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 20742 USA E-mail: wereley@eng.umd.edu

Phone: (301) 405-1927, FAX: (301) 314-9001

2 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, 17-21 March 2002

REVISED

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.

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

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 PS to PH 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

5

to PL 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 Qa and the flow rates in valves�� and�� have Qb, where

Qa >> Qb.�

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

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 (=bd3/12) of the

valve cross-section, the fluid viscosity µ, and the pressure drop over the valve length,

∆P/La. The dimensional volume flux through the valve can be determined (Wereley and

Pang, 1998; Wereley and Lindler, 1999)

−++−∆=

+−∆=

∆=

δδµδδµ

δδµ

µ

31

23)2/1()1(

12

)2/1()1(12

12

22

3

23

3

apoBV

apoBP

apoN

LPbdQ

LPbdQ

LPbdQ

(1)

where QN is for Newtonian flow, QBP is for Bingham-plastic flow and QBV is for

biviscous Poiseuille flow. Here, the non-dimensional plug thickness, d/δδ = and non-

dimensional viscosity ratio, µ , which is defined as the ratio of the post-yield differential

viscosity ( poµ ) to the pre-yield differential viscosity ( prµ ), have been introduced.

7

Normalizing each volume flux by the Newtonian value of volume flux yields the non-

dimensional volume fluxes for each of the flow models

NBVBV

NBPBP

N

QQQ

QQQQ

/)3

1(23)2/1()1(

/)2/1()1(

1

22

2

=

−++−=

=+−=

=

δδµδδ

δδ (2)

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, 1=Q implies Newtonian flow and 0=Q implies that the valve has

blocked the flow.

Note that the MR valve behavior, based on a biviscous MR fluid constitutive

model, is not capable of blocking the flow completely since 0>BVQ for all 10 ≤≤ 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 flow through the inactive valves.

Actuator Performance

The volume flux through each valve in Figure 1 can be defined as

)(12

)(12

3

3

LSba

b

HSaa

a

PPQL

bdQ

PPQL

bdQ

−=

−=

µ

µ (4)

The total flow rate, QS from the motor and the flow rate for moving the actuator, QW are

defined as

uAQQQQQQ

pbaW

baS

=−=+=

(5)

8

The force equilibrium equation at the hydraulic actuator is

FAPP pLH =− )( (6)

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:

+−−=Sp

babapa

S

PAFQQQQ

ALPbdu )()(

24

3

µ (7)

The maximum velocity of the actuator shaft and maximum force of the actuator can be

expressed as:

Spa

ba PALQQbdu

µ24)(3

max

−= (8)

Spba

ba PAQQQQF

+−=

max (9)

The maximum velocity and force are functions of the pressure source, PS. 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

{ }FQQQQPbd

LQQ babaS

aWW )()(

2112

3 +−−== µ (10)

where, SpPAFF /= . The maximum value of F is 1 and WQ is 0.5. If a current is

applied to the shaded valves � and � in Figure 1, we can define for the rectangular

duct:

flowNewtonian for ,1=aQ

9

−++−

+−=

flow biviscousfor )3

1(23)2/1()1(

flow plastic-Binghamfor )2/1()1(2

2

2

δδµδδ

δδbQ (11)

Corresponding to the MR fluid model used, the trends of bQ 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 1=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 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:

ba

ba

bbaa

bbaa

QQQQ

QPQPQPQP

+−=

+−==

system supply toPower load todeliveredPower η (10)

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:

b

b

QQ

+−=

121),( µδη (11)

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 1=δ can be derived as:

µµµδη

δ +−=

= 121),(

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

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-301-060, 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 471.24 cc/min (7.854X10-6 m3/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

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, PS measured the source pressure and

PH and PL 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 PS to PH 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 PL to the reservoir through valve �. The activated valves � and��

have fairly low shear rates compared to valves � and �.

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 ( sec0=t ) the high and low side

pressures, PH and PL, 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.

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

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., 1997. “Position Control of an

ER Valve-Cylinder System via Neural Network Controller,” Mechatronics, 7(1):37-52.

Dyke, S. J., Spencer, B. F., Sain, M. K. and Carlson, J. D., 1998. “Experimental Study of

MR Dampers for Seismic Protection,” Smart Materials and Structures, 7(5):693-703.

Gordaninejad, F. and Kelso, S. P., 2000. “Fail-safe Magneto-Rheological Fluid Dampers

for Off-Highway, High-Payload Vehicles,” Journal of Intelligent Material Systems and

Structures, 11(5):395-406.

Kamath, G. M., Hurt, M. K. and Wereley, N. M., 1996. “Analysis and Testing of

Bingham Plastic Behavior in Semi-Active Electrorheological Fluid Dampers,” Smart

Materials and Structures, 5(5):576-590.

16

Kordonski, W. I. and Golini, D., 2000. “Fundamentals of Magnetorheological Fluid

Utilization in High Precision Finishing,” Journal of Intelligent Material Systems and

Structures, 10(9):83-689.

Lee, U., Kim, D., Hur, N. and Jeon, D., 2000. “Design Analysis and Experimental

Evaluation of an MR Fluid Clutch,” Journal of Intelligent Material System and

Structures, 10(9):701-707.

Lindler, J. and Wereley, N. M., 2000. “Analysis and Testing of Electrorheological

Bypass Dampers,” Journal of Intelligent Material Systems and Structures, 10(5):363-376.

Milgram, J., Chopra, I., and Straub, F. 1998. “Rotors with Trailing-Edge Flaps: Analysis

and Comparison with Experimental Data,” Journal of the American Helicopter Society,

43(4):319-332.

Stanway, R., Sproston, J. L. and El-Wahed, A. K., 1996. “Applications of Electro-

Rheological Fluids in Vibration Control: A Survey,” Smart Materials and Structures,

5(4):464-482.

Watton, J., 1989, Fluid Power Systems, Prentice Hall.

17

Wereley, N. M. and Lindler, J., 1999. “Biviscous Damping Behavior in

Electrorheological Dampers,” ASME Symposium on Adaptive Structures and Materials

Systems, AD-Vol. 59/MD-Vol.87, Nashville, TN, pp. 67-75.

Wereley, N. M. and Pang, Li, 1998. “Nondimensional Analysis of Semi-Active

Electrorheological and Magnetorheological Dampers using Approximate Parallel Plate

Models,” Smart Materials and Structures, 7(5):732-743.

Yoo, J.-H., Sirohi, J., and Wereley, N. M., 2001. “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):148-158.

Zheng Lou, Robert D. Ervin and Frank E. Filisko, 1991. “Behaviors of Electrorheological

Valves and Bridges,” ER Fluids: Mechanisms, Properties, Structure, Technology, and

Applications, 15-16 October 1991, Edited by R. Tao, pp. 398-423.

NOMENCLATURE

Ap Piston area

b Circumference width of the MR valve

d Gap of the MR valve

F Output force of the cylinder

FB Block force

La Active length of the MR valve

18

PH High side pressure in the cylinder

PL Low side pressure in the cylinder

Ps Source pressure from the pump

Q Mass flow rate

u Velocity of the cylinder

Q Non-dimensional volume flux

∆P Pressure difference between the MR valves

δ Plug thickness

δ Non-dimensional plug thickness

η System efficiency

µ Viscosity

µ Nondimensional viscosity (µpo/µpr)

µpo Viscosity in the post-yield region

µpr Viscosity in the pre-yield region

Subscript

N Newtonian flow

BP Bingham plastic flow

BV Biviscous flow

19

Table 1. Valve Dimensions.

Outer Diameter 25.4 mm

Bobbin Diameter 14 mm

Flange Length/each 3 mm

Air gap 0.5 mm

No. of windings 160 turns

Max. Tesla at the gap 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 471.24 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

20

Figure 1. Schematic of hydraulic actuator system with MR valves.

Similarly shaded valves are on or off simultaneously.

21

0 20 40 60 80 100Shear Rate (1/s)

0

4

8

12

She

ar S

tress

(kP

a)

0.14 T

0.28 T

0.42 T

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).

22

0 20 40 60 80 100Shear Rate (1/s)

0.1

1

10

100

1000

Vis

cosi

ty (P

a.s)

Figure 3. Apparent viscosity as a function of shear rate.

23

42

φ25.

4

Details in (b)3 15

R8.

0R

8.5

CW CCW

42

φ25.

4

Details in (b)3 15

R8.

0R

8.5

CW CCW

(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).

24

Figure 5. Photograph of the MR valve parts.

25

0 0.2 0.4 0.6 0.8 1Plug Thickness, δ [1]

0

0.2

0.4

0.6

0.8

1

Vol

ume

Flux

, Q

[1]

Bingham-plastic model (µ=0.0)

Biviscous model

µ=0.4

µ=0.2

µ=0.1

µ=0.05

Figure 6. Flow characteristics of the rectangular duct valve model.

26

0 0.1 0.2 0.3 0.4 0.5Working Flowrate, QW

0

0.2

0.4

0.6

0.8

1

Forc

e, F

δ =1, ideal

δ = 0.8

δ = 0.6

δ = 0.4 δ = 0.2

Figure 7. The performance of the actuator for an MR modeled as a Bingham plastic.

27

0 0.1 0.2 0.3 0.4 0.5Working Flow Rate, QW ( δ =1)

0

0.2

0.4

0.6

0.8

1

Forc

e, F

µ = 0.2

µ = 0.4

µ=0.05

ideal valve µ = 0.1

Figure 8. The performance of the actuator for an MR fluid modeled as a biviscous model.

28

0 0.2 0.4 0.6 0.8 1Non-dimensional plug thickness, δ

0

0.2

0.4

0.6

0.8

1

Effic

ienc

y, η

µ =0, B

ingham-plastic

µ = 0.05

µ = 0.1

µ = 0.2

µ = 0.4

Figure 9. Efficiency of the actuator.

29

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

30

PL

PH

��

�� ��

��

PS

F

MR valves

Accumulator

Reservoir

12

34

P

M

PL

PH

��

�� ��

��

PS

F

MR valves

Accumulator

Reservoir

12

34

P

M

Figure 11. Configuration of the hydraulic actuator with schematic diagram.

31

0 2 4 6Applied current (A)

0

0.2

0.4

0.6

0.8

1

Mag

netic

flux

den

sity

(Te)

Test result, airSimulation, airSimulation, MR

Figure 12. Performance of the magnetic flux density at the gap with MR fluid

permeability (simulation) and with air permeability (test and simulation, Permalloy).

32

-2 0 2 4 6 8 10Time (sec)

0

200

400

600

800

Pres

sure

(kPa

)

0

10

20

30

40

Dis

p. (m

m)

PH

PL

Figure 13. A case of experimental pressures and displacement of actuator shaft.

33

0.4 0.6 0.8 1 1.2 1.4 1.6Applied Current, A

5

10

15

20

Velo

city

, mm

/s

F =0.76

F =0.70

F =0.65

F =0.55

Figure 14. The experimental actuator velocity as a function of applied current.

34

0 0.1 0.2 0.3 0.4 0.5Working Flow Rate, QW

( µ=0.0)

0

0.2

0.4

0.6

0.8

1

Forc

e, F

1.6 A1.0 A0.6 A0.4 A

Figure 15. The experimental non-dimensional actuator performance with Bingham-

plastic model simulation (Symbols: Test, Lines: Simulation).

35

0 0.1 0.2 0.3 0.4 0.5Working Flow Rate,

QW ( µ=0.05)

0

0.2

0.4

0.6

0.8

1

Forc

e, F

1.6 A1.0 A0.6 A0.4 A

Figure 16. The experimental non-dimensional actuator performance with biviscous model

simulation (Symbols: Test, Lines: Simulation).

36

0.4 0.8 1.2 1.6 2Applied Current, A.

0.5

0.6

0.7

0.8

0.9

1

Effic

ienc

y, η

F =0.76 F =0.70 F =0.65 F =0.55

Figure 17. The experimental results for the system efficiency.

37

0 0.04 0.08 0.12Cylinder velocity, u [m/sec] ( µ =0.05)

0

20

40

60

80

100

Bloc

k Fo

rce,

FB

[N]

PS = 500 PSI

400 PSI300 PSI200 PSI

100 PSI

Figure 18. The predicted performance of the actuator system as a function of pressure

supplied by pump.