Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Set

CHINESE JOURNAL OF MECHANICAL ENGINEERING●124●Vol. 22. No. 1, 2009DO: 10.3901/CJME. 2009.01.124, available online at www.jmenet.com; www cjmenet.com.cnNonlinear Dynamic Characteristic Analysis of the Shaft Systemin Water Turbine Generator SetMA Zhenyue and SONG Zhiqiang*School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116023, ChinaReceived May 18, 2008; revised November 13, 2008; accepted November 24, 2008; published elctronically February 20, 2009Abstract: A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropowerhouse foundation. The method of determining guide bearing dynamic characteristic coefficients according to the swing of the shaft isproposed, which can be used for studying the self-vibration characteristic and stability of the water turbine generator set. The methodfully considers the complex supporting boundary and loading conditions; especially the nonlinear variation of guide bearing dynamiccharacteristic cofficients and the coupling efet of the whole power-house foundation. The swing and critical rotating speed of anactual generator set shaft system are calculated. The simulated results of the generator set indicate that the coupling vibration model andcalculation method presented in this paper are suitable for stability analysis of the water turbine generator set.Key words: water turbine generator set, dynamic characteristic cofficients, nonlinerity, coupling vibration, citical speedis operating, under the influence of nonlinear variation of1 Introductionthe loads, the displacement of shaft, the rotating centrifugalforce, and the guide bearing oi-flm distribution changesIn recent years, a number of studies on the vibration ofgetting along with time; hence the dynamic characteristicthe water turbine generator set have been conducted- 4.coefficients of the guide bearings change accordingly.Because of the complexity of this matter, those researchesFurthermore, the natural frequency and the crtical rotatingover simplified the loadings, supporting and boundaryspeed of the shaft system depend on not only the rotatingconditions, etc, which may seriously affect the vibrationspeed but also the constraint conditions of the shaft that isof the shaft system. LIU, et al5], calculated the swing ofathe guide bearing dynamic characteristic coefficients. Fig.1shaft on the basis of finite element method, with lineardescribes a three-guide bearings suspension-type unit shaftapproximate model of the system constructed on thesysteml).premise of the shaft disturb only in a small region near theequilibrium point. Owing to the nonlinear essence of thebeannggenerator set, the linear system was not suitable at allRotorcpwhen the diturbance became larger. QIAO, et al6, tookFmt Magnetic foreinto account the nonlinear characteristic of the oil-film,ower guidecalculated the response of a shaft system, while ignoredthe influence of the whole hydropower house and the pierfoundation. He did not analyze the critical rotating speedor the stability of the generator set further. KANG, et al7),were devoted to the study of foundation effects on the144 Tubpne euidedynamic characteristics of rotor-bearing system. TheirTurbineC- 2simulation and analysis based on the finite elementFig. 1. Sketch of the shaftmethod. They put forward the design criteria of theand guide bearingfoundation for rotating machinery avoiding resonance andsuppressing response.For the vertical water turbine generator set, the guideThe中国煤化工frequencies and thebearings are the force tansmission gears between generatorguide t.2.FromFig.2wecan seeMYHC N M H Gwith the stifnes inset and whole bydro-power house. When the generator setan approximate linearity. The deviation of the first stepnature frequency is about土10% when the deviation of the，Corresponding author. E-maili Shiq200@.126.comstiffness reaches土25% taking 2.0 MN/mm as the referenceThis projeet is supported by National Natural Science Foundation ofCHINESE JOURNAL OF MECHANICAL ENGINEERING●125●point; while 20%，when the deviation of the stiffnessThe geometric sketch of water turbine generator setreaches 土50%. Frequency curves of the second and thirdguide bearing is shown in Fig. 3.steps have a similar trend, which indicates that the journalguide bearing stiffiness heavily influences on the naturefrequency. If the non-linear feature of the siffness couldnot be exactly examined, the correct calculation of thenatural frequency would be impossible, to say nothing of二0critical rotating speed.一First step ---econd step -- Third step20垦15Fig. 3. Guide bearing geometric sketch10.0.5Generally, since the rotating speed of a generator set isitifness K/MN.mmr)quite slow, oil-flm flow field belongs to laminar flow.Fig. 2. Curves of frequency sifnesssIgnoring the effect of the squeeze film, the generalReynolds equation of the steady flow field isIn this research, we have a deep consideration of thequestion how to determine the guide bearing oil-filmdistribution and the sifness coefficients further accordinga(h亚)t a(hp)=6u2h(1)x(μxJf z(μa,ax'to the nonlinear variation of the loads and the shaftdisplacement. Since the supporting structures of the shaftsystem (consisted of bearing pedestal- -bracket-pier-house, whereU= Rw is the linear speed in the circumnferentialetc) and the force ransfomation way were very complex, drection. Let r=Ro, =(L2), the boundary conditions are .the coupling effect of the whole house and pier foundationas fllows:was considered in the numerical simulation calculation.The simulation and analysis in this paper are based on finiteelement method. The guide bearing dynamic characteristich=t1,h=h/c,p= p(e/R) /uo.y=(D/l).coefficients’nonlinear variation with the shaft centerposition (eccentricity and orientation angle) is considered;meanwhile, we also take the coupling efet of the whole Where p is a symbol for the oil-fIm pessure; c representshouse and pier foundation into account. The shaft swing isthe bearing radius gap; R means the joumal radius; D iscalculated via transient analysis under the normnal loads.noted as the diameter; L is the width of the bearing pad, andThe siffiess of the guide bearings at this swing and thoseof the spprting srucure (bracket and pier foundation) are h the thickness of the oi-im. The dimensionless Reynoldsassembled in series. Total supporting siffiness of the shaft equation is deduced using the transformation above assystem was obtained. Finally, natural frequency and critical follows:rotating speed of the generator set are solved by means ofsubspace iteration; stability could be evaluated by which.(2)2 Dynamic Response Analysis of the ShaftSystemThe dimensionless oil-film thickness is2.1 Calculations for the guide bearing nonlineardynamic characteristic eoefficientsThe vertical-type guide bearing dynamic characteristic中国煤化工s(β_ q)+cofficients are analyzed by finite element method. EachYHCNMHG(3)pad's dynamic characteristic cofficients are calculateddirectly with pressure parameter and partial derivativemethods.Definey=c/R as the gap ratio, δ as the swing angle●126.MA Zhenyue, et al: Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Setof the pad. Assume that the oil-flm speeds are u and v injoumal and circumferential direction， respectively, theKq=@KgOT, Cq =@CgφT.(10)dynamic Reynolds equation can be expressed in a form:The nonlinearity of the guide bearing dynamiccharacteristic generally includes the aspects, such as the品(票+r最瓜票)-shaft center displacement, speed and dynamic oil-ilm。ahaφ+ 6(usinp + vcos).(4fracture boundary conditions, etc. The nonlinearity in thisresearch only considers the shaft center displacement whichis the most important factor. As to the effect of shaft centerPressure parameter I function is introduced byspeed, taking the speed as linear factor is reasonablebecause general large water turbine generator set has a verylow speed, most are around 100 r/min.Iπ=h°p.(5)As shown in Fig. 4, the swing amplitude and track of theshaft center are calculated in global coordinate system x y,the dynamic characteristic coefficients of each guideTben Reynolds equation can be written asbearing pad are calculated in local coordinate system X-Y.The angle is the orientation angle of the dynamic loads2n ,22n-adI=h-'xwhich is denoted by y between the axis or and axis Oy.The orientations of the dynamic loads change constantly,0φa(6) therefore, the orientation of the coordinate axis oY in the .| 60 + 6(usinp + vecosp)global coordinate system, ie., the orientation angle y，changes constantly. The load capacity and dynamiccharacteristic coficients are only one-dimensionalfunctions of the eccentricity ratio E in the X -Y coordinatewheresystem; they are two-dimensional functions of theeccentricity ratio ε and orientation angle V in x ycoordinate system. The over eccentricity and the constant(7) changes of orientation angle are the main factors whichh aφ2cause the nonlinearity of the oil-film dynamic characteristiccofficients.The triangle plane element type is chosen to deduce thefinite element equations. Then the oil-film capacities in twodirections are obtained:_0Fx|f.-=-2[J。h-sπ sinpdpdh,o/(8)-RFwhere h and p are the dimensionless form of the oil-flmthickness and pressure.Fig. 4. The global and local coordinatesStiffness and damping cofficients can be obtained bycalculating the partial derivative of the oil -film capacities tothe displacement and speed as follows:Pressure parameter and partial derivative methods aboveare programmed on the basis of finite element theory. WithKg='f. (,Cg= ,i=x,y;s=x,y.(9)sufficient small pan sten of the eccentricity ratio ε andorientat中国煤化工long a cyle in thewhole 1YRCNM H G, adjust each padEach pad's dynamic characteristic cofficients in localcoordinatescould be obtained by coordinate location parameters (the oil inlet edge, the oil out edge andtransformation:the angle of the fulcrum) relative to axis OY in the localCHINESE JOURNAL OF MECHANICAL ENGINEERING●127●coordinates. So each pad characteritic cofficients couldSo the nonlinear calculation could come true: firstbe calculated when the shaft center has an arbitrarycurrent value and direction of the guide bearings dynamiceccentricity and orientation angle. Two-dimensional datacharacteristic coefficients are adjusted according to thefiles were constructed for each pad to call. The swing of theshaft center position (eccentricity and orientation angle)obtained by previous step; second, new unit dynamic loadsshaft system was calculated on the coupling model throughare applied for next step calculation. This method considersANSYS. The guide bearing dynamic characteristicsufficiently the effect of the shaft center displacementcoefficients could be obtained by interpolation in the data nonlinearity. The moment of the oil-film is zero and thefiles when the shaft center arive arbitrary position. The force of the oil-flm is through the fulcrum when the pad isat a balance status for every pad of the tilting pad guidewhole calculation flow chart is shown in Fig. 5.bearing. Each pad dynamic characteristic cofficients couldbe applied in the couplingmodel directly withoutUnit and powerhouscoordinate transformation, taking the radial as the directioncoupling modetlof the siffness and damping, thanks to commerce package|Oit film and beanng modelANSYS supports cylinder coordinates system. At the sameInitial unit dynamic loads |time, the spring element's feature which could only bearPressure parameter andpressure is realized by judging with APDL. The table arrayANSYS transent analy sispartal dervaive methodsparameters of ANSYS are chosen for interpolation. TheseFccentricity and angle、DaDale files of siffness and dampingray parameters have a characteristic which theirof the shat jourmalwhen jourmal at arbtrany postionsubscripts are alowed to be non-integral number. So weModtf real contantsSstufiess and dampingcould take advantage of the table array parameters whichof oil-film elementsof ceach padscould be indexed by the subscripts of rows and columns.Unit dynamic loads change2.2 Calculations for the shaft swingThis paper takes an dctual unit and powerhouse located- Next step calculatonin the Northeast of China as an example. The parameters ofthe guide bearings, the unit and the powerhouse are listedFig.5. Flow chart of the calculation for swing of the shaftin Table 1. .Table 1. Parameters about the coupling model of the unit and powerhousePadDynamicOil flm thicknessBearing widhJoumal radiusBearingB/m/mInter radiusradiusRadian Spaceviscosityat pad centern/mr/m0/(°)6J(C) pW(N.s.m)h/mm0.587. L.621.620 361.685502.55x 100.36RotorTurbineRotating speedShaft materialUnitDiameter WeightRatingRunawaymodulusPossion ratio Density LengthD/mW/tn/(r* min ')n/(r●min ')p/(lkg*m )L/mE/GiPa5.6320.327012187.5210.3_7 800Air cowlPierWhole houseInteOuter diameterHeightHeighThicknessLengthWidthHousediameterD/(m)H/m .(/mT/mb/mH/mD.:/m718.25.762.444.50- -5.2242.0724.752.2Both the nonlinearity of the guide bearing dynamic guide bearing: k3; =kg,=1.71 GN/m. The guide bearings arecharacteritic coefficients and the coupling effect of the simulated by two spring elements which are perpendicularwhole hydro-power house foundation have heavily and keeping constant sifness and damping cofficients.influences on the shaft system swing calculation. Three The spring elements are supported on the rigid foundationmodels are constructed to compare the effect of the two directl!中国煤化工Tlers the nonlinearfactors. The first model takes the guide bearing dynamic variaticamic characteristiccharacteristic coefficients as a constant by experience. The coffic|YHCN M H Gristic of only bearapproximate calculation method of the coefficients is pressure. The guide bearings are simulated with fivedetailed in Ref. [9]: upper guide bearing: knx=k1,=1.62 (because there are five pads) spring elements which areGN/m, lower guide bearing: kz, k2y=1.63 GN/m, turbine around the shaft and have variation stifness and damping●128●MA Zhenyue, et al: Nonlinear Dynamic Charateristic Analysis of the Shaft System in Water Turbine Generator Setceoffcents. The spring elements are supprted on the rigid Otherwise, the shaft center amplitude of the third model isfoundation. The third model simulates the flexibility of the larger than that of the second model, because of thewhole hydro-power house and pier foundation, besides the coupling efect of the whole bydro-power house and thenonlincar variation of the guide bearing dynamic pier foundation. For the supporting sifness and thecharacteristic ceficients. The simulation method of the constraint decreased, the amplitude of shaft center vibrationguide bearings is same as the second, except that the guideincreases. The same conclusion can be obtained from thebearings were supported on the pier foundation through the nodes at the location of the upper and lower bearings, sobrackets. The connection structures such as the bracket other results needn't be given. In addition, the nodes at thesupporting arms are simulated by four or six springrotor and the turbine location had larger response amplitudeelements, the siffness coefficients of them were calculated than any node at other locations. It is because of the efetas Ref. [10]. The bracket center structure is taken as the of the unbalance magnetic pull on the rotor, the huge massrigid ring. It is the connection structure of the bearings and of the rotor and turbine, and no guide bearing const raint atthe bracket supporting arms. The third model is sbown in bottom of the turbine.Fig. 6.0r-Modell --Model2 ...ode330-;程60-/三40of/0.0020.40.60.81.0121.41.61.82.0Time lsFig. 6. Coupling mode! between theFig. 7. Shaft center ampliude at urbine guide bearinggenerator set and pier foundationFig. 8 gives the tracks of the shaft center at the turbineThe generator set dynamic loads at the thirtieth node (theguide bearing location. Fig. 8(a) and Fig. 8(b) sbow thatrotor location), the twenty-sixth node (the stator foundationalthough the two models had the same original position andlocation) and the first node (the turbine location) aresimilar contour, the track radius of the first model is aboutsimplfied as sine and cosine function in two horizontal six times larger than that of the second model. It is proveddirections as follows:that nonlinear variation of the guide bearing dynamiccharacteristic coefficients restrain the vibration of the shaft[F3()= 240sinp = 240sincot，center effectively in all borizon directions. However, the| F,3o(1)= 240cosφ = 240cosaot,track radius of the third model (Fig. 8(C)) is larger than thatof the first model. It indicates that house structure acting as| Fx26()= 126sinp = 126sinat，(11)the elastic suppring boundary of shaft system distrted| F2()= 126cosφ= 126cosart,the constraint, i.e., boosting the vibration amplitude. FromFig. 8(d) comparing with model one and model two, the| F.()= 388singp = 388sinaot,track contour of the model three is more complex and[F,()= 388c08 = 388cosor,disturbed. This indicates that the nonlinearity and couplingdisturb the stability of the generator set. But the generatorwherepis the orientation angle of the loads, wis the set is in a stability status all the same, the shaft centerrotating speed of the generator set.motions along with the circumference and swing to and froFig. 7 gives the transieat analysis results of the node at in the joumal diretion at the same time, it is a dynamicthe turbine location in the first four generator set dynamic balance. So neither model one nor model two reflets theloads rotating periods, i.e, 1.92 s. It can be seen from Fig. essence of the system, deviation is inevitable. Owing to the7 that the shaft center amplitude of the second model is nonlinear characteristic of the oil-flm itself and thevery small, smaller than that of the first model. It is proved coupling effect between generator set and the bouse, thethat the nonlinear variation of the guide bearing dymamicgeneratqmentmodel whichcharacteristic ceficients restrain the vibration of the shaft conside中国煤化工he guide bearingffectively. As the sbaft eccentricity increases, the guide dynamiCNMHGtakes the wholebearing gap decreases, and the siffness and damping houseing stucure (that-officients increase accordingly, the furtber increase of is model three) is in line with real situations, hence is ofeccentricity was restrained, until it comes to a steady state. more credibility.CHINESE JOURNAL OF MECHANICAL ENGINEERING●129●the dynamic characteristic of the shaft system would not bereflected exactly. So the natural frequency of the shaft20-system is researched independently. The total supportingstiffness were composed of three parts: the oil-film stiffnessobtained by the swing calculation above; the bracket0-supporting arms sifness as above; the stiffness of the10Fconcrete pier foundation obtained by the finite elementmethodl. The thrust bearing could be simulated by atorsion spring element. There is a hydraulic unbalance-30~-20-10010203040force at the turbine location due to the seal gap around isAmpliude in X direction A/μmasymmetry. There are an unbalance magnetic pull and a(a)Modellsrmoment at the rotor location owing to the asymmetry gapbetween the rotor and the stator generates. They are allequivalent to the elastic recovery force and moment.According to the ltte influence, the damping effect isignored in calculation.3.2 Matrix analysis methodThe shaft could be regarded as the uniform section beam.The rotary inertia and the gyroscopic efect must be42 tconsidered due to large lateral size and shear deformation.Amplitude in X direction A/urThe rotor and the turbine are simplified as single discs(b)Model 2which have centralized mass and centralized rotary inertia.150rThe total mass and stifness matrices are formed directly.he centralized mass, centralized rotary inertia and thecentralized stifness coefficients were added to thecorresponding elements in the total mass and stiffinessmatrices. The total dynamic balance equation can beexpressed as-100Mi+ Ku=0.-15980-60-40-20020406080Ampltude in X direction A/umThe motion of rotor (turbine) during the vibration is a(C)Model3composite motion. The rotor rotates around the shaft by the- - - -ModelI一Model2 ....Mode3angular frequency 0。; the shaft rotates around the generatorset axis by the angular frequency 0 at the same time. So the50total rotary inertia of the rotor is6》(13)where -148, is the general rotary moment; 10, is just-1504060 80Amplitude in X direction A4/umthe gyroscopic inertia moment which depends on the(d)Companng of three modelsvibration frequencyw; Is and I。 are the diameter andFig. 8. Tracks of the shaft centerpolar rotary inertia moment. The gyroscopic momentmakes the dynamic equation mentioned above (Eq, (12))at the turbine guide bearingnonlinear.Subspace iterative method was used for solving the3 Calculation for the Nature Frequency andabove question for the eigenvalue and eigenvector of everyCritical Speed of the Shaft Systemstep.1中国煤化工obaied frther..1 Boundary conditions3.3TYHCNMH GDue to the dynamic characteristic of the shaft system isThe results of the first six steps natural frequencies aremuch distinct from whole hydro-power house, if took the listed in Table 2. The first step natural frequency is 14.46shaft system and the house as a whole structure to calculate, Hz, and the first critical rotating speed is 867.6 r/min,●130.MA Zhenyue, et al: Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Gencrator Setwhich is higher than the rating rotating speed 125 r/min and the generator set mainly depends on the rotor's andalso higher than the runaway rotating speed 187.5 r/min. So turbine's mode shapes and vibration amplitude s during thethe resonance couldn't appear, and the generator set is operation. While the track of the shaft center at the turbinesteady. The conclusion of resonance examination is location shows that the largest vibration amplitude at theconsistent with the results obtained from the swing turbine guide location is 0.14 mm. This result is relativecalculation mentioned above. The comparing of the results smaller comparing with the main axis swing measuredobtained by diferent guide bearing siffness is also shown history displacement curve in Fig. 10. That is because thein Table 2. The natural frequency of the first, the second calculation in this research only takes into account theand the fourth step have a large difference; the most periodic loads such as mechanical and hydraulic imbalancediference could reach to 23%. The reason of that is the on the turbine, ignores the random loads which were causedsiffness coficicnts obtained by two methods have larger by fluctuating bydraulic pesure when the generator set isdiference. So if calculate the slfviration caracerisi operatig. Either the calculation resuts or the measuredwith the experience sifnesss coficints drecetl, there date tlls the generator set is rnning in a steadty staus. ltiswould be large error in the results.proved that the method proposed in this research is feasiblewhich gets the guide bearing oil-film sifness coefficientsTable 2. Natural frequency of the shaftaccording to the swing of the shaft and calculates theself-vibration characteristic of the shaft system further.Calculation siffnessExperience sifness FrequencyStep No.frequencyerrorfJHzfJHz_el%__0.24r14.4611.1323.030.1218.36 .14.2922.1728.3924.91-0.12-45.3054.6420.62132.42135.752.51. -0.24-145.94154.876.12612345678910The first two mode shapes are described in Fig. 9. It canTime tisbe seen that the first and the second mode shapes areFig. 10. History displacement curve of main axismainly the rotor's and turbine s vibrations.254 Conclusions写2((1) Due to the nonlinearity of the guide bearing dynamicls-/characteristic cofficients and the complex supportingofboundary conditions, creating the 3D finite clement modelof the water turbine generator set shaft system whichconsiders the coupling with the whole house foundation,!0f.calculating the dynamic response and evaluating thestability are very necessary and feasible.-Sδ246.810古14(2) The nonlinear variation of the dynamic characteristicVertical coordinate Z/m(a) The first stepcoefficients with the shaft center position restrains thevibration of the shaft effectively. However, the couplingwith the powerhouse foundation weakens the supportingboundary conditions of the shaft system, increases the4+vibration amplitude. The more complex and distur bed shaftcenter track, as shown in Fig. 8, shows that the stability of2the generator set decreases. The first step critical rotating1十speed is higher than the rating and runaway rotating speed,othe generator set is steady.(3) The method getting the guide bearing dynamicb士4 68101214characteristic coefficients through the swing, analyzing the(b) The second stepself-v中国煤化工tical rotating speedof theFid easy to operation.Fig. 9. Model shapes of the shaftThe m(| YHC N M H CGharaceristic of theguide bearings and the coupling effect of the powerhouseThe relative vibration amplitude at the two locations is foundation. The method which has credible nmumericalthe largest in the whole shaft system. Thus the stability of simulation results may benefit to the security design andCHINESE JOURNAL OF MECHANICAL ENGINEERING.●131●steady operation of the water turbine generator set.Mechanical Srength, 2005, 27(3); 312 -315. (in Chinese)(4) The way of the force transmission and the dynamic[7] KANG Y, CHANG Y-P, TSAI J_W, et al. An investigation insifness efects on dynamics of rotorbearing-foundation sytem[J].characteristic and response of the powerhouse foundationJournal of Sound and Vibration, 20000 231(2): 342-374.need to be studied further when consider the coupling with[8] YANG Xiaoming. Suability analysis and ani-vibration design ofthe generator set.shaft system in hydro generator set[J]. Water Resoures and Power,2005, 23(4): 70- 72. (in Chinese)References[9] BAI Yannian. Design and calculation of water turbine generator[1] CAVALCA K L, CAVALCANTE P F, OKABE E P. Anse{[M]. Beiig: China Machine Pess, 1982. (in Chinese)investigation on the infuence of the supporting structure on the[10] WU Shaozhong. Upper bracker wibration sensitivity analysis aboutdynamic of the rotor system[J]. Mechanical System and Signal9# shaft system in FengMar Power Plan([D]. Dalian: DalianProcessing, 2005, 19: 157-174.University of Technology.2005. (in Chinese)[2] CARDUNALI R, NORDMANN R. SPERBER A. Dynamic [川 YANG Jing, MA Zhenyue, CHEN Jing. Stfhesss checking ofsimulation of non-linear models of hydroeletrie machinery(U].turbine foundation composite structure of Zhanghewan pumped-Mechanical System and Signal Processing. 1993, 7(1): 29-44.storage power station[], Water Power, 2006, 32(12): 33-35. (n3] MA Zhenyue, DONG Yuxin. Dynamic of water turbine generatorChinese)ser{M]. Dalian: Dalian University of Technology Press, 2003. (inBiographical notes[4] ROUTH K E, McMAINS T H, STEPHENSON R W,et al. MA ZHZhenyue, bormn in 1962, is currently a professor in DalianModeting of complex rotor system by combining rotor and University of Technology, China. He received his PhD degreesubstructure models(J] Finite Element in Analysis and Design,from Dalian University of Technology, China, in 1988. H1991(10): 89-100.research interests include dynamics of water turbine generator set,[5] uu Baoguo, ZHANG Xinzhi. Study on computer simulaion structures analysis on builigs of hydropower station.technique of nonlinear dynamic problem for shaft 。Tel: +86-411-84708519; E-mail: dmzy@du.edu.cnhydro-generating unitJ]. China Mecharical Engineering, 200,12(8): 939- -942. (in Chinese)SONG Zhiqiang, bom in 1981, is curently a doctoral candidate in6] QIAO Weidong. MA Wei, LIU Hongzhao. Analysis of coupling School of Civil and Hydraulic Engineering, Dalian University ofdynamic behaviors for rotor-bearing system of hydreoletric Technology, China.machines based on nonlinear dynamics mode[J]. Joumal of E-mail: szhiq2004@126.com中国煤化工MYHCNMHG