A Magneto-rheological Fluid Squeeze Film Damper for Rotor Vibration Control

A Magneto-rheological Fluid Squeeze Film Damper for Rotor Vibration Control Changsheng Zhu Department of Electrical Engineering, Zhejiang University Hangzhou, 310027, Zhejiang, P. R. of China David A. Robb David J. Ewins Centre of Vibration Engineering, Mechanical Engineering Department Imperial College of Science, Technology and Medicine, London SW7 2BX, UK ABSTRACT: Using the special characteristic of magneto-rheological (MR) fluid with a rapid, reversible and dramatic change in its rheological properties, particularly its apparent viscosity, by application of an external magnetic field, a novel controllable magneto-rheological fluid squeeze film damper(sfd) is developed in this paper. The controllability of the MR fluid SFD on the dynamic characteristics of a rotor system and the effectiveness of the MR fluid SFD for attenuating rotor vibration are experimentally studied in a two-disk flexible rotor. It is shown that not only can the dynamical characteristics of the MR fluid SFD be controlled by a simple external magnetic field, but also the magnetic field required to change dramatically the dynamic behaviour of the MR fluid SFD is not high and can be easily produced by a low voltage electromagnetic coil, and that the MR fluid SFD is very effective in controlling and attenuating the rotor system vibration. 1 INTRODUCTION Squeeze film damper (SFD) is one of the most effective supports for adding external damping to rotor systems of high-speed aero-engines. This is because of its relative constructional simplicity and effectiveness in attenuating vibration amplitudes of the rotor system and in reducing transmitted forces through the bearing in the properly designed case. However, some undesired operational states characterised by higher rotor vibrations and transmitted forces possibly occur in the rotor system supported on the SFD due to high non-linearity of the oil film force generated by the SFD. Besides, the behaviour of the conventional SFD cannot be easily controlled on-line to meet different dynamic requirements of the rotor system in different conditions, especially when the rotor system passes through several critical speeds. Therefore, the effectiveness of the conventional SFD is greatly limited in this case. It seems natural to develop controllable SFDs based on the conventional SFD. Electro-rheological (ER) and magneto-rheological (MR) fluids are smart fluids whose rheological property, especially apparent viscosity, can be dramatically and reversibly varied by application of an external electrical or magnetic field in a very short time. Such special characteristics of the ER/MR fluid provide a good interface between a mechanical device and an electrical control system, which can be used to make the dynamic characteristics of traditional fluid dampers controllable. Nikolajsen and Hoque [1] first proposed a multi-disk ER fluid damper operating in shear mode and shown the possibility to control the vibration of the rotor system by using the multi-disk ER fluid damper, then Vance and Ying [2] studied the dynamics of the rotor system supported on the multi-disk ER fluid damper on the basis of Nikolajsen and Hoque s test. Morishita and Mitsui [3] presented an ER fluid SFD based on squeeze film-operating mode which has a more simple structure than the disk-type ER damper and showed that by changing the electric field strength, the ER fluid SFD can effectively attenuate the vibration of a rotor system for a wide range of rotational speeds. On leave from Department of Mechanical Engineering, Imperial College, London, SW7 2BX, UK, e-mail: cszhu@hotmail.com 516

However, for the ER fluid dampers, a 2-3 kvolts is applied to the surfaces between fixed and moving components of the dampers, if these components with high-voltage touch or the electrical insulation is not perfect, there is an arcing which would greatly reduce the reliability of the dampers, so the ER fluid SFD is seemingly very difficult to be used directly in real rotating machinery. In comparison with the properties of the ER fluid, the MR fluids inherently have higher yield strength, therefore are capable of generating greater dynamic force levels than ER fluids. Furthermore, the MR fluids are activated by an external magnetic field, which can be easily produced by a simple, low-voltage electromagnetic coil, which avoids the arcing occurring in the ER fluid SFD. However, no paper published has dealt with the application of the MR fluids in the fluid journal bearings and SFDs for rotating machinery. In order to improve the controllability and effectiveness of the conventional SFD, a novel controllable MR fluid SFD was developed and a rotor test rig with the MR fluid SFD was built in order to demonstrate the controllability of the MR fluid SFD on the dynamic characteristics of a rotor system and the effectiveness of the MR fluid SFD in controlling and attenuating rotor vibrations. In this paper, the authors first describe the concept and structure of the MR fluid SFD and of the rotor test rig. The controllability and the effectiveness of the MR fluid SFD in the rotating state are investigated experimentally in a two-disk flexible rotor. Finally the existing problems in the MR fluid squeeze film damper and theoretical model of the MR fluid SFD are discussed. 2 STRUCTURE OF MR FLUID SFD AND ROTOR SYSTEM The basic structure of the controllable MR fluid SFD under study is shown in Fig. 1. It is very similar to that of the conventional SFD, but includes a coil wound circumferentially in an additional journal rigidly mounted on the outer race of the ball bearing. The annulus between the outside diameter of the additional journal and the inside diameter of the damper housing are filled with the MR fluid. There is no seal element in the two sides of the MR fluid SFD. The MR fluid is supplied to a central circumferential groove in the journal through a hole, which separates the damper into two parts. The MR fluid flowing out of the damper gathered in a reservoir and was circulated into the MR fluid tank placed about 1 m above the damper after mixing in the reservoir in order to reduce the sediment of the magnetic particle in the MR fluid and ensure that the MR fluid remains the same volume fraction of the magnetic particle suspension. This is very important in the test because changes in the volume fraction are likely to affect the yield stress of the MR fluid and the repeat of the test results. Damping housing Oil film Journal Ball bearing Shaft Coil Magnetic path Figure 1. Cross-section of MR fluid SFD Figure 2 Rotor test rig with a MR fluid SFD The first two flexible critical speeds of the rotor system were 24.25 Hz (1455 rpm) and 43.125 Hz (2588 rpm), respectively. The first rigid critical speed of the rotor system was 32.25 Hz (1935 rpm). Note when the radial clearance of the SFD is filled with fluid, the flexible critical speeds will slightly increase. For the purpose of investigation unbalance response of the rotor-mr fluid SFD system, the rotor was balanced and an additional unbalance mass was then attached to the disks in order to obtain the rotor imbalance required. The measurement and control systems are shown in Fig. 3. The measurement system shown in the dotted lines was based on the HP-VXI system with a maximum of 16 data channels. The control system shown in the solid lines was based on the d-space system with a maximum of 4 output channels. Only two of them were used in these tests, one was for controlling the acceleration rate of the motor operation, the other for controlling the DC power to the coil. The vibrations of the rotor system in both horizontal and vertical directions at the journal and disk positions were measured by three pairs of eddy current transducers. The signals were A/D converted and recorded on a computer hard disk, then processed to obtain the vibration amplitudes and the motion orbits of 517

(a). 1600 rpm Figure 3. Measurement and control systems rotor system. In addition, a multi-channel oscilloscope was connected so that the signals could be viewed online. The DC power supply for the magnetic coil was a programmable DC voltage power (HP 4553 type) with maximum output voltage 60V and maximum output current 2.5A. The output voltage could be easily controlled by computer according to the requirement of control strategies. The response time for the DC power system to reach a maximum voltage of 50V was less than 0.03 second. All measurement and control could be automatically done when the acceleration rate of rotor run-up or run-down was given. 3 EXPERIMENTAL RESULTS AND ANALYSES The main purposes of the rotating unbalance test of the two-disk rotor-mr fluid SFD system are to answer three problems: are the dynamic characteristics of the rotor system mounted on the MR fluid SFD controllable? If yes, how is fast of the response of rotor system to the external voltage? and the effectiveness of the MR fluid SFD for attenuating and controlling the rotor vibration? 3.1 The controllability of the MR fluid SFD on the dynamic characteristics of rotor system First, for a given steady rotational speed and rotor imbalance, the whirl orbits of the rotor system at the disks and journal positions were measured for different applied voltages in order to verify the controllability of the MR fluid SFD on the dynamic characteristics of the rotor system. Figure 4 shows the variations of the journal and disk whirl orbits with the applied voltage at the rotational speeds of 1600 rpm, 2000 rpm and 2600 rpm, which are close to the first flexible critical speed, first rigid critical speed and the second flexible critical speed, (b). 2000 rpm (c). 2600 rpm Figure 4. Rotor orbits at speeds of 1600, 2000 and 2600 rpm with different applied voltages (The arrow stands for the direction of increasing voltage in order of 0, 1, 2, 3, 4, 5, 7 and 10V) respectively. The applied voltages are 0, 1, 2, 3, 4, 5, 7 and 10V, respectively. For clearly, different scales are used in the Fig. 4. The arrows in the figures stand for the direction of increasing the applied voltage. In the speed regions near the first two flexible critical speeds, as in Figs. 4a and 4c, both the disk and journal whirl orbits decreased as the applied voltage increased. Especially, the journal whirl orbits were very small and the disk whirl orbits did not significantly change when the applied voltage was more than 5 V. It means that the MR fluid has been solidified under the influence of the magnetic field with the voltage of 5 V and the solidified MR fluid almost locked up the journal. In these speed regions, the journal motion is small, but the small journal motion can produce an optimal combination of the system stiffness and the damping, which can effectively damp the disk vibration. However, the disk whirl orbits did not always decrease with an increase in the applied current. In the region of rotational speeds near the first rigid critical speed, as shown in Fig. 4b, the journal whirl orbits decreased as the applied current increased, but the disk whirl orbits increased. It is shown that in this region, as the applied current increased, the solidified MR fluid SFD produced a small damping but a high stiffness, which leads to the MR fluid SFD in the locked-up state behaving like a rigid and undamped support, and high disk vibration. 518

While the applied voltage was switched on or off between 0V and 10V at the rotational speed of 2500 rpm, the rotor orbits and transient vibration signals in the vertical direction both at the disk and journal positions are shown in Fig. 5. After the applied voltage was switched on or off, the rotor would smoothly jump to a new stable state with a different vibration level from a steady state without causing instability. When a voltage of 10V was suddenly applied, the rotor system would reach a new state only after about 5 revolutions (i.e., about 0.2 second); however the rotor system needed about 30 revolutions (i.e., about 1.2 second) to reach a new steady stste when the voltage was switched off. Repeated switching on/off in different steady rotational speed showed that the time period required for the transient response to decay depends on not only the applied voltage, but also on the rotational speed. The larger the current variation is, the shorter the time for the transient response to decay. The response of the journal to the applied voltage is faster than that of the disks due to the inertial effect of rotor motion. The reason for this is that the equivalent dampings of the rotor system between with the applied voltage and without the applied voltage are much different. Generally speaking, the journal motion can reach a new steady state within 0.25 second, but the disk motion about 0.25-1.5 second. The detail results about the response time of the rotor-mr fluid SFD system will be reported in other paper. Figure 5. Transient orbits and vibration signals while switching on from 0V to 10V at the speed 2000 rpm a and b for the over-hung disk; c and d for the journal; e and f for the middle disk It is clear that the change of the rotor whirl orbits at different rotational speeds with the applied voltage is very obvious and very sensitive to the applied voltage, and it is not necessary to apply a high voltage in the coil; an applied voltage of 10V is enough to change dramatically the dynamic characteristics of the rotor system by the MR fluid SFD. The dynamic characteristics of the MR fluid SFD are shown to be controllable. 3.2 Effect of the applied voltage on the rotor unbalance response Figure 6 shows the unbalance response curves of the rotor system with different applied voltages, which provides the entire rotor vibration information in the operating speed region. The applied voltage is 0, 1, 2, 3, 4, 5, 7, and 10V, respectively. When no voltage was applied in the coil, there are two resonant peaks. The maximum rotor amplitudes in both the journal and the disk occurred at the 1517 rpm and 2529 rpm, respectively, which basically corresponded to the first two flexible critical speeds of the rotor system. As the applied voltage was increased, the journal vibration amplitudes decreased in the whole operation speed region, the disk vibration amplitudes in the regions of the first-two flexible critical speeds were diminished until, at a optimum value of applied voltage, the disk motions were completely damped out. In the case with the optimal applied voltage, the vibration of the journal was not a minimum, but the damper produced an optimal damping and stiffness for the rotor system in the whole rotational speed region to attenuate effectively the disk vibrations. The optimum values of applied voltage for different speed regions were slightly different since the dynamic characteristics of the MR fluid SFD were not exactly linear. However, if the applied voltage was increased beyond the optimum applied voltage, the vibration amplitudes in the disk positions would increase with the applied voltage in the region of the first rigid critical speed, and the resonant peaks shifted to higher speed. When the applied voltage of 10V was applied in the coil, the rotational speed with maximum journal or disk vibration amplitude was about 1995 rpm, which is close to the rigid critical speed of the rotor system. Therefore upon applying a voltage of 10V, the solidified MR fluid make the rotor-mr fluid SFD system behave with a small damping and high stiffness. It is shown that when an external magnetic field is applied in the MR fluid, not only can the MR fluid SFD change the damping of the rotor system, but also its stiffness. Since the dynamic characteristics of the MR fluid SFD can be continuously controlled, it is possible to give the optimum supporting damping for every vibration mode present in the rotor system. 519

Figure 7. Variation of control objective with rotational speed at different applied voltages (The arrow stands for the direction of increasing voltage in order of 0, 1, 2, 3, 4, 5, 7 and 10V) Figure 6. The effect of applied voltages on unbalance response of rotor system (The arrow stands for the direction of increasing voltage in order of 0, 1, 2, 3, 4, 5, 7 and 10V) 3.3 Effectiveness of on-off control on the rotor vibration by the MR fluid SFD Although it is possible to use the optimum applied voltages in different speed regions to attenuating rotor vibration, since the dynamic characteristics of the MR fluid SFD are controllable, it is not necessary to set the applied voltage in the optimal applied voltage within these speed bands, the disk vibration amplitude can be minimised by actively controlling the dynamic characteristics of the MR fluid SFD. Within certain speed regions, the disk amplitude basically either continuously increased or decreased with an increase on the applied voltage, as shown in Fig. 6, therefore it is also not necessary to continuously control the applied voltage, only discrete changes in applied voltage is enough to achieve the required objective. Within these speed bands, the applied voltage of the MR fluid SFD should be set at either the 0V state (for the minimum stiffness) or the 10V state (for the maximum stiffness), respectively. In order to investigate the effectiveness of the MR fluid SFD for active control rotor vibration, a simple on-off control algorithm based on rotational speed feedback (Zhu et al.[4]) was used in the primary stage. From Fig. 6, it is found that the vibration of the over-hung disk in the region of the first flexible critical speed is high, but small in the region of the second flexible critical speed; the vibration of the middle-disk is small in the region of Amplitude, mm Amplitude, mm Amplitude, mm 0.8 0.6 0.4 0.2 (a). Over hung disk 0 1000 1500 2000 2500 3000 3500 4000 0.6 0.4 0.2 (b). Journal ver 0 1000 1500 2000 2500 3000 3500 4000 0.8 0.6 0.4 0.2 (c). Middle disk 0 1000 1500 2000 2500 3000 3500 4000 Rotational speed, rpm Figure 8. Unbalance response of rotor system after on-off control the first flexible critical speed is very small, but large in the region of the second flexible critical speed. In order to control both the vibration of the over-hung disk in the region of the first flexible critical speed and the vibration of the middle disk in the region of the second flexible critical speed, the maximum vibration of the two disks is chosen as the control objective. Taking the rotor system with a small imbalance as an example, the variation of the control objective with the rotational speed at the different applied voltage is shown in Fig. 7. It is shown that when the rotational speed was below 1795 rpm, the voltage of 10V was applied in the coil to make the MR fluid SFD in the maximum stiffness mode, the voltage was switched off at 1795 520

rpm, and then kept the zero voltage state until the voltage switched on 10V again at 2380 rpm. The unbalance response of the rotor system after the onoff control is shown in Fig. 8 as a solid thick line. As expected, the unbalance response curve after the onoff control is in good agreement with the open loop results in different regions of rotational speeds. When the applied voltage was switched on or off at the switching points, the rotor would run in the expected path after a brief transient response with relative larger vibration amplitudes. The transient response takes a short period to decay, general less than 1 second. Comparison with the original rotor vibration, after applying on-off control, the maximum vibration amplitude of the journal and the middle disk in the whole region of rotational speeds is less than 0.1 mm, and the maximum vibration amplitude of the over-hung disk is less than 0.25 mm. It is shown that the rotor vibration amplitude is effectively controlled and the onoff control is very effective to reach the required objection. 4. DISCUSSION 4.1 Effect of unbalanced magnetic pull force In the absence of a current in the coil, the dynamic behaviour of the MR fluid SFD are the same as the conventional SFD, which only depend on the characteristics of the centralising spring and the oil film force of the SFD. Upon application of an external magnetic field in the MR fluid SFD, there is an unbalanced magnetic pull force between the journal and damper housing due to the eccentricity of the journal with respect to the damper housing, and a eddy-current damping force produced by moving conductor in the magnetic field, in addition to the oil film force produced by the squeeze oil film effect and the restoring force by the centralising spring. Therefore, the dynamic characteristics of the MR fluid SFD will depend on not only the centralising spring and the oil film force, but also the unbalanced magnetic pull force and eddy current damping force. The unbalanced magnetic pull force at a given journal eccentricity ratio is almost direct proportion to the square of current (Berman[5]), if the applied current is above a critical value, the unbalanced magnetic pull force will be larger than the sum of the radial oil force and the restoring force of the centralising spring, and pull the journal to the damper housing and lock-up the journal like a rigidly mounted bearing. Further increase in the voltage almost does not affect the rotor system behaviour. The higher the centralising spring stiffness or the smaller the journal eccentricity in the steady state is, the higher the critical applied voltage will be. For example, the critical applied voltage was 18V in the two-disk rotor system and 22V for the one-disk rotor system for the same setup. When the two-disk rotor system is running at any rotational speed, if a voltage of 25V is applied, the journal would immediately be pulled to the damper housing; if the applied voltage of 25V was switched off, the journal returned to its original position. Fortunately, the above test results show that the applied voltage required to change dramatically the dynamic characteristics of the rotor-mr fluid SFD system is much lower than the critical applied voltage. With a low voltage, the unbalanced magnetic pull force is much smaller and cannot pull the journal to the damper housing. However, this problem should be considered when designing the centralising spring and choosing applied voltage level. If not, the unbalanced magnetic pull force will lock up the journal and further increase in the applied voltage did not have any effect on the dynamic characteristics of the MR fluid SFD. 4.2 Theoretical model of the MR fluid SFD From above discussion, it is clear that there are four forces existed in the MR fluid SFD, which are (a) the oil film force produced by the squeezing effect, (b) the restoring force produced by the centralising spring, (c) the unbalanced magnetic pull force, (d) the eddy current damping force. Either ER fluid or MR fluid basically behaves Bingham fluid model, the theoretical analyses on the ER/MR fluid having done are almost based on the Bingham fluid model. Therefore, after modifying the Reynolds equation of the conventional SFD, the oil film force generated by the ER/MR fluid SFD can be obtained (Tichy [6], Yang and Choi[7], Zhu[8]), but most of them is focusing on the theoretical model of the ER fluid SFD. For the MR fluid SFD, the Reynolds equation will be more complex than that in the ER fluid SFD, since the magnetic field distribution in the circumferential direction is not uniform and the rheologic relation of the MR fluid is not clear. Both the unbalanced magnetic pull force produced by the journal eccentricity with respect to the damping housing and the eddy-current damping force generated by the moving journal in magnetic field has been studied in the electrical machines, but there is not a suitable approximate analysis or close solution for the simple magnetic field in the MR fluid SFD. The unbalanced magnetic pull force depends on the journal eccentricity and the magnetic field. If the journal is centralised, the unbalanced magnetic pull force will be zero. The eddy-current damping force is directly proportional to the velocity of the journal motion. It is 521

observed in experiments that for a MR fluid SFD with a low voltage, the oil film force generated by the squeeze effect dominates the unbalanced magnetic pull force and eddy-current damping force, therefore the dynamic characteristics of the rotor-mr fluid SFD system are completely controlled by the oil film force of the MR fluid SFD. However, the effect of unbalanced magnetic pull force and eddy-current damping force on the rotor-mr fluid SFD system in quantity should further be studied. 4.3 MR fluid sediment, magnetic materials and others Sediment is one of existing problems in MR fluids to be solved. The lower the initial viscosity of the MR fluid in the absence of magnetic field is, the easily the sediment will appear. In order to reduce the MR fluid sediment, the MR fluid should be mixed in the experiment or supplied by pump with high fluid rate. In design the MR fluid SFD, we should also pay attention on properly choosing the magnetic path material. The residual magnetic field of the magnetic material used in MR fluid SFD should be as small as possible since it will hasten the MR fluid sediment. From the FRF tests of the rotor system in non-rotating condition and the rotor unbalance response tests, it is also shown that the solidified voltage in the rotating state is much higher than that in the non-rotating case. The reason for this is that it is more difficult for the MR fluid to solidify in the rotating state with a higher squeezing velocity than in the non-rotating state only with a lower squeezing velocity. It is also observed that when no voltage or small applied voltages was applied in the MR fluid SFD, the MR fluid flowed out in whole area of the radial clearance, even in the region with the smallest radial clearance. However, upon applying a higher voltage, the flow of the MR fluid from the radial clearance was non-uniform, the MR fluid did not flow out in some regions where the MR fluid had been solidified. In this case, the dynamic characteristics of the MR fluid SFD were not symmetrical, therefore it is the reason for that the two resonant peaks were observed experimentally in the rotor MR fluid SFD with high applied voltages. 5. CONCLUSION A new controllable SFD based on the MR fluid has been presented which uses the special characteristic of MR fluid with rapid, reversible and dramatic change in its apparent viscosity caused by an external magnetic field. The results of the rotating imbalance response tests show that the dynamic characteristics of the MR fluid SFD can be easily controlled by a low voltage magnetic coil, and that the MR fluid SFD is very effective for attenuating and controlling the vibration of a rotor system. The applied voltages in the coil required to change the dynamic characteristics of the rotor system by the MR fluid SFD is a few tens of votes, which is much lower than that in the ER fluid SFD and easily be used in the real rotating machinery. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the European Community BRITE/EURAM program under contract BRPR-CT97-0544 IMPACT project. REFERENCES 1. Nikolajsen,J.L. and Hoque M.S., 1988, An Electro-viscous Damper, Proceedings of Workshop on Rotor-dynamic Problems in High- Performance Turbo-Machinery, Texas A&M. University, NASA CP-3215, pp:65-73, Texas. 2. Vance, J.M., and Ying, D., 1999, Experimental Measurements of Actively Controlled Bearing Damping with an Electrorheological Fluid, ASME 99-GT-17. 3. Morishita,S., and Mitsui,J., 1990, Journal Squeeze Film Damper as an Application of Electrorhological Fluid, Proceedings 3 rd International Conference on Rotor Dynamics, pp:277-282, Lyon, France. 4. Zhu, C.S., Robb,D.A., and Ewins, D.J., A Variable Stiffness Squeeze Film Damper for Passing through the Critical Speeds of Rotors, Proceedings of IMAC-19: A Conference on Structure Dynamics, Florida, USA, Feb. 5-8, 2001, Vol:2, pp:1264-1269 5. Berman,M., 1993, On the Reduction of Magnetic Pull in Induction Motors with Off-centre Rotor, IAS Annual Meeting, IEEE Industry Application, Vol:1, pp:343-350. 6. Tichy, J.A., Behavior of Squeeze Film Damper with an Electrorheological Fluid, STLE Tribology Transactions, 36(1), pp:127-133, 1993. 7. Jung, S.J., and Choi,S.B., Analysis of a Short Squeeze Film Damper Operating with Electrorheological Fluids, STLE Tribology Transactions, 38(4), pp:857-862, 1995. 8. Zhu, C.S., Robb,D.A., and Ewins, D.J., "Analysis Models on the Behaviour of a Smart Squeeze Film Damper Operation with ER/MR Fluid", SPIE s 7 th Annual International Symposium on Smart Structures and Materials, March 5-9, 2000, CA, USA. 522