Performance of a MR Hydraulic Power Actuation System *

Transcription

1 REVISED Performance of a MR Hydraulic Power Actuation System * JIN-HYEONG YOO AND NORMAN M. WERELEY Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering University of Maryland, College Park, Maryland USA wereley@eng.umd.edu Phone: (301) , FAX: (301) April 2003 Revised ABSTRACT The performance of a magnetorheological hydraulic power system is analytically and experimentally assessed. Four MR valves are implemented as a Wheatstone bridge hydraulic power circuit to drive a hydraulic actuator using a gear pump. The compact hydraulic power actuation system is a Wheatstone bridge network driving a conventional hydraulic actuator. A key advantage of using MR valves in Hydraulic actuations systems is that the valves have no moving parts. This reduces the complexity and enhances the durability compared to conventional mechanical valves. In such a system, MR fluid is used as the hydraulic fluid. A constant volume pump is used to pressurize the MR fluid which eliminates the effect of fluid compliance to a large degree. If a change in direction is required, the flow through each of the valves in the Wheatstone bridge can be controlled smoothly via changing the applied magnetic field. A magnetic field analysis is conducted to design a high-efficiency compact MR valve. The behavior and performance of the MR valve is expressed in terms of non-dimensional parameters. The performance of the hydraulic actuator system with Wheatstone bridge network of MR valves is derived using three different constitutive models of the MR fluid: an idealized model * Presented at the 2002 SPIE Conference on Smart Structures and Integrated Systems, San Diego, CA, March 2002

2 (infinite yield stress), a Bingham-plastic model, and a biviscous model. The analytical system efficiency in each case is compared to experiment, and departures from ideal behavior, that is, a valve with infinite blocking pressure, are recognized. Introduction Magnetorheological (MR) fluid can be implemented in a variety of smart semi-active actuation systems (Stanway et al, 1996), including optical polishing (Kordonski and Golini, 2000), fluid clutches (Lee et al, 2000), and aerospace, automotive (Lindler and Wereley, 2000; Gordaninejad and Kelso, 2000), and civil damping applications (Dyke et al, 1998). Alternatively, MR fluid can be used in a fully active actuator with the help of a conventional pump. Many industrial applications require high reliability, precisely controllable and high energy density actuators. Choi et al (1997) presented a position control system that used a single-rod cylinder activated by an electrorheological (ER) valve. Lou et al (1991) analyzed ER valves and bridges to evaluate in its ability to control the flow and pressure conditions. In this paper, magnetorheological (MR) valves and bridges will be analyzed and designed to develop a compact hydraulic power actuation system for application to unmanned air vehicles and helicopters. The higher yield stress of MR fluid enables the actuator to be more compact than a similarly capable system that uses ER fluid. The MR valve is a key component of the actuation system. Driving force, stroke, bandwidth and efficiency are the key evaluation parameters in a general hydraulic actuator (Watton, 1989). Durability and miniaturization are stumbling blocks to expand the scope of applications for conventional mechanical valves. These problems can potentially be overcome by replacing the mechanical valves with MR valves. 2

3 There are many advantages to using MR valves in hydraulic actuation systems. In particular, MR valves have no moving parts, thereby eliminating the complexity and durability issues associated with conventional mechanical valves. In such a system MR fluid is used as the hydraulic fluid. Especially, in this study, a commercially available MR fluid, namely MRF-132AD (Lord Corporation) was used for the simulation and test. A constant volume pump is used to pressurize the MR fluid. If a change in direction is required, the flow through each of the valves in the Wheatstone bridge can be controlled smoothly via changing the applied magnetic field. Above all, the most important advantage of the MR valves will be the miniaturization and weight savings compared to a mechanical valve. This miniaturization can expand the application area to the aerospace industry, making it a feasible means of actuating trailing-edge flaps in helicopter blades (Milgram et al, 1995) as an example. Two potential disadvantages may be the block force and the cut-off frequency of this actuator. The block force depends on the yield stress of the MR fluid and MR valve geometry, and the cut-off frequency is a function of the response time of the MR fluid. In a preliminary study (Yoo et al, 2001; Yoo and Wereley, 2001), the performance of a hydraulic actuator with MR valves was evaluated based on experimental test data and a performance assessment of MR valves. A magnetic field analysis was conducted to design a high-efficiency compact MR valve (Yoo and Wereley, 2001). The magnetic circuit consisted of a bobbin, with 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 3

4 shaft diameter decreases. Through numerical simulation, a target magnetic flux density at the gap was achieved in an optimized valve design, and its performance was validated via experiment. In this study, a MR fluid based power actuation system is analyzed and experimentally validated by testing a prototype. A set of four MR valves is implemented within a Wheatstone bridge hydraulic power circuit to drive a hydraulic actuator using a gear pump. A non-dimensional analysis will be developed for describing the performance of the valve and the actuation system. The system efficiency defined as the power transferred to the load divided by the MR valve supply power will be derived. The Bingham-plastic and the biviscous constitutive model were adopted for the fluid flow analysis, and the simulation results based on these models agreed well with test results. The performance of the hydraulic actuator with MR valves is shown to be very dependent on the output mechanical load and driving current to the MR valves. On increasing the source pressure the performance of the actuator system was increased. But there are certain limitations on performance due to the finite yield stress of the MR fluid. ACTUATOR ANALYSIS Figure 1 shows the schematic diagram of the hydraulic actuator system where the load attached to the cylinder generates a force F. A motor drives a pump and the pump forces fluid through the accumulator and MR valves configured as a Wheatstone bridge. Applying current to valves and, activates these valves and the fluid flows predominantly from P S to P H through valve. The flow into the lower chamber of the hydraulic actuator causes the piston to move up and the fluid in the upper chamber flows 4

5 to P L to the reservoir through valve. Under ideal conditions or infinite blocking pressure, valves and/ permit no flow. However, in a real system, valves and/ permit a relatively low volume flux as compared to valves and. Assuming well balanced symmetric conditions in the Wheatstone bridge configuration, the flow rates in valves and /are defined as Q a and the flow rates in valves/ and/ have Q b, where Q a >> Q b./ The performance of the hydraulic actuator with MR valves will be evaluated using three models: 1) 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. Figure 2 shows test results of shear stresses of a commercially available MR fluid, namely MRF-132AD (Lord Corporation). The tests are conducted with rotational viscometer (MCR300 with MR cell, MRD180, Paar Physica) for a range of fairly low shear rates. Measured apparent viscosity of the MR fluid is shown in Figure 3. For the simulation, the MR fluid is assumed to have a nominal plastic viscosity of 6 Pa s, which is suitable for the predicted shear rates (< 10 s -1 ) in the activated valves. 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 Figure 4. The core is wound with insulated wire. A current applied through the wire coil around the bobbin creates a magnetic field in the gap between the flange and the flux return. The magnetic field increases the yield stress 5

6 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 Figure 4 (b) with the dimensional definitions. The primary parts of the MR valve design are pictured in Figure 5. A 1-D axisymmetric analysis is given by Kamath, Hurt and Wereley (1996), and an approximate rectangular duct analysis was provided by Wereley and Pang (1998). Gavin (2001) provided an analysis for annular valves with more appropriate radial field dependence. But in our analysis, we assume a uniform field across the valve gap. Following this latter study, we consider the approximate rectangular duct analysis of a flow mode valve system containing MR fluid. For Newtonian flow, the volume flux Q through the annulus is a function only of the area moment of inertia I (=bd 3 /12) of the valve cross-section, the fluid viscosity µ, and the pressure drop over the valve length, P/L a. The dimensional volume flux through the valve can be determined (Wereley and Pang, 1998; Wereley and Lindler, 1999) Q Q Q N BP BV 3 bd P = 12µ L po 3 bd P = 12µ L po 3 bd P = 12µ L po a a a (1 δ ) 2 (1 δ ) (1 + δ / 2) 2 3 δ (1 + δ / 2) + µ δ (1) where Q N is for Newtonian flow, Q BP is for Bingham-plastic flow and Q BV is for biviscous Poiseuille flow. Here, the non-dimensional plug thickness, δ = δ / d and nondimensional 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. 6

7 Normalizing each volume flux by the Newtonian value of volume flux yields the nondimensional volume fluxes for each of the flow models Q Q Q N BP BV = 1 2 = (1 δ ) (1 + δ / 2) = Q / Q (2) δ = (1 δ ) (1 + δ / 2) + µ (1 ) δ = Q 2 3 BP Figure 6 shows the trends of the non-dimensional volume flux as a function of the plug thickness δ, for Bingham-plastic and biviscous models, for the case of rectangular duct. In this figure, Q = 1 implies Newtonian flow and Q = 0 implies that the valve has blocked the flow. N Note that the MR valve behavior, based on a biviscous MR fluid constitutive model, is not capable of blocking the flow completely since Q > 0 for all 0 δ 1. 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 flow through the inactive valves. BV / Q N BV Actuator Performance The volume flux through each valve in Figure 1 can be defined as Q a Q b 3 bd = 12µ L a 3 bd = 12µ L a Q ( P a Q ( P b S S P H ) P ) L (4) The total flow rate, Q S from the motor and the flow rate for moving the actuator, Q W are defined as Q Q S W = Q a = Q a + Q b Q b = A u p (5) 7

8 The force equilibrium equation at the hydraulic actuator is ( P P ) A F (6) H L p = The force F includes friction force and output force of the cylinder. It follows that the steady-state force equilibrium of equation (6) and the velocity of the actuator will be: 3 bd P S u = ( Qa Qb ) ( Qa + Qb ) 24µ La Ap F A p PS (7) The maximum velocity of the actuator shaft and maximum force of the actuator can be expressed as: u max bd ( Q Q ) 3 a b = PS (8) 24µ La Ap F Q = Q A P a b p S (9) max Qa + Qb 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 non-dimensional 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. From equation (7), the non-dimensional actuator performance equation can be stated Q 12µ QW L = bd P 1 {( Q Q ) ( Q Q F} a W = a b a + b) 3 S 2 (10) where, F F / = A p PS. The maximum value of F is 1 and W Q is 0.5. If a current is applied to the shaded valves and in Figure 1, we can define for the rectangular duct: Q a = 1, for Newtonian flow 8

9 2 (1 δ ) (1 + δ / 2) for Bingham - plastic flow 2 Q b = 2 3 δ (11) (1 δ ) (1 + δ / 2) + µ (1 ) δ for biviscous flow 2 3 Corresponding to the MR fluid model used, the trends of Q b will follow the simulation results of Figure 6. Figure 7 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 Figure 8. As can be seen in Figure 8, the biviscous model cannot reach the maximum performance of the actuator. The maximum performance with δ = 1 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 Figure 7. System Efficiency The system efficiency, defined as the power transferred to the load divided by the MR valve supply power, is given by: = Power delivered to load Power supply to system = P Q P Q Q = Q a a b b a b η (10) Pa Qa + Pb Qb Qa + Qb In this definition of efficiency, only the hydraulic efficiency is considered. From the above, system efficiency of the actuator model can be derived as follows: 2Q (, µ ) = 1 1+ Q b η δ (11) b 9

10 Figure 9 shows the efficiency for the actuator when the working MR fluid behaves as a biviscous fluid. In this case, the maximum efficiency at δ = 1 can be derived as: η( δ, µ ) = 1 2µ µ δ = 1 1+ (12) Thus the system efficiency is a function of both δ of the valve and µ of the fluid. ACTUATOR IMPLEMENTATION To validate the nonlinear valve performance based on Bingham plastic model, a set of four MR valves was implemented within a Wheatstone bridge hydraulic power circuit to drive a hydraulic actuator using a gear pump. The experimental setup is shown in Figure 10. The actuator consists of three main parts: a hydraulic cylinder, a set of four MR valves with Wheatstone bridge configuration and a gear pump as a hydraulic source, as pictured in Figure 11. MR 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 important to the performance of the valve and actuator. A high efficiency design was explored for meso-scale MR valves (<25 mm OD). 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 10

11 decreases. Through numerical simulation, a target magnetic flux density at the gap was achieved in an optimized valve design, and its performance was validated via experiment. A thin film (FH , F.W.BELL) Hall sensor was used to measure the magnetic flux density at the gap and a hand-held Gauss meter (F.W.BELL, model 5080) was used to calibrate the Hall sensor. Figure 12 compares the experimental data with the analytical prediction from ANSYS/Emag 2-D for the valve with an air gap. Taking the error of the Hall sensor into consideration, the results in Figure 12 are in good agreement with each other. With these results, it was concluded that simulation using ANSYS/Emag 2-D was sufficiently accurate to predict the steady state performance of the magnetic field at the gap when filled with MR fluid. Thus, at 1.6 Ampere of applied current, a magnetic flux density of 0.8 Tesla will have been induced, which is sufficient for fluid energisation. Table 1 summarizes the valve parameters. The current to the MR valve was supplied from a DC power supply. Hydraulic Pressure Source A ¼-HP electric motor drove the pump through a flexible coupling at the bottom of the test rig as shown in Figure 10. The fixed displacement gear pump (D05 series, Parker) has a flow rate of 1.87 cc/rev. The motor speed was controlled by the motor controller and the speed was set to nominally 252 RPM, so that the flow rate of the system was nominally cc/min (7.854X10-6 m 3 /sec). To regulate the pressure from the gear pump, an accumulator was connected just after the gear pump as shown in Figure 11. Hydraulic Cylinder The hydraulic cylinder in this system had ½ inch bore diameter with ¼ inch shaft diameter. The maximum stroke of the actuator is 32 mm. To measure the displacement 11

12 response, a potentiometer was attached with a rigid bar, as shown in Figure 10. Table 2 shows specification of the apparatus and operational conditions. EXPERIMENTAL SETUP Experiments were performed to measure the output power of the actuator as a function of driving current to the MR valve. Figure 11 shows the configuration of the actuator in more detail with schematic diagram. The actuator had four MR valves in a Wheatstone bridge circuit. Three pressure transducers and two pressure gauges monitored the pressure inside the circuit. The pressure transducer, P S measured the source pressure and P H and P L measured the high and low side pressure, respectively. The accumulator regulated the source pressure from the gear pump and the reservoirs controlled the amount of fluid inside the actuation system according to the operational condition. The signal conditioner collected the output signal from three pressure transducers (PX600, Omegadyne Inc.) and an LVDT (TR50, Novotechnik) connected to the hydraulic actuator. Finally, all the data was transferred to a digital oscilloscope (TDS420A, Tektronix) for monitoring of the signal and data acquisition. Deadweights were hung off the end of the output hydraulic actuator and the position of the output hydraulic cylinder was measured using the LVDT. The bias pressure was set to about 70PSI because the pressure limit of the reservoir was 80 PSI. Applying a current to valves and, in Figure 11 activated the valves and the fluid flowed predominantly from P S to P H through valve. The flow into the lower chamber of the hydraulic actuator caused the piston to move up and the fluid in the upper chamber flowed to P L to the reservoir through valve. The activated valves and/ have fairly low shear rates compared to valves and. 12

13 For optimal performance, it is desired to have a zero shear rate condition in the actuator valve, but this may not be achievable in practical as described above. EXPERIMENTAL RESULTS In Figure 13, the experimental pressure and displacement response of the actuator shaft are plotted. As the current is applied to MR valves ( t = 0sec ) the high and low side pressures, P H and P L, increases and decreases, respectively. Before the shaft started to move, the low side pressure gradually decreased and high side increased. After the shaft of the actuator started to move, the pressure of each side remained constant until the shaft stopped. The velocity is plotted in Figure 14 as a function of the applied current. On increasing the deadweight, the velocity of the actuator shaft tended to decrease. On increasing the applied current, the velocity of the shaft increased but after 1.0 A, the velocity saturated. This implies that the maximum performance of the valve was reached. In Figure 15, the non-dimensional actuator performance of the test is compared with the simulation results from the Bingham-plastic model. The simulation results (lines) are shown from 0.4 to 1.6 A and the test results (symbols) are for the range of 0.6 to 1.6 A. Generally the predicted performance from the simulation was higher than the test results, but the trends of these results as a function of the current are fairly similar to each other. Introducing the biviscous model, as in Figure 16, the predictions can be made more consistent with test results. The rectangular symbols show the case of 0.6 A test and the coarse dashed line corresponds to its corresponding prediction. Above 1.0 A current input, the performance of the actuator almost reaches to the maximum performance line. 13

14 Figure 17 shows the efficiency of the system. The efficiency tended to increase on increasing the input current and deadweights. The maximum performance of the actuator system as a function of the pressure source is shown in Figure 18. As mentioned in equation (8) and (9), on increasing the pressure supplied by the pump, the maximum performance of the actuator will also increase, but is limited to an upper performance bound by the finite yield stress of the MR fluid. CONCLUSION A MR fluid based actuation system was analyzed and experimentally validated by testing a prototype. The hydraulic actuation system was constructed with four MR valves which have a Wheatstone bridge configuration and gear pump. The gear pump forces the fluid through the MR valves and the MR valves control the direction of flow through to the actuator. The controlled fluid flow makes the piston move. A non-dimensional volume flux was defined for describing the performance of the valve and the performance of the actuation system 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 was derived and it was found that the efficiency is a function of non-dimensional plug thickness, δ and viscosity ratio µ. The low pressure capacity of the reservoir limited the output power of the system, but the test results agree fairly well with predictions. The biviscous model showed better agreement with the test data than a Bingham-plastic model, and on increasing the deadweight, the tested efficiency was increased. The performance of the hydraulic actuator with MR valves is very dependent on the output mechanical load and driving current to the MR valves. The performance of the actuator system was increased on 14

15 increasing the source pressure. However, performance of the system is limited by the finite blocking pressure of the MR valve, because of yield stress of the MR fluids also finite. Even though the actuator investigated in the present study is an experimental prototype, scaling techniques using non-dimensional performance metrics derived in this paper, make it possible to expand use of this actuator system to applications requiring substantially different force, stroke or speed requirements. REFERENCES Choi, S.-B., Cheong, C.-C., Jung, J.-M. and Choi, Y.-T., Position Control of an ER Valve-Cylinder System via Neural Network Controller, Mechatronics, 7(1): Dyke, S. J., Spencer, B. F., Sain, M. K. and Carlson, J. D., Experimental Study of MR Dampers for Seismic Protection, Smart Materials and Structures, 7(5): Gordaninejad, F. and Kelso, S. P., Fail-safe Magneto-Rheological Fluid Dampers for Off-Highway, High-Payload Vehicles, Journal of Intelligent Material Systems and Structures, 11(5): Kamath, G. M., Hurt, M. K. and Wereley, N. M., Analysis and Testing of Bingham Plastic Behavior in Semi-Active Electrorheological Fluid Dampers, Smart Materials and Structures, 5(5):

16 Kordonski, W. I. and Golini, D., Fundamentals of Magnetorheological Fluid Utilization in High Precision Finishing, Journal of Intelligent Material Systems and Structures, 10(9): Lee, U., Kim, D., Hur, N. and Jeon, D., Design Analysis and Experimental Evaluation of an MR Fluid Clutch, Journal of Intelligent Material System and Structures, 10(9): Lindler, J. and Wereley, N. M., Analysis and Testing of Electrorheological Bypass Dampers, Journal of Intelligent Material Systems and Structures, 10(5): Milgram, J., Chopra, I., and Straub, F Rotors with Trailing-Edge Flaps: Analysis and Comparison with Experimental Data, Journal of the American Helicopter Society, 43(4): Stanway, R., Sproston, J. L. and El-Wahed, A. K., Applications of Electro- Rheological Fluids in Vibration Control: A Survey, Smart Materials and Structures, 5(4): Watton, J., 1989, Fluid Power Systems, Prentice Hall. 16

17 Wereley, N. M. and Lindler, J., Biviscous Damping Behavior in Electrorheological Dampers, ASME Symposium on Adaptive Structures and Materials Systems, AD-Vol. 59/MD-Vol.87, Nashville, TN, pp Wereley, N. M. and Pang, Li, Nondimensional Analysis of Semi-Active Electrorheological and Magnetorheological Dampers using Approximate Parallel Plate Models, Smart Materials and Structures, 7(5): Yoo, J.-H., Sirohi, J., and Wereley, N. M., Design of an MR Hydraulic Power Actuation System, SPIE Symposium on Smart Structures and Materials, Smart Structures and Integrated Systems Conference, 5-8 March, 2001, Newport Beach, CA, 4327(22): Zheng Lou, Robert D. Ervin and Frank E. Filisko, Behaviors of Electrorheological Valves and Bridges, ER Fluids: Mechanisms, Properties, Structure, Technology, and Applications, October 1991, Edited by R. Tao, pp NOMENCLATURE A p b d F F B L a Piston area Circumference width of the MR valve Gap of the MR valve Output force of the cylinder Block force Active length of the MR valve 17

18 P H P L P s Q u Q P δ δ η High side pressure in the cylinder Low side pressure in the cylinder Source pressure from the pump Mass flow rate Velocity of the cylinder Non-dimensional volume flux Pressure difference between the MR valves Plug thickness Non-dimensional plug thickness System efficiency µ Viscosity µ Nondimensional viscosity (µ po /µ pr ) µ po Viscosity in the post-yield region µ pr Viscosity in the pre-yield region Subscript N BP BV Newtonian flow Bingham plastic flow Biviscous flow 18

19 Table 1. Valve Dimensions. Outer Diameter Bobbin Diameter Flange Length/each Air gap No. of windings Max. Tesla at the gap 25.4 mm 14 mm 3 mm 0.5 mm 160 turns 0.80 Tesla Table 2. Specification and operational conditions of the apparatus. Apparatus Specification Operational Condition Electric Motor ¼ HP 252 RPM Gear Pump 1.87 cc/rev cc/min, about 100PSI Hydraulic Actuator ½ bore, ¼ shaft Max. 32 mm stroke DC power supply 20V, 10A. Max. 0.6 A. to 1.6 A. Load 1 lbs weight, 600g Rig 0, 0.6, 1, 1.5 Kg 19

20 Figure 1. Schematic of hydraulic actuator system with MR valves. Similarly shaded valves are on or off simultaneously. 20

21 Shear Stress (kpa) T 0.28 T 0.14 T Shear Rate (1/s) Figure 2. Shear stress versus shear rate diagram for the MR fluid, MRF-132AD (Lord Corporation, Measured on a Paar Physica Rheometer Model MCR300 with MR cell). 21

22 1000 Viscosity (Pa.s) Shear Rate (1/s) Figure 3. Apparent viscosity as a function of shear rate. 22

23 3 15 Details in (b) R8.5 R8.0 CW CCW φ (a) Valve cross section. All units in mm (b) Velocity Profile Figure 4. Schematic of the valve (a) and typical velocity profile for a Bingham plastic flow over the active valve length (b). 23

24 Figure 5. Photograph of the MR valve parts. 24

25 1 Volume Flux, Q [1] Bingham-plastic model (µ=0.0) Biviscous model µ=0.05 µ=0.4 µ=0.2 µ= Plug Thickness, δ [1] Figure 6. Flow characteristics of the rectangular duct valve model. 25

26 1 0.8 δ = 0.8 Force, F δ = 0.6 δ = 0.4 δ =1, ideal 0.2 δ = Working Flowrate, Q W Figure 7. The performance of the actuator for an MR modeled as a Bingham plastic. 26

27 1 0.8 ideal valve µ = 0.1 Force, F µ = 0.2 µ = 0.4 µ= Working Flow Rate, Q W ( δ =1) Figure 8. The performance of the actuator for an MR fluid modeled as a biviscous model. 27

28 1 Efficiency, η µ =0, Bingham-plastic µ = 0.05 µ = 0.1 µ = 0.2 µ = Non-dimensional plug thickness, δ Figure 9. Efficiency of the actuator. 28

29 Figure 10. Experimental setup for the evaluation of the actuator. 29

30 Accumulator M P Reservoir P S MR valves N X 3 N X 4 N Y 1 2 N Y P H P L F Figure 11. Configuration of the hydraulic actuator with schematic diagram. 30

31 Magnetic flux density (Te) Test result, air Simulation, air Simulation, MR Applied current (A) Figure 12. Performance of the magnetic flux density at the gap with MR fluid permeability (simulation) and with air permeability (test and simulation, Permalloy). 31

32 40 Disp. (mm) Pressure (kpa) PH PL Time (sec) Figure 13. A case of experimental pressures and displacement of actuator shaft. 32

33 20 Velocity, mm/s F =0.55 F =0.65 F =0.70 F = Applied Current, A Figure 14. The experimental actuator velocity as a function of applied current. 33

34 A 1.0 A 0.6 A 0.4 A Force, F Working Flow Rate, Q W ( µ=0.0) Figure 15. The experimental non-dimensional actuator performance with Binghamplastic model simulation (Symbols: Test, Lines: Simulation). 34

35 A 1.0 A 0.6 A 0.4 A Force, F Working Flow Rate, Q W ( µ=0.05) Figure 16. The experimental non-dimensional actuator performance with biviscous model simulation (Symbols: Test, Lines: Simulation). 35

36 1 Efficiency, η F =0.76 F =0.70 F =0.65 F = Applied Current, A. Figure 17. The experimental results for the system efficiency. 36

37 Block Force, F B [N] PS 200 PSI 100 PSI = 500 PSI 400 PSI 300 PSI Cylinder velocity, u [m/sec] ( µ =0.05) Figure 18. The predicted performance of the actuator system as a function of pressure supplied by pump. 37