A Magnetorheological Hydraulic Actuator Driven by a Piezopump

Transcription

1 A Magnetorheological Hydraulic Actuator Driven by a Piezopump Jin-Hyeong Yoo Jayant Sirohi Norman M. Wereley Inderjit Chopra Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering University of Maryland, College Park, MD, 2742 ABSTRACT Magnetorheological (MR) fluids can be used in a variety of smart semi-active systems. The MR damper shows an especially great potential to mitigate environmentally induced vibration and shocks. Another aspect of MR fluids is the construction of MR valve networks in conjunction with a hydraulic pump resulting in a fully active actuator. Conventional hydraulic pumps, however, are bulky, contain many moving parts, and do not scale favorably with decreasing size motivating development of high energy density piezohydraulic pumps. These devices are simple, have few moving parts and can be easily miniaturized to provide a compact, high energy density pressure source. The present study describes a prototype MR-piezo hybrid actuator that combines the piezopump and MR valve actuator concepts, resulting in a self-contained hydraulic actuation device without active electro-mechanical valves. Durability and miniaturization of the hybrid device are major advantages due to its low part count and few moving parts. An additional advantage is the ability to use the MR valve network in the acuator to achieve controllable damping. The design, construction and testing of a prototype MR-piezo hybrid actuator is described. The performance and efficiency of the device is derived using ideal, biviscous and Bingham-plastic representations of MR fluid behavior, and is evaluated with experimental measurements. This will provide a design tool to develop an actuator for a specific application. The prototype actuator achieved an output velocity of 5.34mm/sec against a mass load of 5.5kg with a piezopump weighing 3gm. Keywords: ER(Electrorheological) and MR(Magnetorheological) valve, Piezo electric driven pump. Hybrid actuator, ER/MR damper, Hydraulic actuator.. INTRODUCTION Magnetorheological (MR) fluids can be used in a variety of smart semi-active systems, such as in optical polishing and fluid clutches, 2 as well as in aerospace, automotive, 3,4 and civil damping applications. 5 In active systems, the ER/MR fluid can be used as a fully active actuator in conjunction with a conventional hydraulic pump. 6,7 In such a system, MR fluid is used as the hydraulic fluid, and a network of MR valves functions as a directional control valve. However, the hydraulic pump assembly is complex and needs to be externally powered by a motor or some other similar power source. Many industrial and aerospace applications need highly reliable, precisely controllable and high energy density actuators. In order to address this need, there has been some interest recently in developing high energy density piezohydraulic actuators. These hybrid devices are self-contained, electrically-driven linear actuators, consisting of a hydraulic pump driven by piezoelectric stacks, acting in conjunction with a conventional hydraulic output cylinder and a fast-acting set of valves. The pump-valve-cylinder system is used to rectify and convert the high frequency, low amplitude motion of the piezostacks to lower frequency, higher displacement motion of the hydraulic cylinder. Piezohydraulic hybrid devices have been proposed for a variety of aerospace 8 and automotive applications. 9 Several prototype piezohydraulic actuators have been designed and tested over the past few years, 8,,9, clearly demonstrating proof of the concept. Due to their mechanical simplicity, and operation off an electric power supply, piezopumps show great promise in applications requiring a miniature hydraulic power source. Further author information: (Send correspondence to N.M.W.) J.H.Y.: Research Scientist, jhyoo@eng.umd.edu, Tel: J.S.: Research Associate, sirohij@eng.umd.edu, Tel: N.M.W.: Associate Professor, wereley@eng.umd.edu, Tel: I.C.: Alfred Gessow Professor and Director, chopra@eng.umd.edu, Tel:

2 The present study describes a novel actuator that combines the advantages of the piezopump and the MR valve concept, resulting in a self-contained actuator with few moving parts. In this hybrid MR-piezo device, the mechanical directional control valves typically present in conventional hydraulic actuation systems are replaced by a Wheatstone bridge of MR valves and the hydraulic pump/driving motor assembly is replaced by a piezopump. The MR fluid functions as a hydraulic fluid and a conventional hydraulic cylinder is coupled to the system to extract useful work. The hybrid MR-piezo actuator would have a low number of moving parts, a simple design, and can be scaled down favorably. The moving parts inside of the system are the actuator shaft with two rod seals, two reed valves and the piston in the piezo pump. An additional advantage of such a system is the high compliance of the device while operating as a semi-active MR damper. The actuator can adapt to large changes in disturbace mass loading and can achieve reliable and precise control in severe environments. The objective of this study is to develop a prototype MR-piezo position (or force) control actuator with a controllable MR damping effect. Hence, this system behaves not only as a controllable MR damper, but also as a fully activated actuator that can be used for position or force control. The MR valve and piezopump are the key components of the actuation system. Driving force, stroke, cut-off frequency and efficiency are the main evaluation parameters for this actuator. 2 The performance of a prototype MR-piezo actuator is determined experimentally by suspending deadweights from the end of the actuator and measuring its output velocity. This test is performed at various pumping frequencies and applied magnetic field in the MR valve. The experimental results are compared with performance trends predicted using biviscous and Bingham-plastic MR fluid constitutive models as well as to an ideal mechanical valve case (infinite blocking pressure in the MR valve). There are two main challenges in this system. Firstly, the piezoelectric pump has a low flow rate. Secondly, the MR valve has a low blocked force. However, through previous studies, we have already optimized the piezoelectric pump and MR valve performance 3,4 with given volume. In this study, we will develop a prototype of MR-piezo hybrid actuator, and evaluate its performance. Some experimental results will be presented, along with simulations. This will provide a design tool to develop an actuator for a specific application. 2. MR VALVE NETWORK CONCEPT AND CONSTRUCTION The MR-piezo hybrid actuator is a combination of an MR valve network and a piezopump. A schematic of the device is shown in Fig.. The device consists of 4 MR valves arranged in a Wheatstone bridge configuration, an accumulator, a piezopump and a conventional hydraulic cylinder. The accumulator is used to apply a bias pressure to the hydraulic circuit. The device can function in two modes: an active mode and a semi-active mode. A description of operation of the MR valve network as well as the MR valve is given below. 2.. MR valve network operation In the active mode, shown in Fig. (a), the piezopump functions as a pressure source to the system and the output displacement of the device can be controlled by activating the MR-valve network. In the semi-active mode, shown in Fig. (b), the MR-valve network operates independently of the pump and the 4 valves can provide a more precise control over a broad range as a semi-active damper. In Fig. (a), the load attached to the output cylinder generates a force F. The piezopump forces fluid through the accumulator and MR valves configured as a Wheatstone bridge. Applying current to valves and 4 activates these valves and the fluid flows predominantly from the output port of the pump at a pressure P S to the high pressure arm at a pressure P H, through valve 3. The flow into the lower chamber of the hydraulic actuator causes the piston to move up and the fluid in the upper chamber flows through the low pressure arm, at a pressure P L, to the reservoir through valve 3. Under ideal conditions, or infinite blocking pressure, valves and 4 permit no flow. However, in a real system, valves and 4 permit a relatively low volume flux as compared to valves 2 and 3. Assuming well balanced symmetric conditions in the Wheatstone bridge configuration, the flow rates in valves 2 and 3 are defined as Q a and the flow rates in valves and 4 have Q b, where Q a Q b. The performance of the hydraulic actuator with MR valves will be evaluated using three models: ) an idealized valve in which infinite blocking pressure is assumed, 2) a Bingham-plastic model with finite blocking pressure, and 3) a biviscous model, also with finite blocking pressure. With these assumptions, system efficiency can be derived based on knowledge of the field dependent yield stress of the MR fluid.

3 Output cylinder P L Accumulator Output cylinder Accumulator 2 2 P S 3 4 Piezopump 3 4 Piezopump P H MR Valve network MR Valve network (a) Active operation (b) Semi-active operation Figure. Schematic of hybrid MR-piezo actuator 2.2. MR Valves The MR valves used in this study consist of a core, flux return, and an annulus through which the MR fluid flows, as shown in Fig. 2(a). The core is wound with insulated wire. A current applied through the wire coiled around the bobbin creates a magnetic field in the gap between the flange and the flux return. The magnetic field increases the yield stress of the MR fluid in this gap. This increase in yield stress alters the velocity profile of the fluid in the gap and raises the pressure difference required for a given flow rate. For Bingham-plastic flow, the typical velocity profile is illustrated in Fig. 2(b). The primary parts of the MR valve design are pictured in Fig R6. CW CCW R Region 3 (Post-yield) Region 2 (Pre-yield) δ d 33.2 Region (Post-yield) y (a) Cross-section of MR valve (b) Flow profile in the annulus Figure 2. MR Valve Concept End Cap Bobbin Hydraulic Cylinder/ Flux Return Figure 3. Parts of the MR valve

4 A -D axisymmetric analysis is given by Kamath et. al., 5 and an approximate rectangular duct analysis was provided by Wereley and Pang. 6 Gavin 7 provided an analysis for annular valves with more appropriate radial field dependence. In our simplified analysis, we assume a uniform field across the valve gap. 6 Following this latter study, we consider the approximate rectangular duct analysis of Poiseuille flow through a valve system containing MR fluid. For Newtonian flow, the volume flux Q through the annulus is a function of the area moment of inertia I(= bd 3 /2) of the valve cross-section, the fluid viscosity, and the pressure drop over the valve length, P/L a in the case of the rectangular duct model. The dimensional volume flux through the valve can be determined. 6,3 Q N = bd3 P 2µ po L a Q BP = bd3 P ( 2µ po L δ) 2 ( + δ/2) a Q BV = bd3 P 2µ po L a [( δ) 2 ( + δ/2) + 32 µ ( δ 2 3 ) ] δ () where Q N denotes for Newtonian flow, Q BP denotes Bingham-plastic flow and Q BV denotes biviscous flow. Here, the non-dimensional plug thickness, δ = δ/d and non-dimensional viscosity ratio, µ, which is defined as the ratio of the post-yield differential viscosity (µ po ) to the pre-yield differential viscosity (µ pr ), have been introduced. Normalizing each volume flux by the Newtonian (field off) value of volume flux yields the non-dimensional volume flux for each of the flow models Q N = Q BP = ( δ) 2 ( + δ/2) = Q BP /Q N Q BV = [( δ) 2 ( + δ/2) + 32 ( µ δ 2 ) ] (2) δ = Q BV /Q N 3 Figure 4 shows the trends of the non-dimensional volume flux as a function of the plug thickness δ, for Binghamplastic and biviscous models, for the case of rectangular duct. In this figure, Q = implies Newtonian flow and Q = implies that the valve has blocked the flow. Volume flux, Q [] Biviscous model µ =.4 µ =.5 µ =.2 µ =. Bingham-plastic model (µ = ) Plug thickness, δ [] Figure 4. Non-dimensional volume flux as a function of plug thickness Note that the MR valve behavior based on a biviscous MR fluid constitutive model, is not capable of blocking the flow completely since Q BV for all δ. This implies that the two activated valves in the hydraulic circuit will experience leakage, which is a key source of efficiency loss in the actuator system. This efficiency loss will occur even though the fluid will tend to predominantly flow through the inactive valves. Yield stress characteristics of a MR fluid change as a function of the applied magnetic field. Therefore, the magnetic field applied to the MR fluid is very

5 important to the performance of the valve and actuator. A high efficiency design was explored for meso-scale MR valves. The magnetic circuit consisted of a bobbin, which a coil wound about its shaft. Surrounding the bobbin was a tubular magnetic flux return. Key geometric properties were the bobbin shaft diameter, bobbin flange thickness, and gap between bobbin flange outer diameter and the flux return. A lower limit to miniaturizing the MR valves was that the bobbin shaft saturates magnetically at lower field strengths as the shaft diameter decreases. Table summarizes the valve parameters. Table. Valve dimensions Outer diameter Bobbin diameter Flange length Air gap No. of windings Material 6.4 mm. mm.6 mm.5 mm 4 turns HIPERCO-5A 3. PIEZOPUMP CONCEPT AND CONSTRUCTION The piezopump concept is illustrated in Fig. 5. An exploded view of the prototype pump used in the present study is shown in Fig. 5(a). A description of the design and testing of this piezopump coupled to an output hydraulic actuator can be found in Ref. 8. The main components of the piezopump are the piezostack assembly, piston assembly, pump body, pumping head and preload assembly (Fig. 5(b)). The piezostack assembly consists of two commercially available low voltage piezostacks (model P-84., Physik Instrumente 9 ), that are bonded together, end to end. The overall size of this assembly is 36mm mm mm. One end of the piezostack assembly is bonded to a preload mechanism and the other end is pushed up against a piston-diaphragm assembly. The preload assembly serves to adjust the position of the piezostack assembly relative to the pump body as well as to provide a compressive preload to the piezostacks. The piston-diaphragm assembly consists of a steel piston of diameter inch, which has a tight running fit with a bore in the pump body, bonded to a.2 thick C-95 spring steel diaphragm. The diaphragm seals the pump body from the hydraulic fluid in the pumping chamber, and the piston serves to constrain the deflected shape of the diaphragm to remain flat over most of its surface, thus maximizing the swept volume of the pump per cycle. While one face of the pumping chamber is formed by the movable piston, the other face is formed by the pumping head, that contains two oppositely oriented passive check valves. The piezostacks are actuated by a sinusoidal voltage from - V, resulting in an oscillatory flow of fluid in the pumping chamber. The check valves rectify this flow and provide a uni-directional output flow from the pump. The piezopump has an outer diameter of.25, a length of 3.5 and weighs 3gm. The major parameters of the complete device are given in Table. 2. Table 2. Piezopump parameters Piezostack Model P-84. Number of piezostacks 2 Length.3937 in Width.3937 in Height.787 in Blocked Force (- V) 33 lbs Free displacement (- V) u.5 mil Maximum voltage 2 V Minimum Voltage -24 V Capacitance 7 µf Pumping Chamber Diameter in Height.5 in

6 Connecting ports Pumping head Valve assembly Spacer Piston assembly Pump body Piston Piezostack assembly Preload Hydraulic Fluid Piezostacks Preload base Check Valves Diaphragm (a) Exploded view of piezopump assembly (b) Schematic of the piezopump Figure 5. Piezopump Concept 4. MR-PIEZO HYBRID ACTUATOR The volume flux through each valve in Fig. (a) can be defined as Q a = bd3 P 2µL a Qa (P S P H ) Q b = bd3 P 2µL a Qb (P S P L ) (3) The total flow rate Q S from the pump and the flow rate for moving the actuator Q W are defined as Q S = Q a + Q b Q W = Q a Q b = A p u (4) The force equilibrium equation at the hydraulic actuator is (P H P L )A p = F (5) The force F includes friction force and output force of the cylinder. It follows that the steady-state force equilibrium of equation (5) and the velocity of the actuator will be [ ] u = bd3 P S ( 2µL a A Q a Q b ) ( Q a + Q F b ) (6) P A p P s The maximum velocity of the actuator shaft and maximum force of the actuator can be expressed as

7 u max = bd3 ( Q a Q b ) 24µL a A p P S F max = Q a Q b Q a + Q b A p P S (7) The maximum velocity and force are functions of the pressure source, P S. In the case of an ideal valve, the velocity and force will increase as the source pressure increases. However, in the case of an MR valve, the nondimensional volume flux, Q is also a function of the supply pressure, so that the maximum velocity and force is dependent on the non-dimensional volume flux. In the piezopump, P S and the flow rates are functions of driving frequency and external loads. From equation (6), the non-dimensional actuator performance equation can be stated Q W = 2µQ W L a bd 3 = [ ( Qa P S 2 Q b ( Q a + Q b ) F ] (8) where, F = F/Ap P S. The maximum value of F is and Q W is.5. If a current is applied to the shaded valves and 4 in Fig. (a), we can define for the rectangular duct Q a = Q b = ( δ) 2 ( + δ/2) Q b = ( δ) 2 ( + δ/2) ( δ 2 3 ) δ For Newtonian flow For Bingham-plastic flow For Biviscous flow (9) Corresponding to the MR fluid model used, the trends of Q b will follow the simulation results of Fig. 4. Fig. 6 shows the actuator performance predicted by the Bingham-plastic model as a function of the non-dimensional plug thickness, δ. On increasing the current to the valve, the magnetic flux density at the gap will be increased. This causes an increase in the plug thickness of the MR fluid flowing through the gap. The performance of the actuator will approach the ideal case, as the plug thickness increases. In the case of biviscous model, the performance as a function of the viscosity ratio is shown in Fig. 7. As can be seen in Fig. 7, the biviscous model cannot reach the maximum performance of the actuator. The maximum performance with δ = is dictated by the value of the viscosity ratio, µ. On decreasing the current to the valve, the performance of the actuator also decreases, following the trends of Bingham-plastic model, in Fig. 6. The pressure from the piezo pump is a function of driving frequency and external loads..8 δ =.8 Force, F [] δ =.6 δ =.4 δ =.2 δ =, ideal Working Flowrate, QW [] Figure 6. Force and flow rate as a function of plug thickness, Bingham-plastic model

8 .8 Force, F [].6.4 µ =, ideal µ =. µ =.2 µ =.4 µ = System Efficiency Working Flowrate, QW [] Figure 7. Force and flow rate as a function of viscosity ratio, biviscous model, δ = The system efficiency, defined as the power transferred to the load divided by the power supplied to the MR valves, is given by η = Power delivered to load Power supply to system = P aq a P b Q b P a Q a + P b Q b = Q a Q b Q a + Q b () From the above, system efficiency of the actuator model can be derived as follow η( δ, µ) = 2 Q b + Q b () Figure 8 shows the efficiency for the actuator when the working MR fluid behaves as a biviscous fluid. In this case, the maximum efficiency at δ = can be derived as η( δ, µ) δ = 2 µ + µ (2) Efficiency, η [] µ =, Bingham-plastic µ =.5 µ =. µ =.2 µ = Non-dimensional plug thickness, δ [] Figure 8. Efficiency as a function of plug thickness, biviscous model Thus the system efficiency is a function of both δ of the valve and µ of the fluid. 5. EXPERIMENT To validate the nonlinear hybrid actuator performance, a set of four MR valves was implemented within a Wheatstone bridge hydraulic power circuit to drive a hydraulic actuator using a piezopump. The configuration of the hybrid actuator is shown in Fig. 9. The actuator consists of three main part: a hydraulic cylinder, a set of four MR valves with Wheatstone bridge configuration and a compact designed piezopump as a hydraulic source.

9 Hydraulic cylinder MR valves Piezopump Accumulator LVDT Figure 9. MR-piezo hybrid actuator configuration 5.. Experimental Setup Experiments were performed to measure the output power of the actuator as a function of driving current to the MR valves and driving frequency to the piezopump. The hydraulic cylinder in this system as shown in Fig. 9, had 7/6 bore diameter with.87 shaft diameter. The maximum stroke of the cylinder is 2-/2. To measure the displacement response, a potential meter(lvdt, TR5 Novotecknik) was attached with a rigid bar. The accumulator regulated the source pressure from the piezopump. Figure shows the schematic diagram for the experimental setup. The piezopump was driven by a high voltage amplifier and the MR valve was driven by a power supply, directly. Deadweights were hung off the end of the output hydraulic cylinder and the displacement was measured using the LVDT. The bias pressure was set to about 3psi. Figure shows simulation results of yield stress of a commercially available MR fluid, namely MRF-32AD (Lord Corporation) with the MR valve design in this study. For the simulation the magnetic analysis was performed with ANSYS/Emag 2-D. Power Supply Actuator Assembly High Voltage Amplifier Oscilloscope LVDT Loads Figure. MR-piezo hybrid actuator test setup

10 5 Yield stress, τy [kpa] Data Sheet Curve Fit 2 3 Current, i [A] Figure. Yield stress as a function of applied current, MRF-32Ad(Lord Corporation) 5.2. Experimental Results In Fig. 2, the experimental velocity response of the actuator shaft are plotted. On increasing the deadweight, the velocity of the actuator tended to decrease. On increasing the applied current, the velocity of the shaft increased. For the case of high loads condition has more enhancement of velocity response according to the applied current. It shows the possiblity of performance enhancement of this actuator. The performance of this actuator mainly depends on the flow rate from the piezopump and blocking pressure of the MR valve. These parameters can be optimized according to the application. The external force and velocity are the key design parameters for each application. The actuator in this study can move 5.5 Kg with 5.34mm/sec velocity. The conditions of driving is 4V p p at 25Hz for the piezopump and.8 Ampere for MR valves. 6 Pzt pump: 25 Hz Velocity, u [mm/sec] Kg 2.88 Kg 4. Kg 5.5 Kg Applied Current, i [A] Figure 2. Output velocity as a function of applied current and external load In Figs. 3(a), 3(b) and 3(c), the non-dimensional actuator performance test with MR valve is compared with the test of the ideal valve. The driving frequency of the piezo pump is 2, 25 and 3 Hz, respectively. The driving current for the MR valve is.8 Ampere. In the low loads region shows fluctuating data trend than the high loads condition. On increasing the driving frequency of the piezo pump, the fluctuation region on low loads site is diminishing. However, the scattering in high loads site is emerged for the ideal valve. In general, on increasing the driving frequency of piezopump and on increasing the deadweight, the performance of the actuator is stabilizes.

11 Figure 3(d) shows the efficiency of the system as a function of pump frequencies and load. The efficiency at 3 Hz driving frequency for the piezopump was highest among those frequencies tested. We are continuing testing of this actuator to better characterize its efficiency..8 Pzt pump: 2 Hz, MR vavle.8 A Ideal Valve Test with Ideal Valve Test with MR Valve.8 Pzt pump: 25 Hz, MR vavle.8 A Ideal Valve Test with Ideal Valve Test with MR Valve Force, F [].6.4 Force, F [] Working flow rate, Qw [] Working flow rate, Qw [] (a) Actuator performance correlation, 2 Hz pumping frequency,.8 A current (b) Actuator performance correlation, 25 Hz pumping frequency,.8 A current.8 Pzt pump: 3 Hz, MR vavle.8 A Ideal Valve Test with Ideal Valve Test with MR Valve Hz 25 Hz 3 Hz Force, F [] Efficiency, η [%] Working flow rate, Qw [] (c) Actuator performance correlation, 3 Hz pumping frequency,.8 A current Force, F [] (d) System efficiency Figure 3. Performance of the MR-piezo actuator 6. CONCLUSIONS AND FUTURE WORK A MR-Piezo hybrid actuation system was analyzed and experimentally evaluated by testing a prototype. The actuation system was constructed with four MR valves with Wheatstone bridge configuration and piezo pump. The piezopump forces the MR fluid through the MR valves and MR valves control the direction of flow through to the hydraulic cylinder. The controlled fluid flow makes the piston move. A non-dimensional volume flux was defined and the performance of the actuation systme was evaluated with the non-dimensional equation. The system efficiency defined as the power transferred to the load divided by the MR valve supply power. Through this study we can conclude that. With 25 Hz driving frequency for piezopump and.8 Ampere driving current for MR valve, the hybrid actuator moves 5.5 Kg mass with 5.34 mm/sec velocity. 2. On increasing the driving frequency of piezopump, the performance of the actuator system stabilized and the efficiency increased.

12 The behavior of this MR-hybrid actuation system is determined by two separate non-linear systems: the MR valve network and the piezopump. In the MR valves, the yield stress of the MR fluid has a non-linear dependence on applied current. The plug thickness also depends on the pressure difference and flow rate. Furthermore, the flow rate generated by the piezopump is a complex function of the driving frequency and external force. Future work will involve the development of a non-linear model to predict the exact performance of this hybrid system. With this model, an optimized design can be generated depending on the application. Additionally, the damping effectiveness of the system in the semi-active mode will be evaluated. REFERENCES. W. I. Kordonski and D. Golini, Fundamentals of magnetorheological fluid utilization in high precision finishing, Journal of Ineglligent Material Systems and Structures (9), pp , U. Lee, D. Kim, N. Hur, and D. Jeon, Design analysis and experimental evaluation of an mr fluid clutch, Journal of Ineglligent Material Systems and Structures, pp. 7 77, September J. Lindler and N. M. Wereley, Analysis and testing of electrorheological bypass dampers, Journal of Ineglligent Material Systems and Structures (5), pp , F. Gordaninejad and S. P. Kelso, Fail-safe magneto-rheological fluid dampers for off-highway, high-payload vehicles, Journal of Ineglligent Material Systems and Structures, pp , May S. J. Dyke, B. F. Spencer, M. K. Sain, and J. D. Carlson, Experimental study of mr dampers for seismic protection, Smart Materials and Structures 7, pp , October S. B. Choi, C. C. Cheong, J. M. Jung, and Y. T. Choi, Position control of an er valve-cylinder system via neural network controller, Mechatronics 7, pp , February Z. Lou, R. D. Ervin, and F. E. Filisko, Behaviors of electrorheological valves and bridges, in Proceedings of the International Conference on ER fluid, pp , 5-6th October L. D. Mauck and C. S. Lynch, Piezoelectric hydraulic pump development, Journal of Intelligent Material Systems and Structures, pp , October K. Konishi, H. Ukida, and K. Sawada, Hydraulic pumps driven by multilayered piezoelectric elements - mathematical model and application to brake device, Proceedings of the 3th Korean Automatic Control Conference, K. Nasser, D. J. Leo, and H. H. Cudney, Compact piezohydraulic actuation system, Proceedings of the 7th SPIE Conference on Smart Structures and Integrated Systems, Newport Beach, CA 399, pp , March 2.. J. Sirohi and I. Chopra, Design and testing of a high pumping frequency piezoelectric-hydraulic hybrid actuator, Proceedings of the 9th SPIE Conference on Smart Structures and Integrated Systems, San Diego, CA 47, pp , 7-2 March J. Watton, Fluid Power Systems, Prentice Hall, J.-H. Yoo and N. M. Wereley, Performance of a mr hydraulic power actuation system, in Proceedings of the 9th SPIE Conference on Smart Structures and Integrated Systems, 47, pp. 9 9, (San Diego, CA), 7-2 March J.-H. Yoo and N. M. Wereley, Design of a high-efficiency magnetorheological valve, in 8th International Conference on Electrorheological Fluid (ER) and Magnetorheological (MR) Suspensions, (Nice, France), 9-3 July G. M. Kamath, M. K. Hurt, and N. M. Wereley, Analysis and testing of bingham plastic behavior in semi-active electrorheological fluid dampers, Smart Materials and Structures 5, pp , N. M. Wereley and L. Pang, Nondimensional analysis of semi-active electrorheological and magnetorheological dampers using an approximate parallel plate model, Smart Materials and Structures 7, pp , H. P. Gavin, R. D. Hanson, and F. E. Filisko, Electrorheological dampers, part i: analysis and design, Journal of Applied Mechanics ASME 63, pp , J. Sirohi and I. Chopra, Design and testing of a high pumping frequency piezoelectric-hydraulic hybrid actuator, Proceedings of the 3th International Conference on Adaptive Structures Technology, Potsdam, Germany, October Physik Instrumente (PI), Products for Micropositioning, US-edition, 997.