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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.
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FIGURE 1.1. A compressor assembly with passive isolators.FIGURE 1.1. A compressor assembly with passive isolators.
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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.
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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.
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22--3. Passive Isolation Systems3. Passive Isolation Systems
FIGURE 2.1. Design of a passive isolator.FIGURE 2.1. Design of a passive isolator.
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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.
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22--5. Passive Isolation Systems5. Passive Isolation Systems
FIGURE 2.2. Design of a passiveFIGURE 2.2. Design of a passive hydromounthydromount..
FLUID
FLUID
ORIFICE ORIFICE
MOUNTING
LOCATION
MOUNTING
LOCATION
ELASTOMERSURROUNDING
FLUID
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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
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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
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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
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22--9. Passive Isolation Systems9. Passive Isolation Systems
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
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22--10. Passive Isolation Systems10. Passive Isolation Systems
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
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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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--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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--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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--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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--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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--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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--3. ER/MR Fluid Isolator Systems3. ER/MR Fluid Isolator Systems
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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--4. ER/MR Fluid Isolator Systems4. ER/MR Fluid Isolator Systems
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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33--7. Bingham Plastic Model Of MR Fluids7. Bingham Plastic Model Of MR Fluids
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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33--8. Bingham Plastic Model Of MR Fluids8. Bingham Plastic Model Of MR Fluids
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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33--9. Bingham Plastic Model Of MR Fluids9. Bingham Plastic Model Of MR Fluids
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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33--11. MR Fluid Working Modes11. MR Fluid Working Modes
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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33--12. MR Fluid Working Modes12. MR Fluid Working Modes
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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33--13. MR Fluid Working Modes13. MR Fluid Working Modes
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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33--14. MR Fluid Working Modes14. MR Fluid Working Modes
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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44--4. Simulation Of The Passive Isolator4. Simulation Of The Passive Isolator
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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44--5. Simulation Of The Passive Isolator5. Simulation Of The Passive Isolator
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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44--6. Simulation Of The Passive Isolator6. Simulation Of The Passive Isolator
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
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44--7. Simulation Of The Passive Isolator7. Simulation Of The Passive Isolator
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.
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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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44--9. Simulation Of The Semi9. Simulation Of The Semi--Active IsolatorActive Isolator
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
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44--10. Simulation Of The Semi10. Simulation Of The Semi--Active IsolatorActive Isolator
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
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44--11. Simulation Of The Semi11. Simulation Of The Semi--Active IsolatorActive Isolator
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
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44--12. Simulation Of The Semi12. Simulation Of The Semi--Active IsolatorActive Isolator
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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44--13. Simulation Of The Semi13. Simulation Of The Semi--Active IsolatorActive Isolator
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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44--14. Simulation Of The Semi14. Simulation Of The Semi--Active IsolatorActive Isolator
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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44--15. Simulation Of The Semi15. Simulation Of The Semi--Active IsolatorActive Isolator
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
==
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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 +++=
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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.
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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.
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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
)
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44
--21. Filter Design21. Filter Design
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
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44
--22. Filter Design22. Filter Design
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..
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44--23. Filter Design23. Filter Design
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
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44
--24. Filter Design24. Filter Design
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.
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44--25. Filter Design25. Filter Design
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
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44
--26. Filter Design26. Filter Design
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.
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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
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44--28. Control Law Design28. Control Law Design
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
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44--29. Control Law Design29. Control Law Design
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
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44--30. Control Law Design30. Control Law Design
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
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44--31. Control Law Design31. Control Law Design
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.
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44--32. Control Law Design32. Control Law Design
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.
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44--33. Control Law Design33. Control Law Design
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.
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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.
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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)
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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.
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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.
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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.
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44--39. Detailed Design Of The MR Isolator39. Detailed Design Of The MR Isolator
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)
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44--40. Detailed Design Of The MR Isolator40. Detailed Design Of The MR Isolator
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.
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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.
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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
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55--3. Results For The Passive Isolator Design3. Results For The Passive 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 5.2. 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
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55--4. Results For The Passive Isolator Design4. Results For The Passive Isolator Design
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.
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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
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55--7. Results For The Semi7. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--8. Results For The Semi8. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--9. Results For The Semi9. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--10. Results For The Semi10. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--11. Results For The Semi11. Results For The Semi--Active Isolator DesignActive Isolator Design
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
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 2.1 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
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 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
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 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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55--12. Results For The Semi12. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--13. Results For The Semi13. Results For The Semi--Active Isolator DesignActive Isolator Design
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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55--14. Results For The Semi14. Results For The Semi--Active Isolator DesignActive Isolator Design
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