Semi-Active Magnetorheologic, Greg Stelzer

8/13/2019 Semi-Active Magnetorheologic, Greg Stelzer

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Smart Structures Bio-Nano Laboratory

A MAGNETORHEOLOGIC SEMI-ACTIVE

ISOLATOR TO REDUCE NOISE AND VIBRATIONTRANSMISSIBILITY IN AUTOMOBILES

Gregory J. Stelzer

Delphi Automotive Systems

Chassis Systems Test Center, Dayton, OH 45401-1245

Mark J. Schulz, Jay Kim, Randall J. Allemang

Department of Mechanical EngineeringUniversity of Cincinnati, Cincinnati, OH 45221-0072


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OUTLINE1. INTRODUCTION1. INTRODUCTION

2. BACKGROUND2. BACKGROUND

3. MODELING OF RHEOLOGIC FLUIDS3. MODELING OF RHEOLOGIC FLUIDS

4. MODELING OF ISOLATION SYSTEMS4. MODELING OF ISOLATION SYSTEMS

5. RESULTS5. RESULTS

6. MR ISOLATOR COIL DESIGN6. MR ISOLATOR COIL DESIGN

7. CONCLUSIONS7. CONCLUSIONS

8. RECOMMENDATIONS OF FUTURE WORK8. RECOMMENDATIONS OF FUTURE WORK


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11--1. INTRODUCTION1. INTRODUCTION Passive vibration isolators are inexpensive and simple. For thePassive vibration isolators are inexpensive and simple. For these reasons,se reasons,

most isolation systems in automobiles use passive isolators.most isolation systems in automobiles use passive isolators.

When using a passive vibration isolator, there is a tradeoff betWhen using a passive vibration isolator, there is a tradeoff between Noise,ween Noise,Vibration, and Harshness (NVH) performance and durability characVibration, and Harshness (NVH) performance and durability characteristics.teristics.

Passive isolators cannot provide both optimal isolation and optiPassive isolators cannot provide both optimal isolation and optimalmal

durability.durability.

The object of this thesis is to develop an advanced vibration isThe object of this thesis is to develop an advanced vibration isolatorolator

design for automotive components that can provide substantial andesign for automotive components that can provide substantial and costd cost--

effective improvements in NVH performance.effective improvements in NVH performance.

The new work in this thesis will provide:The new work in this thesis will provide:

1.1. Information on the advantages and limitations of semiInformation on the advantages and limitations of semi--active isolation.active isolation.

2.2. A detailed nonlinear model of the isolator.A detailed nonlinear model of the isolator.

3.3. The results of extensive simulation studies of a practical desigThe results of extensive simulation studies of a practical design.n.


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11--2. INTRODUCTION2. INTRODUCTION In the automotive industry, noise control expectations from theIn the automotive industry, noise control expectations from the end userend user

are becoming more strict, and consequently the Original Equipmenare becoming more strict, and consequently the Original Equipmentt

Manufacturer (OEM) has responded by placing higher expectationsManufacturer (OEM) has responded by placing higher expectations on theon the

suppliers.suppliers.

Noise control specifications have now become standard on many ofNoise control specifications have now become standard on many ofthethe

smallest components in the vehicle.smallest components in the vehicle.

A customer will now use component performance to develop a listA customer will now use component performance to develop a list ofof

acceptable candidates, and then use NVH to determine where the bacceptable candidates, and then use NVH to determine where the businessusiness

is awarded.is awarded.

This increased emphasis on noise reduction and operator comfortThis increased emphasis on noise reduction and operator comfort isis

requiring that more attention be paid to the use of vibration anrequiring that more attention be paid to the use of vibration and noised noise

isolation and attenuation systems in automobiles.isolation and attenuation systems in automobiles.


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11--3. INTRODUCTION3. INTRODUCTION A compressor, used in an automobiles leveling systems, will beA compressor, used in an automobiles leveling systems, will be used asused as

an example in this research.an example in this research.

A leveling system is used to keep a vehicle level with respect tA leveling system is used to keep a vehicle level with respect to roado roadsurface,surface, ieie, when a load is placed in the back of the truck, the rear, when a load is placed in the back of the truck, the rear

suspension is compressed more than the front. A leveling systemsuspension is compressed more than the front. A leveling system willwill

raise the back end of the vehicle so that it is once again levelraise the back end of the vehicle so that it is once again level with thewith the

front.front.

The compressor pumps air into the vehicle shocks, and this is whThe compressor pumps air into the vehicle shocks, and this is whatat

raises the back end of the vehicle.raises the back end of the vehicle.

When the compressor runs, it generates high frequency vibrationWhen the compressor runs, it generates high frequency vibration that isthat is

transmitted to the vehicle structure.transmitted to the vehicle structure.


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11--4. INTRODUCTION4. INTRODUCTION In this research, the compressor will be modeled as a mass withIn this research, the compressor will be modeled as a mass with a forcea force

that produces high frequency excitation.that produces high frequency excitation.

The isolator design will minimize the transmitted force from theThe isolator design will minimize the transmitted force from thecompressor to its structural base, a vehicle body.compressor to its structural base, a vehicle body.

From this point, the component generating the high frequency excFrom this point, the component generating the high frequency excitationitation

will be referred to as a compressor.will be referred to as a compressor.



FIGURE 1.1. A compressor assembly with passive isolators.FIGURE 1.1. A compressor assembly with passive isolators.



22--1. VIBRATION ISOLATORS1. VIBRATION ISOLATORS A vibration isolator is a flexible device that is used to attachA vibration isolator is a flexible device that is used to attach thethe

compressor to a mounting base.compressor to a mounting base.

The purpose of the isolator is to reduce the vibration or forceThe purpose of the isolator is to reduce the vibration or forcetransmitted between the compressor and the base.transmitted between the compressor and the base.

Different possible approaches for vibration isolation of automobDifferent possible approaches for vibration isolation of automobileile

components are described and compared.components are described and compared. The following systems areThe following systems arediscussed:discussed:

1.1. Passive isolation systems.Passive isolation systems.

2.2. SemiSemi--active isolation systems.active isolation systems.

3.3. Active isolation systems.Active isolation systems.

4.4. Smart materials for actuators.Smart materials for actuators.



22--2. Passive Isolation Systems2. Passive Isolation Systems In a passive isolation systems, no controls are needed for the iIn a passive isolation systems, no controls are needed for the isolator.solator.

The design consists of a simple natural rubber material, or a coThe design consists of a simple natural rubber material, or a comparablemparable

synthetic material.synthetic material.

This is the cheapest option because it is the simplest design anThis is the cheapest option because it is the simplest design and thed the

easiest to manufacture.easiest to manufacture.

The durability of the isolator can be improved by stiffening theThe durability of the isolator can be improved by stiffening the isolator.isolator.

This can be done simply by increasing theThis can be done simply by increasing the durometerdurometerhardness of thehardness of the

material or by changing material.material or by changing material.

However, as the stiffness of the isolators is increased, the noiHowever, as the stiffness of the isolators is increased, the noisese

performance of the compressor will be compromised, because a stiperformance of the compressor will be compromised, because a stifferffer

isolator will generally transmit higher frequency vibration.isolator will generally transmit higher frequency vibration.



22--3. Passive Isolation Systems3. Passive Isolation Systems

FIGURE 2.1. Design of a passive isolator.FIGURE 2.1. Design of a passive isolator.



22--4. Passive Isolation Systems4. Passive Isolation Systems AA hydromounthydromount is a more complex passive isolator. A fluid isis a more complex passive isolator. A fluid is

incorporated into the design to provide extra damping.incorporated into the design to provide extra damping.

Fluid is forced through an orifice within the isolator. The resFluid is forced through an orifice within the isolator. The resistanceistanceprovided by the orifice provides damping for the isolated compreprovided by the orifice provides damping for the isolated compressor.ssor.

The increased damping allows the isolator to be designed of a leThe increased damping allows the isolator to be designed of a less stiffss stiff

material. The combination of reduced stiffness and increased damaterial. The combination of reduced stiffness and increased dampingmpingallows theallows the hydromounthydromount to provide better isolation without compromisingto provide better isolation without compromising

durability.durability.

However, the added damping increases the transmitted force, andHowever, the added damping increases the transmitted force, and

therefore, the system is not an optimal solution.therefore, the system is not an optimal solution.




FIGURE 2.2. Design of a passiveFIGURE 2.2. Design of a passive hydromounthydromount..

FLUID

FLUID

ORIFICE ORIFICE

MOUNTING

LOCATION

MOUNTING

LOCATION

ELASTOMERSURROUNDING

FLUID



22--6. Passive Isolation Systems6. Passive Isolation Systems A transmissibility model was developed to show some of theseA transmissibility model was developed to show some of these

concepts. It shows the compressor mounted to its structural basconcepts. It shows the compressor mounted to its structural basee

through an isolator that has only passive stiffness and passivethrough an isolator that has only passive stiffness and passive dampingdamping

components (k and c, respectively).components (k and c, respectively).

FIGURE 2.3. Transmissibility model.FIGURE 2.3. Transmissibility model.

c

Compressor

x

y

k

Base



22--7. Passive Isolation Systems7. Passive Isolation Systems The transmissibility model is used to create a ratio between forThe transmissibility model is used to create a ratio between force seence seen

in the compressor due to rotation unbalance and force transmittein the compressor due to rotation unbalance and force transmittedd

through the isolator into the base.through the isolator into the base.

The ratio is developed by summing the forces in the model.The ratio is developed by summing the forces in the model.

(2.1)(2.1)

Assuming x and y are sinusoidal displacements for the compressorAssuming x and y are sinusoidal displacements for the compressorandand

base, respectively, velocity and acceleration can be calculatedbase, respectively, velocity and acceleration can be calculated by takingby taking

the derivative of the displacement. The result is:the derivative of the displacement. The result is:

(2.2)(2.2)

where X and Y are amplitudes of vibration andwhere X and Y are amplitudes of vibration and is the rotational speedis the rotational speed

of the compressor.of the compressor.

( )

+= =+ xycxykxmF &&

cXjcYjkXkYm += 2



22--8. Passive Isolation Systems8. Passive Isolation Systems The equation is rewritten as:The equation is rewritten as:

(2.3)(2.3)

Solving, the amplitude of the mass, X, divided by the amplitudeSolving, the amplitude of the mass, X, divided by the amplitude of theof the

base, Y, gives the transmissibility.base, Y, gives the transmissibility.

(2.4)(2.4)

YcjkXcjmk

+=+ 2

cjmkcjk

YX

++

= 2




FIGURE 2.4. Transmissibility as a function of the stiffness ofFIGURE 2.4. Transmissibility as a function of the stiffness of the isolator.the isolator.

XX

YY




FIGURE 2.5. Transmissibility as a function of the damping of thFIGURE 2.5. Transmissibility as a function of the damping of the isolator.e isolator.

XX

YY



22--11. Semi11. Semi--Active Isolation SystemsActive Isolation Systems A semiA semi--active isolator can only remove energy from the system.active isolator can only remove energy from the system.

However, a semiHowever, a semi--active isolator is capable of changing one or moreactive isolator is capable of changing one or more

properties in response to a command signal.properties in response to a command signal.

The ability to change system properties gives the system designeThe ability to change system properties gives the system designer morer more

control while using very little input power.control while using very little input power.

An example of a semiAn example of a semi--active system is a shock absorber with a variableactive system is a shock absorber with a variable

orifice that allows the damping coefficient to be changed as neeorifice that allows the damping coefficient to be changed as needed.ded.


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22

--12. Active Isolation Systems12. Active Isolation Systems

Active isolation systems can be controlled by computers throughActive isolation systems can be controlled by computers through inputinput

signals from sensors.signals from sensors.

Unlike passive and semiUnlike passive and semi--active systems, active systems are able to addactive systems, active systems are able to addenergy to the system.energy to the system.

The goal of active isolation is to provide energy equal in magniThe goal of active isolation is to provide energy equal in magnitude andtude and

opposite in phase of the vibration input. In doing so, an activopposite in phase of the vibration input. In doing so, an active isolatione isolationsystem can improve noise performance and durability performance.system can improve noise performance and durability performance.

An example of an active system is an electromechanical actuatorAn example of an active system is an electromechanical actuator

arranged to generate force by responding to a velocity or displaarranged to generate force by responding to a velocity or displacementcement

feedback signal.feedback signal.


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22

--13. Active Isolation Systems13. Active Isolation Systems

However, active systems are very design intensive and require seHowever, active systems are very design intensive and require sensorsnsors

and processors to provide real time data to the isolator.and processors to provide real time data to the isolator.

Large amounts of power are also required to operate an active isLarge amounts of power are also required to operate an active isolator.olator.

These necessary features of the active isolation system make itThese necessary features of the active isolation system make it the mostthe most

expensive isolation design.expensive isolation design.

Because of the expense, active isolation systems are very uncommBecause of the expense, active isolation systems are very uncommon.on.


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22

--14. Smart Materials As Actuators14. Smart Materials As Actuators

Several different materials have been developed to allow designeSeveral different materials have been developed to allow designers tors to

use them as actuators in a system.use them as actuators in a system.

Piezoelectric materials experience a dimensional change when anPiezoelectric materials experience a dimensional change when anelectrical voltage is applied to them.electrical voltage is applied to them.

Conversely, these materials produce an electrical charge when aConversely, these materials produce an electrical charge when a

pressure is applied to them.pressure is applied to them.

This rare property allows the piezoelectric material to be usedThis rare property allows the piezoelectric material to be used as aas a

sensor or an actuator.sensor or an actuator.

The best known such material is leadThe best known such material is lead--zirconatezirconate--titanatetitanate (PZT).(PZT).

However, the use of PZT for vibration isolation is limited due tHowever, the use of PZT for vibration isolation is limited due to the smallo the small

strain capability of the material.strain capability of the material.


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22

--15. Smart Materials As Actuators15. Smart Materials As Actuators

Shape memory alloy (SMA) material possesses the interesting propShape memory alloy (SMA) material possesses the interesting propertyerty

in that a metal remembers its original shape and size and chanin that a metal remembers its original shape and size and changesges

back to that shape and size at a characteristic transformationback to that shape and size at a characteristic transformation

temperature.temperature.

Materials that exhibit these characteristics include: goldMaterials that exhibit these characteristics include: gold--cadmium,cadmium,

brass, and nickelbrass, and nickel--titanium.titanium.

The alloys inherent properties have become very useful to the meThe alloys inherent properties have become very useful to the medicaldical

field.field.

TheThe SMAsSMAs ability to generate high forces at low frequency allows theability to generate high forces at low frequency allows the

material to be used as an actuator.material to be used as an actuator.

However, the use of SMA in engineering applications has been limHowever, the use of SMA in engineering applications has been limitedited

because of slow response time and due to the limited temperaturebecause of slow response time and due to the limited temperature rangerange

in which it can be effective.in which it can be effective.


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33

--1. MODELING OF RHEOLOGIC FLUIDS1. MODELING OF RHEOLOGIC FLUIDS

AA rheologicrheologic fluid changes properties as an external field is applied.fluid changes properties as an external field is applied.

These fluids can be used as controllable energy dissipaters.These fluids can be used as controllable energy dissipaters.

The control used is semiThe control used is semi--active, and with this approach small controlactive, and with this approach small control

energy can produce large actuation forces.energy can produce large actuation forces.

The following characteristics of aThe following characteristics of a rheologicrheologic fluid will be discussed:fluid will be discussed:

1.1. ER/MR fluid isolator systems.ER/MR fluid isolator systems.

2.2. Bingham plastic model of MR fluids.Bingham plastic model of MR fluids.

3.3. MR fluid isolator systems.MR fluid isolator systems.


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--2. ER/MR Fluid Isolator Systems2. ER/MR Fluid Isolator Systems

A great deal of research has been conducted on semiA great deal of research has been conducted on semi--active controlactive control

to look for a compromise between passive and active isolationto look for a compromise between passive and active isolation

systems.systems.

These systems can be used for vibration suppression or isolationThese systems can be used for vibration suppression or isolation

and require minimal power as compared to an active system.and require minimal power as compared to an active system.

With a semi active system, noise performance can be improvedWith a semi active system, noise performance can be improvedwithout dramatically hindering durability capabilities.without dramatically hindering durability capabilities.


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Extensive studies have been conducted on ElectroExtensive studies have been conducted on Electro--RheologicRheologic (ER)(ER)

and Magnetoand Magneto--RheologicRheologic (MR) fluids for use in semi(MR) fluids for use in semi--active systemsactive systems

that are used for vibration suppression.that are used for vibration suppression.

The two materials were discovered in the late 1940s.The two materials were discovered in the late 1940s.

JackJack RabinowRabinow reported on a MR fluid experimental program at thereported on a MR fluid experimental program at the

U.S. National Bureau of Standards for the Armys Chief ofU.S. National Bureau of Standards for the Armys Chief ofOrdinance in 1948.Ordinance in 1948.

Winslow published his account of a lengthy research programWinslow published his account of a lengthy research program

investigating the properties and applications of ER fluid in 194investigating the properties and applications of ER fluid in 1949.9.


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Initial testing with ER fluids showed problems with the fluid, nInitial testing with ER fluids showed problems with the fluid, namelyamely

operating temperature limitations and storage stability problemsoperating temperature limitations and storage stability problems..

Over time improvements have been made, but new problems haveOver time improvements have been made, but new problems havearisen.arisen.

Today, ER fluids are considered to have low shear strengths. ThToday, ER fluids are considered to have low shear strengths. Thee

fluid provides shear strengths that are two to ten times lower tfluid provides shear strengths that are two to ten times lower thanhanneeded for many practical applications.needed for many practical applications.

High voltages are required to operate ER fluids.High voltages are required to operate ER fluids.

There is a lack of universal fluid for ER technology.There is a lack of universal fluid for ER technology.

Because of these limitations, commercial success of ER fluids haBecause of these limitations, commercial success of ER fluids hass

been elusive.been elusive.


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33--5. ER/MR Fluid Isolator Systems5. ER/MR Fluid Isolator Systems

MR fluids are more practical.MR fluids are more practical.

When compared to ER fluids, MR fluids offer higher order yieldWhen compared to ER fluids, MR fluids offer higher order yield

stresses and provide a better operating temperature range.stresses and provide a better operating temperature range.

At the same time, companies such as Lord Corporation haveAt the same time, companies such as Lord Corporation have

commercial MR products.commercial MR products.

Because of the advantages of MR fluid over ER fluid, MR fluid wiBecause of the advantages of MR fluid over ER fluid, MR fluid willll

be considered from this point.be considered from this point.


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33--6. Bingham Plastic Model Of MR Fluids6. Bingham Plastic Model Of MR Fluids

MR fluids are traditionally modeled as a Bingham plastic, whereMR fluids are traditionally modeled as a Bingham plastic, where

there is a passive and active component to the fluid. Wherethere is a passive and active component to the fluid. Where

(3.1)(3.1)

is the equation used to model the fluid.is the equation used to model the fluid.

The passive component is a function of the fluid rThe passive component is a function of the fluid resistanceesistancefrom the viscosity, which is a property of the fluid and cannotfrom the viscosity, which is a property of the fluid and cannot bebe

controlled.controlled.

The active component is derived from the yieldThe active component is derived from the yield stress,stress,

which changes proportionally with the applied magnetic field.which changes proportionally with the applied magnetic field.

+=+=

yMRyxMRcyieldfMRF

R

c

yieldf


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Initial research showed the passive resistance could be modeledInitial research showed the passive resistance could be modeled asas

a constant.a constant.

Figure 3.1. Shear stress versus shear strain rate for aFigure 3.1. Shear stress versus shear strain rate for a

Bingham plastic material.Bingham plastic material.

Fo=0

F1

F2

F3

INCREASING

FIELD

STRENGTH

y(F1)

y(F2)

y(F3)

0 0


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However, further investigation showed that viscosity is a functiHowever, further investigation showed that viscosity is a function ofon of

shear rate, with the viscosity increasing dramatically at lowershear rate, with the viscosity increasing dramatically at lower shearshear

rates.rates.

Figure 3.2. Viscosity of a MR fluid is a function of shear rateFigure 3.2. Viscosity of a MR fluid is a function of shear rate..

0 50 100 150-1

0

1

2

3

4

5MR Fluid Characteristics - MRF 132LD - Lord Corporation

Shear Rate (1/s)

Viscosity(Pas)


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The active component is derived from resistance due to yieldThe active component is derived from resistance due to yield

stress, which is a function of the magnetic field created by a cstress, which is a function of the magnetic field created by a coiloil

that is incorporated into the isolator.that is incorporated into the isolator.

Figure 3.3. Yield stress as a function of magnetic field.Figure 3.3. Yield stress as a function of magnetic field.

0 0.5 1 1.5 2 2.5 3

x 105

0

1

2

3

4

5x 10

H (Amp/m)

Y

ield

S

tress

(P

a)

MR Fluid Characteristics -- MRF 132 LD - Lord Corporation


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33--10. MR Fluid Working Modes10. MR Fluid Working Modes

MR fluid has three different types of working modes, depending oMR fluid has three different types of working modes, depending onn

how the fluid is loaded. The modes include:how the fluid is loaded. The modes include:

1.1. Shear mode.Shear mode.2.2. Flow mode.Flow mode.

3.3. Squeeze mode.Squeeze mode.

Different equations are used to calculate resistive force for eaDifferent equations are used to calculate resistive force for each ofch ofthe different modes.the different modes.


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Figure 3.4. Three working modes of a MR fluid (a) shear, (b) flFigure 3.4. Three working modes of a MR fluid (a) shear, (b) flow,ow,

and (c) squeeze. B is the magnetic flux direction.and (c) squeeze. B is the magnetic flux direction.

B

Flux Guide

Moving Surface

B

TensionCompression

COIL

Flux Guide

Moving Surface

v

F

COIL

Flux Guide

Bp1 p2

COIL

(a) (b) (c)


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The shear mode works when one surface moves through the fluid wiThe shear mode works when one surface moves through the fluid withth

respect to another surface.respect to another surface.

The magnetic field is perpendicular to the direction of motion.The magnetic field is perpendicular to the direction of motion.

A MR based clutch is a good example of working the fluid in theA MR based clutch is a good example of working the fluid in the shearshear

mode.mode.

The equation corresponding to the shear mode is:The equation corresponding to the shear mode is:

(3.2)(3.2)

where f is the resultant force based on the plate area, and S, Lwhere f is the resultant force based on the plate area, and S, L, b, and h, b, and hare the surface area, length, width, and height, respectively.are the surface area, length, width, and height, respectively. Is theIs the

viscosity of the fluid and is the yield strength of thviscosity of the fluid and is the yield strength of the fluid.e fluid.

yLbhSLbf +=

y


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The flow mode is characterized by two static flux guides with thThe flow mode is characterized by two static flux guides with thee

magnetic field normal to the flow.magnetic field normal to the flow.

The magnetic field can be used to control flow resistance and prThe magnetic field can be used to control flow resistance and pressureessuredrop across the valve.drop across the valve.

Automotive shock absorbers work in the flow mode.Automotive shock absorbers work in the flow mode.

The equation corresponding to the flow mode is:The equation corresponding to the flow mode is:

(3.3)(3.3)

where Q is the flow rate of the fluid.where Q is the flow rate of the fluid.

yhL

bh

QLHFER

PHF

PP 33

12,,0 +=+=


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The squeeze mode works when two parallel surfaces are used toThe squeeze mode works when two parallel surfaces are used to

compress the fluid.compress the fluid.

The magnetic field is parallel to the motion of the surfaces.The magnetic field is parallel to the motion of the surfaces.

The magnetic flux density can be used to adjust the normal forceThe magnetic flux density can be used to adjust the normal force toto

resist the motion.resist the motion.

The squeeze mode has been shown to damp vibrations with high forThe squeeze mode has been shown to damp vibrations with high forcesces

and low amplitudes.and low amplitudes.

The equation corresponding to the squeeze mode is:The equation corresponding to the squeeze mode is:

(3.4)(3.4))()(

0

30

2x

thh

aF

=


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44--1. MODELING THE ISOLATION SYSTEM1. MODELING THE ISOLATION SYSTEM

A single degree of freedom model is used to model the compressorA single degree of freedom model is used to model the compressor

system.system.

The model simulates a compressor mounted to a vehicle body.The model simulates a compressor mounted to a vehicle body.

To simplify the model, the motion of the vehicle body is modeledTo simplify the model, the motion of the vehicle body is modeled as a 1as a 1

Hz sine wave. This simulates the vehicle body bouncing at the nHz sine wave. This simulates the vehicle body bouncing at the naturalatural

frequency of the suspension system.frequency of the suspension system.

Two seconds of data are simulated.Two seconds of data are simulated.

Halfway through the model, a speed bump is introduced. The speeHalfway through the model, a speed bump is introduced. The speedd

bump is a severe test of the isolators durability.bump is a severe test of the isolators durability.


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44--2. MODELING THE ISOLATION SYSTEM2. MODELING THE ISOLATION SYSTEM

Two models are created. One for the passive system and the otheTwo models are created. One for the passive system and the other forr for

the semithe semi--active system.active system.

The following discussion is included:The following discussion is included:

1.1. Simulation of the passive isolator.Simulation of the passive isolator.

2.2. Simulation of the semiSimulation of the semi--active isolator.active isolator.

3.3. NewmarkNewmark--Beta explicit time integration.Beta explicit time integration.4.4. Filter design.Filter design.

5.5. Control law design.Control law design.

6.6. System inputs.System inputs.

7.7. System outputs.System outputs.

8.8. Detailed design of the MR isolator.Detailed design of the MR isolator.


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44--3. Simulation Of The Passive Isolator3. Simulation Of The Passive Isolator

The passive model was used to create baseline performance standaThe passive model was used to create baseline performance standardsrds

for the existing isolator, and to show trend lines when stiffnesfor the existing isolator, and to show trend lines when stiffness ands and

damping parameters are changed.damping parameters are changed.

The passive model can be seen in Figure 4.1. The model shows thThe passive model can be seen in Figure 4.1. The model shows thee

compressor mounted to the vehicle body through an isolator thatcompressor mounted to the vehicle body through an isolator that hashas

only passive stiffness and passive damping components (only passive stiffness and passive damping components (kkpassivepassive andand

ccpassivepassive, respectively)., respectively).

1.1. The free body diagram for the passive system can be seen in FiguThe free body diagram for the passive system can be seen in Figure 4.2.re 4.2.

This diagram helps show how the equation of motion and the equatThis diagram helps show how the equation of motion and the equationion

for transmitted force are developed.for transmitted force are developed.


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Figure 4.1. Passive model.Figure 4.1. Passive model. Figure 4.2. Passive free body diagram.Figure 4.2. Passive free body diagram.

cPASSIVEkPASSIVE

VEHICLE BODY

COMPRESSOR

x(t)

y(t)

F COMPRESSOR

COMPRESSOR

F COMPRESSOR ASSUME x>y

VEHICLE BODY

)( yxkPASSIVE )(

yxcPASSIVE


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The equation of motion is created by summing the forces seen inThe equation of motion is created by summing the forces seen in thethe

free body diagram, given by:free body diagram, given by:

(4.1)(4.1)

This summation of forces is:This summation of forces is:

(4.2)(4.2)

Rearranging gives:Rearranging gives:

(4.3)(4.3)

The acceleration of the compressor,The acceleration of the compressor, , is then calculated as:, is then calculated as:

(4.4)(4.4)

=+

xmF

( )COMPRESSOR

FyxPASSIVEcyx

PASSIVEkxm +=

COMPRESSORFx

PASSIVEcy

PASSIVEcx

PASSIVEky

PASSIVEkxm ++=

( )

++=

COMPRESSOR

Fxy

PASSIVE

cxy

PASSIVE

k

m

x1

x


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The force transmitted into the vehicle body is also seen in theThe force transmitted into the vehicle body is also seen in the free bodyfree body

diagram. A transmitted force is considered any force created frdiagram. A transmitted force is considered any force created from theom the

relative motion between the vehicle body and the compressor thatrelative motion between the vehicle body and the compressor that actsacts

upon the vehicle body.upon the vehicle body.

The transmitted force is computed using:The transmitted force is computed using:

(4.5)(4.5)

Including the spring and damper force in (4.5) gives:Including the spring and damper force in (4.5) gives:

(4.6)(4.6)

=+TRANS

FF

( )

+= =+ yxPASSIVE

cyx

PASSIVE

k

TRANS

FF


43/115



The compressor assembly consists of three baseline isolators andThe compressor assembly consists of three baseline isolators and thethe

compressor.compressor.

Each isolator is a simple passive isolator with the following prEach isolator is a simple passive isolator with the following properties:operties:

Synthetic rubber material of 60Synthetic rubber material of 60 durometerdurometer..

Rated to withstand temperatures up to 110 C.Rated to withstand temperatures up to 110 C.

Measured stiffness of k=50,000 N/m and damping ratio of zeta=0.1Measured stiffness of k=50,000 N/m and damping ratio of zeta=0.1.. Height of 20 mm, outer diameter of 14 mm, and mass of 6.8 grams.Height of 20 mm, outer diameter of 14 mm, and mass of 6.8 grams.

The compressor has the following properties:The compressor has the following properties:

230 mm long, 180 mm wide, and 110 mm tall.230 mm long, 180 mm wide, and 110 mm tall. Mass of 3 kg (6.6 lbs.)Mass of 3 kg (6.6 lbs.)

For the model, it was assumed that oneFor the model, it was assumed that one--third of the mass (1 kg) was onthird of the mass (1 kg) was on

each isolator.each isolator.


44/115


44--8. Simulation Of The Semi8. Simulation Of The Semi--Active IsolatorActive Isolator

The semiThe semi--active isolator was modeled to replace the passive isolator.active isolator was modeled to replace the passive isolator.

The fluid was modeled as a Bingham plastic, where there is a pasThe fluid was modeled as a Bingham plastic, where there is a passivesive

and active component to the fluid.and active component to the fluid.

The equations used to model the fluid are as follows:The equations used to model the fluid are as follows:

(4.7)(4.7)

(4.8)(4.8)

+= yxMRcyieldfMRF

+= yR


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TheThe ccMRMR component of the fluid is the passive part of the fluid.component of the fluid is the passive part of the fluid.

It is a function of the viscosity of the fluid, , the shear raIt is a function of the viscosity of the fluid, , the shear rate of the fluid, ,te of the fluid, ,

and the geometry of the flow path.and the geometry of the flow path.

The shear rate of the fluid is a function of the relative velociThe shear rate of the fluid is a function of the relative velocity and thety and the

fluid gap width. The viscosity of the fluid is a function of thfluid gap width. The viscosity of the fluid is a function of the shear rate.e shear rate.

TheThe ffyieldyield is the active isolation component of the MR fluid.is the active isolation component of the MR fluid.

It is a function of the yield strength of the fluid, .It is a function of the yield strength of the fluid, .

The yield strength of the MR fluid is related to the resistanceThe yield strength of the MR fluid is related to the resistance forceforcethrough the gap area of the isolators flow channels and the strthrough the gap area of the isolators flow channels and the strength ofength of

the magnetic field surrounding it.the magnetic field surrounding it.

y


46/115



Figure 4.3. SemiFigure 4.3. Semi--active model of the MR isolator.active model of the MR isolator.

Processor With

Control LawControl

Filter

IntegratorVehicle Body

Compressor

Amplifier For

MR Coil

MRcpassive

kpassive

y(t)

x(t)

Fcomponent


47/115



Figure 4.4. SemiFigure 4.4. Semi--active free body diagram.active free body diagram.

COMPRESSOR

F COMPRESSOR ASSUME x>y

VEHICLE BODY

FMR)( yxkPASSIVE )(

yxcPASSIVE


48/115



The equation of motion is created by summing the forces seen inThe equation of motion is created by summing the forces seen in thethe

free body diagram, given by:free body diagram, given by:

(4.9)(4.9)

However, in the semiHowever, in the semi--active system, forces created by the MR fluid areactive system, forces created by the MR fluid are

included in the equation of motion.included in the equation of motion.

(4.10)(4.10)

Rearranging gives:Rearranging gives:

(4.11)(4.11)

The acceleration of the compressor, , is then calculated asThe acceleration of the compressor, , is then calculated as::

(4.12)(4.12)

=+

xmF

( )COMPRESSOR

FMR

FyxPASSIVEcyx

PASSIVEkxmF += =+

COMPRESSORFMRFxPASSIVEcyPASSIVEcxPASSIVEkyPASSIVEkxm ++=

( )

++=

COMPRESSORF

MRFxy

PASSIVEcxy

PASSIVEk

mx

1

x


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The transmitted force equation for the semiThe transmitted force equation for the semi--active system is very similaractive system is very similar

to the passive equation.to the passive equation.

The transmitted force is computed using:The transmitted force is computed using:

(4.13)(4.13)

But once again, the forces generated by the MR fluid need to beBut once again, the forces generated by the MR fluid need to beconsidered.considered.

(4.14)(4.14)

It is important to note that the MR force is transmitted into thIt is important to note that the MR force is transmitted into the vehiclee vehiclebody. For this reason, the control of the MR fluid is very impobody. For this reason, the control of the MR fluid is very important.rtant.

=+ TRANSFF

( )MR

FyxPASSIVEcyx

PASSIVEk

TRANSFF ++= =+


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To generate the passive and active force components from the MRTo generate the passive and active force components from the MR fluid,fluid,

the pressure drop through the isolator must be analyzed.the pressure drop through the isolator must be analyzed.

(4.15)(4.15)

From (4.15), the force components can be derived using the areaFrom (4.15), the force components can be derived using the area of theof the

flow channel,flow channel, AAgapgap, and the area of the isolator plunger, A, and the area of the isolator plunger, Aii..

The derivation of the active component follows:The derivation of the active component follows:

(4.16)(4.16)

It is important to note that the active component of the MR fluiIt is important to note that the active component of the MR fluid isd is

directly proportional to the yield stress of the fluid.directly proportional to the yield stress of the fluid.

3123 bhQLyhLP

+=

yhiroryhgap

Ayield

f

== 2233


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The derivation of the passive component is a little more complicThe derivation of the passive component is a little more complicated.ated.

The passive force is related to the viscosity and flow rate.The passive force is related to the viscosity and flow rate.

(4.17)(4.17)

However, the flow rate is a function of relative velocity.However, the flow rate is a function of relative velocity.

(4.18)(4.18)

When the velocity is factored out, the passive component is seenWhen the velocity is factored out, the passive component is seen asas

being proportional to the viscosity of the fluid and the geometrbeing proportional to the viscosity of the fluid and the geometry of they of the

isolator.isolator.

(4.19)(4.19)

312 bhQLyxMRc =

3

22212

312

312

bh

Lyxi

r

iror

bh

Lyxi

A

gapAbh

QLgapAyxMR

c

=

==

322212

3

22212

bh

Li

rorir

bh

Li

r

irorMR

c

==


52/115


44--16. Simulation Of The Semi16. Simulation Of The Semi--Active IsolatorActive Isolator Simplifying, the equation for the passive component of the MR flSimplifying, the equation for the passive component of the MR fluid isuid is

found.found.

(4.20)(4.20)

Combining the passive rubber components and the MR components ofCombining the passive rubber components and the MR components of

the isolator, the MR based isolator is modeled as follows:the isolator, the MR based isolator is modeled as follows:

(4.21)(4.21)

312 bhgapAiAMRc

=

( ) ( )yield

fyxMRccyxk

IsolatorF +++=


53/115


44--17. Simulation Of The Semi17. Simulation Of The Semi--Active IsolatorActive Isolator The control of theThe control of the ffyieldyield component is very important.component is very important.

The goal of theThe goal of the ffyieldyield term is to control road input frequencies withoutterm is to control road input frequencies without

transmitting higher frequencies created by the compressor.transmitting higher frequencies created by the compressor.

This done by controlling the active MR component to model the paThis done by controlling the active MR component to model the passivessive

damping provided by the isolator, but using a low pass filter todamping provided by the isolator, but using a low pass filter to eliminateeliminate

the higher frequencies created by the compressor.the higher frequencies created by the compressor.


54/115


44--18.18. NewmarkNewmark--Beta Explicit Time Integration MethodBeta Explicit Time Integration Method This is an integration method with force balance iteration usedThis is an integration method with force balance iteration used to moveto move

from one time point to the next because the equations of the isofrom one time point to the next because the equations of the isolatorlator

system are nonlinear and cannot be solved in closed form.system are nonlinear and cannot be solved in closed form.

The integration method requires initial displacement, velocity,The integration method requires initial displacement, velocity, andand

acceleration components. It then calculates displacement and veacceleration components. It then calculates displacement and velocitylocity

for the next time point, and inputs them into the equation of mofor the next time point, and inputs them into the equation of motion.tion.

Ten iterations are run for each point, allowing the calculationsTen iterations are run for each point, allowing the calculations toto

converge.converge.

This is an accurate, flexible, and simple method for solving nonThis is an accurate, flexible, and simple method for solving nonlinearlinear

equations. However, a small time step is required.equations. However, a small time step is required.


55/115


44

--19. Filter Design19. Filter Design

The lowThe low--pass filter was designed as a second order Butterworth filter.pass filter was designed as a second order Butterworth filter.

The filter was designed with a cutoff frequency of 30 Hz in ordeThe filter was designed with a cutoff frequency of 30 Hz in order to turnr to turn

off the actuator at 50 Hz so the compressor vibration is not troff the actuator at 50 Hz so the compressor vibration is not transmittedansmittedto the automobile frame.to the automobile frame.

Figure 4.5 shows how the filter introduces amplitude distortionFigure 4.5 shows how the filter introduces amplitude distortion based onbased on

frequency.frequency.

It also shows how the filter introduces phase lag into the respoIt also shows how the filter introduces phase lag into the response of thense of the

active MR component.active MR component.


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44--20. Filter Design20. Filter Design

Figure 4.5. Characteristics of a second order Butterworth filteFigure 4.5. Characteristics of a second order Butterworth filter.r.

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

Second Order Butterworth Low Pass Filter Properties -- 30 Hz

Frequency (Hz)

Magn

itu

de

0 20 40 60 80 100 120 140 160 180 200-200

-150

-100

-50

0

Frequency (Hz)

P

hase

(deg

)


57/115


44


The following shows how the lowThe following shows how the low--pass filter works:pass filter works:

The active variable v is set equal to the relative velocity betwThe active variable v is set equal to the relative velocity between theeen the

compressor and the structural base.compressor and the structural base.

It is then filtered, producing a variable z with the compressorIt is then filtered, producing a variable z with the compressor excitationexcitation

content removed.content removed.

The variable z is then scaled to produce the yield stress of theThe variable z is then scaled to produce the yield stress of the fluid.fluid.

v = relative velocityv = relative velocity vv FilterFilter zz yield stress=z*scaleyield stress=z*scale


58/115


44


The variable v is exactly in phase with the passive isolation foThe variable v is exactly in phase with the passive isolation force.rce.

If the filter was a perfect filter, there would be no phase lagIf the filter was a perfect filter, there would be no phase lag in variable z,in variable z,

and it too would be exactly in phase with the passive isolationand it too would be exactly in phase with the passive isolation force.force.

However, as seen in Figure 4.6, when the vehicle hits the bump,However, as seen in Figure 4.6, when the vehicle hits the bump, thethe

response of the active component lags behind the passive componeresponse of the active component lags behind the passive componentnt

by roughly ninety degrees.by roughly ninety degrees.

Because the active component lags, it cannot be as effective asBecause the active component lags, it cannot be as effective as

possible.possible.

If the amplitude of the active MR component is scaled too high,If the amplitude of the active MR component is scaled too high, thisthis

phase lag can cause a phase lag induced instability in the modelphase lag can cause a phase lag induced instability in the model..


59/115



Figure 4.6. Showing the phase lag with a Butterworth low pass fFigure 4.6. Showing the phase lag with a Butterworth low pass filter.ilter.

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-15

-10

-5

0

5

10

15

Time (s)

Active com ponent lags behind the passive com ponent .

Dampin

gForce(N)

passive

active


60/115


44


Several ideas were explored to resolve this phase lag issue andSeveral ideas were explored to resolve this phase lag issue and improveimprove

results.results.

A phase lag compensator can be used to correct the phase lag.A phase lag compensator can be used to correct the phase lag.

Displacement and velocity feedback control with phase lag can beDisplacement and velocity feedback control with phase lag can be

resolved into corrected displacement and velocity components.resolved into corrected displacement and velocity components.

This feedback can be used in a linear control law.This feedback can be used in a linear control law. The limitation of this technique is that both position and velocThe limitation of this technique is that both position and velocityity

feedback are needed.feedback are needed.

Another idea is the concept of an ideal filter, as seen in FigurAnother idea is the concept of an ideal filter, as seen in Figure 4.7.e 4.7.

This filter would have no phase lag at any frequency.This filter would have no phase lag at any frequency.

The amplitude cutThe amplitude cut--off is perfect at the cutoff frequency.off is perfect at the cutoff frequency.


61/115



Figure 4.7. Characteristics of an ideal lowFigure 4.7. Characteristics of an ideal low--pass filter.pass filter.

Frequency (Hz)

Frequency (Hz)

0

180

180

0

1

0

-1

0 30

Phase

Magnitude

Ideal Low Pass Filter


62/115


44


To get the desired results for this type of control system, reseTo get the desired results for this type of control system, researcharch

showed that the design of the low pass filter is a very importanshowed that the design of the low pass filter is a very important factor.t factor.

Research also showed that compensating for phase lag is veryResearch also showed that compensating for phase lag is verycomplicated.complicated.

While this subject needs further research, a simpler approach waWhile this subject needs further research, a simpler approach was takens taken

for this model.for this model.

To illustrate the adverse affects of the low pass filter, the fiTo illustrate the adverse affects of the low pass filter, the filter waslter was

simply turned off when the compressor was off.simply turned off when the compressor was off.

The filter was there for the sole purpose of taking out the compThe filter was there for the sole purpose of taking out the component inonent in

the relative velocity response due to the compressor.the relative velocity response due to the compressor.

If the compressor is not running, there is no reason to have theIf the compressor is not running, there is no reason to have the filter on.filter on.


63/115


44--27. Control Law Design27. Control Law Design

A skyhook control algorithm was considered for the control of thA skyhook control algorithm was considered for the control of thee

isolator.isolator. It was based on the following logic:It was based on the following logic:

Figure 4.9. Diagram of skyhook control law.Figure 4.9. Diagram of skyhook control law.

Positive absolute velocity (+)

Negative absolute velocity (-)

Negative relative velocity (-)

Positive relative velocity (+)

Negative relative velocity (-)

Positive relative velocity (+) Controller ON

Controller OFF

Controller ON


64/115



A careful evaluation of the results showed that the active MR coA careful evaluation of the results showed that the active MR componentmponent

would not react immediately to the bump in the model.would not react immediately to the bump in the model.

Figure 4.10. Skyhook control law does not allow theFigure 4.10. Skyhook control law does not allow the

isolator to react properly to a bump.isolator to react properly to a bump.

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-15

-10

-5

0

5

10

15

Time (s)

Skyhook control does not allow the active component to react properly.

Damp

ing

Forc

e(N)

passive

active


65/115



A relative skyhook control algorithm was investigated. It was bA relative skyhook control algorithm was investigated. It was based onased on

the logic below. It was quickly noted that this control was thethe logic below. It was quickly noted that this control was the same assame as

always having the control on.always having the control on.

Figure 4.11. Diagram of relative skyhook control law.Figure 4.11. Diagram of relative skyhook control law.

Positive relative velocity (+)

Negative relative velocity (-) Negative relative velocity (-)

Positive relative velocity (+) Controller ON

Controller ON


66/115



With no skyhook control, the isolator is able to react properly.With no skyhook control, the isolator is able to react properly.

Figure 4.12. No skyhook control allows the isolator to react prFigure 4.12. No skyhook control allows the isolator to react properly.operly.

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-15

-10

-5

0

5

10

15

Time (s)

No sky hook control allows the active component to react properly.

DampingF

orce(N)

passive

active


67/115



In the control system shown in Figure 4.3, an accelerometer is lIn the control system shown in Figure 4.3, an accelerometer is locatedocated

on the compressor and another accelerometer is located on the veon the compressor and another accelerometer is located on the vehiclehicle

body.body.

The acceleration signals can be integrated and then subtracted tThe acceleration signals can be integrated and then subtracted to giveo give

the velocity of the compressor relative to the vehicle body.the velocity of the compressor relative to the vehicle body.

This relative velocity is used as a feedback signal in the contrThis relative velocity is used as a feedback signal in the contrololalgorithm.algorithm.

While this approach is feasible, the two channels of data acquisWhile this approach is feasible, the two channels of data acquisition andition and

the signal processing would add complication and cost to the isothe signal processing would add complication and cost to the isolatorlator

system.system.


68/115



Another approach is to design a direct relative velocity sensorAnother approach is to design a direct relative velocity sensor that isthat is

built into the isolator.built into the isolator.

The velocity of the piston in the isolator with respect to the bThe velocity of the piston in the isolator with respect to the base is thease is therelative velocity that must be measured.relative velocity that must be measured.

It may be possible to have a magnet built into the piston rod anIt may be possible to have a magnet built into the piston rod and a smalld a small

coil of wire attached to the isolator housing which is attachedcoil of wire attached to the isolator housing which is attached to theto thebase.base.

The magnet moving through the coil of wire around the piston rodThe magnet moving through the coil of wire around the piston rod willwill

produce a voltage in the coil that will be proportional to the vproduce a voltage in the coil that will be proportional to the velocity ofelocity of

the magnet relative to the coil.the magnet relative to the coil.


69/115



Another possible approach is to use a Linear Variable DifferentiAnother possible approach is to use a Linear Variable Differentialal

Transformer.Transformer.

These devices are used to measure relative displacement and mayThese devices are used to measure relative displacement and may bebeadapted to measure velocity, or the derivative of the relativeadapted to measure velocity, or the derivative of the relative

displacement may be taken to obtain relative velocity.displacement may be taken to obtain relative velocity.

A design with a sensor in each isolator would have the added posA design with a sensor in each isolator would have the added possibilitysibilityand advantage of individually controlling each isolator. This wand advantage of individually controlling each isolator. This wouldould

provide rotational isolation for the component and is a potentiaprovide rotational isolation for the component and is a potentially simplelly simple

approach to achieve multiapproach to achieve multi--degreedegree--ofof--freedom control.freedom control.

The development of such a sensor should be investigated in futurThe development of such a sensor should be investigated in futuree

work.work.


70/115


44--34. System Inputs34. System Inputs

The unbalance force due to the compressor rotation is simulatedThe unbalance force due to the compressor rotation is simulated as aas a

sinusoidal force input to the compressor mass.sinusoidal force input to the compressor mass. As discussed earlier,As discussed earlier,

the compressor is turned on and off during the simulation.the compressor is turned on and off during the simulation.

The vehicle body motion is modeled as a body heave mode, with aThe vehicle body motion is modeled as a body heave mode, with a

speed bump input midway through the simulation.speed bump input midway through the simulation.

Both inputs can be seen in Figure 4.13.Both inputs can be seen in Figure 4.13.


71/115


44--35. System Inputs35. System Inputs

Figure 4.13. Model inputs for the compressor and vehicle body.Figure 4.13. Model inputs for the compressor and vehicle body.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-20

-10

0

10

20

No

ise

Sourc

eInpu

t(N)

Model Inputs

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.05

0

0.05

Ve

hicleBo

dy

Mo

tion

(m)

Time (s)


72/115


44--36. System Outputs36. System Outputs

The main outputs from the simulation are:The main outputs from the simulation are:

Power spectral density of the transmitted force at 50 Hz, thePower spectral density of the transmitted force at 50 Hz, the

frequency of the compressor.frequency of the compressor. The PSD is calculated during the timeThe PSD is calculated during the timeperiod that the compressor is on. An example of the PSD is seenperiod that the compressor is on. An example of the PSD is seen inin

Figure 4.14.Figure 4.14.

Maximum relative displacement between the compressor and theMaximum relative displacement between the compressor and thevehicle body.vehicle body. This occurs shortly after the bump. This isThis occurs shortly after the bump. This is

considered a measure of durability of the isolator.considered a measure of durability of the isolator.


73/115


44--37. System Outputs37. System Outputs

Figure 4.14. Example of a power spectral density plot.Figure 4.14. Example of a power spectral density plot.

0 50 100 150 200 250 300 350 400 450 50010

-6

10-4

10-2

100

102

Frequency (Hz)

Power Spectral Density

(N2

/Hz)

Power spectral density of the transmitted force.


74/115


44--38. Detailed Design Of The MR Isolator38. Detailed Design Of The MR Isolator

Once the control and filter issues were resolved, a fluid was chOnce the control and filter issues were resolved, a fluid was chosen.osen.

Lord Corporations web site was used to get fluid properties onLord Corporations web site was used to get fluid properties on theirtheir

product MRF 132LD. This fluid was chosen because it had low visproduct MRF 132LD. This fluid was chosen because it had low viscositycosityproperties.properties.

The properties of MRF 132LD can be seen in Figure 4.15.The properties of MRF 132LD can be seen in Figure 4.15.


75/115



Figure 4.15. Properties of MRF 132LD.Figure 4.15. Properties of MRF 132LD.

0 50 100 150

0

2

4

MR Fluid Characteristics - MRF 132LD - Lord Corporation

Shear Rate (1/s)

V

iscosity(Pas)

0 0.5 1 1.5 2 2.5 3

x 105

0

1

2

3

4

5x 10

4

H (Amp/m)

Yield

Stress(Pa)

0 0.5 1 1.5 2 2.5 3

x 105

0

0.5

1

H (Amp/m)

B(Tesla)


76/115



Using the fluid properties, the size of the isolator needed to oUsing the fluid properties, the size of the isolator needed to obtain thebtain the

performance necessary was determined.performance necessary was determined.

The power capability and coil design needed to generate the poweThe power capability and coil design needed to generate the power wasr wasalso determined.also determined.

Final design parameters, such as weight, size, fluid volume, coiFinal design parameters, such as weight, size, fluid volume, coill

length,etc., were determined.length,etc., were determined.

Results are compared.Results are compared.

The goal is to show that the semiThe goal is to show that the semi--active design can give the sameactive design can give the same

maximum relative displacement as the passive baseline, but, in amaximum relative displacement as the passive baseline, but, in addition,ddition,provide a significant reduction in noise transmission.provide a significant reduction in noise transmission.


77/115


55--1. RESULTS1. RESULTS

The results of the passive and semiThe results of the passive and semi--active models are plotted. Theactive models are plotted. The

maximum relative displacement and transmitted force seen with thmaximum relative displacement and transmitted force seen with thee

passive system are plotted. These results are used to develop tpassive system are plotted. These results are used to develop thehe

baseline performance of the passive isolator.baseline performance of the passive isolator.

The following four designs are discussedThe following four designs are discussed::

Design Case 1Design Case 1 Passive rubber isolator.Passive rubber isolator.

Design Case 2Design Case 2 Passive rubber isolator with passive MR fluid.Passive rubber isolator with passive MR fluid.

Design Case 3Design Case 3 Passive rubber isolator with active MR fluid withPassive rubber isolator with active MR fluid with

Butterworth filter.Butterworth filter.

Design Case 4Design Case 4 Passive rubber isolator with active MR fluid withPassive rubber isolator with active MR fluid with

filter off.filter off.

The forces seen in the different isolator components are evaluatThe forces seen in the different isolator components are evaluated.ed.

The change in viscosity of the fluid is analyzed.The change in viscosity of the fluid is analyzed.


78/115


55--2. Results For The Passive Isolator Design2. Results For The Passive Isolator Design

The power spectrum of the transmitted noise at 50 Hz is seen toThe power spectrum of the transmitted noise at 50 Hz is seen to increaseincrease

as the stiffness of the isolator increases.as the stiffness of the isolator increases.

Figure 5.1. The effect of passive stiffness seen on transmittedFigure 5.1. The effect of passive stiffness seen on transmitted force.force.

Power Spectrum Of Transmitted Noise @ 50 Hz

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

0 10000 20000 30000 40000 50000

Stiffness (N/m)

PSOfTransmittedNoise(

N^2/Hz)

PASSIVE RESULTS

Baseline Transmission


79/115



The maximum relative displacement is seen to decrease as the stiThe maximum relative displacement is seen to decrease as the stiffnessffness

of the isolator increases.of the isolator increases.

Figure 5.2. The effect of passive stiffness seen onFigure 5.2. The effect of passive stiffness seen on

maximum relative displacement.maximum relative displacement.

Maximum Relative Displacement

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0 10000 20000 30000 40000 50000

Stiffness (N/m)

MaxRelDisp

(mm)

PASSIVE RESULTS

Baseline Displacement


80/115



From the previous two figures, the baseline performance of the iFrom the previous two figures, the baseline performance of the isolatorsolator

is determined. This is seen below.is determined. This is seen below.

(i)(i) Maximum relative displacement of 2.3 mm.Maximum relative displacement of 2.3 mm.

(ii)(ii) Maximum transmitted force from the compressor of 6.3 NMaximum transmitted force from the compressor of 6.3 N22/Hz./Hz.


81/115


82/115


55--6. Results For The Semi6. Results For The Semi--Active Isolator DesignActive Isolator Design

The maximum relative displacement is seen to decrease as the stiThe maximum relative displacement is seen to decrease as the stiffnessffness

of the isolator increases.of the isolator increases.

Figure 5.4. The effect of passive stiffness seen onFigure 5.4. The effect of passive stiffness seen on

maximum relative displacement.maximum relative displacement.

Maximum Relative Displacement

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0 10000 20000 30000 40000 50000

Stiffness (N/m)

MaxRelDisp

(mm)

PASSIVE RESULTS

MR INACTIVE RESULTS

MR ACTIVE RES ULTS -- Butterworth Lowpass Filter

MR ACTIVE RESULTS -- Ideal Low Pass Filter

Baseline Displacement


83/115



The results show the passive component of the MR fluid has aThe results show the passive component of the MR fluid has a

significant affect on results.significant affect on results.

As expected, the maximum relative displacement is reduced, and tAs expected, the maximum relative displacement is reduced, and thehetransmitted force increases.transmitted force increases.

The following effects were seen when the active component of theThe following effects were seen when the active component of the MRMR

fluid is introduced with the Butterworth filter.fluid is introduced with the Butterworth filter.

The maximum relative displacement at low stiffness is reduced.The maximum relative displacement at low stiffness is reduced.

However, there is little effect at higher stiffness.However, there is little effect at higher stiffness.

The transmitted noise is not affected much by the active componeThe transmitted noise is not affected much by the active component.nt.


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When the filter is turned off, the active fluid is in phase andWhen the filter is turned off, the active fluid is in phase and the resultsthe results

improve significantly.improve significantly.

With the filter turned off, the following effects are seen in thWith the filter turned off, the following effects are seen in the results:e results:

The transmitted force is not affected.The transmitted force is not affected.

The maximum relative displacement is reduced at each stiffness.The maximum relative displacement is reduced at each stiffness.


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Figure 5.5. Improvement to relative displacement with MR fluid.Figure 5.5. Improvement to relative displacement with MR fluid.

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6-8

-6

-4

-2

0

2

4

6

8x 10

-3

Time (s)

Re

lative

Disp

lacemen

t(m)

Passive

Pass ive M R

Active M R


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The results can be seen in Table 5.1.The results can be seen in Table 5.1.

Shown in the table are the following properties:Shown in the table are the following properties:

(i)(i) Isolator stiffness.Isolator stiffness.

(ii)(ii) Isolator passive damping ratio.Isolator passive damping ratio.

(iii)(iii) Compressor mass per isolator.Compressor mass per isolator.

(iv)(iv) Natural frequency of the isolator.Natural frequency of the isolator.

(v)(v) Maximum relative displacement.Maximum relative displacement.

(vi)(vi) Compressor transmitted force.Compressor transmitted force.

(vii)(vii) Maximum forces seen by the isolator components.Maximum forces seen by the isolator components.


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Table 5.1. Summary of simulation results.Table 5.1. Summary of simulation results.

PASSIVE RESULTS POWER SPECTRUM

stiffness mass zeta nat. freq. scale max. rel. displacement comp. transmitted spring damper passive fluid active fluid total

(N/m) (kg) (Hz) (mm) (N 2/Hz) (N) (N) (N) (N) (N)

50000 1 0.1 35.6 0 2.3 6.300 113.7 26.6 0 0 116.0

30000 1 0.1 27.6 0 3.0 1.300 91.4 21.7 0 0 93.3

10000 1 0.1 15.9 0 6.2 0.100 62.0 11.9 0 0 62.9

5000 1 0.1 11.3 0 12.8 0.030 63.8 14.7 0 0 65.1

1000 1 0.1 5.0 0 26.3 0.003 26.3 5.0 0 0 27.7

MR INACTIVE RESULTS POWER SPECTRUM



50000 1 0.1 35.6 0 2.1 6.50 105.0 27.6 15.7 0 110.5

30000 1 0.1 27.6 0 2.6 2.10 79.2 21.1 15.5 0 84.5

10000 1 0.1 15.9 0 4.3 0.70 42.5 12.0 15.3 0 47.0

5000 1 0.1 11.3 0 7.1 0.54 35.5 11.5 20.9 0 42.0

1000 1 0.1 5.0 0 15.6 0.43 15.6 3.8 15.2 0 21.4

MR ACTIVE RESULTS -- Butterworth Lowpass Fil ter POWER SPECTRUM



50000 1 0.1 35.6 10000 2.1 6.75 104.4 27.4 15.6 7.4 112.4

30000 1 0.1 27.6 10000 2.6 2.06 78.4 21.5 15.8 8.8 88.0

10000 1 0.1 15.9 10000 4.0 0.66 40.2 13.4 15.2 50.4 56.7

5000 1 0.1 11.3 30000 5.0 0.43 24.8 11.5 20.6 56.4 80.5

1000 1 0.1 5.0 30000 6.0 0.32 6.0 3.8 17.1 13.7 57.8

MR ACTIVE RESULTS -- Ideal Low Pass Filter POWER SPECTRUM


(N/m) (kg) (Hz) (mm) (N 2/Hz) (N) (N) (N) (N) (N)50000 1 0.1 35.6 45000 1.5 7.70 75.7 26.7 15.2 121.6 158.5

30000 1 0.1 27.6 45000 1.7 2.10 49.6 20.9 15.3 122.5 152.9

10000 1 0.1 15.9 45000 2.5 0.60 25.2 12.2 15.5 124.1 144.7

5000 1 0.1 11.3 45000 3.2 0.40 15.7 8.5 15.2 121.7 141.4

1000 1 0.1 5.0 45000 3.6 0.30 3.6 3.7 14.8 118.4 136.9

MAXIMUM FORCES

MAXIMUM FORCES

MAXIMUM FORCES

MAXIMUM FORCES


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The maximum forces are shown in the right columns of Table 5.1.The maximum forces are shown in the right columns of Table 5.1. TheyThey

give an indication of how the forces seen by the different compogive an indication of how the forces seen by the different components ofnents of

the isolator compare to each other.the isolator compare to each other.

The columns are linked to the following forces:The columns are linked to the following forces:

(i)(i) Spring force resulting from the passive stiffness component k.Spring force resulting from the passive stiffness component k.

(ii)(ii) Damper force resulting from the passive damping component c.Damper force resulting from the passive damping component c.

(iii)(iii) Fluid force resulting from the passive component of the MR fluidFluid force resulting from the passive component of the MR fluid..

(iv)(iv) Fluid force resulting from the active component of the MR fluid.Fluid force resulting from the active component of the MR fluid.

(v)(v) Total force resulting from the sum of all the isolator forces.Total force resulting from the sum of all the isolator forces.


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The results show the force resulting from the passive stiffnessThe results show the force resulting from the passive stiffness andand

damping components decreases as the passive stiffness of the isodamping components decreases as the passive stiffness of the isolatorlator

decreases.decreases.

This explains why transmitted noise decreases when stiffness andThis explains why transmitted noise decreases when stiffness and

damping decrease.damping decrease.

Also, the results show the negative affect on relative displacemAlso, the results show the negative affect on relative displacement, andent, and

thus durability, when the stiffness decreases.thus durability, when the stiffness decreases.


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The active results show why turning the filter off is necessary.The active results show why turning the filter off is necessary.

When the Butterworth low pass filter is used, the active componeWhen the Butterworth low pass filter is used, the active component ofnt of

the MR fluid is roughly the same size as the passive component othe MR fluid is roughly the same size as the passive component of thef theMR fluid. If the active force is scaled higher than this, the iMR fluid. If the active force is scaled higher than this, the isolato

Documents

Semi-Active Magnetorheologic, Greg Stelzer