Causality of the damages in high power rotating system elements: Experimental testing and modeling

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1 Cuslity of the dmges in high power rotting system elements: Experimentl testing nd modeling V. Brzditis 1, M. Bogdevičius 2 1 Kuns University of Technology, Engineering Mechnics Deprtment, Lithuni vytuts.rzditis@ktu.lt, 2 Vilnius Technicl University, Deprtment of Trnsport Technologicl Equipment, Lithuni mrius@vtu.lt Astrct This rticle concerns dynmics of high power rotting system with toothed wheel coupling. The elstic contcts locted etween pltes nd etween plte s pckets nd semi couplings teeth. Friction etween pltes inside pcket nd teeth genertes fretting corrosion phenomenon nd dmges pltes. Theoreticl modeling nd simultion of rotting system ws provided y finite element method. Complex model involved rotting system, hydrodynmic erings nd coupling. The dynmics of semi couplings nd pltes hve een simulted end experimentlly monitored. The experimentl testing of rotting system ws provided y sttionry mchine condition monitoring nd dignostic system. High frequency solute virtion ccelertion, however, mke it possile to determine the technicl condition of toothed wheel coupling, which is difficult to determine y pplying the shfts virtion. Keywords: : dynmics, modeling, rotting system, erings, dignostic. Introduction The reliility nd efficiency is min prolem tht supports renovtions of the high power generting mchines. Experimentl testing in situ with modeling nd simultion of dynmics of these rotting systems supports filure preventive methods design nd instlltion. In this rticle the dynmics of two stem turines rotting systems with flexile coupling is presented. The high pressure cylinder rotor (1, HPR) medium nd low pressure cylinder rotor (2, MLPR) is joined with nonliner flexile coupling (, NFC). The rotting system is shown in Figure 1. Two semi couplings with 80 teeth ech re connected y plte s pckets. Ech pcket contins three pltes. pckets nd with teeth. Becuse of friction etween pltes inside pcket nd plte s pckets nd teeth the fretting corrosion phenomenon tke plce tht dditionlly dmges pltes s shown in Fig. 2. Fretting corrosion is cused y reltive motion of mted contct surfces nd results s contct filures. The evlution of technicl condition of rotting system with NFC through motion of plte s pckets nd virtion of semi couplings is the tsk of this rticle. Z 1 2 Y X 1B 2B B 4B Fig. 1. Rotor nd ering system: 1 high pressure cylinder rotor (HPR); 2 medium nd low pressure cylinder rotor (MLPR); nonliner flexile coupling (NFC); kb journl erings, k=1,..,4 Trnsferring the torque the rotting system virtes minly y the dynmic forces cting from unlnce, mislignment nd from NFC elements motion. The dynmics of NFC depends on ech plte motion in the pcket, plte s pockets motion nd reltive motion etween ech semi couplings. The high rotting velocity genertes lrge inerti forces cting on pltes. The pltes rdil motions re limited y the cylinder tht is fixed on the HPR semi coupling. Pltes motions in the coupling is complicted, initited metllic contct etween pltes nd plte s inside the Fig. 2. Generl view of dmged pltes Experimentl testing in situ The proximity proes mesures reltive displcements of shfts in the erings nd virtion displcements of the shfts reltive to erings ut not the motion of coupling or its elements. Modeling nd simultion of rotting system with NFC ws provided using experimentl dt. For monitoring virtion of rotting system the solute virtion of the erings nd reltive virtion displcements of the shfts were used [-5]. With sttionry instlled monitoring system the pek-to-pek shfts reltive displcements S( p p), rdil gps Δ X nd Δ Y, unlnce vectors, ect., hve een mesured nd the mximum vlues of virtion 11

2 displcement S mx were clculted referring to ISO One of the sic differences in the opertion of driving nd driven semi couplings lies in the erings design - the 2 nd ering is rdil while the rd one is rdil-xil. The rdil-xil ering significntly chnges the orit of the motion of the rd ering shft together with driven semi coupling, Fig.,. The squred ellipticl re of the 2 nd ering orit is greter compred with the non-ellipticl orit of the rd ering shft. When chnging the lod the sme rtio of the limited orits res remins s stle ut different shpes of the orits. New coupling Fig.. HPR 2 nd ering shft kinetic orit s mx2 =158 µm t 51 MW power Dmged coupling Fig. 4. The two spectr of verticl virtion ccelertion of the HPR 2 nd ering t 54 MW lod, fter one yer in continuous run of mchine The TWC genertes dynmic forces tht dmge the pltes.as shown in Fig. 4, dmged coupling genertes higher intensity virtion ccelertion in comprison with new coupling. The virtion excited y the coupling plte s pckets fll into the high frequency zone nd is chrcterized y solute virtion ccelertions of the 2 nd nd rd erings. The design nd opertion of TWC is similr s gering. The high frequency virtion ccelertion spectr of 2 nd nd rd ering look nlogous. The typicl spectrum s the 2 nd ering ccelertion is shown in Fig.. The previling high frequency ~4000 Hz virtion ccelertion mplitude. Fig. MLPR rd ering shft kinetic orit s mx =55 µm t 51 MW power This cuses the chnges of the eccentricity rtios of the 2 nd nd rd erings, ffects lignment of HPR nd MLPR nd chnges design xil positions of oth semi couplings. Eccentricity rtio of 1 st nd 2 nd erings lso depends on instilities of the stem control system of the HPR nd MLPR. The TWC genertes high frequency virtion pproching 4000 Hz nd 2X hrmonic (80 teeth with plte s pckets t 50 Hz rottion velocity). The reltive virtion displcement of 2 nd nd rd erings either prtilly evluted or entirely do not represent the high frequency virtion excited y the NFC. The frequency difference nd virtion ccelertion intensity is the indictor tht pltes nd plte s pckets hving een uneqully loded or dmged. These chnges re cused not only due to irregulrities of the teeth pitches, devitions of the teeth geometric shpe, mechnicl nd temperture unlnce, etc., ut minly cused y HPR semi coupling rdil virtion displcements, cused y unlnce nd mislignment of HPR semi coupling nd HPR reltive to MLPR, Fig. 4. Fig. 5. Mximum vlues of virtion displcement S mx of the 1 st,2 nd nd rd erings shfts under vrying lod The vlule chnges in verge shfts centerline positions strongly depends on loding nd indirectly indicte tht driving nd driven semi couplings possess chnges in lignment tht genertes dynmic forces cting on pltes nd pltes pckets. According solute virtion intensity v rms vlues mchine cn run sfely in long term continuous opertion mode. But 1 st nd 2 nd erings shfts reltive virtion 12

3 mximum vlues of displcements (S (p-p)mx =2 S mx, Fig.) re to high for sfe long-term continuous opertion ecuse reched virtion severity zone D (S (p-p)mx >20 µm, ISO :2001). The shfts reltive virtion displcement mximum vlues S mx should e considered in condition monitoring of mchine. Models of rotting system The rotting system shown in Fig. 1 consists of two rotors supported y oil-film erings with NFC. The following generl ssumptions hve een mde: the mteril of rotors nd coupling re elstic; sher forces re tken into ccount; the deflection of the rotor is produced y the displcement of points of the centre line; the xil motion of the rotors is neglected; the semicouplings re treted s rigid. The rotor dynmics is simulted y the finite element method when the finite element consists of two nodes nd five degrees of freedom (DOF) t ech node. The first nd the second DOF re displcements long y nd z xes nd the lst three DOF re ngles round X, Y nd Z xes. The equtions of motion of the rotor finite element re derived y pplying Lgrnge eqution of the second order nd cn e written s follows: [ M ( q) ]{} q& + ([ C] + [ G] ){ q& } + [ K ]{ q} = { F( q, q& )} (1) where [ M ( q) ],[ C ], [ G ] nd [ K] re mss, dmping, gyroscopic nd stiffness mtrices of the finite element, respectively; { F ( q, q& )} is the lod vector of the finite element. Under the ssumption of smll displcements of the journl centre, the fluid-film force components in the horizontl nd verticl directions, Fy nd Fz, re s follows turns out to e where c c v& k k v czy czz w & k zy k zz w v& v + K, (2) w& w kij nd the c ij ( i, j) = ( y, z) re stiffness nd yy yz yy yz { F } = + = [ C ] [ ] dmping coefficients, respectively (Fig. ). The equtions of motion of the coupling cn e presented y the mtrix eqution or [ M c1 ] [ 0] [] 0 [ M ] Fcg1 + Fcg2 q&& c1 + q&& { F } + { F } c w, [ Gc1] [ 0] [] 0 [ G ] q& c1 = q& [ M ]{ q& } + [ G ]{ q& } = { F } coupl & coupl coupl coupl coupl, () The mss nd gyroscopic [ mtrices nd lod vectors [ ci M ] ] { F } cgi G ci of semi coupling re otined y using second order Lgrnge s eqution. { F w } is lod vector of weight force. Z kyy cyy kyz cyz Results nd discussions Rigid journl 0 Fluid kzz czz film Fig.. Fluid-film model Two steel rotors with toothed wheel coupling rotting t 000 rpm nd supported t the four hydrodynmics erings re considered (Fig. 1). The vlues of stiffness coefficients of the erings re s follows: k yy = N / m, k yz = N / m, k zy = N / m, k zz = N / m, c yy zz / yy = c zz = 0 = c = Ns m, c. The density nd elstic modulus of the rotors nd coupling mteril re ρ = 7850 kg m, 9 2 E N m =, respectively. Ech rotor is divided into 22 finite elements. The numer of notches is equl to NZ = 80, the gp etween the plte pcket nd semicoupling is design δ = m. The coefficients of stiffness nd dmping of plte pcket re 9 9 k y = N m, k z = N m, = Ns m, respectively, nd the friction coefficient etween the plte nd semi-coupling is equl to f = The rdii of the coupling re R0 = m, R = R m. The geometricl prmeters of the c y 1 2 = coupling re 1 = 2 = m, = m. The mss, polr nd trnsverse moments of the semicoupling re m1 = m2 = 241 kg J cp = m 4, 4 J cd = m kzy czy. The journl dimeter is equl to Y 1

4 0.00 m with the length of 0.00 m ; ering rdil clernce lemon type is ~ m. The simultion results re shown in Fig. 7 nd Fig. 8 s virtion ccelertion spectr in verticl nd horizontl directions. 0, 0, In comprison with experimentl dt in Fig. the simultion results hve the sme shpe nd indictes the cceptnce of physicl modeling results. More clcultions mde on dynmics of pltes in the coupling. The virtion displcements results re showed in Fig. 9 nd Fig. 10, s virtion displcement vlues of plte in XYZ coordinte system. The virtion displcements S(p-p) vlues received in simultion re vlule in dignostics, ecuse to mesurement of virtion displcements of the semi couplings is very complicted nd expensive ,8 0, 0,4 0, Fig. 7. The spectr of solute virtion ccelertions of the HPR semi-coupling when the lod is 40 MW: horizontl direction, verticl direction Fig. 9. Virtion displcements of HPR semi coupling during full four rottions in the XYZ coordinte system t 40 MW power lod: verticl direction; horizontl direction, v, w [10 m ] 0, 0, , 0, Fig. 8. The spectr of solute virtion ccelertions of the LMPR semi-coupling when the lod is 40 MW: horizontl direction, verticl direction Fig. 10. Virtion displcements of MLPR semi coupling during full four rottions in the XYZ coordinte system t 40 MW power lod: verticl direction; horizontl direction, v, w [10 m]. Conclusions Rotors nd the ering system with nonliner flexile coupling were modeled nd simulted through the use of the finite element method. Both the gyroscopic effect due 14

5 to rotor spin motion nd dynmic properties of the oil-film erings were tken into ccount in the model. The dynmic model of rotting system estimtes the dynmics of semi-couplings nd plte pckets. The simultion of the dynmic model of toothed wheel coupling nd the nlysis of the virtion displcements of semi-couplings nd plte pckets determine the conditions of the fretting corrosion. The simultion results provide the sic knowledge in the estimtion of the dynmics of semi-couplings nd pltes ecuse experimentl mesurement of these prmeters is complicted in comprison with shfts virtion displcements inside the journl erings. Asolute virtion ccelertion of high frequencies is the min prmeter tken into ccount in prctice when evluting the technicl condition nd reliility of the whole rotting system. References 1. Brzditis V., Bogdevičius M., Gečys S. Virtion prolems of high power ir lower mchine. The 2-nd Interntion Symposium on Stility Control of Rotting Mchinery (ISCORMA-2). Gdnsk. 4-8 August 200. P ISO (199) Mechnicl virtion. evlution of mchine virtion y mesurements on non-rotting prts. Prt 2. Lrge sed stem turine genertor sets in excess of 50 MW, 8 p.; P.20. ISO (2001) Mechnicl virtion evlution of mchine virtion y mesurements on rotting shfts. Prt 2: Lnd sed stem turines nd genertors in excess of 50 MW with norml operting speeds of 1500 r/min, 1800 r/min, 000 r/min nd 00 r/min. P.20.. Brzditis V., Brzditis V.V., Didžioks R., Pocius Z. Inconsistence of solute nd reltive virtion in rotors dignostics. Mechnik. ISSN Kuns: Technologij Nr.(41). P Brzditis V., Činiks G. Monitoring nd dignostics of rotor mchines. Monogrph. Kuns: Technologij P Aldjev V., Bogdevičius M., Prentkovskis O. New softwre for mthemticl pckge Mple of releses, 7 nd 8. Monogrph. Vilnius: Technik P.404. V. Brzditis, M. Bogdevičius Didelės glios rotorinės sistemos elementų sužlojimo priežstys: eksperimentinii tyrimi ir modelivims Reziumė Ngrinėjm didelės glios rotorinė sistem, kurioje rotorii sujungti sudėtingos konstrukcijos mov. Movoje yr štuonisdešimt išdrožų su komplektu plokštelių. Perduodnt sukimo momentą, trp pusmovių ir plokštelių tsirnd kintms kontkts ir veiki kintmos trinties jėgos, o esitrinnčiuose kūnų pviršiuose - fretingo korozij. Atlikti rotorinės sistemos eksperimentinii ir teorinii tyrimi. Rotorinės sistemos dinminii procesi išngrinėti igtinių elementų metodu. Rotorinės sistemos eksperimentinii tyrimi tlikti nudojnt stcionrią monitoringo ir dignostikos sistemą. Guti rotorius soliučiųjų pgreičių spektri. Sunku išmtuoti movos ir plokštelių virpesius. Pteikt spudi