DESIGN OF A HIGH-EFFICIENCY MAGNETORHEOLOGICAL VALVE JIN-HYEONG YOO AND NORMAN M. WERELEY Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering University of Maryland, College Park, Maryland 2742 USA E-mail: jhyoo@glue.umd.edu A high efficiency design was explored for meso-scale MR valves (<25 mm O.D.). The main design issues in the MR valve involve the magnetic circuit and nonlinear fluid mechanics. The performance of the MR valve will be limited by saturation phenomenon in the magnetic circuit and by the yield stress of the MR fluid. The non-dimensional plug thickness is evaluated as a basis for evaluating the valve efficiency. In this paper, design parameters of the MR valve were studied and an optimal performance was designed using these parameters. A maximum magnetic flux density at the gap was achieved in the optimized valve design based on a constraint on the outer diameter limitation. Valve performance was verified with simulation. A flow mode bypass damper system was fabricated and was used to experimentally validate the valve performance. Introduction The substantial field-induced yield stresses exhibited by MR fluids make possible numerous industrial applications. [] Furthermore, there are several studies to develop active devices with electrorheological (ER) [2] or magnetorheological (MR) fluids [3] in hydraulic actuation systems. There are many advantages of using MR valves in hydraulic actuation systems, including: valves have no moving parts, eliminating the complexity and durability issues in conventional mechanical valves. A wheatstone bridge based hydraulic actuator is being developed at the University of Maryland for compact actuation application in unmanned air vehicles and helicopters. The MR valve is a key component of the actuation system. The actuator relies on flow rates for a given pump flow rate, and avoids, to a large degree, fluid compliance. 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, most important advantages of MR valve 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 [4] as an example. Two disadvantages are the block force and the cut-off frequency of this actuator. The block force depends on the yield stress of the MR fluid, and the cut-off frequency is a function of the response time of MR fluid. In this paper, MR valves will be analyzed and evaluated experimentally to determine its ability to control flow and pressure conditions. Also, magnetic field analysis will be conducted to optimize the electromagnetic performance with given material properties. The pressure differences achieved in the MR valve due to the applied current are also measured to validate the design methodology. The performance of the MR valve is compared using the experimental non-dimensional plug thickness to clarify the efficiency of the valve. ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM /
2 MR Valves MR valves used in this study consist of a core and a flux return, and an annulus through which the MR fluid flows, as shown in Figure. The bobbin shaft is wound with insulated wire. A current applied through the wire coil around the bobbin creates a magnetic field in the gap between the core and the flux return. The magnetic field increases the yield stress of the MR fluid between the core and the flux return. This increase in yield stress alters the velocity profile of the fluid in the gap by creating a plug flow, decreases the volume flux, Q, and raises the pressure difference, P, required for a given flow rate. We now consider the approximate parallel plate analysis of the flow mode valve system containing MR fluid, which follows the Bingham-plastic flow model. The typical velocity profile is illustrated in Figure. The total volume flux [5] is 3 bd 2 Q = ( δ ) ( + δ / 2) P () 2µ La where the non-dimensional plug thickness is δ = δ / d and δ = for Newtonian flow. Here, b is the circumference of the MR valve and µ is the differential post-yield viscosity. To verify the performance of the valve, an MR bypass damper was designed and fabricated. A schematic of a flow mode bypass damper is shown in Figure 2. The volume flux displaced by the hydraulic cylinder head is proportional to the cylinder head velocity, v, or Q=A p v, where A p is the area of the cylinder head minus the area of the shaft. Solving for the force acting at the shaft, the pressure drop becomes F 2µ La Ap P = = v 3 2 (2) Ap bd ( δ ) ( + δ / 2) Measuring shaft force, F and velocity, v experimentally, we obtain δ from 2 3 3 2µ La Ap v δ δ + = (3) 2 2 3 bd F In evaluating the valve performance, the non-dimensional plug thickness in equation () plays a substantial role. Namely, in the case of δ =, there is no flow through the valve as in the case of an ideal valve. Because the non-dimensional plug thickness is a function of flow rate and pressure difference in the valve, and has a value between and, it is a good measure of valve efficiency. 3 Magnetic Circuit for the Valve A meso-scaled MR valve design was explored. The valve main parts are pictured in Figure 3. MR fluid has changing characteristics of its yield stress according to the applied magnetic field. Therefore, the magnetic field applied to the MR fluid must be correlated with prediction or measurement. Considering the magnetic circuit, the main design parameters are gap distance, bobbin shaft diameter, bobbin core length, thickness of flux return and number of windings in the coil, which is related to the length of the bobbin shaft. To achieve an efficiency magnetic circuit, the area of the path of magnetic flux should be maintained constant. Theoretically, the smaller air gap distance will be better because the permeability of the MR fluid at the gap is much less than the iron-based bobbin and flux return. Practical gaps typically range from.25 to 2 mm for ease of ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 2/2
manufacture and assembly. A constant gap between the core and flux return should be maintained for uniformity of the magnetic flux in the gap. Furthermore, the distance of the gap should be considered in the concept of fluid flow. The gap determines the flow rate for a given pressure difference as shown in equation (). In this study, the gap will be set to.5 mm. The flux return has two functions: one is as an element in the magnetic circuit and the other is as a connector to the tubing adapter with a seal as shown in Figure 3. In most cases of small valve design, the wall thickness of the flux return will be determined by the size of threads for the adapter. In this paper, the magnetic field finite element analysis for the valve system is conducted using ANSYS/Emag 2D. The purpose of the analysis is to identify the effect of the saturation phenomenon in the magnetic circuit and to evaluate the effect of the design parameters at the valve. The magnetization data of Permalloy [6] steel and Hiperco 5-A material are used in this analysis. Throughout this analysis, two optimized models of MR valve are introduced. The first is a flux return with an outer diameter of 2 mm (Model ), and second with an outer diameter of 25.4 mm (Model 2). 3. Bobbin diameter The bobbin shaft radius is the most sensitive design parameter limiting the magnetic performance. In Figure 4, the magnetic flux density at the gap is plotted versus the bobbin shaft radius for a low permeability Permalloy steel, and a high permeability Hiperco 5A powder metallurgical alloy. It is desired to have as high a flux as possible. Both materials provide adequate flux above 4 mm bobbin shaft radius. However, the low permeability Permalloy rolls off below 4 mm much faster than the high Permeability Hiperco 5A, due to saturation. Therefore, to reduce the bobbin shaft and the valve diameter, higher permeability, more costly, magnetic materials must be used. 3.2 Core length Figure 5 shows the trend of magnetic flux density at the gap as a function of core length. In the case of Permalloy, as the length of the core decreases, the magnetic flux density at the gap tends to increase because the magnetic flux density at the bobbin shaft decreases with decreasing core length. Decreasing the core length results in higher magnetic flux density at the gap by reducing saturation at the bobbin shaft. To verify this effect, the magnetic flux density at the gap was calculated for cases of, 4 and 2 mm core length, as shown in Figure 6. In the case of 2 mm core length has better performance. Figure 7 shows the magnetic flux density along the air gap with various active core lengths. In this narrow range of core lengths, as core length increases, the uniformity of the magnetic field across the active length improves, but the level of magnetic flux density also decreases. 3.3 Magnetic material The maximum magnetic flux density at the gap is about.4 Tesla with Permalloy material in the case of Model. Considering the shear stress versus magnetic inductance of MRF-32LD (Lord Corp., 999) and magnetization curve for Permalloy [6],.8 Tesla is the maximum magnetic flux density achievable with these materials. To achieve.8 Tesla at the gap, we should increase the outer diameter to 25.4 mm as Model 2. The maximum magnetic flux density of this valve will be about.8 Tesla with.6-ampere ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 3/3
input current, as shown in Figure 8. Table shows the main design parameters of the each model. In the case of high permeability material (Hiperco 5-A) in Figures 4 and 5, the bobbin shaft can be reduced, and the core length increased, while still obtaining the same performance as the larger valve made of Permalloy steel. 4 Measurement of the Magnetic Flux density In this experiment, a thin film (FH-3-6, F.W.BELL) hall sensor is used to measure the magnetic flux density at the small gap and 58 hand-held gauss meter (F.W.BELL) is used for calibrating the hall sensor. Figure 8 compares the experimental data with the analytical prediction from ANSYS/Emag 2-D for Model 2. Taking the sensing error of the hall sensor into the consideration, the results in Figure 8 are in good agreement with each other. With these results, we can conclude that the simulation result with ANSYS/Emag 2-D will be accurate enough to predict the performance of the magnetic field at the gap when filled with MR fluid. 5 Analytical results Due to the non-linearity of the MR-fluid, determination of the performance of the valve requires numerical analysis. In the following analysis, we use a commercially available MR-fluid data, namely MRF-32LD (Lord Corp., 999). To evaluate the valve performance, the pressure difference and flow rate will be calculated. For the Binghamplastic model, the material properties of the dynamic yield stress, τ y, and plastic viscosity, µ, of the MR-fluid will be required as a function of applied magnetic field. The dynamic yield stress for this fluid can be approximated by a cubic equation of the magnetic field, so that 3 2 τ y = a3 B + a2 B + a B + a. The polynomial coefficients were determined by least-squares fit of the dynamic yield stress data as a function of magnetic field from Lord Corporation (999), and are: a =-.877 kpa, a =7.42 kpa/te, a 2 =22.56 kpa/te 2 and a 3 =-86.5 kpa/te 3. To simplify the analysis, the MR fluid is assumed to have a nominal plastic viscosity of.6 Pa sec. The pressure difference versus flow rate diagram is shown in Figure with experimental results for the case of Model. As increasing the applied currents, the enhancement of pressure difference decrease cause the effect of saturation at the bobbin shaft. The shear stress of the MR fluid in the case of the Model 2 is shown in Figure 9. The maximum shear stress is about 47 kpa with.6-ampere input current. Comparing the pressure differences according to the flow rate in Figure with Figure, the valve performance of the Model 2 is higher than the Model. 6 Experimental results To validate this non-dimensional analysis using the nonlinear Bingham-plastic shear flow and the magnetic circuit design with ANSYS/Emag 2-D, a high stroke ( 2cm ) MR damper was constructed. The damper consists of four main parts: a hydraulic cylinder, ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 4/4
industrial tube fittings, an accumulator and an MR bypass valve as pictured in Figure. The damper is charged with MR fluid, MRF-32LD (Lord Corporation). The accumulator connected to the cylinder increase the overall pressure inside the damper for the purpose of reducing the amount of air bubbles inside and preventing cavitation. For the experimental validation of the flow mode bypass valve equations, force measurement from triangular displacement cycles were recorded on a servo-hydraulic testing machine. The MR bypass valve damper shaft mounted in the clevises, triangularly oscillates the shaft of the damper, measures the shaft displacement using an LVDT in MTS hydraulic actuator and measures the applied load using a 25 lb load cell. In Figure, the flow characteristics of the Model and Model 2 valve are plotted along with simulation results. The yield stress data of MR fluid is applied from LORD Corporation s data sheet. Comparing Figure with Figure, the enhancement of the flow characteristics is apparent. Figure 2 shows the test results of non-dimensional plug thickness of Model and Model 2 valve with simulation results, respectively at a constant current input. From the valve performance point of view, we can say that the Model 2 valve has a higher efficiency than Model because the input current and number of windings are same for the each model. Figure 3 shows the time responses of the each valve with same input step current. As the results of pressure difference are different, the response is not directly comparable. Figure 3 shows the normalized step responses for each valve. Comparing the step responses of each valve, the time response of the Model 2 is comparable to that of Model, in spite of the higher-pressure difference at the valve. 7 Conclusion Considering the shear stress versus magnetic inductance of the MR-fluid (MRF-32LD, Lord Corp., 999) and magnetization curve for Permalloy [6], a maximum magnetic flux density at the gap was achieved with optimized design and was verified with simulation and experiment. As the results, we can get following conclusions:. Using low permeability Permalloy steel material, 5kPa block pressure can be achieved with our MR valve design with a 25.4 mm outer diameter. 2. Using high permeability material, the size of the valve can be reduced and the active core length can be increased. 3. Comparing the non-dimensional plug thickness, the efficiency of the Model 2 valve is higher than Model. References. Carlson, J. D. Catanzarite, D. M. Clair, K. A. S. Commercial Magnetorheological Fluid Devices Technology, International Journal of Modern Physics B, v., n.22-23, 996, p.2857 2. Zheng Lou, Robert D. Ervin and Frank E. Filisko, Behaviors of Electrorheological Valves and Bridges, Proceedings of the International Conference on ER fluid, 5-6 October 99, pp.398-423. 3. J. -H. Yoo, J. Sirohi and N. M. Wereley, Design of a MR hydraulic power actuation system, SPIE s 8th Annual International Symposium on Smart Structures and Materials, 4-8 March 2, Long Beach CA. Paper No. 4327-22. ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 5/5
4. Milgram, J. H. and Chopra, I., Parametric design study for actively controlled trailing edge flaps, Journal of the American Helicopter Society, v.43, n.2, 998, p-9. 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, v. 5, n. 5, pp.576-59. 6. Herbert C. Roters, Electromagnetic Devices, John Wiley & Sons, Inc., 94. Table. The dimensions of the valves Outer Dia. Bobbin Dia. Core L/each Air gap No. of windings Max. Te at the gap Model 2. mm 7 mm 2 mm.5 mm 6 turns.4 Tesla Model 2 25.4 mm 4 mm 3 mm.5 mm 6 turns.8 Tesla Figure. Schematic of the valve and velocity profile. Figure 2. Test configuration for the MR valve Figure 3. Photograph of a design of the MR valve parts. Magnetic flux densit (Te).2.8.6.4.2 Magnetic flux density (Te).8.6.4.2 Hiperco 5A Permalloy Core Bobbin shaft.4 Hiperco 5A Permalloy.2 2 3 4 5 Bobbin shaft radius (mm) Figure 4. Magnetic flux density at the gap as a function of the bobbin shaft radius. (gap =.5 mm, air) 2 4 6 8 2 3 Core length (mm) Figure 5. Magnetic flux density at the gap as a function Figure 6. The magnetic flux density at the gap with of the core length. (gap=.5 mm, air) various core lengths. (Permalloy, Model ) - -5 5 8 2 Relative position along the air gap(mm) Figure 7. Magnetic flux density along the gap with various core lengths. (Permalloy, Model 2, i=amp) Magnetic flux density (Te) Magnetic flux density (Te).8.7.6..8.6.6.4.2 L=mm L=2mm L=3mm L=4 mm Core L = 2 mm Core L = 4 mm Core L = mm ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 6/6
Magnetic flux density (Te).8.6.4.2.4.8.2.6.8.6.4.2 Simulation Test result 2 4 6 Figure 8. Performance of the magnetic flux density at the gap with MR Figure 9. Shear stress of the MR fluid permeability. comparison between test and simulation, air. fluid at the gap. (Permalloy, (Permalloy, Model 2) Model 2) Shear Stress (kpa) 5 4 3 2.4.8.2.6 DC Power supply Hydraulic Cylinder MR Valve Accumulator Signal Conditioning Amplifier Load cell Pressure Difference (kpa) 25 2 5 5 MTS Hydraulic Actuator MTS Controller Digital Oscilloscope Figure. Experimental setup for performance measurement of the MR valve..6 A.2 A.8 A.6 A.4 A 2 3 4 5 6 Flow Rate (cc/sec) 2 3 4 5 6 Flow Rate (cc/sec) 5 5 2 25 Pressure Difference (kpa) Figure. Flow characteristics of the Model and Figure 2. Comparison of the non-dim. δ Model 2 MR valve. (Symbols: test and between Model and Model 2. Lines: simulation) (i =.6 Amp.) δ.8.6.4 Model 2 Model Simulation test Pressure Response (kpa) 8 4 Model 2 Model 8 4 Pressure Response (kpa) Normalized Response.6.2.8.4 Model 2 Model..2 Time (sec)..2 Time (sec) Figure 3. Comparison of the time responses of pressure difference and normalized pressure difference between Model and Model 2. (Test results) ERMRp7.doc submitted to World Scientific 8/24/2: :2 AM 7/7