplied with high pessue ai. (2) location of micophone and acceleomete mounting. Fig. 5 Flowchat of measuement post pocessing Shown in Fig. 5 is the flow chat of the data measuement and post pocessing of the measued signal. The measued signal was e-sampled in the angula domain with an intege numbe of

6 samples pe evolution, tiggeed by a measued once pe-ev tacho signal, often efeed to as ode tacking. This has the advantage that the e-sampled signal can have fluctuations due to changes in shaft speed easily emoved. This is done by time domain synchonous aveaging the ode tacked signal, with a peiod equal to shaft speed this also allows sepaation of the discete and andom components. The powe spectum was then calculated using a hanning weighted, 75% ovelapping, Welch-type aveaging, esulting in a spectum with 1 Hz fequency esolution. Results Expeimental esults wee obtained fo an input shaft speed of 2000 pm, with measuement of casing wall pessue, casing acceleation and tacho signal. Analytical esults ae also shown fo the simulated pessue signal, fo the same opeating conditions as the expeimental test ig; i.e. 19 oto blades, 6 stato blades, and 2000pm shaft speed. The powe spectum, ove a limited ange of the measued pessue and acceleation signals can be seen in Fig. 6. The esidual signal is ovelaid on the synchonously aveaged discete signal. The discete signals can be seen to be made up of multiple discete peaks at hamonics of shaft speed, with the lagest peak at a multiple of BPF. The esidual signal in Fig. 6(a) can be seen to be elatively flat with double peaks eithe side of multiples of shaft speed, the zoomed spectum in Fig. 7 shows this moe clealy. The same oveall stuctue of the esidual signal is appaent in the casing vibation signal, with the addition of boad stuctual esonance peaks, indicated by the aows. This is the fundamental diffeence in the esults which ae seen between the pessue and casing vibation signals. This is owing to the fact that the casing vibations ae diven by the intenal pessue foce, so the casing vibations should esemble the pessue signal afte it has passed though the stuctual tansfe function, a Linea Time Invaiant Filte. db el. 1E (a) fequency Hz db el. 1E (b) fequency Hz Fig. 6 (a) PSD of measued pessue signal, sepaated discete and esidual signal ovelaid on each othe, (b) measued casing acceleation signal. Aows indicate the stuctual esonance peaks in the acceleation signal.

7 The zoomed spectum shown in Fig. 7, highlights the naow band peaks cented aound multiples of shaft speed. Shown by the solid vetical lines ae the multiples of shaft speed, the othe vetical dashed lines show the coesponding half multiples of shaft speed the blade natual fequency, ie blade natual fequency. Thee is a discepancy between the measued pessue signal and that which is modelled in accodance with the ealie deived pessue signal. Fig. 8 shows the simulated pessue signal, which contains the same sets of two naow band peaks. Howeve they ae shifted by an amount of half shaft speed, i.e. they ae cented aound whole numbes of shaft speed; shown is times shaft speed blade natual fequency. It is believed this diffeence can be explained by discete fequencies which exist at half multiples of shaft speed in the expeimental esults, as seen in Fig. 9. The discete fequencies in Fig. 9 ae extacted by taking the synchonous aveage of the angula e-sampled signal at double the shaft speed peiod. As can be seen in Fig. 9 the half shaft speed hamonic and paticulaly the one and a half shaft speed hamonic ae of the same ode as the intege multiples of shaft speed. The existence of these half ode discete shaft ode hamonics, pesumably caused by paametic excitation, could then cause this modulation, o half shaft speed shift which is not at pesent allowed fo in the theoetical model. Despite the diffeences between the esults, the impotant ability to detemine the blade natual fequency is still able to be established, which can be estimated by the space between these two naow peaks. The diffeence between the two naow peaks can be shown to be: diff 2 Blade nat. f q (6) The value of q can be found by plotting the diff value veses q and obseving whee the plot passes though zeo. This howeve equies knowledge of the blade natual fequency to at least within shaft speed. In these esults, the space is on aveage 5 Hz, and the blade natual fequency is known to be aound 117 Hz, fom measuements taken while the shaft is stationay [17]. A blade natual fequency can thus be calculated to be appoximately 119 Hz. This coesponds well with the expected incease in natual fequency which would esult fom centifugal stiffening *Nat.f db el. 1E fequency Hz Fig. 7 Zoomed spectum of the measued esidual pessue signal. Vetical line at shaft speed spacing, vetical line at shaft speed blade natual fequency, vetical line at shaft speed + blade natual fequency

8 *Nat.f db el. 1E fequency Hz Fig. 8 Zoomed spectum of the analytic esidual pessue signal. Vetical line at shaft speed spacing, vetical line at shaft speed blade natual fequency, vetical line at shaft speed + blade natual fequency db el. 1E ode numbe Fig. 9 Spectum of the discete synchonous aveage components, with synchonous aveage length twice shaft speed length Conclusions Measued casing wall pessue and casing vibations have been pesented along with the analytical fomulations of the intenal pessue signal fo a simplified tubine test ig. Results fo the simulated pessue signal shown hee and in pevious wok [7, 8] have been shown to contain the same signal featues as those which have been measued, namely; discete peaks at multiples of shaft speed and naow band peaks at multiples of shaft speed blade natual fequency, although thee cuently exists a half shaft speed fequency shift between the two esults which is thus fa not fully explained. Despite this discepancy, the impotant featue of

9 being able to estimate the blade natual fequency fom wall pessue measuements o casing vibations is still able to be achieved. Acknowledgements Gateful acknowledgment is made fo the financial assistance given by the Austalian Defence Science and Technology Oganisation, though the Cente of Expetise in Helicopte Stuctues and Diagnostics at UNSW. Refeences 1. Majjigi, R.K. and P.R. Gliebe, Development of oto wake/votex model, in NASA-CR , NASA contact NAS Chiang, H.-W.D. and R.E. Kielb, Analysis system fo blade foced esponse. Jounal of Tubomachiney, Tansactions of the ASME, (4): p Zielinski, M. and G. Zille, Noncontact Blade Vibation Measuement System fo Aeo Engine Application. Ameican Institute of Aeonautics and Astonautics, 2005(ISABE). 4. Heath, S., A New Technique fo Identifying Synchonous Resonances Using Tip-Timing. Jounal of Engineeing fo Gas Tubines and Powe, (2): p Heath, S., et al. Tubomachiney blade tip measuement techniques. in Advanced Non-Intusive Instumentation fo Populsion Engines Bussels, Belgium. 6. Fobes, G.L. and R.B. Randall. Simulated Gas Tubine Casing Response to Roto Blade Pessue Excitation. in 5th Austalasian Congess on Applied Mechanics Bisbane, Austalia. 7. Fobes, G.L. and R.B. Randall. Sepaation of excitation foces fom simulated gas tubine casing esponse measuements. in EURODYN Southampton, UK. 8. Fobes, G.L. and R.B. Randall. Detection of a Blade Fault fom Simulated Gas Tubine Casing Response Measuements. in 4th Euopean Wokshop on Stuctual Health Monitoing Kakow, Poland. 9. Mathioudakis, K., E. Loukis, and K.D. Papailiou. Casing vibation and gas tubine opeating conditions Toonto, Ont, Can: Publ by Ameican Soc of Mechanical Enginees (ASME), New Yok, NY, USA. 10. Mathioudakis, K., et al., Fast esponse wall pessue measuement as a means of gas tubine blade fault identification. Jounal of Engineeing fo Gas Tubines and Powe, Tansactions of the ASME, (2): p Dedoussis, V., K. Mathioudakis, and K.D. Papiliou. Numeical simulation of blade fault signatues fom unsteady wall pessue signals Hague, Neth: Publ by ASME, New Yok, NY, USA. 12. Stamatis, A., N. Aetakis, and K. Mathioudakis. Blade fault ecognition based on signal pocessing and adaptive fluid dynamic modelling Olando, FL, USA: ASME, New Yok, NY, USA. 13. Mailach, R., L. Mulle, and K. Vogele, Roto-stato inteactions in a fou-stage low-speed axial compesso - Pat II: Unsteady aeodynamic foces of oto and stato blades. Jounal of Tubomachiney, (4): p Hendeson, A.D., G.J. Walke, and J.D. Hughes, The influence of tubulence on wake dispesion and blade ow inteaction in an axial compesso. Jounal of Tubomachiney, (1): p Dullenkopf, K. and R.E. Mayle, Effects of incident tubulence and moving wakes on lamina heat tansfe in gas tubines. Jounal of Tubomachiney, Tansactions of the ASME, (1): p Dimitiadis, G., et al., Blade-tip timing measuement of synchonous vibations of otating bladed assemblies. Mechanical Systems and Signal Pocessing, (4): p Clak, M., Tubine Blade Diagnostics, in School of Mechanical and Manufactuing Engineeing. 2006, Univesity of New South Wales: Sydney.