DYNAMIC CHARACTERISATION OF A MULTI STAGE AXIAL COMPRESSOR TEST RIG ROTOR SYSTEM

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1 DYNAMIC CHARACTERISATION OF A MULTI STAGE AXIAL COMPRESSOR TEST RIG ROTOR SYSTEM Abstract Ramakrishna N. Bhat 1, N. C. Mahendrababu, Ajith Kumar 1- (Engg.) Student, -Professor and Centre Manager (MD), Centre for Rotating Machinery Design M. S. Ramaiah School of Advanced Studies, Bangalore - Scientist, Gas Turbine Research Establishment, Bangalore Dynamic properties of support structures play major role in controlling the vibration amplitudes of test rigs involved in the development of gas turbine engines rotors. These rotors often operate in the supercritical speed regimes, which necessitates the prediction of their dynamic characteristics more accurately. In the present study, numerical simulation of dynamic characteristics of a multi-stage compressor test rig rotor supported on rolling element bearings and a Squeeze Film Damper (SFD) has been carried out. A methodology using numerical methods and analytical relations, was developed to evaluate the stiffness of the bearing support structur. Bearing support structure stiffness values were evaluated using finite element method,, employing the developed methodology. Finite element analysis of rotordynamics was carried out, taking into account the non-linear properties of both rolling element bearings and SFD. A sensitivity analysis was carried out on SFD parameters to understand the behaviour of the system under different geometry and operating conditions. Comparison of results obtained for the present rotor system showed that the non-linearities in the SFD play major role in the dynamics of the system, compared to the non-linearity in the bearings. Sensitivity studies carried out for the range of SFD parameters revealed that the SFD clearance, viscosity and unbalance are important parameters that determine the maximum amplitude of response and also force transmitted to bearings, whereas the supply pressure was one of the least affecting parameters. Key Words: Gas Turbine Engines Rotors, Squeeze Film Damper, Oil Viscosity, Non-linear,, Finite Element Method Nomenclature C Squeeze film radial clearance (mm) D Ball diameter (mm) E Young s modulus (MPa) e Eccentricity (mm) F Force (N) K Stiffness (N/m) L Land length (mm) l Roller length (mm) M Mass (kg) nz No. of balls or rollers Ps Supply pressure (kpa) r1, r, r Radius (mm) μ Poisons ratio δ Deflection (micron) ε Eccentricity ratio (e/c) 1. INTRODUCTION Engineering components concerned with the subject of rotor dynamics are rotors in machines, especially of turbines, generators, motors, compressors, blowers and the like. At its most basic level rotordynamics is concerned with one or more rotors supported by bearings. Major objectives of rotordynamic studies are to predict critical speeds and corresponding mode shapes, unbalance response of the system and determine design changes for critical speed placements. In the present study, dynamic characterisation of an axial compressor test rig rotor was carried out. The test rig rotor is an aero engine compressor rotor, having six stages. The rotor blades are attached to the disc as shown in Figure 1. The entire rotor is supported by two bearings. The front bearing is a ball bearing with squeeze film damper arrangement, whereas the rear bearing is roller bearing. Both ball and roller bearings are housed in the support casings. The rotor is driven by a gas turbine type prime mover through gearbox and flexible coupling. A rotor needs to be supported on a stationary structure and this is done through support bearings. They appear to be rigid but in several cases they are flexible enough to interact significantly with the rotor dynamics. Their stiffness characteristics is also a nonlinear function of speed. Rolling element bearings are most commonly employed in rotating machinery. Rolling element bearings have very little in built damping, necessitating use of an external damper such as Squeeze Film Damper (SFD). The rolling element bearings and SFD have non-linear characteristics, which must be accounted for in the rotordynamic analysis. Most of the analysis of rotor bearing systems carried out on a highly linearised model of the SFD based on the simplified analytical approach derived from short bearing model. Support structure stiffness plays important role in the dynamics of the rotor bearing system. J.-J. Sinou et al. [1], studied numerically and experimentally, the effects of the bearing support flexibility on the rotordynamics and the first forward and backward critical speeds. Anandvel et al. [], studied experimentally and numerically using FEM techniques, the stiffness of squirrel cage bearing used in the aero engines. Good correlation between the analytical and experimental results was obtained. Schneider [], carried out stiffness analysis of the front and rear casings of an aero engine with the aid of a three dimensional finite element code. A known vertical load was applied at the bearing in the form of sinusoidally SASTECH 41 Volume 9, Issue 1, April 010

2 distributed load from which the overall spring rate was calculated. One of the most direct demonstrations of the ability of an uncentralised squeeze film to control the orbit amplitude of an unbalanced shaft was made by Kossa and Cookson [4]. It was seen that for the same level of vibration amplitude, the squeeze film assembly can withstand an increase in unbalance of some 5 times. Rezvani and Hahn [5], have obtained good agreement between the experimentally measured and theoretically predicted unbalance behaviour of flexible rotor bearing systems with an uncentralised squeeze film damper. Current analysis of rotor bearing systems is carried out on a highly linearised model of SFD based on the simplified analytical approach derived from short bearing model. Zeldan et al. [6] have studied the rotor system using non-linear properties of SFD. Tang and Han [7] have carried out the experiments on model rotor supported on flexible bearing housing with squirrel cage at one end and a rigid support at the other end. The vibration amplitudes of the flexible supports were decreased by decreasing the support stiffness, whereas the stress level increased by decreasing the support stiffness. They concluded that there is an optimum value of support stiffness for which the damping and the stress limits are acceptable. Fleming et al. [8] have carried out rotordynamic analysis using the non-linear properties of the ball bearing. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Zeldan et al. [6] have studied the response characteristics of simple rotor system supported on ball bearing and SFD by changing the SFD parameters. They reported that if damping is too large, the SFD acts as a rigid constraint and transmits large force to the bearing structure. If damping is too small, then the damper is ineffective and likely to permit large amplitude of motions with possible subsynchronous frequencies. While most of the papers reviewed by the authors have accounted for either the non-linear behaviour of squeeze film dampers or rolling element bearings, there are no published literature available accounting the nonlinear behaviour of both. Even the non-linearities considered were for a simple experimental rotor-bearing system. There is very little literature available for the rotordynamic analysis of complex rotor-bearing system like a multi-stage axial compressor rotor supported on Fig. 1 Multistage rotor system rolling element bearing and SFD, considering the effect of both the non-linearities. Lot of experimental data is available in literature regarding performance of SFD with operational and geometric parameters like viscocity, clearance etc. But, numerical modelling of SFD was not cited in any of the literature reviewed by the author. In the present work, dynamic characterisation of a multi-stage axial compressor test rig rotor was carried out by considering the non-linear effects of both the rolling element bearing and SFD. Numerical modelling of uncentralised SFD was carried out to study the effects of SFD parameters on unbalance response of the system.. NON-LINEARITIES IN BEARINGS The force deflection characteristics of rolling element bearings are very complex as they depend on the geometry and number of rolling elements in a bearing, material and lubricant properties. For the purpose of analysis, a single ball in a radial ball bearing, as shown in Figure, is considered. Fig. Deformation of the single ball [9] It is assumed that the races are relatively rigid compared to the balls. The deformation δ under the force F is determined by Hertzian theory as [9],.5 (1 ) r r 1/ 1 [ F E r1 r For standard ball bearing, of material with Young s modulus of.06*10 5 MPa and Poisson s ratio of 0., the deflection δ is a function of the geometry of the bearing. The force dependent non-linear equation for stiffness of rolling element bearings is as given below [10]. ] SASTECH 4 Volume 9, Issue 1, April 010

3 / z 1/ Ball Bearing stiffness: k 1.89 n d F 0.8 1/10 Roller Bearing Stiffness: k 4 nz l F The stiffness given by the above equation show that the stiffness of rolling element bearings is highly non-linear. The stiffness is zero when there is no force applied on the bearing and rapidly increases as the force is initially increased. For large loads on the bearing, the stiffness tends to become constant. In the above equations, ideal condition, which assumes no radial play between the inner and outer races, was considered. For a bearing with play, the displacements are larger and therefore the stiffness is lower [10].. NON-LINEARITIES IN SFD Squeeze film dampers derive their action from a lubricant being squeezed in the annular space between a non-rotating journal and bearing housing. The analysis method for the dynamic characteristics of the squeezed film is based on the theory of hydrodynamic lubrication [6]. Fig. SFD Nomenclature [11] The basic lubrication equation governing the oil film is the Reynolds equation [11]. For a short bearing approximation, the pressure field of the squeezed oil film is described as.. L cos sin p (, x) 6 x R 1 cos 0.9 1/ 1 1 p s x 4 The radial and the transverse forces emanating from the SFD are obtained by integrating the pressure distribution along and normal to the line of centers of the journal and bearing. For a special case where P s is zero, the forces for a cavitated π film are given by, by RL c 1 F r F RL c / 1 The stiffness and damping co-efficient are given k c RL C 1 RL C / 1 The forces and coefficients are non-linear and functions of whirl speed and eccentricity ratio. In rotor system dynamic analysis, SFD is regarded as highly non-linear, providing forces obtained from the relationships based on the instantaneous journal centre eccentricity [6]. Currently, the analyses of rotor bearing systems are carried out on a highly linearised model of the SFD based on the simplified analytical approach derived from short bearing model (π film cavitation). 4. ROTORDYNAMIC ANALYSIS The rotordynamic analysis of the compressor test rig rotor was carried out using finite element method using the analysis package SAMCEF Rotor. At the front side, rotor is supported on ball bearing with uncentralised SFD whereas at the rear; the rotor is supported on roller bearing. These bearings are supported and held in position by front and rear casings. Numerical evaluation of stiffness of support structures was carried out using Ansys. Evaluation of non-linear stiffness of bearing elements was carried out using analytical relations. Simulation of non-linear stiffness and damping of SFD was carried out using SAMCEF Rotor. 4.1 Evaluation of Support Structure Stiffness For the evaluation of the stiffnesses of bearing housing and casings D finite element models were used. overall stiffness was calculated using a known vertical load applied at the bearing location in the form of sinusoidally distributed load [,]. The overall stiffness was then calculated as the ratio of total vertical load to the average vertical deflection at the point of loading. Effective stiffness was then taken as stiffness of spring in series [1]. Table 1 gives summary of stiffness calculated for the support structure. Table 1. Summary of effective stiffness calculations Bearing Location Housing Stiffness (MN/m) Casing Stiffness (MN/m) Equivalent Stiffness (MN/m) Front Rear Rotordynamic Model The rotating assembly was modelled using axi-symmetric finite elements called Fourier multiharmonic elements in SAMCEF Rotor (Figure 4). Rotor blades, nuts, gears etc. were simulated as lumped masses. Bolted and spline joints have been modelled as rigid body by merging the nodes at the interface [1]. Appropriate material properties were taken for each component. Bearing support structures were simulated as isotropic spring elements with stiffness values evaluated as described in the previous section. The descretised axi-symmetric rotor model is shown in the Figure 4. Rotor blade aerofoils, fasteners and bearing inner races could not be modelled and hence they were lumped at appropriate nodes. A bush element having non-linear properties was created in SAMCEF at the front and rear bearing location. The following relations between force and displacement for the bush element was used. SASTECH 4 Volume 9, Issue 1, April 010

4 For front ball bearing, F 1/ k 4.*10 * F u 1.5 Hence, F 764* u *10 and for rear roller bearing F k 50.6*10 * F u Hence, F 9* u /10 *10 The force term in the above equation is due to the residual unbalance in the rotor, which is calculated as, F imb me For a given residual unbalance, the imbalance force is a function of rotational speed alone. Hence stiffness of bearing varies with the speed. The rotor is composed of mainly three different materials. The material properties required for the analysis is given in the Table. Material Table. Material properties Young s Modulus (MPa) Poisson s ratio Fig. 4 Descretised model of the rotor Density (kg/m ) Ti E Inco E Steel 00 E Numerical Simulation of SFD SAMCEF has SFD element to simulate the squeeze film damper. This element is formulated using short bearing approximation and π film theory. This element allows introducing the dynamic forces associated with a squeeze-film damper. The element is defined by two nodes with six degrees of freedom per node. SFD element requires input as annulus description (diameter, length, and clearance), fluid properties (viscosity, saturation pressure) and boundary conditions on pressure. Different typical configurations like SFD with or without end seals, with pressure input, and with end seal leakage are possible. Values input for the SFD parameters are given in Table Critical Speed Analysis Critical speed analysis was carried out using the above model and the input parameters. To determine the critical speeds, a Campbell diagram was drawn to find the intersection points of the whirl speeds with the one per revolution excitation (1X line). 4.5 Unbalance Response Analysis Rotor unbalance is considered as one of the major source of excitation, causing amplitudes of synchronous vibration to reach high value while passing through critical speeds. Unbalance also transmits rotational forces to rotor bearings and to the supporting structure. A known unbalance (1000 gm-mm in this case) was put at the stage 1 disc location and the unbalance response was plotted for the case without SFD and also with SFD. Table. SFD element parameters SFD Parameters Values Inlet Pressure (bar) Oil Viscosity (mm /s) 5 E-9 Diameter (mm) 59 Length (mm) 41 Clearance (mm) 00 E- 4.6 SFD Parametric Study The dynamic response of the system with SFD may be markedly different from that without SFD. Also the severity of response curves at the critical speeds depends upon the SFD parameters. Hence a sensitivity study was carried out on un-centralised SFD to understand the effect of major SFD parameters on the response and also on the force transmitted to the bearing. Fig 5 Campbell Diagram for non-linear bearing properties (without SFD) 5. RESULTS AND DISCUSSIONS Figure 5, shows the Campbell diagram without SFD but including the non-linear bearing properties.1x line intersects the first forward (IF) frequency line at 9150 rpm. This is called the first critical speed. At around 1100 rpm, 1X line intersects the second forward frequency line (II F). This is called the second SASTECH 44 Volume 9, Issue 1, April 010

5 critical speed. Hence there were two critical speeds coming within the operating speed. Mode shapes corresponding to these critical speeds are given in the Figure 6 and Figure 7. There is significant bending in the shaft corresponding to first critical. The second mode shape is essentially drive shaft bending mode. From the mode shapes it is evident that the both the bearings participate in the first critical. Second mode shape is more sensitive to the rear bearing stiffness. Comparison of Campbell diagram for linear (Figure 9) and non-linear case (Figure 5) showed that the difference in the critical speeds were 0.4 % respectively for the first and second critical speed. The non-linearities in the bearings were evident in the Campbell diagram till certain speed. Up to a speed of around 4000 rpm, for the given unbalance, the stiffness was found to vary non-linearly. After that the variation was linear. In the speed regime where critical speeds occur, the stiffness was almost linear. Hence, not much of a difference was observed in the critical speed values. Fig. 6 Mode shape at 9150 rpm Fig. 7 Mode shape at 1100 rpm The response at both the bearing location with SFD in position is shown in Figure 8. The shape of the response curve is non-linear as SFD introduces more non-linearities to the system. No peak is observed at all corresponding to the first critical speed of 9150 rpm. Response peaks were observed at rpm at both the bearing locations. The maximum amplitude observed was about 0.05mm at speed of rpm. Introduction of SFD in the analysis adds one more response peak at 160 rpm, which was not evident from the Campbell diagram. Fig. 9 Campbell Diagram using linear bearing properties Figure 10 and Figure 11 show the response curves drawn with linear and non-linear properties. For comparison purposes, SFD was not put in both the cases. Two peaks were observed in both the cases related to first and second critical speeds. Compared to linear case, the response amplitudes were markedly on the higher side for the non-linear case. These results were in line with the observations available in the literature [14]. 5. Comparison of Analysis Results with SFD and without SFD Response of the rotor system at the bearing location with SFD and without SFD was compared. Response curves were plotted for the case with SFD (Figure 8) and without SFD (Figure 11). Fig. 8 Response with non-linearities and with SFD 5.1 Comparison of Linear and Non-linear Bearing Stiffness Results Rotordynamic analysis of the test rig rotor was carried out in the previous section by considering the effect of non-linearities arising out of non-linear forces in bearing and SFD. For the purpose of comparison, analysis was carried out with linear bearing parameters also. In both the cases, SFD was not present. The Campbell diagram for the linear case is shown in Figure 9. The first critical speed was observed at 910 rpm and the second at around 1150 rpm. Fig. 10 Response with linear properties Without SFD, there were two peaks, corresponding to first and second critical speeds observed in the Campbell diagram, were observed in the response SASTECH 45 Volume 9, Issue 1, April 010

6 curves. Maximum amplitude observed was 0.09 mm at the front bearing location for the first critical speed, whereas maximum amplitude of 0.08 mm was observed at the rear bearing location for the second critical speed. micron, a peak appeared at 80 rpm. For other clearance values, there were no peaks at this speed. Hence, a higher clearance value at this speed is beneficial. The speed for the peak response was different for different clearances at the second critical speed. The peak speeds shifted to lower speeds as the clearance values were increased. At this speed, less clearance is preferred. The reaction forces at the bearing increased with the decrease in the clearance at all the speeds. Hence, a suitable clearance value must be selected for which both the response and the bearing reaction forces are acceptable. Fig. 11 Response with non-linearities and without SFD The shape of the response curve with SFD was different as SFD introduced more non-linearities to the system. There was no peak observed at all corresponding to the first critical speed of 9150 rpm. Response peaks were observed at rpm at both the bearing locations. The maximum amplitude observed was about 0.05 mm corresponding to a speed of rpm. Introduction of SFD in the analysis added one more response peak at 160 rpm, which was not observed in the Campbell diagram. This response peak was also not observed in the case of rotor without SFD. The maximum amplitude of response also decreased due to the addition of SFD. 5. SFD Performance Variation with Clearance In order to understand the effect of annulus clearance on the response of the rotor bearing system, analyses were carried out for different values of clearances. A known unbalance of 1000 gm-mm was introduced at the stage 1 disc location. Analyses were carried out for the clearance ranging from 100 micron to 400 micron in steps of 50 micron, keeping the other parameters like viscocity, pressure and type of SFD same as in Table. Fig. 1 Response variation with oil viscosity It is reported that if the orbit amplitudes are greater than 0.4 times the squeeze film clearance then the orbit becomes unstable resulting in very large amplitudes [15]. But for the range of clearance values analysed here, no such phenomenon was noticed. It was reported that within the range of clearances, where the damper gives better damping effects, the transmissibility is large for smaller clearances [16]. These findings are in line with the results reported here. 5.4 SFD Performance Variation with Oil Viscosity Analyses were carried out for different values of viscosities ranging from E-9 mm /s to 0E-9 mm /s. A known unbalance of 1000 gm-mm was introduced at the stage 1 disc location. Analyses were carried out keeping other parameters like clearance, pressure and type of SFD same as in Table. Fig. 1 Response variation with SFD clearance Figure 15 shows response variation with SFD clearance at front bearing. For a clearance of 100 Fig. 14 Bearing reaction force variation with oil viscosity SASTECH 46 Volume 9, Issue 1, April 010

7 Figure 1 shows response variation with oil viscocity. The response peaks were found at the second critical and beyond. It was observed that the high viscocity was better from the response point of view. Bearing reactions were computed for the same oil viscocity values (Figure 14). The reaction forces at the bearing increased with the increase in the oil viscocity, for all speeds. These findings are in line with the results available in the literature [17]. Fig. 15 Response variation with unbalance 5.5 SFD Performance variation with unbalance To know the effectiveness of SFD during the normal unbalance and at high unbalance that may happen during the possible blade off event, analyses were carried out for different values of unbalances ranging from 500 gm-mm to 5000 gm-mm. As shown in the Figure 15, the response and bearing reaction forces increased continuously with increase in the unbalance levels. Even at the high unbalance levels of 5000 gm-mm, the response was found to have the maximum value of 0.1 mm. This shows the capability of SFD in successfully containing the amplitude of vibration, even for the case of partial blade off condition. Fig. 16 Response variation with oil supply pressure 5.6 SFD Performance Variation with Supply Pressure Oil supply pressure to the SFD is one of the operational parameter affecting the damping capacity of the SFD. Analyses were carried out for different values of pressures ranging from 100 kpa to 50 kpa. The response curves are plotted in Figure 16. A known unbalance of 1000 gm-mm was introduced at the stage 1 disc location. Analyses were carried out keeping other parameters same as in Table. For the range of pressures tested, no significant variation was found either in the response curves and or in the bearing reaction force. 6. CONCLUSION In the present work, dynamic characterisation of the multistage compressor rig rotor was carried out using the stiffness properties derived from the FE analysis. Non-linear effect of both the rolling element bearing and SFD were considered in the analysis. A parametric study was also conducted to understand the effects of operational and geometric parameters on the response of the system for the uncentralised SFD configuration. Based on the results obtained in the present work, following conclusions can be drawn. Use of linear or non-linear model for bearings does not affect the critical speed. The difference noticed was of the order of 1.7% and 0.4 % respectively for the first and second critical speed. However, the response amplitudes for non-linear case was on the higher side compared to linear case. The effect of non-linearities in the uncentralised SFD was found to be much stronger on the results than that of the bearing non-linearities. There were a marked differences in the response curves between the rotor systems with and without SFD. Smaller clearance was found to be better from the response point view. But the bearing reaction force was more for xmaller clearance. High viscocity oil was found to be better from the response point of view. But, it was found to increase the reaction forces at the bearing at all speeds. The response and the bearing reaction forces increased continuously with increase in the unbalance levels. The supply pressure does not significantly alter the response or bearing reaction forces 7. REFERENCES [1] Sinou J.J, Villa. C., F. Thouverez, Experimental and Numerical Investigations of a Flexible Rotor on Flexible Bearing Supports, International Journal of Rotating Machinery, pp , 005. [] Anandvel.K, S.K.Patel, N.Nagaraj, K.Ramachandra, Stiffness evaluation of Aero Engine Squirrel cage bearing, Proceedings of the fourth National Conference on Air Breathing Engines NCABE [] Schneider.M.H. Thermal expansion accommodation in a jet engine frame, ASME Journal of Engineering for Power, Vol 10, pp ,1981. [4] Kossa S.S, Cookson R.A, The Vibration Isolating Properties of Uncentralised Squeeze Film Damper Bearings Supporting a Flexible Rotor, Proceedings of A.S.M.E. Gas Turbine Conference Houston Texas, SASTECH 47 Volume 9, Issue 1, April 010

8 [5] Rezvani M. A. and Hahn E. J., An experimental evaluation of squeeze film dampers without centralizing springs, Tribology International Vol. 9, pp , [6] Zeldan Foud Y, Andres Louis San, Vance John M, Design and Application of Squeeze film dampers in rotating machinery, Proccedings of the 5th Turbomachinery symposium, [7] Tang Yan Li, Han Li Qi, Experiments on the vibration characteristics of a rotor with flexible damped support, ASME Journal of Engineering for Power, Vol. 10, pp ,1981. [8] Fleming David, Jerzy T. Sawicki,J.V. Poplawski, Unbalance Response Prediction for Accelerating Rotors With Load-Dependent Nonlinear Bearing Stiffness NASA/TM 1801,005. [9] Rao.J.S, Vibratory Condition Monitoring of Machines, The Vibration Institute of India,1998. [10] Dogdag Mourad, N. E. Totouche, M.Djaoui, Ouli Mohammed, The calculation of ball bearing nonlinear stiffness- Theorical and experimental study with comparisons, Journal of Engineering and applied sciences, (11), pp 87-88, 008. [11] Fulei Chu, Roy Holmes, The damping capacity of the squeeze film damper in suppressing vibration of a rotating assembly, Tribology International, Vol, pp 81-97, 000. [1] L.San Andres, O.De Santiago, Imbalance response of Rotor supported on flexural pivot tilting pad journal bearings in series with integral squeeze film dampers, ASME Journal of Engineering for Gas Turbine and Power, Vol. 15, pp , 00. [1] Iqbal Momin, Ajit Kumar, A.V.Balasankaran, N.Nanjudarao, Rotordynamic analysis of power turbine assembly of Kaveri derivative gas turbine engine, Proceedings of the fourth National Conference on Air Breathing Engines, National Conference on Air Breathing Engines, 006. [14] Lee Dong Soo and Choi Dong- Hoon (1997), A dynamic analysis of a flexible rotor in ball bearings with nonlinear stiffness characteristics, International Journal of Rotating Machinery, Vol., No., pp. 7-80, [15] White D.C. The Dynamics of a Rigid Rotor Supported on Squeeze Film Bearings. Vibration in Rotating Systems Conference, pp. 1-9, 197. [16] Yan Li Tang, Li Qi Han, Experiments on the vibration characteristics of a rotor with flexible damped support, ASME Journal of Engineering for Power, Vol. 10, pp ,1981. [17] Bonneau Oliver, Frene Jean,Non-linear behaviour of a flexible shaft partly supported by a squeeze film damper, Journal of Wear, vol 06, pp 44-50, SASTECH 48 Volume 9, Issue 1, April 010

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