MR Fluid MTech Seminar

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VIBRATION CONTROL USING

MAGNETORHEOLOGICAL FLUIDS

AE 694 - M.Tech Seminar

By

NITHIN S NAIR(10301036)

Under the guidance of

Prof. Ms. Mira Mitra

Department of Aerospace Engineering,

Indian Institute of Technology, BombayNovember, 2010


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Table of contents

Chapter Page No.

1. Introduction 1

1.1 Smart Materials 1

1.2 Magnetorheological (MR) Fluids 1

1.3 Theory 2

1.4 The Bingham Plastic Model for MR Fluids 3

1.5 Pre-Yield Response 4

1.6 Post-Yield Flow 4

1.7 Carrier Fluids 6

1.8 Other Effects 6

2. Applications of Magnetorheological Fluids 7

2.1 Commercial MR Fluids 7

2.2 Heavy Duty Vehicle Seat Suspensions 7

2.3 Control of Seismic Vibrations in Structures 82.4 Seal-Less Vibration Damper 9

2.5 MR fluids in structural applications 9

3. The Application of MR Damper for Semi-Active Control of

Vehicle Suspension System 11

3.1 Introduction 11

3.2 MR Damper and Parameter Estimation 11

3.3 BOUC WEN Model and Parameters Estimation 13

3.4 Semi-Active Control of Vehicle Suspension System 14

3.5 Discussion 16

4. Seismic Response Control Using Multiple MR Dampers 18

4.1 Introduction 18

4.2 MR damper Modeling 18

4.3 Clipped-Optimal Control Algorithms 19


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4.4 Five Story Structure - Two MR Dampers 21

4.5 Discussion 21

5 Conclusion 23


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List of figures

Figure No. Title Page No.

1.1 A MR fluid under magnetic field 1

1.2 The schematic of off state and on state of MR fluids 2

1.3 Shear stress versus shear strain rate for the Bingham model 3

1.4 Operational modes of MR fluid devices 4

1.5 Shear stress shear strain relationship of MR material 42.1 Rheonetic RD-1001/4 MR Fluid Damper 7

2.2 Schematic of MR Fluid Seismic Damper 8

2.3 Rheonetic RD-1013-1 vibration damper 9

2.4 Three-layered adaptive beam configuration with MR material 10

3.1 Schematic Diagram of the MR Damper 12

3.2 Responses of force vs. time and force vs. displacement underdifferent electric currents 13

3.3 Equivalent damping coefficient vs. velocity under variouselectric currents 13

3.4 Bouc Wen model 14

3.5 Simplified quarter car model 15

3.6 Acceleration response of sprung mass 16

4.1 Simple Mechanical Model of the MR Damper 18

4.2 Graphical Representation of Algorithm for Selecting the

Command Signal 20

4.3 Block Diagram of Semi-Active Control System 21


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ABSTRACT

Vibration control is a set of technical means aimed to reduce the undesired vibrations in a

structure. There are several techniques used in vibration control. Mainly these techniques can

be classified as passive, active and hybrid. Passive methods have no feedback systems, butactive system incorporates real-time recording instrumentation and feedback system to

control vibration. Hybrid is a combination of both active and passive. In this seminar the role

of smart materials, mainly Magnetorheological fluids (MR), is highlighted.

Magnetorheological fluids are those field responsive fluids which change their rheological

properties when a magnetic field is applied. These fluids can be used in structures to reduce

the vibration by changing its damping force using a magnetic field. To study the variation of

properties of a MR fluid, a suitable model should be developed to explain the variation.Several models like Bingham plastic model, Bouc-Wen model etc. has been proposed. This

seminar deals with mainly Bouc-Wen model which is suitable to explain the behaviour of

MR fluid when used in a damper. The MR fluids when used in a damper can be used in

automobile suspensions, aircraft landing gear, seismic vibration damping system etc. In this

report, the role of MR fluids in seismic vibration reduction in buildings and vehicle

suspension is discussed.


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CHAPTER-1

INTRODUCTION

1.1 Smart Materials

Smart materials are those materials which can alter some of their properties on the

application of an external field. Materials exhibiting ferroelectricity, pyroelectricity,

piezoelectricity, a shape memory effect, electrostriction, magnetostriction, electro-chromism,

photomagnetism are some examples. These materials are mostly used in their solid state.

There is another class of s mart materials known as field -responsive fluids which are soft,

typically dispersions or gels, rather than solids. Magnetorheological fluids, electrorheological

fluids, ferrofluids and certain types of polymeric gels are included in this kind. Field

responsive fluids constitute dispersions of particles in a carrier liquid and some aspect of their

rheology can be controlled by an external electric field or magnetic field. In this seminar, the

focus is on Magnetorheological fluids (MR fluids).

1.2 Magnetorheological (MR) Fluids

Magnetorheological fluids come under the category of field-responsive fluids. Their

rheological properties may be rapidly varied by applying a magnetic field. They are

suspensions of particles in inert carrier liquids. When exposed to a magnetic field, the

suspended particles polarize and interact to form a structure aligned with the magnetic

field that resists shear deformation or flow. The particles are of size of the order of 1 to 10

m and these are added to fluids such as mineral oils or silicone oils. The weight fractions of

these particles are large and vary in the range 30% to 50%. MR fluids also contain small

amounts of additives so as to affect the polarisation of the particles and stabilize the

suspension against settling.

Figure 1.1 A MR fluid under magnetic field [9]


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The change in properties of MR fluids is due to the realignment of particles in the fluid to

form fibrils, or long strands of suspended particles, that resist shear. The process of fibration

occurs in a few milliseconds after the application of the field. In the absence of an external

field, MR fluid may be characterized as Newtonian, i.e., resisting shear strain is proportional

to shear stress. But actually, because of the additives they contain and the heavy loading of

solid particles, they act as non-Newtonian even when no field is applied.

1.3 Theory

As explained above the change in properties is due to the realignment of the particles.

This alignment is related to the displacements and torque produced in the medium by the

field and the translational motion and relocation of particles to positions that have local

minimum potential energy. This results in an increase in viscosity and an increase in shear

strength of the material.

When MR fluid flows, or when there is a relative motion between the walls of its

container, shear stress distribution develops across the fluid due to the shear strain occurring

in the fluid. When a magnetic field oriented perpendicular to the direction of flow is applied,

fibrils are formed across the flow, and because of the motion of fluid or the walls these fibrils

are broken and then reformed again. This continuous breaking and reforming of these particle

chains result in a force resisting the motion of the fluid or walls. This results in the formation

of a field-dependent component of shear stress. This component of shear stress is much larger

than the viscous shear stress. This large and controllable shear stress is useful in mechanical

systems. When MR fluid reaches magnetic saturation, the upper limit of the induced shear

stress is reached.

Figure 1.2 The schematic of off state and on state of MR fluids [5]


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1.4 The Bingham Plastic Model for MR Fluids

The formation of the fibrils within the MR fluid br ings only little change in the fluids

viscosity actually. The effect of the fibrils is to produce a shear stress which is independent of

the strain rate [1]. This stress is referred to as yield stress and denoted as y . This term is added

to the general Newtonian model of fluids and the total stress is obtained.

( ) y F is the viscosity of the fluid, is the strain rate of the fluid and is the applied field.

Here yield stress, y is given as a function of the applied field. It is typically proportional to

the field strength raised to a power between 1 and 2. The response by this model is plotted

and shown below. Thus MR fluids are characterized in part by their zero-field viscosity and

field-dependent yield stress.

Figure 1.3 Shear stress versus shear strain rate for the Bingham model [6]

In experiments, the dynamic viscosity, is determined by a linear fitting of a line to

experimental plotted data, and the intersection of this line with the shear stress axis is takenas y . Initiating the motion or flow requires overcoming a static yield stress , y s , and this is

larger than the dynamic yield stress , y d . But this quickly falls to the dynamic value once

motion is there. Once shear stress has reached its dynamic value, it tends to follow the fitted

straight line towards y as decreases. This behaviour may be due to the reattachment to

the walls of the field-induced fibrils, which were broken near their ends by the bulk shear of

the fluid accompanying the flow. Also , y s can rise significantly after long periods of static

state.


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Figure 1.4 Operational modes of MR fluid devices [2]

1.5 Pre-Yield Response

The Bingham plastic model proposed that stress less than yield stress y produces no

flow of the fluid; but in real case the fluid responds to stress in this range. Even if y

increases with F , the yield occurs at approximately the same strain, regardless the field

strength. For many purposes MR fluids are regarded as viscoelastic solid.

The shear stiffness of viscoelastic solids are represented by the complex shear modulus*G G jG , where the real part G is called the storage modulus which measures the

materials ability to elastically store strain energy and the imaginary part G is called the loss

modulus which is associated with the dissipation of energy during deformation.

1.6 Post-Yield Flow

Figure 1.5 Shear stress shear strain relationship of MR material [8]

When a magnetic field is applied, only a small portion of the fluid is subjected to the

applied field while the rest is free to flow as a conventional, low viscosity fluid. Two

possibilities are explained to illustrate how shear is created in the fluid [1]. When the fluid is

forced through a gap under pressure or when the confining boundaries move with respect to


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the other, shear may be produced. The gap considered is small in the direction of the field.

This close spacing is required in order to produce a field strong enough to activate the fluid.

If adequate field can be generated, the fibrils will form over a greater distance within the

fluid.

The analysis of the above possibilities can be done with the help of elementary fluid

mechanics. A differential control volume within the fluid shows how the pressure gradient

p produces a shear stress distribution through the fluid layer. This distribution is of the

form

( )2h

z p z

wheredp

p dx = constant and h is the thickness of the gap.

This distribution is independent of the nature of the material in the gap. But as the fluid

exhibits a yield stress, a critical pressure is required for the flow to occur. This critical

pressure is related to the gap geometry and fluid yield stress and is given by

2 y

c

dpdx h

The flow will occur if the pressure exceeds this critical level this flow will be characterized

by shear of a layer near each boundary while the central portion of the fluid remains

unyielding. This resembles a plug flow. The volumetric flow rate can be obtained by

integration of the distribution of velocity across the gap. It gives the result

2

2

2

12

y y p h p hQb p

This result can be written in the non-dimensional form3 2 3* * * *(1 3 ) 4 0 P T P T

where3

*

12

bh p P

Q ,

2

*

12 ybhT

Q

There are approximations which can be done to this equation, depending upon the flow rate.

When*

T > 0.5, the equation becomes* *1 3 P T

and for low flow conditions corresponding to*

T > 200, the approximation is


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* *2

23

P T .

1.7 Carrier Fluids

The carrier liquid in an MR fluid plays a very important role. The function of a carrier

liquid is to provide a liquid in which the magnetically active phase particulates are

suspended. The approximate relative volume fractions of the liquid phase range between 0.5

and 0.9. Silicone oils, synthetic or semi-synthetic oils, mineral oils, lubricating oils and

combination of these can be used as carrier liquids [5]. It is important to consider the boiling

temperature, vapour pressure at elevated temperatures and freezing point while selecting the

carrier liquids. The carrier liquid should also be highly non-reactive toward the components

or materials used in the device. It is important to minimise the off-state viscosity of the

carrier liquid and choose liquids that do not show significant variation in the viscosity at a

given temperature. A new family of material emerged which called MR elastomers replaces

the fluid component by cross-linked material like rubber or silicone. Additives are also

incorporated into MR fluids to enhance their performance and make the fluids and devices

more durable.

1.8 Other Effects

MR fluids give weaker responses to changes in their environment. Temperature variations

affect the fluid predominately through the inert liquid phase of the suspension. The carrier

fluid may expand or contract with temperature changes, affecting the effective volume

fraction of the particles, and its viscosity can also vary with temperature. The influence of

particle volume fraction is studied by using the property, relative viscosity, which is defined

as the ratio of viscosity of the MR suspension to the viscosity of the carrier fluid.


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Chapter 2

APPLICATIONS OF MAGNETORHEOLOGICAL FLUIDS

2.1 Commercial MR Fluids

MR fluid caters to various applications depending on the modes used. These range from

automotive to optics and also defence applications. Lord Corporation has commercialized

several MR fluids and various MR fluid based systems including an MR fluid brake for use in

the exercise industry and a controllable MR fluid damper for use in truck seat suspensions.

Most devices that use controllable fluids can be classified as having either fixed poles

(pressure driven flow mode) or relatively moveable poles (direct-shear mode). The basic

composition of these four fluids is given in the table .

Table 2.1 Properties of commercial MR fluids [2]

Some of the significant applications include

2.2 Heavy Duty Vehicle Seat Suspensions

In heavy duty vehicle seat applications, flow mode is employed. Flow mode is usually

applied in Dampers and shock absorbers wherein the fluid is forced across field in a direction

in which movement is to be controlled.

Figure 2.1 Rheonetic RD-1001/4 MR Fluid Damper [2]


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extended period as a seismic event is often sudden and non-dynamic. MRX -140ND is an

MR fluid used for such a use. This fluid is given a small yield strength which gives it a

greasy consistency preventing the particles from gravitational settling.

2.4 Seal-Less Vibration Damper

Figure 2.3 Rheonetic RD-1013-1 vibration damper [2]

Seal less vibration dampers work in flow mode. A small controllable MR fluid

vibration damper used for industrial application is shown in figure. A small steel disc is

moved in a chamber of MR fluid. Axial motion is primarily achieved producing a

damping force of 0-125N although secondary lateral and flexing motions are also

possible. It uses elastomer rubber elements instead of dynamic sliding seals owing to

relatively small amplitudes. The device can also be used as a locking device.Since the natural rubber diaphragms are not compatible with hydrocarbon oil based

fluids, water based fluids like MRX-242AS are used, which are exceptionally stable due

to the wide choice of surfactants.

2.5 MR fluids in structural applications

Magnetorheological materials are potentially applicable to structures and devices

when a tuneable system response is required [7]. When incorporated into an adaptive

structural system, they can yield higher variations in the dynamic response of the structure.

Magnetorheological (MR) materials, due to their semi-active control capabilities, are

candidate materials, which can cause changes in both damping and stiffness of the structure

simultaneously [8]. Their utilization in these applications is based on the concept of

optimized control with minimum energy addition via semi-active control. The MR fluid layer

is embedded in a laminated composite to control its vibration. The relationship between the

magnetic field and the complex shear modulus of MR materials in the pre-yield regime is

researched using oscillatory rheometry techniques. Vibration characteristics of MR adaptive

structures are predicted for different magnetic field levels by structural dynamic modelling.


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Figure 2.4 Three-layered adaptive beam configuration with MR material [8]

A test beam is modelled some principle like the following [8]. The surface plates must be

made of elastic materials, the surface plates should not affect the distribution and strength of

the magnetic field, the MR layer should be uniform between the surface plates, and thefabricated MR test beam should be uniform and straight. Permanent magnets are used to

generate magnetic field over the test beam. Variations in the magnetic field level are obtained

by changing the distance between the permanent magnets by using a simple screw

mechanism.


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Chapter 3

THE APPLICATION OF MR DAMPER FOR SEMI-ACTIVECONTROL OF VEHICLE SUSPENSION SYSTEM

3.1 Introduction

Semi-active suspensions can be nearly as effective as fully active suspensions inimproving ride quality and were proposed in the early 1970s. The semi-active suspension can

still work in passive condition even when the control system fails. The semi-active

suspension system combines the advantages of both active and passive suspensions; i.e. it

provides good performance compared with passive suspensions and is economical. It does

not require either higher-power actuators or a large power supply.

A MR damper is designed and fabricated first in this paper. A nonparametric model for the

damper is constructed and parameter estimation is done for the MR damper based on the

experimental results. The model results are compared with those of experimental results. A

car model is established with the model of MR damper and the governing equation is

obtained for the suspension system. Sky-hook control, a semi-active control strategy, is

adopted to control the vibration of suspension system over random road excitation.

Simulation is carried out and results are compared with those of passive suspension. The

potential application of MR damper in vehicle suspension system is proved.

3.2 MR Damper and Parameter Estimation

3.2.1 Design of MR damper and experimental setup

The MR damper used works in flow mode. The damper is218 mm long in its extended

position, and has 25 mm stroke. The main cylinder houses a piston, a magnetic circuit, an

accumulator and MR fluid. MR 132 LD is used in the damper. The MR fluid valve is

contained within the piston and consists of an annular flow channel with 1.5 mm gap. The

magnetic field is applied radially across the gap, perpendicular to the direction of fluid flow.

The total axial length of the flow channel is 6 mm which exposed to the applied magnetic

field. Viscosity of MR fluid in the valve will be increased by increasing the electric current

through the electromagnet, thus resisting the MR fluid flow through the valve and increasing

the damping force of the MR damper.

The property of the damper should be determined first and then a model must be developed

that can accurately reproduce the behaviour of the MR damper in order to apply the MR

damper in vibration control of vehicle suspension system. To determine the property of the

MR damper an experimental test rig is set up. This set up also helps in obtaining the dynamic

data necessary for estimating the parameters of the model. A computer-controlled INSTRON


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Test Machine (Model 8874) is used and the MR damper is fixed in it. The INSTRON Test

Machine has a load cell and a displacement sensor in it to measure the force produced by the

MR damper and the displacement of the piston. Two types of excitations, sinusoidal and

triangular, are used. The excitation frequencies are 1, 2 and 4 Hz and the amplitudes of

excitation are 1, 2 and 4 mm, respectively.

Figure 3.1 Schematic Diagram of the MR Damper [4]

The applied electric current is from 0 to 1 A with increment of 0.25 A. The force and

displacement responses of the damper are sampled simultaneously by the computer via an

A/D converter. The excitation signal is also produced by the computer and sent out to the

hydraulic actuator via a D/A converter. Velocity response can be obtained by differentiating

the displacement. All experiments are carried out at the room temperature of 23 C.

3.2.2 Experimental Results

The effect of the magnetic field on damping force is studied by applying 1 Hz excitation

under five constant electric currents. The result obtained is shown in the figure. With the

increasing of the applied electric current, the damping force will increase remarkably,

however when the applied electric current is more than 0.75 A, the increase of the damping

force is no longer significant. This means that saturation of the MR effect occurs at 0.75 A.

The force produced by the damper is not exactly centred at zero. This is due to the presence

of highly compressed air in the accumulator in the MR damper and the existence of air in the

cylinder which occupies among the MR fluid. The maximum force of MR damper at 1 A is

approximately equal to eight times of that without electric field. Experiments are done with

triangular excitation to obtain the relation of equivalent damping coefficient to velocity and

electric current. The equivalent damping coefficient of the damper against velocity under

various electric currents is shown in figure. From the figure, at low velocity, equivalent

damping coefficient will increase significantly.


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Figure 3.2 Responses of force vs. time and force vs. displacement under different electric

currents [3]

As the velocity increases, the equivalent damping coefficient under high electric current

decreases rapidly whereas that without electric current decreases slowly. At high velocity, the

effect of current on equivalent damping coefficient is also not so significant. This

phenomenon means that the MR damper cannot be treated as a viscous damper under high

electric current.

Figure 3.3 Equivalent damping coefficient vs. velocity under various electric currents [3]

From the experiments, it is seen that the designed MR damper has very large changeable

damping force range under magnetic field, although the saturated magnetic field is not so big.

Since the MR damper cannot be treated as a viscous damper under high electric current, a

suitable model is necessary to be developed to describe the MR damper.

3.3 BOUC WEN Model and Parameters Estimation

The model of the MR damper should be continuous in all the ranges and be numerically


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tractable for application of MR damper in vibration control. The Bouc-Wen model is adopted

here. The schematic of the model is shown in the figure. The force in this system is given by

0 0 F c x k x z ,

where the evolutionary variable z is governed by1n n

z x z z x z Ax ,

where , and A are parameters related to the shape of hysteresis loop.

These parameters are adjusted to control the linearity in the unloading and the smoothness of

the transition from the pre-yield to the post-yield region.

To estimate the parameters of the model, an error function is introduced as an objective

function

21

N ei pi

i

J F F ,

Where e F is the experimental damping force, p F is the estimated damping force and N is

the number of experimental data. The parameters are calculated. It is seen that the estimated

model can capture the properties of the MR damper except at the region where the velocity is

near zero. So the Bouc Wen model can be used to characterize the property of the MR

damper.

Figure 3.4 Bouc Wen model [3]

3.4 Semi-Active Control of Vehicle Suspension System

3.4.1 Vehicle suspension model

A simple quarter car installed with a MR damper in the suspension system is used. It is

shown in the figure. This is a two-degrees-of-freedom system, mass 2m represents the sprung


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mass while mass 1m means the unsprung mass; 2k represents the stiffness of suspension

system and 1k means the stiffness of tire. The property of the MR damper is determined by

the force equation of the Bouc-Wen model. 0 x is the road excitation. The governing equation

of quarter car model can be obtained by the dynamic analysis as

1 1 0 2 1 2 2 1 1 1 0( ) ( ) ( )m x c x x k x x k x x z ,

2 2 0 2 1 2 2 1( ) ( )m x c x x k x x z ,

where the evolutionary variable z is governed by1

2 1 2 1 2 1( ) ( )n n

z x x z z z x x A x x .

Figure 3.5 Simplified quarter car model [3]

T

1 2x x x

Then the governing equation can be written in the matrix form as

x Cx Kx Fy

where

C

0 0

1 1

0 0

2 2

c cm m

c cm m

, K

1 2 2

1 1

2 2

2 2

k k k

m m

k k

m m

, F

1

1 2

2

0

a k

m m

a

m

and T0y z x .

Let T

X x x . Then the governing equation can be written in the state space as

X AX Bu

where


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C K A

I 0

,F 0

B0 0

, and Tu y 0 0

3.4.2 Control Strategy

The state variables are the relative velocity between the sprung mass and the unsprungmass, as well as the velocity of sprung mass. When the relative velocity between sprung mass

and unsprung mass is in the same direction of the velocity of sprung mass, an electric current

is applied to the MR damper, otherwise no damping force is required. But for MR damper it

is impossible to provide a zero force, so we should minimize the semi-active damping force

without any electric current. So semi-active sky-hook control policy can be described using

the form

2 2 1

2 2 1

( ) 0 Max,

( ) 0 Min.

x x x F

x x x F

3.4.3 Simulation Results

The results show the acceleration response of sprung mass under different control

strategies. The suspension travel response around the body resonance is reduced significantly

under constant control and semi-active control, but they are unable to reduce the suspension

travel response around the wheel hop.

Figure 3.6 Acceleration response of sprung mass [3]


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CHAPTER 4

SEISMIC RESPONSE CONTROL USING MULTIPLE MR DAMPERS

4.1 Introduction

Magnetorheological (MR) dampers can be implemented as semi-active control devices

for seismic response reduction. For this purpose a clipped-optimal control algorithm based on

acceleration feedback was proposed. So a linear optimal controller was designed and

combined with a force feedback loop to determine the appropriate command voltage to send

to the MR damper. This investigation demonstrates that the MR damper, combined with the

clipped-optimal control algorithm, is effective for controlling a multi-story structure with

multiple MR dampers.

4.2 MR damper Modelling

The damper is 21.5 cm long in its extended position, and the main cylinder is 3.8 cm in

diameter. The main cylinder houses the piston, the magnetic circuit, an accumulator and 50

ml of MR fluid, and the damper has a 25 cm stroke. the magnetic field produced in the

device is generated by a small electromagnet in the piston head. The current for the

electromagnet is supplied by a linear current driver, which generates a 0 1 amp current that is

proportional to an applied DC input voltage in the range 0 3 V. The peak power required is

less than 10 watts. Forces of up to 3000 N can be generated with the device. A simple

mechanical idealization of the MR damper depicted below.

Figure 4.1 Simple Mechanical Model of the MR Damper [4]

The force predicted by this model is given by


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0 0 1 0f ( ) ( ) ( ) z c x y k x y k x x

where the evolutionary variable is governed by1

( ) ( )n n

z x y z z x y z A x y

and

0 00 1

1( ) y z c x k x y

c c

Here, 1k is the accumulator stiffness, the viscous damping observed at larger velocities by 0c .

A dashpot, represented by 1c , is included in the model to introduce the nonlinear roll-off that

was observed in the experimental data at low velocities, 0k is present to control the stiffness

at large velocities, and x0 is the initial displacement of spring 1k

associated with the nominaldamper force due to the accumulator. By adjusting the parameters of the model , and A,

one can control the shape of the hysteresis loops for the yielding element.

The dependence of the force on the voltage applied to the current driver and the resulting

magnetic field can be accounted by

( ) a bu u , 1 1 1 1( ) a bc c u c c u , 0 0 0 0( ) a bc c u c c u

where u is given as the output of a first-order filter given by

( )u u v

and v is the commanded voltage sent to the current driver. This equation is necessary to

model the dynamics involved in reaching rheological equilibrium and in driving the

electromagnet in the MR damper.

4.3 Clipped-Optimal Control Algorithm

Since semi-active control devices are inherently stable, high authority control strategies

may be designed and implemented. But, because these devices are intrinsically nonlinear,

appropriate nonlinear control algorithms must be developed to make use of their uniquecharacteristics. In addition, in determining the control action, the control algorithms should

use readily available measurements. A clipped-optimal controller based on acceleration

feedback was proposed and turned out to be effective for controlling a structure with a single

MR damper. This control algorithm is extended to consider the case in which multiple control

devices are employed to control a structure.

Consider a seismically excited structure controlled with n MR dampers. It is assumed that the

forces provided by the MR dampers are adequate to keep the response of the primarystructure from exiting the linear region, and then the equations of motion can be written as


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z Az Bf Ex g

Where x g

is a one-dimensional ground acceleration, 1 1f f f .... f n is the vector of

measured forces generated by the MR dampers, and z is the state vector. The measurement

equation is given by

y Cz Df n

where y is the vector of measured outputs, and n is the measurement noise vector. In this

application, the measurements typically available for control force determination include the

acceleration of selected points on the structure, the displacement of the MR dampers and the

measurement of the control forces provided by the MR dampers.

Consider the ith MR damper used to control the structure to discuss the algorithm used for

determining the control action. The response of the MR damper is dependent on the relative

structural displacements and velocities at the point of attachment of the damper, and so the

force generated by the MR damper cannot be commanded; only the voltage iv applied to the

current driver for the ith MR damper can be changed directly. To induce the MR damper to

generate approximately the corresponding desired optimal control force ci f , the command

signal iv is selected as follows. When the ith MR damper is providing the desired optimal

force (i.e., i ci f f ), the voltage applied to the damper should remain at the present level. If

the magnitude of the force produced by the damper is smaller than the magnitude of the

desired optimal force and the two forces have the same sign, the voltage applied to the

current driver is increased to the maximum limit so as to increase the force produced by the

damper to match the desired control force. Otherwise, the commanded voltage is set to zero.

This algorithm is graphically represented the figure below.

Figure 4.2 Graphical Representation of Algorithm for Selecting the Command Signal [4]


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The proposed control strategy does not require a model for the MR damper, although the

model of the MR damper is important to system analysis. This is one of the attractive features

of this control strategy.

Figure 4.3 Block Diagram of Semi-Active Control System [4]

4.4 Five Story Structure - Two MR Dampers

Sometimes it is not only important to ensure that the structure is not damaged, but the

contents as well (e.g. sensitive computer or laboratory equipment). To ensure this, the

absolute accelerations of the floors of the structure where this equipment is situated must beminimized. Therefore, the focus of this example is to demonstrate that a high reduction in the

floor accelerations can be achieved while simultaneously maintaining a significant reduction

in the inter-story displacements. In this example, the nominal linear controller was designed

by weighting the absolute acceleration of the top floor of the structure.

Two MR dampers are employed to control a five story structure. The first MR damper is

attached between the base and first floor of the structure (providing control force 1 f ), and

the second is attached between the first and second floors of the structure (providing controlforce 2 f ). Two floors with the same mass, stiffness, and damping were added to the three-

story structure to form the five story structural model. The measurements used for feedback

include the absolute accelerations of the five floors of the structure, and the displacements of

both MR dampers.

4.5 Discussion

The performance of the semi-active control system is compared to that of two passive

systems. Since the properties of the MR damper can be varied dynamically, the semi-activesystems achieved greater response reduction than either of the two passive cases.


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Additionally, the semi-active control systems using the MR damper were shown to be

effective at reducing both the structural displacements and accelerations. The results of this

study are that it is possible to achieve large reductions in the floor while simultaneously

achieving a significant reduction in the inter-story displacements.


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CHAPTER 5

CONCLUSION

MR fluids and devices have made considerable progress towards commercialisation.

Adaptive control devices implementing MR dampers are one of the most promising semi-

active devices for use in vibration control applications. These are used to produce the

required forces in a very short interval of time and help to make a damaged structure behave

like an undamaged structure. The semi-active systems using MR damper achieves greater

response reduction than passive systems because of the dynamically variable MR fluid

properties. MR damper has a very broad changeable damping force range under magnetic

field and the damping coefficient increases with the electric current. These systems using MR

damper are very effective in reducing both the structural displacements and accelerations.

There are still challenges in this area. The major challenge lies in the durability of MR

fluids and the devices with the same. Higher and lower temperature performance of MR

fluids over larger periods of time is also a concern. Also each MR fluid based device is

unique and will therefore need a specially formulated MR fluid. The damping force decreases

with the increase in the excitation amplitude. Under electric current, the MR damper cannot

be treated as a viscous damper and the property of the damper can be described by the Bouc-

wen model.


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References

[1] A. V. Srinivasan and D. Michael McFarland, Smart Structures - Analysis and Design,

The press syndicate of the University of Cambridge, United Kingdom, 2001

[2] Mark R. Jolly, Jonathan W. Bender, and J. David Carlson, Properties and Applications of

Commercial Magnetorheological Fluids , Thomas Lord Research Centre, Lord Corporation,

405 Gregson Drive Cary, NC 27511, SPIE 5th Annual Int. Symposium on Smart Structures

and Materials, San Diego, CA, 15 March, 1998

[3] G.Z. Yao, F.F. Yap, G. Chen, W.H. Li, S.H. Yeo , MR damper and its application for

semi- active control of vehicle suspension system, School of Mechanical & Production

Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798,

Singapore

[4] S.J. Dyke1 and B.F. Spencer, Jr., Seismic Response Control Using Multiple MR

Dampers, Dept. of Civil Engineering Washington University, St . Louis, MO 63130, U.S.A.

2Dept. of Civil Engineering and Geol. Sci., University of Notre Dame, Notre Dame, IN

46556, U.S.A.

[5] Dr. Pradeep P. Phul, Magnetorheological (MR) fluids: Principles and applications,

Department of Materials Science & Engineering, University of Pittsburgh, and New Age

Materials Inc, Pittsburgh, PA, USA

[6] Mel Schwartz, Encyclopaedia of SMART MATERIALS, Volume 1 and Volume 2 ,

Wiley-Interscience Publication, 2002

[7] Tjahjo Pranoto, Kosuke Nagaya, Atsushi Hosoda, Vibration suppression of plate using

linear MR fluid passive damper , Department of Mechanical Engineering, Gunma

University, Kiryu, Gunma 376-8515, Japan, Journal of Sound and Vibration 276 (2004) 919

932

[8] Qing Sun, Jin-Xiong Zhou, Ling Zhang , An adaptive beam model and dynamiccharacteristics of Magnetorheological materials , Department of Engineering Mechanics,

Xian Jiaotong Un iversity, Xian Ning Road 28, Xian 710049, China, Journal of Sound and

Vibration 261 (2003) 465 481

[9] http://avcdefense.com/development/

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