MR&ITS APPS

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MR Damper and Its Application in Vehicle Suspension System

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Abstract

In this paper,a brief introduction to vehicle primary suspension system is

presented along with numerical analysis of a semiactive suspension system with MR

damper is presented. In an automotive system, the vehicle suspension usually

contributes to the vehicle's handling and braking for good active safety and driving

pleasure and keeps the vehicle occupants comfortable and reasonably well isolated

from road noise, bumps and vibrations.Suspension is the term given to the system of

springs, shock absorbers andlinkages that connects a vehicle to its wheels and allows

relative motion between the two. Isolation from the forces transmitted by external

excitation is the fundamental task of any suspension system.

Time response sprungmass is analyzed for a half car model. Simulation results

shows MR damper based semi-active suspension system reduces both the peak values

and RMS values of vertical displacements of sprungmass and gives better damping of

oscillations for various road inputs which improves the ride comfort.

Keywords: MR damper, semi-active suspension system,sprungmass,unsprungmass
http://en.wikipedia.org/wiki/Spring_(device)http://en.wikipedia.org/wiki/Shock_absorberhttp://en.wikipedia.org/wiki/Linkage_(mechanical)http://en.wikipedia.org/wiki/Vehiclehttp://en.wikipedia.org/wiki/Wheelhttp://en.wikipedia.org/wiki/Wheelhttp://en.wikipedia.org/wiki/Vehiclehttp://en.wikipedia.org/wiki/Linkage_(mechanical)http://en.wikipedia.org/wiki/Shock_absorberhttp://en.wikipedia.org/wiki/Spring_(device)


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Table of Contents

1. Introduction: ......................................................................................................................................... 3

1.1 Suspension functions: ................................................................................................................... 3

1.2 Vehicle Primary Suspensions ........................................................................................................ 4

2. Advantages of a Semi-Active Suspension System ............................................................................... 12

3. Damper Background ........................................................................................................................... 13

3.1 Controllable Fluids and Devices .................................................................................................. 15

4. Magneto-Rheological Dampers........................................................................................................... 19

4.1 Magneto-Rheological Fluids ........................................................................................................ 19

4.2 Construction of an MR Damper .................................................................................................. 20

4.3 Performance of the MR Damper ................................................................................................. 22

5. Vehicle Ride Model: ............................................................................................................................ 25

5.1 Road Input Modeling: ................................................................................................................. 26

6 Results: ................................................................................................................................................ 29

7 Conclusion ........................................................................................................................................... 36

8 References ........................................................................................................................................... 37


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1. IntroductionSuspension is the term given to the system of springs, shock absorbers and

linkages that connects a vehicle to its wheels and allows relative motion between the

two. Isolation from the forces transmitted by external excitation is the

fundamental task of any suspension system. Generally there are three types of

suspension systems namely, passive, semi-active and active suspensions.

1.1 Suspension functions:The automotive suspension on a vehicle typically has the following basic tasks [1] :

1) To isolate a car body from road disturbances.

In order to provide good ride quality Ride quality in general can be quantified

by the vertical acceleration of the passenger locations. The presence of a well-designed

suspension provides isolation by reducing the vibratory forces transmitted from the axle

to the vehicle body. This in turn reduces vehicle body acceleration. In the case of the

quarter car suspension, sprung mass acceleration can be used to quantify ride quality.

2) To keep good road holding.

The road holding performance of a vehicle can be characterized in terms of its

cornering, braking and traction abilities. Improved cornering, braking and traction are

obtained if the variations in normal tire loads are minimized. This is because the lateral

and longitudinal forces generated by a tire depend directly on the normal tire load.

Since a tire roughly behaves like a spring in response to vertical forces, variations in

normal tire load can be directly related to vertical tire deflection. The road holding

performance of a suspension can therefore be quantified in terms of the tire deflection

performance.

3) To provide good handling.

The roll and pitch accelerations of a vehicle during cornering, braking and

traction are measures of good handling. Half-car and full-car models can be used to

study the pitch and roll performance of a vehicle. A good suspension system should

ensure that roll and pitch motion are minimized.

4) To support the vehicle static weight.

This task is performed well if the rattle space requirements in the vehicle are

kept small. In the case of the quarter car model, it can be quantified in terms of the

maximum suspension deflection undergone by the suspension.
http://en.wikipedia.org/wiki/Spring_(device)http://en.wikipedia.org/wiki/Shock_absorberhttp://en.wikipedia.org/wiki/Linkage_(mechanical)http://en.wikipedia.org/wiki/Vehiclehttp://en.wikipedia.org/wiki/Wheelhttp://en.wikipedia.org/wiki/Wheelhttp://en.wikipedia.org/wiki/Vehiclehttp://en.wikipedia.org/wiki/Linkage_(mechanical)http://en.wikipedia.org/wiki/Shock_absorberhttp://en.wikipedia.org/wiki/Spring_(device)


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1.2 Vehicle Primary SuspensionsPrimary suspension is the term used to designate those suspension components

connecting the axle and wheel assemblies of a vehicle to the frame of the vehicle. This

is in contrast to the suspension components connecting the frame and body of the

vehicle, or those components located directly at the vehicles seat, commonly called the

secondary suspension. There are two basic types of elements in conventional

suspension systems. These elements are springs and dampers. The role of the spring in a

vehicles suspension system is to support the static weight of the vehicle. The role of

the damper is to dissipate vibrational energy and control the input from the road that is

transmitted to the vehicle. The basic function and form of a suspension is the same

regardless of the type of vehicle or suspension. Primary suspensions will be divided into

passive, active adjustable and semi-active systems, as will be discussed next, within the

context of this study.

A] Passive Suspensions

A passive suspension system is one in which the characteristics of the

components (springs and dampers) are fixed. These characteristics are determined by

the designer of the suspension, according to the design goals and the intendedapplication. Passive suspension design is a compromise between vehicle handling and

ride comfort, as shown in Figure 1.

Figure 1.1.)Damping Compromise for Passive Dampers


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A heavily damped suspension will yield good vehicle handling, but also

transfers much of the road input to the vehicle body. When the vehicle is traveling at

low speed on a rough road or at high speed in a straight line, this will be perceived as a

harsh ride. The vehicle operators may find the harsh ride objectionable, or it may

damage cargo. A lightly damped suspension will yield a more comfortable ride, but can

significantly reduce the stability of the vehicle in turns, lane change maneuvers, or in

negotiating an exit ramp. Good design of a passive suspension can to some extent

optimize ride and stability, but cannot eliminate this compromise.

B] Active Suspensions

In an active suspension, the passive damper or both the passive damper andspring are replaced with a force actuator, as illustrated in Figure 1.2.

Figure1.2.)Passive and Active Suspensions

The force actuator is able to both add and dissipate energy from the system,

unlike a passive damper, which can only dissipate energy. With an active suspension,

the force actuator can apply force independent of the relative displacement or velocityacross the suspension. Given the correct control strategy, this results in a better

compromise between ride comfort and vehicle stability as compared to a passive

system, as shown in Figure 1.3 for a quarter-car model.


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Figure 1.3.) Passive and Active Suspension Comparison (adapted from reference [1],

p.201)

A quarter-car model, shown in Figure1.4is a two-degree-of-freedom model that

emulates the vehicle body and axle dynamics with a single time (i.e., one-quarter of a

car).

Figure 1.4.)A Quarter-Car Model.

In a study by Chalasani [1], a quarter car model was used to investigate the

performance gains possible with an active suspension system. In this study, the road


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input was modeled as a white noise velocity input. The study found that within practical

design limitations, an active suspension can reduce the RMS (root mean square)

acceleration of the sprung mass by 20%. This suspension configuration exhibited

approximately the same level of suspension travel and wheel-hop damping ratio as a

lightly damped, soft passive suspension. In a further study [2], similar simulations and

analysis were performed for half car model. This study estimated that active

suspensions could reduce the RMS value of the sprung mass acceleration by 15%.

Active suspension systems have the added advantage of controlling the attitude of a

vehicle. They can reduce the effects of braking, which causes a vehicle to nose-dive, or

acceleration, which causes a vehicle to squat. They also reduce the vehicle roll during

cornering maneuvers. Active suspension systems, though shown to be capable ofimproving both ride and stability, do have disadvantages. The force actuators necessary

in an active suspension system typically have large power requirements (typically 4-5

hp). The power requirements decrease the overall performance of the vehicle, and are

therefore often unacceptable. Another detraction to active suspension systems is that

they can have unacceptable failure modes. In the case of actuator failure the vehicle

would be left undamped, and possibly unsprung. This is a potentially dangerous

situation for both the vehicle and operator.

B.1] Adjustable Suspensions

An adjustable suspension system combines the passive spring element found in

a passive suspension, with a damper element whose characteristics can be adjusted by

the operator. As shown in Figure 1.5, the vehicle operator can use a selector device to

set the desired level of damping based on their subjective feel.


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Figure 1.5.) Adjustable Suspension (adapted from reference [3], p. 107)

This system has the advantage of allowing to operator to occasionally adjust the

dampers according to the road characteristics. It is however, unrealistic to expect the

operator to adjust the suspension system to respond to time inputs such as potholes,

turns, or other common road inputs.

C] Semiactive Suspensions

Semiactive suspension systems were first proposed in the early 1970s. In this

type of system, the conventional spring element is retained, but the damper is replaced

with a controllable damper as shown in Figure 1.6.)

Figure 1.6.) Passive and Semiactive Suspensions

Whereas an active suspension system requires an external energy source to

power an actuator that controls the vehicle, a semiactive system uses external power

only to adjust the damping levels, and operate an embedded controller and a set of

sensors. The controller determines the level of damping based on a control strategy, and

automatically adjusts the damper to achieve that damping. One of the most common

semiactive control policy is skyhook control which adjusts the damping level to emulate

the effect of a damper connected from the vehicle to a stationary ground, as shown in

Figure 1.7.


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Figure 1.7.) Quarter Car Model with Skyhook Damper

Mathematically, skyhook control is described as:

X1*(X1-X2) 0 C = high damping

X1*(X1-X2) < 0 C = low damping ()

In this equation

1. X is the velocity of the upper mass and

2 X is the velocity of the lower mass.

This type of skyhook control is called on-off, or bang-bang control since the

damper switches back and forth between two possible damping states. When the upper

mass is moving up, and the two masses are getting closer, the damping constant should

ideally be zero. Due to the physical limitations of a practical damper, a damping

constant of zero is not practical and a low damping constant is used. When the upper

mass is moving down and the two masses are getting closer, the skyhook control policy

ideally calls for an infinite damping constant. An infinite damping constant is not

physically attainable, so in practice, the adjustable damping constant is set to a

maximum. The effect of the skyhook control scheme is to minimize the absolute

velocity of the upper mass. This is shown in figure 1.8.


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Figure 1.8.) Skyhook Control Policy [4]

It has been shown that a continuously variable semiactive suspension system is

able to achieve performance comparable to that of a fully active system [5]. It is also

possible to develop acontrol policy in which the damper is not just switched between a

high and low state, but has an infinite number of positions in-between. This type of

system is called a continuously variable semiactive system. The ranges of damping

values used in these two systems are illustrated in Figure 1.9.

Figure 1.9.) Range of Damping Values

Further research indicated that performance of an on-off semiactive suspension

system would be very close to the performance of a continuously variable semiactive

system [6]. In the case that the controllable damper necessary in a semiactive

suspension fails, it will simply revert to a conventional damper. Semiactive systems not


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only have a less dangerous failure mode, but are also less complex, less prone to

mechanical failure, and have much lower power requirements compared to active

systems.


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2.Advantages of a Semi-Active Suspension SystemCompared to fully active suspension systems, semi-active systems consume

significantly less power. The power consumption in a semi-active system is only for

purposes of changing the real-time dissipative force characteristics of the semi-active

device. For example, power is used to change the area of the piston orifice in a variable

opening damper or to change the current in the elecromagnetic coil of a MR damper.

External power is not directly used to counter vibratory forces. Another advantage of

semi-active systems over active systems is that they cannot cause the suspension system

to become unstable. This is due to the fact that they do not actively supply energy to the

vibratory suspension system but only dissipate energy from it.


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3. Damper BackgroundA damper is a device that dissipates energy in the form of heat. Energy is

changed to heat by forcing a viscous fluid through an orifice. In a vehicle, energy from

the road, rather than being transmitted to the vehicle, is changed into a temperature rise

of the fluid inside of the damper. Two types of dampers are commonly used in

vehicular applications, twin-tube and monotube dampers. Both twin-tube and monotube

dampers typically have bilinear damping characteristics. This means that the slope of

the damper force vs. relative velocity is greater at low velocities than it is at high

velocities, as shown in figure 3.1.

Figure 3.1.) Bilinear Force vs. Velocity Curve for a Conventional Damper

Figure 3.2.) Twin-Tube and Monotube Dampers


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In both cases, the shock absorber has a piston that traverses back and forth

inside a cylinder. In a monotube damper, the piston travels in a single cylinder that

contains a fluid chamber and pressurized air chamber. A floating piston is used to

separate the fluid and air chambers. The air chamber is used to accommodate the

change in the fluid chamber volume, due to the volume of the piston rod. As the piston

rod pushes in, it reduces the fluid chamber volume, which is gained back by the floating

piston moving down against the compressible air chamber. Conversely, when the rod is

pushed out, the fluid chamber volume increases and the floating piston moves up to fill

the excess volume, in order to avoid the creation of a vacuum in the fluid chamber. If a

vacuum is created in the fluid chamber, then the fluid will cavitate as it passes through

the damper piston and the damping effect will be significantly diminished. In the twin-tube configuration, there is air in part of the outer tube. The compressible air is in direct

contact with the incompressible fluid. As the piston rod enters the damper, the air

compresses to compensate for the change in volume available to the fluid. Likewise,

when the piston rod is withdrawn from the damper, the air expands in order to avoid the

creation of a vacuum. In the twin-tube damper configuration, it is necessary for the air

to remain at the top of the outer cylinder. If the air did not remain at the top of the

damper and were to pass through the damper valving, the damping effect will be

significantly diminished, as in the case where the fluid cavitates. Since there is not a

barrier at the fluid-air interface, the air will only remain at the top of the outer cylinder

if the damper is operated in its upright position. In either style of damper, the damping

force is the result of viscous friction arising from the passage of the working fluid

through an orifice. The level of the damping force that results is a function of properties

of both the orifice and the fluid. The size and shape of the orifice as well as the

viscosity of the fluid determine how easy it is for the fluid to pass through the orifice. A

semiactive suspension system uses a damper in which the level of damping force can be

adjusted. Dampers in which the damping force can be externally adjusted are called

controllable dampers A controllable damper has a range over which the level of

damping can be varied. This is shown in Figure 3.3.


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Figure 3.3.) Damping Range of a Controllable Damper

The most immediately apparent way to achieve this variable damping is to

include a mechanism that is capable of varying either the size and shape of the

dampers internal orifices, or the number of active orifices. Either of these methods

leads to the inclusion of more moving parts inside of the damper, which could

potentially lead to decreased reliability and a shortened lifetime. In order to make a

controllable damper without mechanically changing the character of the internal

orifices, it is necessary to vary the properties of the working fluid. The fluid itself mustbe able to change from a low viscosity, free flowing fluid to a high viscosity, semi-solid

in a short time span. The class of fluids whose characteristics can be externally varied in

this manner are called controllable fluids.

3.1 Controllable Fluids and DevicesThis section gives background information on both controllable fluids and the

devices which make use of their unique properties.

A] Controllable Fluids

A controllable fluid is a fluid whose rheological behavior can be externally

controlled, typically by the application of either an electric or a magnetic field. Fluids in

which the yield strength, and hence effective viscosity, can be changed by the

application of an electrical field are called electrorheological (ER) fluids. Fluids that

can be controlled by the application of a magnetic field are called Bingham magnetic

fluids or magnetorheological (MR) fluids. Of these two types of controllable fluids, it is


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the MR fluids that are currently deemed to be best suited to most variable damper

applications. Both ER and MR fluids were initially developed independently in the

1940s. ER fluids were developed by Winslow [7] and MR fluids were developed by

Rabinow [8]. Initially it was ER fluids that received the most attention, but were

eventually found to be not as well suited to most applications as the MR fluids. In their

non-activated or off state, both MR and ER fluids typically have similar viscosity, but

MR fluids exhibit a much greater increase in yield strength, and therefore viscosity,

than their electrical counterparts, as shown in Table 3.1.

Table 3.1.) Summary of MR and ER Properties (adapted from reference [10], p.3)

Property ER Fluid MR Fluid

Yield Strength (Field) 2-5 kPa (3-5 kV/mm)

field limited by breakdown

50-100 kPa (150-250

kA/m)

field limited by saturation

Viscosity (no field) 0.2-0.3 Pa-s @ 25 ?C 0.2-0.3 Pa-s @ 25 ?C

Operating Temperature +10 to +90 ?C (ionic, DC)

-25 to +125 ?C (non-ionic,

AC)

-40 to +150 ?C

(limited by carrier fluid)

Current Density 2-15 mA/cm2 (4 kV/mm,

25?C)

(x10x100 @ ?C)

can energize with

permanent magnets

Specific Gravity 1-2.5 3-4 3-4

Ancillary Materials Any (conductive surfaces) Iron/Steel

Color Any, Opaque or Transparent Brown, Black,

Gray/Opaque

A device based on an ER fluid will have roughly the same overall power

requirement as similar device based on an MR fluid, though the ER device will require

high voltage, low current power, while the MR device will require low voltage, high

current power [10]. The extremely high voltage requirements for ER fluids make them


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impractical for most commercial applications. Additional advantages of MR fluids over

ER fluids are that ER fluids are sensitive to contaminants whereas MR fluids are not.

Also, MR fluids have a much broader useful temperature range than ER fluids [10].

B] Magnetorheological Fluid Based Devices

Magnetorheological fluids have application in many types of devices. Lord

Corporationmanufactures MR devices under the Rheonetic brand name. One such

device, shown in Figure 3.4, is a vibration damper that can be used in a controllable

mount.

Figure 3.4.) MR Vibration Absorber for Use in a Controllable Mount [11]

Another such device, shown in Figure 3.5, is a large scale damper used forseismic vibration control.

Figure 3.5.) MR Damper for Seismic Vibration Control (adapted from reference [12], p.

5)

Another such device, shown in Figure 3.6, is a rotary brake that is being used in

programmable exercise equipment.


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Figure 3.6.) MR Rotary Brake [4]

The most important part of any MR fluid device is an MR throttle valve [10].

The MR throttle valve is a resistance to fluid flow that is externally controllable. When

a field is applied normal to the flow direction, it becomes more difficult for the fluid to

pass through the valve, increasing the pressure drop across the valve. In this way the

overall damping of the device is modulated.


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4. Magneto-Rheological DampersThe purpose of this section is to introduce the theoretical and practical

applications of magneto-rheological (MR) fluid for a controllable MR damper. First,

the concept of MR fluid will be introduced. Next, the practical realization of an MR

damper will be discussed. Finally, the performance of the MR damper used for this

research will be investigated.

Magneto-rheological dampers are the most promising semi-active devices

used nowadays in automotive engineering the MR damper is not very different

from a conventional viscous damper. The difference is the magneto-rheological oil

and the presence of a solenoid embedded inside the damper which produces a magnetic

field. When a current is passed through the solenoid a magnetic field is developed

which will cause the fluid to change its state from the fluid to semi-solid state

thereby increasing the damping properties. Hence by controlling the amount of

current through the solenoid we can control the damping rate of the damper.

4.1 Magneto-Rheological FluidsMagneto-rheological fluids are materials that exhibit a change in rheological

properties (elasticity, plasticity, or viscosity) with the application of a magnetic field.

[17] The MR effects are often greatest when the applied magnetic field is normal to

the flow of the MR fluid. Another class of fluids that exhibit a rheological change is

electro-rheological (ER) fluids. As the name suggests, ER fluids exhibit rheological

changes when an electric field is applied to the fluid. However, there are many

drawbacks to ER fluids, including relatively small rheological changes and extreme

property changes with temperature. Although power requirements are approximately

the same, MR fluids require only small voltages and currents, while ER fluids requirevery large voltages and very small currents. For these reasons, MR fluids have recently

become a widely studied 'smart' fluid. Besides the rheological changes that MR fluids

experience while under the influence of a magnetic field, there are often other effects

such as thermal, electrical, and acoustic property changes. However, in the area of

vibration control, the MR effect is most interesting since it is possible to apply the

effect to a hydraulic damper. The MR fluid essentially allows one to control the

damping force of the damper by replacing mechanical valves commonly used in


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adjustable dampers. This offers the potential for a superior damper with little concern

about reliability since if the MR damper ceases to be controllable; it simply reverts to a

passive damper.

4.2 Construction of an MR DamperMagneto-rheological fluids are manufactured by suspending ferromagnetic

particles in a carrier fluid. The ferromagnetic particles are often carbonyl particles,

since they are relatively inexpensive. Other particles, such as iron-cobalt or iron-nickel

alloys, have been used to achieve higher yield stresses from the fluid [15]. Fluids

containing these alloys are impractical for most applications due to the high cost of the

cobalt or nickel alloys. A wide range of carrier fluids such as silicone oil, kerosene, and

synthetic oil can be used for MR fluids. The carrier fluid must be chosen carefully to

accommodate the high temperatures to which the fluid can be subjected. The carrier

fluid must be compatible with the specific application without suffering irreversible and

unwanted property changes. The MR fluid must also contain additives to prevent the

sedimentation of, and promote the dispersion of, the ferromagnetic particles. A

functional representation of an MR damper, with schematics of the components

necessary for operation, is shown in Figure 4.1. The fluid that is transferred from above

the piston to below (and vice versa) must pass through the MR valve. The MR valve is

a fixed-size orifice with the ability to apply a magnetic field, using an electromagnet, to

the orifice volume. This magnetic field results in a change in viscosity of the MR fluid,

causing a pressure differential for the flow of fluid in the orifice volume. The pressure

differential is directly proportional to the force required to move the damper rod. As

such, the damping characteristic of the MR damper is a function of the electrical current

flowing into the electromagnet. This relationship allows the damping of an MR damper

to be easily controlled in real time.


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Figure 4.1.)Functional Representation of an MR Damper

The accumulator is a pressurized volume of gas that is physically separated from

the MR fluid by a floating piston or bladder. The accumulator serves two purposes.

The first is to provide a volume for the MR fluid to occupy when the shaft is inserted

into the damper cylinder. The second is to provide a pressure offset so that the pressure

in the low pressure side of the MR valve does not induce cavitation in the MR fluid by

reducing the pressure below the vapor pressure of the MR fluid. The design of the MR

damper developed by Lord Corporation, Koni Incorporated, and the Advanced Vehicle

Dynamics Laboratory at Virginia Tech is shown in Figure 4.2. All of the external

components have been incorporated internally, providing a compact design that is very

similar in size and shape to existing passive vehicle dampers. The only external parts

are the two electrical leads for the electromagnet, which are connected to the current

source.

Figure 4.2.) Lord/Koni MR Damper, (a) Schematic Representation, (b) Actual

Hardware


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4.3 Performance of the MR DamperForce developed by an MR damper is the sum of viscous component F the

field dependent induced yield stress component F.

Where is the off-field viscosity, ythe yield stress (a function of applied magnetic

field, H), vp is the velocity of the piston, L is the magnetic pole length, Ap area

of piston, Ag fluid gap area, ARm mean area and c is a constant depends on the

flow velocity profile (Emanuel Guglielmino et.al,2008)[16].

For typical passive dampers, the damper performance is often evaluated based

on the force vs. velocity characteristics. For an ideal viscous damper, the force vs.

velocity performance is shown in Figure 4.3. The slope of the force vs. velocity line is

known as the damper coefficient, C. Frequently, the force vs. velocity line is bilinear

and asymmetric, with a different value of C for jounce (compression) and rebound

(extension), as shown in Figure 4.4. In the case of a vehicle suspension, the damping

curve is shaped (or tuned) by a ride engineer for each particular application. Therefore,

the operational envelope of a passive damper is confined to a pre-designed force-

velocity characteristic.


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Figure 4.3.)Linear Damper Characteristics.

Figure 4.4.)Bilinear, Asymmetric Damping Characteristics.

In the case of MR dampers, the ideal force vs. velocity characteristics [18] are as

shown in Figure 4.5. This results in a force vs. velocity envelope that can be described

as an area rather than a line in the force-velocity plane. Effectively, the controller can

be programmed to emulate any damper force-velocity characteristic or control policy

within the envelope.


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Figure 4.5.)Ideal MR Damper Performance.

We can model the ideal MR damper according to

FiMRDAMPER=i

Where is a constant and i is the damper current.


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5. Vehicle Ride ModelA variety of vehicle mathematical models has been developed for vehicle

performance assessment. A car can be thought of as being composed of being

composed of two main sub systems: the sprungmass (chassis) .and unsprung

mass(wheels, axles, and linkages),connected through a number of elastic and dissipative

elements and subjected to external inputs coming from the road profile, the steering

system and other external disturbances like wind forces. Vehicle ride is essentially

concerned with car vertical dynamics (bounce, pitch, and roll). A half car model is a

4DOF system having three translational degrees of freedom and one rotational degree

of freedom. It can represent the bounce motion of the chassis, pitch motion of the

chassis and bounce motion of the wheels without taking into account of roll vibration

modes.

Figure5.1.Half car model


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The equations of motion for the half car model are [16]

Where m is the sprung mass, J is the pitch moment of inertia, m1 and

m2 are the front and rear unsprung masses, a and b are the distances of rear and

front of the vehicle from its center of gravity.

5.1 Road Input Modeling:To study the response of vehicle systems various inputs are needed as

there is no single input which gives the same effect as that of real time road

conditions. So various standard inputs [16] are given and then the response is obtained.

In time domain analysis, three different road conditions are considered, namely, bump

road input, road input with limited ramp and sinusoidal road input.


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A] Bump input

First, time responses for the bump road input are presented. This type of road

surface irregularity is one of the most encountered in actuality. Bump road input is

formulated as: (Figure.5.2)

Here, h is the height of the bump road input. figure5.2.)Bump input

B] Road ramp

Secondly, a road input with limited ramp as seen in (Figure 5.3) is

applied to the half car model. This type of road irregularity tests the performance

of the controller when there is a sudden change in the road surface elevation.

Since the change in road surface elevation is permanent, this type of road input also

tests whether the suspension working space is preserved since the actuator uses the

inherent suspension working space while pushing up or pulling down the vehicle

body in order to compensate for the change in road elevation. The road input withlimited ramp is formulated as below where h is the final road surface elevation:


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figure5.3.) Road Ramp input

C] Sinusoidal

For the time domain analysis, a sinusoidal road input (Figure 5.4) is applied to

the half car model in order to test the performance of the controller for severe

periodic road conditions and to see the capability of the controller keep a stable and

comfortable reference value. The sinusoidal road input to the front wheels is

formulated as below with h being the magnitude of the road input.

Figure 5.4.)Sinosoidal Input


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6. ResultsFigure 6.1shows time responses of vertical deflections sprungmass of semi-

active and passive system for the bump input. The semi-active system reduces the

amplitude of oscillation. Percentage reduction in rms value is 43.27. Figure 6.2 shows

the acceleration response of spring mass vertical motion. The rms value is reduced

17.5%. Figure 6.3 and Figure 6.4 depicts the response of pitch motion and pitch

acceleration respectively. Though the peak values and the rms values are higher in the

case of semi-active system the pitch motion gives very good response once the

force is removed. Time responses of displacement for road ramp input are given in

Figure 6.5. It is seen from the figure that the peak of displacement and number of

oscillations are significantly reduced. Percentage reduction in rms value is 1.4. Figure

6.6represents the plot between acceleration vs time. More than 77% reduction in

acceleration is obtained. Similarly Figure 6.7 and figure 6.8 depicts pitch motion and

pitch acceleration for road ramp input. Percentage reduction attained are 71.27 and

29 .2 respectively for pitch motion and pitch acceleration.[20]

Figure 6.1.) Sprung mass response for bump road input


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Figure.6.2.) Sprung mass acceleration for bump road input

Figure 6.3.) Pitch motion for bump road input


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Figure 6.4.) Pitch acceleration for bump road input

Figure 6.5.) Sprung mass response for road ramp input


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Figure 6.6.) Sprung mass acceleration for road ramp input

Figure 6.7.)Pitch motion for road ramp input


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Figure 6.8.)pitch acceleration for road ramp input

Figures 6.9 and 6.10show time response of displacement of sprungmass and

acceleration for a sinusoidal road input. In these cases both rms value and peak values

increases slightly. Figures 6.11 and 6.12 plot time response of pitch motion and pitch

acceleration respectively. Percentage reduction attained in the cases of pitch motion

and pitch acceleration are 15.6 and 36.21 respectively.

Figure 6.9.) Sprung mass response for sinusoidal road input


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Figure 6.10.) Sprung mass acceleration sinusoidal road input

Figure 6.12.) Pitch motion for sinusoidal road input


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Figure 6.13.) Pitch acceleration for sinusoidal road input


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7. ConclusionA semi-active suspension system with MR damper is analyzed and its

performance is evaluated for a half car model. Responses of sprung mass for

both passive and active vehicle suspension system are plotted for various road

inputs. Semi-active suspension system reduces the RMS values of both displacement

and acceleration in most of the cases. Reduction in these values gives an indication of

the effectiveness of MR damper based semi-active control system in the vehicle

suspension system.


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8. References

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Vibration and Acoustics, Vol. 115, No. 3, pp. 340-343, July 1993.

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Flowable Compositions Based on Barium and Strontium Ferrites and Iron Oxides,"

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16. EmanueleGuglielmino, Tudor Sireteanu, Charles W. Stammers, Gheorghe

Ghita,MariusGiuclea, Semi-active Suspension Control, Springer, 2008.

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18. F. Spencer Jr., S.J. Dyke, M.K. Sain and J.D. Carlson, Phenomenological Model of

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active suspension control strategy through LPV technique, Control Engineering

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20. Dr. K Jayaraj. Smijith G B, M R damper and its application in vehicle

suspension system 10th National Conference on Technological Trends (NCTT09)

6-7 Nov 2009.pp.69-74


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