Effects of Unbalance Location on Dynamic Characteristics of High-speed Gasoline Engine Turbocharger with Floating Ring Bearings

Transcription

1 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 9,aNo.,a DOI: /CJME , available online at Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings WANG Longkai, BIN Guangfu*, LI Xuejun, and LIU Dingqu Health Maintenane for Mehanial Equipment Key Lab of Hunan Provine, Hunan University of Siene and Tehnology, Xiangtan 41101, China Reeived June 3, 015; revised September 5, 015; aepted Otober 13, 015 Abstrat: For the high-speed gasoline engine turboharger rotor, due to the heterogeneity of multiple parts material, manufaturing and assembly errors, running wear in impeller and uneven arbon of turbine, the random unbalane usually an be developed whih will indue exessive rotor vibration, and even lead to nonlinear vibration aidents. However, the investigation of unbalane loation on the nonlinear high-speed turboharger rotordynami harateristis is less. In order to disuss the rotor unbalane loation effets of turboharger with nonlinear floating ring bearings(frbs), the realisti turboharger of gasoline engine is taken as a researh objet. The rotordynami equations of motion under the ondition of unbalane are derived by applied unbalane fore and nonlinear oil film fore of FRBs. The FE model of turboharger rotor-bearing system is modeled whih inludes the unbalane exitation and nonlinear FRBs. Under the onditions of four different applied loations of unbalane, the nonlinear transient analyses are performed based on the rotor FEM. The differenes of dynami behavior are obvious to the turboharger rotor systems for four onditions, and the bifuration phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearane of frational frequeny is not idential and the amplitude magnitude is different from the different unbalane loations, and the non-synhronous vibration does not our in the turboharger and the amplitude is relative stable and minimum under the ondition 4. The turboharger vibration and non-synhronous omponents ould be redued or suppressed by ontrolling the applied loation of unbalane, whih is helpful for the dynami design, fault diagnosis and vibration ontrol of the high-speed gasoline engine turbohargers. Keywords: high-speed turboharger, unbalane loation, nonlinear transient analysis, waterfall, dynami harateristis 1 Introdution Automotive turbohargers have beome more and more ommon in passenger vehiles as well as ommerial vehiles. The tehnology of high-speed exhaust automotive turboharger is an important way for energy-saving and ost-reduing of vehiles. The gasoline engine turboharger belongs to the high-speed and light-weight rotors. In the meatime, the nonlinear FRBs are the ommon type used for high-speed turboharger. So the rotor vibration response is omplex and highly nonlinear due to the high operation speed and nonlinear oil film fore. Turboharger rotors are easy to ause random unbalane due to the heterogeneity of multiple parts material, manufaturing and assembly errors, running wear in impeller and uneven arbon of turbine, whih often indues exessive rotor vibration and even leads to nonlinear vibration aidents and redues the NHV * Corresponding author. abin81105@163.om Supported by National Natural Siene Foundation of China(Grant Nos , ), Sientifi Researh Foundation of Hunan Provinial Eduation Department of China(Grant No.15B085), and Postgraduate Innovation Foundation of Hunan University of Siene and Tehnology, China(Grant No. S14000) Chinese Mehanial Engineering Soiety and Springer-Verlag Berlin Heidelberg 016 of vehiles. The turboharger design must ensure smooth and effiient operation at high speed. The demands for higher rotational speed and effiient performane, along with low manufaturing ost, ontinue to motivate the rotordynami investigation of turbohargers. Therefore, it is neessary to study the unbalane reponse of high-speed turboharger. The first exhaust turboharger was presented as early as 191. Until now, many efforts are made to investigate the rotordynamis of turboharger rotor-bearing system. Refs. [1 5] study the dynami model of turboharger rotor bearing system. YING, et al [6], also established a dynami model of a turboharger whih inludes the engine s foundation exitation and nonlinear oil film fore. NGO, et al [7], analyzed the responses of unbalane fore in ase of undamped and damped system based on the finite element method. To determine suitable system onfiguration for stable operation in the design proess, JUNG, et al [8], built simulation model with onentrated mass and inertia for the rotating struture to arry out modal and mass unbalane response analyses with six ases having different shaft diameters and bearing arrangements. Sine the early 1970s, major works in rotordynamis are oriented toward the alulations of ritial speeds and unbalane responses [9].

2 7 WANG Longkai, et al: Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings Rotor unbalane is the main soure for the vibration of rotating mahinery, also the trigger fator for many kinds of self-exited vibration. ZHAI, et al [10], analyzed the shaft dynami response due to the unbalaned mass by using the finite element analysis. GUNTER, et al [11], studied the effets of rotor unbalane and destabilizing Alford type fores ating at the ompressor and turbine wheels. These effets an strongly influene the limit yle orbits. TIAN, et al [1], also employed a numerial integration approah to ondut dynami investigation inluding the traditional unbalane and the engine exitation effets. The results show that the unbalane will plae onsiderable influene on the rotor response at a low working speed. At high speeds, the effet will be prevented by the dominant sub-synhronous vibrations. MA, et al [13], foused on the effets of two loading onditions(the first mode and seond mode unbalane exitation) on the nonlinear responses of the rotor-bearing system, simulation and experiment all show that oil film instability an exite ompliated ombination of frequeny omponents. LI, et al [14 15], investigated how the eentri phase differene between two disks influene the oil film whirl in a rotor-bearing system. The elimination of sub-synhronous vibration is a major task of rotating mahinery engineers. ALSAEED [16] presented a method to suppress the sub-synhronous vibrations by induing the turboharger rotor unbalane. TIAN [17] investigated the nonlinear effets of unbalane and observed the rotor response an be onsiderably affeted by the amount and distribution of the imposed unbalane. STERLING, et al [18], also studied the effet of indued unbalane on sub-synhronous vibrations of automotive turboharger. It is theorized that an inrease in unbalane ould ause a redution in sub-synhronous vibration amplitudes. KIRK, et al [19], also investigated the influene of turboharger unbalane on sub-synhronous vibration amplitude. Using the run-up and run-down simulation methods, TIAN, et al [0], investigated the effet of mass unbalane on the rotordynami harateristis of a real turboharger system from 0 Hz to 3500 Hz, the results show the distint phenomena brought about by the variations of the unbalane offset, whih onfirms that the unbalane level is a ritial parameter for the system response. Most researhers devoted to investigate the influene of the unbalane levels on turboharger dynamis at a fixed unbalane loation. The nonlinear analysis is also less at high speed for these small-sized and light-weight turbohargers. Obviously, the influene of unbalane loations on the rotordynami harateristis has not perfomed suffiient studies. It is well known that rotor unbalane affets the operation performane of turboharger. Unsuitable rotor unbalane will lead to flexure and internal stress of the rotor and may ause onsiderable vibration and noise in the mahine, even auses safety aidents. However, a suitable unbalane ould suppress the sub-synhronous vibrations and improve the response behavior of turboharger as many researhers mentioned before. The turboharger used in automobile is light-weight with wide operating speeds ould above r/min. Due to the unbalane fore and nonlinear FRBs, the nonlinear rotordynami harateristis of turboharger beome more ompliated. The turboharger rotor often exists random unbalane in the turbine and ompressor impellers, there would still exist residual unbalane even after dynami balaning through adding weights or subtrating weights at the nose or bak wall of two impellers due to the speial struture of urved surfae. Interestingly, high temperature and high pressure exhaust gas in turbine often exist okes. So the turbine impeller may exist some unertain oke deposition. That is, high speed turboharger will generate random unbalane in the turbine and ompressor impeller after running a period of time in the atual operating ondition. The unbalane exists in the different loations of turbine and ompressor impellers, whih diretly influenes the high-effiieny operation of the high-speed turboharger and even auses serious nonlinear vibration aident. Aim at different loations of unbalane and onsidering the nonlinear oil film behavior of FRBs, a relatively aurate finite element model of gasoline engine turboharger was built and the nonlinear time transient run-up analyses and time domain analyses were performed to investigate how the unbalane loations affet the nonlinear response harateristis of turboharger. The investigation is helpful to distribute the unbalane loation and be a guide for suppressing the nonsynhronous vibrations for the turboharger design. Rotordynamis of Turboharger Rotor System in FRBs Considering a generalized Laval-Jeffott rotor system with equivalent support stiffness of K x and K y and orresponding visous damping C x and C y in the X and Y diretion, as illustrated in Fig. 1(a). The disk has a mass of m and the enter of gravity is offset from the shaft geometri enter by an eentriity of e. The motion at the disk enter is desribed by two translational displaements (x, y), as illustrated in Fig. 1(b) [1]. Fig. 1. Two-degree-freedom of model For the ase of onstant angular speed of rotation, Ω, the equations of motion for the mass enter an be derived from Newton s laws of motion:

3 CHINESE JOURNAL OF MECHANICAL ENGINEERING 73 d m [ x+ eos( t+ e )] =-C xx-kxx dt d m [ y+ esin( t+ e )] =-C yy-kyy dt Eqs. (1), () an be rewritten as follows:, (1). () + x + x = os( + e ), (3) mx C x K x me t + y + y = sin( + e ), (4) my C y K y me t where e is the phase angle for the mass unbalane position. For single unbalane fore, as in this ase, e an be set to zero without loss of generality. The equations of motion show that the motions in the X and Y diretions are both dynamially and statially deoupled in this simple model. Therefore, they an be solved separately. Sine there are no ross-oupling stiffness oeffiients in this model, it is sometimes referred to as an orthotropi system. For the isotropi systems, the equations of motion for the x and y displaements are idential, exept for the 90 phase differene in unbalane exitations. The steady state solutions to Eqs. (3), (4) have the same form as follows: xt ( ) = x os t+ xsin t= xos( t- ), (5) s yt ( ) = y os t+ ysin t= yos( t- ). (6) s Note that x and y displaements osillate at the same frequeny Ω with different amplitudes( x, y ) and phase angles ( x, ). The negative phase angle is measured in y the diretion of rotation and positive phase angle is measured in the opposite diretion of rotation. The response is lagging the exitation aording to Eqs. (5), (6). The phase lag is due to the presene of the damping term. Floating ring bearing has been widely used in the turboharger appliation where the rotor is light-weight and runs at very high speed. FRB an be treated as two fluid film(plain ylindrial) bearings in series. The inner film bearing has two rotating surfae(shaft and floating ring). The outer film has only one rotating surfae(floating ring). Additional two degrees-of-freedom are introdued for eah FRB due to its non-zero ring mass. For the purpose of simpliity, the bearing feeding holes are not inluded and the oil feeding onditions will not be onsidered in the FRB model. In addition, the isothermal fluid flow ondition is assumed for the proposed model. The Reynolds equations for the inner and outer oil films an be written as follows: 1 R j 3 3 æ hi p ö æ i hi p ö i j+ r hi h i + i 1 i i Z = +, çè ø içè1 i Z iø i t (7) x y 1 R ro 3 3 æ ho p ö æ o ho p ö o r ho h o + o 1 o o Z = + +, çè ø oçè1 o Z oø o t (8) where subsripts i and o identify the parameters of the inner oil film and outer oil film, respetively. Subsripts j and r distinguish the parameters between journal and floating rings. p is the oil film pressure, and μ denotes the lubriating oil film visosity. R j and R ro orrespond to radius and floating ring outer radius, respetively. θ is the angular oordinate for the inner and outer oil films. Z i and Z o denote the axial oordinates of the inner and outer films, respetively. h i, h o represent the oil film thiknesses. Ω j, Ω r are the angular veloity of journal and floating ring. The two Reynolds equations for the inner and outer films an be solved separately and the dynami oeffiients an be determined just like the plain bearing for linear analysis. Considering an automotive turboharger rotor system, sine the partial differential equations given by modeling of the rotor shaft in a ontinuous system are diffiult to be takled, disretizing the ontinuum to a disretized system by the FE method in the form of a set of ordinary differential equations is the only feasible method. In this paper, with the help of FEA software, the rotor physial onstrutor an be disretized by using dynami theory and FE method. The turboharger rotor was modeled to 0 stations, additional two stations for the floating rings. The turboharger rotor is regarded as being rigid [], and the equations of motion are solved by using the New-mark integration method, and these are solved simultaneously with the nonlinear FRBs. The motion governing equations for the investigated turboharger rotor-frbs system are derived as follows: Mx + C x + Kx = F, (9) SG () t where M represents the mass matrix ontained the mass and inertia moments of the rotor with n DOFs. C SG is the damping oeffiients and gyrosopi matrix. K is the system stiffness oeffiients matrix inluded diagonal and ross oupled stiffness. x is the response vetor inluded two translational and two rotational displaements at eah station in the horizontal diretion X and the vertial diretion Y. F () t onsists of unbalane fore F ub (, t), stati gravity fore F s in Y diretion and nonlinear bearing fore Fi ( x, xt, ). So F () t an be rewritten as F() t = F( x, x,) t + F (,) t + F. (10) i ub s As displayed in Eqs. (11), (1), F ub (, t) onsists of Fub and F ub t, whih only exists at the end of ompressor and turbine impellers. m, m t denote the mass of the ompressor and turbine impellers, respetively. e is the unbalane displaement. is the rotor rotating angle around the Z axis, and therefore, represent the angular speed and aeleration, respetively.

4 74 WANG Longkai, et al: Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings F æf ö æme me sin ö, F me me os ø ubx os + ub = = çè uby ø çè sin - F æf ö æme me sin ö. F me me os ø ubxt t os + t ub = t = è ç ubyt ø è ç t sin - t (11) (1) The nonlinear bearing fore F 1 and F in the inertial oordinate system an be written as æf ö 1 Frsin Ft os f1(,,,, ( t)) F æ ö ç + + º i = =ç ç F ç- ç Fr os + Ft sin º f(,,,, ( t)), è ø è ø (13) where F 1, F are the omponent fore in the inertia oordinate (X 1, X ). F r and F t are the omponent fore in the rotating oordinate (r, t). γ is the angular position of journal from negative diretion of X to positive diretion of r. ε is the eentriity of the journal. The radial and tangential fore of bearing fore F i opposite to the journal fore F j, whih are omputed from integrating the oil pressure p(x(φ),z) over the journal fae. i æ L ö Fr R p(, z)os d dz = ò ò 0 0 L Ft = R p(, z)sin d dz ç ò ò çè 0 0 ø F = =-F, (14) where L is the inner width of the FRB. R is the journal radius and φ is the angle for the oil film thikness. The residual mass unbalane of a rotating assembly is usually determined by using the multi-plane balaning mahines. However, with the development of modern tehnology, the balaning preision has ahieved a high level, it is urgent to know how to ontrol the unbalane for small vibration and stable operation in the design proess. It is inevitably that the unbalane existed in the rotation, espeially for the high-speed rotating mahine. These mass unbalane loates at different loations of two impellers with a magnitude of me. As expressed in unbalane fore Eqs. (11), (1) and the governing Eq. (10), it is learly shown that unbalane, F ub, diretly affets the motion of turboharger rotor-bearing system. The motion state will hange with the different loation of unbalane in turbine or ompressor. Therefore, it is neessary to perform suffiient studies to understand the relationship and laws between dynami harateristis and unbalane loation for these small-sized and high-speed automotive turbohargers. 3 FE Modeling for Turboharger System 3.1 Dynami model of FRBs Rotors of the light-weight and high-speed gasoline engine turboharger are supported in FRBs. Compared to j others bearing type, FRBs are heap to produe and the manufature is relative simple. FRB has two oil films, ompared with the traditional single oil film bearings, the main advantages is their improved damping behavior based on the mutual effets of inner and outer oil films. Although the behavior of the FRBs is highly nonlinear, it is desirable to determine the linearized bearing oeffiients in order to perform eigenvalue analysis of turboharger system. The omputation of 8 bearing oeffiients is required for both inner and outer surfaes of the FRB. Aording to the strutural parameters and lubriating onditions, the FRB model was built as shown in Fig.. Fig.. Floating ring bearing Ω j, Ω r Angular veloity of the journal and ring; W Bearing load Note that the two nonlinear bearings for turbine end bearing and ompressor end bearing are onsistent with the same FRB parameters and lubriating onditions. The ring mass is.16 g. The inner and outer lengths are 3.6 mm and 6.15 mm, respetively. The inner and outer diameters are mm and 9.54 mm, respetively. The inner and outer oil film visosities were assumed to be onstant values of p and 9.35 p, with typial 15W 40 supply lubriant, respetively. The ring speed ratio was omputed to be 0.4 aording the frition torque balane of inner and outer oil film. Fig. (b) represents the bearing pressure profile for the turbine bearing at r/min. The inner and outer surfaes of the bearing develop a very different pressure profile. The ross dynami oeffiients are the priniple soure of the ause of sub-synhronous whirl. The FRBs used for the time transient numerial analysis are nonlinear, and the rotor-bearing system is also highly nonlinear. Therefore, it is a very straightforward proedure for the nonlinear time transient analysis by oupling the rotor equation with two Reynolds equations of inner and outer oil films. 3. FE modeling of rotor-bearing system The turboharger is a typial double overhung rotor with a steel turbine and an attahed aluminum ompressor impeller. That is, the turbine and ompressor impellers are outboard of two bearings. The rotor shaft, FRBs, shaft seal, thrust ollar, shaft nut and other parts are inluded in the turboharger. All rotor omponents should be taken into aount in the rotordynami omputation to investigate the rotor vibration response, suh as the frequeny omponents

5 CHINESE JOURNAL OF MECHANICAL ENGINEERING 75 in the waterfall plot, shaft orbit and rotor amplitude of the response vibration in the time domain plot. The ompressor and turbine impeller are generally regarded as rigid disk to model. Due to its omplex struture, the mass of rotating omponents, moment of inertia, and the enter of gravity position an be obtained by using CAE 3-dimensional software to model and alulate, and then add to the rotor-shaft regarded as a disk. Aording to the needs of researh and Saint-Venant priniple, the FEM of rotor made reasonable simplifiation and assumptions, the turbine end omponent of irregular surfae was defined as a ylindrial surfae. Small hanges on the hamfering of rotor shaft were mostly ignored. Aording to the strutural parameters and lubriating onditions, the FEM of the turboharger rotor was built by using the software DyRoBeS, as shown in Fig. 3. nonlinear, it is of onsiderable value to perform a ritial speed analysis of the turboharger. In this analysis, the bearing oeffiients are linearized as mentioned before. So the presented undamped natural frequeny should be onsidered qualitatively rather than quantitatively. By means of a ritial speed analysis, one an determine the relative mode shapes and ritial speed, as shown in Fig. 4. In the proess of rotor finite element modeling, if the error between ritial speed alulated from finite element model and amplitude peak of testing run-down data is within 5%, the rotor and bearing parameters of rotor finite element model are aeptable, otherwise need to hek and revise the parameters appropriately until the alulation result is almost onsistent with the testing data. Fig. 3. Gasoline engine turboharger model The turboharger rotor was modeled with 19 shaft finite elements whih inludes 4 sub-elements. The idential bearings 1 and, at stations 9 and 1, represent the FRBs, respetively. Stations 1 and represent the floating rings as the lumped mass.16 g of single degree of freedom. Stations 5 and 17 represent the enter of gravity of the turbine and ompressor impellers, respetively. Note that the turbine and ompressor impellers are simplified to the tapered struture element without mass, whih the mass and inertia moments are applied to the 5 and 17 stations. The arrow at station 4 represents the unbalane(me) applied to the nose wall of turbine impeller. The irular dot near station 9 represents the gravity enter(c.g.) of the entire system whih is loser to the turbine end bearing. This auses the turbine bearing loads to be a magnitude larger than ompressor end bearing. For the analysis of the different appliations, the bearing modeling methods are different. For linear analysis, the bearing stiffness and damping oeffiients were linearized and imported by seleting the appropriate boundary onditions as mentioned before and the two rings of FRBs were modeled as rigid body. However, for time transient numerial analysis, the Reynolds equation inluding the bearing parameters and lubriating onditions an be embedded into the equations of motion to solve. 3.3 Critial speed analysis Although the FRBs for the turboharger are highly Fig. 4. First four mode shapes of turboharger rotor system

6 76 WANG Longkai, et al: Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings The first four ritial speeds are r/min, 40 4 r/min, r/min, r/min, respetively. Note that the nd mode isn t suseptible to unbalane exitation aused by turbine impeller at r/min. It an be known from Fig. 4(a) Fig. 4(d) that the 1st to nd modes are typial rigid body modes, and the 3rd to 4th modes are typial bending modes. It should be note that the maximum amplitudes our at the ompressor end as shown in the four mode shapes, so the station 19 was hose to be the response measurement point. 4 Effet of Unbalane Loation on Nonlinear Dynami Charateristis for Turboharger The rotordynami behavior of turbohargers has been paid signifiant attention beause of its importane in their healthy operation. For the high-speed and light-weight rotor, and its asymmetri struture aused by different material in turbine, shaft and ompressor impeller, it is inevitably that the unbalane exists in the turbine and impeller end. Considering the ondition of different unbalane loations and the oupling effet of synhronous vibration aused by unbalane fore and self-exited vibration aused by nonlinear oil film fore, thus, it is neessary ondut suffiient studies to determine the nonlinear dynami behaviors of the turboharger. In order to determine the dynami motion of the turboharger in the nonlinear FRBs, a nonlinear time transient numerial analysis must be performed. The time transient analysis was onduted at speeds range from r/min to r/min by using the nonlinear rotor-bearing finite element model under different loation ombinations of unbalane to determine the effets of unbalane loation on dynami harateristis of turboharger supported in nonlinear FRBs. Five solution methods are provided in the time transient analysis: Gear s Method, Runge-Kutta, Wilson-theta, and Newmark-Modified methods. The Newmark-beta method was hosen to be the integration method in this paper, whih is known as the onstant-average-aeleration method. Aording to the pratial struture and unbalane loations of gasoline engine turboharger in engineering, stations 4, 6, 16 and 18 were hose to be the investigated unbalane loations. Note that loations 1 4 represent the unbalane(u=me) applied to the stations 4, 6, 16 and 18 orresponding to the stations as shown in Fig. 3, respetively. Table 1 shows the different applied loations of unbalane applied to the nose and bak wall of eah impeller based on the FE rotor model. Table 1. Four different loations of unbalane Loation Station U/(g mm) Note that 1X frequeny orresponding to the preession speed equals to rotor speed, 0.5X frequeny orresponding to the whirl speed approximately equals to 50% of rotor speed, and 0.1X frequeny orresponding to the whirl speed equals to about 1% of rotor speed 4.1 Nonlinear bifuration phenomena The response spetra intensity plot at station 19 from r/min to r/min for four different applied loations of unbalane is presented in Fig. 5. It an be seen that the response spetral intensity is distint different for the four different unbalane loations. The bifuration phenomena strongly depend on the unbalane loation during the run-up. The start speeds of bifurations from synhronous vibration to sub-synhronous vibration(0.1x) for the loations 1 3 are r/min, r/min and r/min, respetively. The main differene for loation 4 is that bifuration phenomenon does not exist in the onsidered speed range, the rotor performs the pure unbalane osillations(1x) around the equilibrium position. The start speeds of two nonsynhronous omponents(0.1x and 0.5X) are obtained from Fig. 5(a) Fig. 5(), it is useful to give a guide for investigating the rotor motions at the whirl/whip region during the operating speed. The bifuration phenomena are nearly onsistent for the loations 1 and 3, exept the start speeds of non-synhronous frequeny. Most notably, 0.1X and 0.5X frequenies our simultaneously at the speifi rotor speeds for loation, as shown in Fig. 5(b). In this ase, inner and outer oil films may be simultaneously unstable. However, the system is not totally unstable sine the inner and outer oil whirl frequenies are different. 4. Nonlinear response harateristis for different unbalane loations In pratie, it is diffiult to measure the relative displaements between the journal and floating ring of FRB during rotation. Hene, the rotordynami alulation is a useful tool to determine the relative displaements between the journal and floating ring at every rotor speed. If the relative displaements are greater than the limit bearing learane, the bearing will our rub-impat phenomenon. Fig. 6 shows the relative displaements between the journal and floating ring for two bearings at rotor speed of r/min. In order to get more intuitive understanding of the relative displaements between journal and floating ring for four different unbalane loations, the maximum relative displaements for turbine end bearing and ompressor end bearing at every rotor speeds are displayed in Fig. 7 and Fig. 8, respetively. If the relative displaement is positive, the journal moves loser to the floating ring beause the journal displaement is larger than the ring. The urrent thikness of oil film is determined by the bearing learane and relative displaement. When oil thikness is larger than limit oil film thikness, the bearing is fully hydrodynami. The simulation results show that the maximum relative displaement is about mm and mm for the

7 CHINESE JOURNAL OF MECHANICAL ENGINEERING 77 turbine end bearing and ompressor bearing, respetively. It indiates that minimum oil film thikness in the inner bearing learane is about mm with the inner radial learane(threshold) of mm. So no wear will our in the two bearings for four different unbalane loations. Fig. 5. Response spetra intensity plot with an unbalane of 0. g mm applied to different loations Fig. 6. Orbit plot of the relative displaements between the journal and floating ring for loation 1 Fig. 7. Relative displaement between journal and ring at turbine end bearing for four different loations Fig. 8. Relative displaements between journal and ring at ompressor end bearing for four different loations Fig. 9 represents the waterfall plots for the horizontal(x) displaement from rotor speed of r/min to r/min with a given unbalane of 0. g mm for four kinds of unbalane loations, in additional to the onstant gravity fore in negative Y diretion. It shows that 0.1X whirl frequeny(low frequeny self-exited vibration) aused by outer oil film exists when rotor speed is over r/min, r/min and r/min for loations 1 3. The amplitudes of 0.1X frequeny self-exited vibrations inrease rapidly with the rotational speed and dominate the turboharger motion. At higher rotor speed, the 0.1X an still establish the dominane with large amplitude. It may

8 78 WANG Longkai, et al: Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings beome instability system, even leads to wear and failure of turbine or ompressor impeller. Sub-synhronous vibrations may sometimes be disadvantageous in terms of noise generation and auses large vibration. It is learly shown that turboharger may exhibits oil whip when rotor speed exeeds r/min and synhronous vibrations are suppressed for loations 3, as shown in Fig. 9(b) Fig. 9(). What's more, the synhronous vibration disappears when rotor speed exeeds r/min for loation. It is worth noting that the sub-synhronous(0.5x) vibration disappears in the motion when rotor speed over r/min for loations 1 and 4. Fig. 9 Waterfall plots at station 19 for four different applied loations of unbalane with an magnitude of 0. g mm Interestingly, by omparing the waterfall spetra from Fig. 9(a) Fig. 9(d), the results show that the turboharger operate relative well when the unbalane applied to the loations 1 and 4 orresponding to the nose wall of the turbine and the nose wall of ompressor impellers. It also indiates that the unbalane applied to loation 4 is superior to loation 1 for the same magnitude unbalane whih the 0.1X and 0.5X vibrations don t exist in the whole motions from rotor speed of r/min to r/min. As a result, the loation 4 is the relative-optimum applied loation of unbalane. It an be used as referene loation of unbalane to suppress the self-exited vibration and redue the rotor vibration response for the same type of high-speed turbohargers. In order to quantitative investigate the nonlinear rotordynami ompared to the waterfall plot, the time domain analyses are performed at every rotor speed for different loations. The transient peak response value of horizontal(x) displaement at measurement point after running stable for the different applied loations at every speed are alulated and summarized into Fig. 10. The trend of amplitude is nearly onsistent for different loations before r/min, as seen from Fig. 10. However, the amplitude inrease dramatially for loations 3 when rotor speed exeed r/min. For loation 1, the amplitudes derease with the rotor speed before r/min, and then inrease with the rotor speed up to top speed. Interestingly, the amplitudes for loation 4 is relative small ompared to others stations in the onsidered speed range, and an order of magnitude small in the higher speed. The results also show that turboharger operate relatively well when the unbalane applied to the loation 4 orresponding to the nose wall of ompressor impeller. The ondition of loation 4 is the relative optimum applied loation of unbalane. The results are same to the waterfall plots as mention before. Fig. 11 shows the rotor orbits of measurement point at different speeds with an unbalane of 0. g mm applied to the loation 1. The rotor reahes the bounded limit yle due to the good damping effet after running stability, and displaement amplitudes are limited at the rotational speeds. The amplitudes of higher speeds(suh as r/min) are higher than the amplitudes at relative low speed of r/min beause of the large 0.1X frequeny

9 CHINESE JOURNAL OF MECHANICAL ENGINEERING 79 vibration omponent for loation 1. Fig. 10. Transient response for different unbalane loations Fig. 11. Rotor orbits at four different rotor speeds with an unbalane of 0. g mm applied to loation 1 5 Conlusions (1) Under four kinds of applied loations of unbalane, the vibration response harateristis of turboharger are different. From the waterfall plot, the simulation results show that the speed for the appearane of frational frequeny is not idential and the amplitude magnitude is different under the different applied loations of unbalane. Large amplitude of low-frequeny whirl may lead to exessive vibration of turboharger. Speial onsideration should be required at high speed for the different applied loations of unbalane. () The bifuration phenomena our during the startup strongly depend on the applied loations of unbalane. The start speed of bifurations from synhronous vibration to 0.1X frequeny vibration omponent for the loations 1 3 are different. The bifuration phenomena are nearly onsistent for loations 1 and 3, exept the start speeds of nonsynhronous frequenies(0.1x and 0.5X). The main differene for loation 4 is that the bifuration does not exist in the onsidered speed range, the turboharger rotor performs the pure unbalane osillations around the equilibrium position. (3) The response of turboharger rotor-bearing system is losely related to the applied loations of unbalane. The turboharger rotor-frbs system exhibits the best dynami harateristis under the unbalane applied to loation 4. For the loation 4, the turboharger rotor-bearing system operates very well, whih only exists synhronous vibration omponent. The loation 4 is the relative optimum applied loation of unbalane for the four unbalane loations. It an be used as referene loation of unbalane to suppress the self-exited vibration or redue response vibration for the same type of turbohargers. The proposed unbalane loation is an effetive solution to ahieve the small vibration and stable operation. Referenes [1] HUNG N S. Rotordynamis of automotive turbohargers[m]. Berlin: Springer Berlin Heidelberg, 01. [] SCHWEIZER B. Dynamis and stability of turboharger rotors[j]. Arhive of Applied Mehanis, 010, 80(9): [3] WANG Longkai, BIN Guangfu, LI Xuejun, et al. Effets of floating ring bearing manufaturing tolerane learanes on the dynami harateristis for turboharger[j]. Chinese Journal of Mehanial Engineering, 015, 8(3): [4] BOYACI A, LU Daixing, SCHWEIZER B. Stability and bifuration phenomena of Laval/Jeffott rotors in semi-floating ring bearings[j]. Nonlinear Dynamis, 015, 79(): [5] SCHWEIZER B. Total instability of turboharger rotors-physial explanation of the dynami failure of rotors with full-floating ring bearings[j]. Journal of Sound and Vibration, 009, 38(1 ): [6] YING Guanghi, MENG Guang, JING Jianping. Turboharger rotor dynamis with foundation exitation[j]. Arhive of Applied Mehanis, 009, 79(4): [7] NGO V T, XIE Danmei, XIONG Yangheng, et al. Dynami analysis of a rig shafting vibration based on finite element[j]. Frontiers of Mehanial Engineering, 013, 8(3):

10 80 WANG Longkai, et al: Effets of Unbalane Loation on Dynami Charateristis of High-speed Gasoline Engine Turboharger with Floating Ring Bearings [8] JUNG K C, KRUMDIECK S. Rotordynami modelling and analysis of a radial inflow turbine rotor-bearing system[j]. International Journal of Preision Engineering and Manufaturing, 014, 15(11): [9] D LY D, THOUVEREZ F, JÉZÉQUEL L. Unbalane responses of rotor/stator systems with nonlinear bearings by the time finite element method[j]. International Journal of Rotating Mahinery, 004, 10(3): [10] ZHAI L, LUO Y, WANG Z, et al. Failure analysis and optimization of the rotor system in a diesel turboharger for rotor speed-up test[j]. Advanes in Mehanial Engineering, 014, 6: 1 8. [11] GUNTER E J, CHEN W J. Dynami analysis of a turboharger in floating bushing bearings[c]//proeedings of the 3rd International Symposium on Stability Control of Rotating Mahinery(ISCORMA), Cleveland, Ohio, USA, September 19 3, 005. [1] TIAN L, WANG W J, PENG Z J. Dynami behaviours of a full floating ring bearing supported turboharger rotor with engine exitation[j]. Journal of Sound and Vibration, 011, 330(0): [13] MA Hui, LI Hui, NIU Heqiang, et al. Numerial and experimental analysis of the first-and seond-mode instability in a rotor-bearing system[j]. Arhive of Applied Mehanis, 014, 84(4): [14] LI Chaofeng, ZHOU Shifa, JIANG Shijie, et al. Investigation on the stability of periodi motions of a flexible rotor-bearing system with two unbalaned disks[j]. Journal of Mehanial Siene and Tehnology, 014, 8(7): [15] MA Hui, LI Hui, ZHAO Xueyan, et al. Effets of eentri phase differene between two diss on oil-film instability in a rotor-bearing system[j]. Mehanial Systems and Signal Proessing, 013, 41(1 ): [16] ALSAEED A A. A study of methods for improving the dynami stability of high-speed turbohargers[d]. Virginia: Virginia Polytehni Institute and State University, 010. [17] TIAN L. Investigation into nonlinear dynamis of rotor-floating ring bearing systems in automotive turbohargers[d]. Brighton: University of Sussex, 01. [18] STERLING, JOHN A. Influene of Indued Unbalane on Subsynhronous Vibrations of an Automotive Turboharger[D]. Blaksburg: Virginia Polytehni Institute and State University, 009. [19] KIRK R G, STERLING J, SAWYERS W, et al. Influene of turboharger imbalane on subsynhronous vibration amplitude[c]//proeedings of the ASME/STLE International Joint Tribology Conferene(IJTC), Memphis, TN, USA, Otober 19 1, 009. [0] TIAN L, WANG W J, PENG Z J. Nonlinear effets of unbalane in the rotor-floating ring bearing system of turbohargers[j]. Mehanial Systems and Signal Proessing, 013, 34(1 ): [1] CHEN W J, GUNTER E J. Introdution to dynamis of rotor-bearing systems[m]. Vitoria: Trafford Publishing, 005. [] HUNG N S. Nonlinear rotordynami omputations of automotive turbohargers using rotating floating ring bearings at high rotor speeds[c]//10th International Conferene On Vibrations In Rotating Mahines, Berlin, Germany, February 5 7, 013. Biographial notes WANG Longkai, male, born in 1990, is urrently a master andidate at Health Maintenane for Mehanial Equipment Key Lab of Hunan Provine, Hunan University of Siene and Tehnology, China. His researh interests inlude rotordynamis, automotive turbohargers and oil film bearing. Tel: ; Longkai.Heat@hotmail.om BIN Guangfu, male, born in 1981, is urrently an assoiate professor at Health Maintenane for Mehanial Equipment Key Lab of Hunan Provine, Hunan University of Siene and Tehnology, China. He ated as an aademi visitor in University of Ottawa from 008 to 009. He reeived his PhD degree from Beijing University of Chemial Tehnology, China, in 013. His researh interests inlude rotating mahinery dynamis and modal analysis, shafting dynami balane, mehanial dynami testing. Tel: ; abin81105@163.om LI Xuejun, male, born in 1969, is urrently a professor at Health Maintenane for Mehanial Equipment Key Lab of Hunan Provine, Hunan University of Siene and Tehnology, China. He reeived his PhD degree from Central South University, China, in 003. He reeived post-dotor degree from Tsinghua University, China, in 009. His main researh interests inlude mehanial dynamis and fault diagnosis, signal analysis and proessing. Tel: ; hnkjdxlxj@163.om LIU Dingqu, male, born in 1990, is urrently a master andidate at Health Maintenane for Mehanial Equipment Key Lab of Hunan Provine, Hunan University of Siene and Tehnology, China. His researh interests inlude signal analysis and proessing, fault diagnosis and rotordynamis. Tel: ; @qq.om