Design, Analysis, and Experimental Evaluation of a Double Coil Magnetorheological Fluid Damper

13 Pages·2016·3.61 MB·English

Hindawi Publishing Corporation
Shock and Vibration
Volume 2016, Article ID 4184726, 12 pages
http://dx.doi.org/10.1155/2016/4184726
Research Article
Design, Analysis, and Experimental Evaluation of a Double Coil
Magnetorheological Fluid Damper
GuoliangHu,FengshuoLiu,ZhengXie,andMingXu
SchoolofMechatronicEngineering,EastChinaJiaotongUniversity,Nanchang,Jiangxi330013,China
CorrespondenceshouldbeaddressedtoGuoliangHu;[email protected]
Received25May2015;Revised2September2015;Accepted2September2015
AcademicEditor:RafałBurdzik
Copyright©2016GuoliangHuetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Amagnetorheological(MR)damperisoneofthemostadvanceddevicesusedinasemiactivecontrolsystemtomitigateunwanted
vibrationbecausethedampingforcecanbecontrolledbychangingtheviscosityoftheinternalmagnetorheological(MR)fluids.
ThisstudyproposesatypicaldoublecoilMRdamperwherethedampingforceanddynamicrangewerederivedfromaquasistatic
modelbasedontheBinghammodelofMRfluid.Afiniteelementmodelwasbuilttostudytheperformanceofthisdoublecoil
MRdamperbyinvestigatingsevendifferentpistonconfigurations,includingthenumbersandshapesoftheirchamferedends.
Theobjectivefunctionofanoptimizationproblemwasproposedandthenanoptimizationprocedurewasconstructedusingthe
ANSYSparametricdesignlanguage(APDL)toobtaintheoptimaldampingperformanceofadoublecoilMRdamper.Furthermore,
experimentaltestswerealsocarriedout,andtheeffectsofthesamedirectionandreversedirectionofthecurrentsonthedamping
forceswerealsoanalyzed.TherelevantresultsofthisanalysiscaneasilybeextendedtothedesignofothertypesofMRdampers.
1.Introduction these studies showed that damping performance of MR
damperscanbesignificantlyimprovedviaoptimaldesignof
The rheological properties of a magnetorheological fluid themagneticcircuitofthesystems.
(MRF) can be continuously changed within several mil- Yangetal.[21]presentedanoptimaldesignofaparallel
lisecondsbyapplyingorremovingexternalmagneticfields. diskvalvemodeMRdamperwithFEMmethodconsidering
Theseuniquefeatureshaveledtothedevelopmentofmany differentstructuralparametersanddifferentmaterialsforthe
MRF-baseddevicessuchastheMRdamper,MRvalve,MR cylinderandcoveroftheMRdamper,andtheresultsshow
brake,andMRclutch.Amongthem,themostpopularMRF- that both the material and the fluid gap are key factors for
based devices are MR dampers due to their long range MR circuit. Zheng et al. [22] designed a novel MR damper
controllable damping force, fast adjustable response, and with a multistage piston and independent input currents;
low energy consumption [1–4]. Till now, the MR dampers the multiphysics of the novel MR damper was theoretically
have a huge applications in automotive industry including analysedandcarriedout,includingelectromagnetic,thermal
off-road vehicles [5–7], and they are also widely used in dynamic, and flow mechanism. Zhang et al. [23] proposed
naval gun controlling [8, 9], field of landing gear [10, 11], theuseoffiniteelementstoimprovethemagneticdesignof
prostheticknees[12,13],washingmachines[14],highspeed anMRdamper.Khanetal.[24]usedfiniteelementsoftware
trainsuspension[15–17],seismicvibrationcontrolofdifferent to simulate nine different configurations of the pistons for
civilstructures[18–20],andsoon. an MR damper and investigate how these configurations
As well known that the performance of MR dampers would affect and influence the maximum pressure drop.
significantly depended on the activating magnetic circuit, Ferdausetal.[25]established2Dand3DmodelsofanMR
thereforetheperformanceofMRdamperscanbeoptimized damperthatconsideredtheshapeofthepiston,theMRfluid
by the optimal design of the activating magnetic circuit. gap,theairgap,andthethicknessofthedamper’shousing.
Recently,somestudiesintheliteraturehavefocusedonthe The analytical results show that the single coil MR damper
geometric optimization of MR dampers. The results from withlinearplasticairgap,topandbottomchamferedpiston
2 ShockandVibration
end, and medium MR fluid gap has better performance.
Parlak et al. [26] presented a method for optimizing the
design of the target damper force and maximum magnetic
Upper pin
flux density of an MR damper; this new approach used an
electromagnetic analysis of the magnetic field and a CFD
analysis of MR flow together to obtain the optimal value Upper end cover
of the design parameters. Nguyen and Choi [27] presented
an optimal design of a passenger vehicle MR damper that I Damper cylinder
was constrained in a specific cylindrical volume and an
Damper rod
advanced objective function that collectively included the
damping force, the dynamic range, and an inductive time I
1
constant. Parlak et al. [28] investigated the geometrical Coil1
H
optimization of an MR shock damper using the Taguchi
experimentaldesignapproachbyspecifyingfourparameters
Piston head
(gap, flange thickness, radius of piston core, and current
excitation) and by selecting the maximum dynamic range I2 Coil2
requiredasthetargetvalue.Parlaketal.[29]alsoevaluated
II Floating piston
the optimal solutions of the MR damper for the maximum
dynamic range and the maximum damper force separately
III Lower end cover
usingtheTaguchiexperimentaldesignmethod.Goldaszand
Sapinski [30] presented and verified a mathematical model
Lower pin
of a monotube MR shock absorber with an emphasis on
leakage flow mechanisms and their impact on the damping
output. In the study, the authors considered the impact of
highspeedlosses,fluidchambercompressibility,cavitations,
Figure1:SchematicconfigurationofthedoublecoilMRdamper
elastic deformation of cylinder, fluid inertia, floating piston
withannulargap.
inertia,gaschamberpressure,andCoulombfrictionbetween
damper components and the cylinder to make the model
double coil MR damper. There are three chambers in the
moreaccurate.
damper cylinder; chamber I and chamber II are filled with
Asmentionedabove,thoughthemagneticoptimaldesign
MR fluid, and chamber III compensates for the changes
methodscandecreasethecostandthemanufacturingperiod
in volume induced as the piston rod moves is filled with
and improve the performance of the MR dampers, many
pressurized nitrogen gas. As the damper piston rod moves,
factors are needed to consider in developing MR dampers
theMRfluidflowsthroughtheannulargapbetweenchamber
to obtain optimal designs, that is, how to find significant
I and chamber II. Moreover, there is a double coil of wire
geometricaldimensionsandconfigurationsofMRdampers
insidethepistonheadusedforwindingthatisheatresistant
to obtain maximum output mechanical performance, such
and electrically insulated. When a direct current is applied
asdampingforceordynamicrange,whichmakestheprob-
tothedoublecoil,amagneticfieldoccursaroundthepiston
lemverychallengingwhenusingconventionaloptimization
head.Itisnotedthatthedirectionofthecurrentappliedonto
methods.
the double coil can be the same or the reverse, which can
In this study, a double coil MR damper with annular
enlarge the maximumdampingforceorthedynamic range
gap was developed and prototyped; the damping force and
tosomeextent.
dynamic range were also derived. A finite element model
was built to investigate the performance of the double coil
MR damper by considering seven damper pistons with 2.2. Magnetic Circuit and Control Model of the Double Coil
differentconfigurations.Anoptimizationprocedurewasthen MRDamper. Figure2showsthesimplifiedmagneticcircuit
constructed with the ANSYS parametric design language of the double coil MR damper with an annular gap at both
(APDL) to obtain the optimal parameters of the double ends of the flanges and in the middle of the flange, where
coil MR damper. Finally, a series of dynamic experimental the flux lines are perpendicular to the flow direction and
tests,especiallytheeffectsofthesamedirectionandreverse generate a field-dependent resistance to the fluid flow. The
direction of the currents on the damping forces, were also doublecoilMRdamperisshapedtoguidethemagneticflux
carriedout. axially through the damper cylinder, across the length of
the flange of piston head and the gap at one end and then
throughthefluxreturnandacrossthegapandtheflangeof
2.DesignConsiderationsfor theDoubleCoil pistonheadattheoppositeend.Thevolumeoffluidthrough
MRDamperwithAnnularGap whichthemagneticfieldpassesisdefinedasanactivevolume,
and the MR effects only occur within the active volume.
2.1. Principle of the Proposed Double Coil MR Damper. The most effective MR dampers have a high magnetic flux
Figure 1 shows schematic configuration of the proposed density passing through a large active volume, but a lot of
ShockandVibration 3
L V𝑝 (𝑞 = 𝐴𝑝V𝑝).𝜏𝑦1 and𝜏𝑦2 aretheyieldstressesoftheMR
fluidintheendflangeandmiddleflange,respectively.𝑐1and
Rh 𝑐2arecoefficientswhichdependedontheflowvelocityprofile
andhaveavaluerangingfromaminimumvalueof2.07to
h I1 I2 a maximum value of 3.07. The coefficients 𝑐1 and 𝑐2 can be
R1 approximatelyestimatedasfollows:
Rc 12𝑞𝜂
𝑐 =2.07+ ,
1 12𝑞𝜂+0.8𝜋(𝑅 +0.5ℎ)ℎ2𝜏
1 𝑦1
(4)
12𝑞𝜂
Wc 𝑐 =2.07+ .
R 2 12𝑞𝜂+0.8𝜋(𝑅 +0.5ℎ)ℎ2𝜏
1 𝑦2
Asshownin(1),thefirsttermiscalledthecontrollableforce
because it varies with the applied field, whereas the sum
L L L L L
1 c 2 c 1 of the latter two terms is referred to as the uncontrollable
forcebecausetheygenerateaconstantforceaccordingtothe
Figure2:SimplifiedmagneticcircuitofthedoublecoilMRdamper. velocityofthedamperpiston.
Thedynamicrange𝐷isdefinedastheratioofthetotal
dampingforcetotheuncontrollableforce,anditisgivenby
magnetic coils are needed to produce large magnetic fields. 𝐹 +𝐹 +𝐹 𝐹
Anoptimizedcircuitwouldmaintainabalancebetweenthe 𝐷= 𝜏 𝜂 𝑓 =1+ 𝜏 . (5)
𝐹 +𝐹 𝐹 +𝐹
fieldproducedandthepowerrequiredbythemagneticcoils. 𝜂 𝑓 𝜂 𝑓
Whencurrents𝐼1and𝐼2wereappliedoncoil1andcoil2,
respectively,themagneticfluxdensitywillbeproducedinthe Here, the dynamic range 𝐷 was introduced to evaluate the
resistance gaps between the inner damper cylinder and the performance of the double coil MR damper. Normally, it
outerpistonheadaccordingtotheelectromagneticinduction is better to keep the dynamic range as large as possible to
principle.TheviscosityoftheMRfluidintheresistancegaps maximisetheeffectivenessoftheMRdamper.Thedynamic
willincreasewiththeincreaseofthemagneticfluxdensity.So, rangeisproportionaltotheshearforceandisafunctionof
thedampingforcewillbegeneratedtoo.Duetothedouble thesizeofthegap.Thewidthoftheannulargapℎisinversely
coil design of the MR damper, the damping force can be proportional to the controllable force, so a small gap width
controlledwithinawiderangethroughregulatingthevalues willincreasetherangeofthecontrollableforce,butwhenthe
anddirectionsofthecurrentsthatappliedonthedoublecoil. gapℎislessthan0.5mm,theviscousforce𝐹𝜂ismuchfaster
Some of the important dimensions of the double coil thanthecontrollableforce𝐹𝜏;thisreducesthedynamicrange.
MRdamperarealsolistedinFigure2.Dampergeometryis Again when the gap becomes wider, both 𝐹𝜏 and 𝐹𝜂 fall, so
characterizedbythelengthofthepistonhead𝐿,thelength finding an optimal width gap that maximises the dynamic
oftheendflange𝐿1,thelengthofthemiddleflange𝐿2,the range is very important. Moreover, parameters such as the
length of the coil winding 𝐿𝑐, the thickness of the damper lengthoftheflange𝐿1 and𝐿2,theradiusofthepistonhead
cylinder𝑅ℎ,thewidthoftheresistancegapℎ,theouterradius 𝑅, the yield stress 𝜏𝑦1 and 𝜏𝑦2, the thickness of the damper
of the damper cylinder 𝑅, the internal radius of the piston cylinder 𝑅ℎ, and the internal radius of the piston core 𝑅𝑐
core𝑅𝑐,andthewidthofthecoilwinding𝑊𝑐. willalsoplayanimportantroleinsearchingfortheoptimal
The total damping force 𝐹 generated by the double design.
coil MR damper consists of three components: the field-
dependentforce𝐹𝜏duetothemagneticfield,theviscousforce 3.ModelingandOptimalDesignof
𝐹𝜂duetotheviscouseffects,andthefrictionalforce𝐹𝑓: DoubleCoilMRDamperUsingFinite
𝐹=𝐹 +𝐹 +𝐹 , ElementMethod
𝜏 𝜂 𝑓 (1)
The magnetic field in an MR damper is produced by an
where
electromagnet. Here in the ANSYS simulation model the
6𝜂𝐿𝑞𝐴
𝑝 excitationcoilisconsideredtobetheelectromagnet,andthe
𝐹𝜂 = 𝜋(𝑅 +0.5ℎ)ℎ3, (2) magnetic field provided by this excitation coil is needed to
1
energize the MR fluid. By varying the current through the
𝐿 𝐿
𝐹𝜏 =2𝑐1 ℎ1𝐴𝑝𝜏𝑦1sgn(V𝑝)+𝑐2 ℎ2𝐴𝑝𝜏𝑦2sgn(V𝑝), (3) excitation coil, the magnetic flux density can be varied and
theMRfluidisenergizedaccordingly.
where𝐴𝑝isthecross-sectionalareaofthepistonheadand𝜂is
theplasticviscosity.𝑞istheflowratethroughthedoublecoil 3.1.MagneticPropertiesofMRFluidandSteelUsedintheDou-
MRdamper,anditcanbecalculatedfromthepistonvelocity bleCoilMRDamper. TheMRfluidwithtypeofMRF-J01T
4 ShockandVibration
Table1:PerformanceindexofMRfluidwithMRF-J01T. 3.0
Project Parameters
2.5
3
Massdensity 2.65g/cm T)
SOVhipseecarorassttiitroyenswsail(t5the0om0u0pteGmrsaa)tgunreetricanfigeeld(𝛾=10/s,20∘C) −>4005.8∼0P1K3aP0⋅sa∘C Bdensity ( 21..05
x
u
fl
c
80 eti 1.0
n
g
a
M
0.5
60
a) 0.0
kP 0 100 200 300 400
(
𝜏ess 40 Magnetic field intensity H (kA/m)
d str Figure4:𝐵-𝐻curveofsteelmaterial(number10).
el
Yi
20
stressdataasafunctionofmagneticfluxdensity;here𝛼0 =
0.0182kPa,𝛼1 =−48.4644kPa/T,𝛼2 =865.3901kPa/T2,and
00.0 0.1 0.2 0.3 0.4 0.5 0.6 𝛼3 =−984.2742kPa/T3.
Figure4showstherelationshipbetweenthemagneticflux
Magnetic flux density B (T)
densityandthemagneticfieldintensityofthesteelmaterial
(a) Relationshipof𝜏and𝐵 (number 10) used in the damper cylinder and piston head,
1.4 respectively.
1.2
3.2. Modeling of Double Coil MR Damper Considering Dif-
T)
B ( 1.0 ferent Piston Configurations. To investigate how the shape
y ofthedamperpistonaffectstheperformanceofdoublecoil
nsit 0.8 MRdamper,sevenmodelswithdifferentshapedpistonswere
e
x d designed,asshowninFigure5.Model1pistonwasdefinedas
flu 0.6 havingaplainend,Model2pistonwasdefinedashavingeach
c
eti endofthepistonchamfered,Model3pistonwasdefinedas
n 0.4
g havingaradiusoneachend,Model4pistonwasdefinedas
a
M
havingchamfersonthetop,atthebottom,andinthemiddle,
0.2
Model5pistonwasdefinedashavingaradiusonthetop,at
thebottom,andinthemiddle,Model6pistonwasdefinedas
0.0
0 200 400 600 800 havingbothendschamfered,andModel7pistonwasdefined
Magnetic field intensity H (kA/m) ashavingaradiusoneveryedge.
Table 2 and Figure 6 show the results of the magnetic
(b) Relationshipof𝐵and𝐻
flux densities between the seven different models when the
Figure3:SpecificationoftheMRfluidtypeMRF-J01T. appliedcurrentvariesfrom0.1Ato1.0A.Herethemagnetic
flux densities decreased with the number of chamfers on
the damper piston, the maximum density of magnetic flux
provided by the Chongqing Instrument Material Research appeared in Model 1, which means that this piston had
InstituteinChinawasusedinthefollowingsimulationsand theoptimalgeometricalshape.Moreover,themagneticflux
experiments. Table 1 summarizes the performance index of density in the model with a radius was greater than the
theMRfluid,anditsfield-dependentpropertiesareshownin chamferedmodel;thereasoncanbefoundinFigure7which
shows that the distribution of magnetic flux lines along
Figure3.
the resistance gap in Model 1 was more even than that in
ByobservingFigure3(a),thedynamicyieldstressofthe
Models6and7.Thedamperpistonwithchamfershadlarger
MRfluidintheannularresistancegapcanbeapproximated
reluctances at its core because the core was larger and the
by
cross-sectionalareathroughwhichthemagneticfluxpassed
𝜏𝑦 =𝛼3×𝐵3+𝛼2×𝐵2+𝛼1×𝐵+𝛼0, (6) decreased,whichinturncausedthemagneticfluxdensities
inthefluidresistancegaptodecreaseaswell.
where𝛼0,𝛼1,𝛼2,and𝛼3 arepolynomialcoefficientsthatare Figure 8 shows the dynamic range of the proposed
determinedbytheleast-squaresfittingofthedynamicyield MR damper under different piston configurations when
ShockandVibration 5
Table2:Magneticfluxdensitycomparisonamongdifferentmodels.
Current(𝐼) 𝐵forModel1 𝐵forModel2 𝐵forModel3 𝐵forModel4 𝐵forModel5 𝐵forModel6 𝐵forModel7
0.1 0.072 0.070 0.071 0.066 0.069 0.063 0.066
0.2 0.145 0.140 0.142 0.132 0.137 0.124 0.132
0.3 0.212 0.204 0.208 0.193 0.200 0.182 0.193
0.4 0.273 0.264 0.268 0.250 0.259 0.234 0.249
0.5 0.331 0.319 0.325 0.302 0.313 0.284 0.302
0.6 0.382 0.370 0.375 0.350 0.363 0.330 0.351
0.7 0.428 0.414 0.421 0.394 0.408 0.373 0.395
0.8 0.471 0.456 0.464 0.434 0.450 0.412 0.436
0.9 0.510 0.495 0.502 0.473 0.489 0.448 0.475
1.0 0.543 0.529 0.536 0.508 0.524 0.483 0.511
(a) Model1 (b) Model2 (c) Model3 (d) Model4 (e) Model5 (f) Model6 (g) Model7
Figure5:Simulationmodelswithdifferentpistonshapes.
0.6 the pistons increased, and so too did the damping perfor-
mance. Moreover, the dynamic range in the model with
a radius on the edges was greater than the model with
chamfered edges. When the current varied from 0.1A to
0.4 1.0A,thedampingforcesteadilyincreasedandthenstabilised
when the current was close to 1.0A due to the magnetic
T) saturation of MRF in the resistance gap. From Figure 6
B ( to Figure 8, Model 1 with square ends had the maximum
𝐵 value under different currents, while the damping force
0.2
and dynamic range was also better in Model 1 than in the
othermodels.So,Model1withthepistonwithsquareends
was selected as the optimal geometry for the proposed MR
damper.
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
I (A) 3.3.OptimalDesignofDoubleCoilMRDamper. Afterdeter-
miningtheoptimalconfigurationofthedamperpiston,the
Model 1 Model 5
FEMusingtheANSYSparametricdesignlanguage(APDL)
Model 2 Model 6
tool is used to obtain the optimal geometric dimensions
Model 3 Model 7
Model 4 of the MR damper. For vehicle suspension design, the ride
comfort and the suspension travel are the two conflicting
Figure6:Magneticfluxdensityofdifferentmodels.
performanceindices.Inordertoreducethesuspensiontravel,
ahighdampingforceisrequired,whileconsideringtheride
the applied current varied from 0.1A to 1.0A. Here the comfort, a low damping force is expected, and thus a large
dynamic range decreased as the number of chamfers on dynamic range is required. Considering these effects, the
6 ShockandVibration
(a) Model1 (b) Model6 (c) Model7
Figure7:Distributionsofmagneticfluxlinesofdifferentmodels.
12 chosen depending on each specific suspension system. For
unevenorunpavedroad,alargedampingforceisrequired.
Thus,largevaluesof𝛼𝐹and𝛼𝐵arechosen.Ontheotherhand,
9 alargevalueof𝛼𝐷isusedinthedesignofsuspensionsystems
forflatroads.
InordertofindtheoptimalsolutionofthedoublecoilMR
D 6 damper,ananalysislogfileforsolvingthemagneticcircuitof
thedamperandcalculatingtheobjectivefunctionisbuilt.In
the analysis log file, the resistance length of the end flange
3 𝐿1 andtheinternalradiusofdampercore𝑅𝑐 areselectedas
thedesignvariables(DVs),andinitialvalueswereassigned
tothem,respectively.Theprocedurestoachievetheoptimal
0
0.0 0.2 0.4 0.6 0.8 1.0 designparametersusingthefirst-ordermethodareshownin
I (A) Figure9.StartingwithinitialvaluesoftheDVs,themagnetic
fluxdensity,dampingforce,anddynamicrangearecalculated
Model 1 Model 5 byexecutingthelogfile.TheANSYSoptimizationtoolthen
Model 2 Model 6 transformstheoptimizationproblemwithconstrainedDVs
Model 3 Model 7
to an unconstrained one via penalty functions. The dimen-
Model 4 sionless,unconstrainedobjectivefunction𝑓isdenotedas
Figure8:DynamicrangeofMRdamperunderdifferentcurrents.
𝑛
OBJ
𝑓(𝑥)= +∑𝑃 (𝑥),
𝑥 𝑖 (8)
OBJ0 𝑖=1 𝑖
objective function used in the optimization can be defined where OBJ0 is the reference objective function value that is
as selectedfromthecurrentgroupofdesignsets.𝑃𝑥𝑖istheexte-
riorpenaltyfunctionforthedesignvariable𝑥𝑖.Fortheinitial
𝐹 𝐷 𝐵 iteration(𝑗 = 0),thesearchdirectionofDVsisassumedto
OBJ=𝛼𝐹 𝐹𝜏𝑟 +𝛼𝐷 𝐷𝑟 +𝛼𝐵 𝐵𝑟, (7) bethenegativeofthegradientoftheunconstrainedobjective
𝜏 function, and a combination of a golden-section algorithm
and local quadratic fitting techniques are used to calculate
where 𝐹𝜏𝑟, 𝐷𝑟, and 𝐵𝑟 are the referenced field-dependent newvaluesofDVs.Ifconvergenceoccurs,thevaluesofthe
damping force, dynamic range, and magnetic flux density, DVs at this iteration are the optimum. If not, subsequent
respectively; 𝛼𝐹, 𝛼𝐷, and 𝛼𝐵 are the weighting factors for iterations will be performed. In the subsequent iterations,
the field-dependent damping force, dynamic range, and the procedures are similar to those of the initial iteration
magnetic flux density, respectively; and the sum of 𝛼𝐹, 𝛼𝐷, exceptthatthedirectionvectorsarecalculatedaccordingto
and𝛼𝐵is1.However,thevaluesoftheseweightingfactorsare thePolak-Ribiererecursionformula[27].Thus,eachiteration
ShockandVibration 7
Initial values of design
parameters (DV)
Magnetic field density
Run log file Damping force
Calculate equivalent unconstrained Dynamic range
Initial
objective function f(x)
iteration
Find DV direction vector
(negative of the gradient of f(x))
Calcuate new values of DV
(golden-section algorithm)
Run log file
Yes
Convergence Stop
No
Calcuate new values Calcuate equivalent unconstrained
of DV (golden-section objective function f(x) Optimal solution
algorithm)
Find DV direction vector
(Polak-Ribiere recursion formula)
Figure9:FlowchartforoptimaldesignofthedoublecoilMRdamper.
iscomposedofanumberofsubiterationsthatincludesearch Table 3: Physical dimensions of the proposed double coil MR
directionandgradientcomputations. damper.
Figures 10 and 11 show the results of magnetic flux
Initial
density and damping force between the initial design and Optimal
Parameters Symbol value
optimal design, respectively. It is obviously seen that the value(mm)
(mm)
magneticfluxdensityandthedampingforcewithanoptimal
Totallengthofdampercylinder 𝐻 235 235
design were greater than the initial design, although the
differencebetweenbothofthemimprovedsignificantlywhen Maximumstrokeofthedamper 𝑆 40 40
theappliedcurrentexceeded0.5A. Resistancegap ℎ 1 1
Outerradiusofdampercylinder 𝑅 30 31
4.ExperimentalEvaluationof Internalradiusofthepistoncore 𝑅𝑐 13 14
DoubleCoilMRDamper Lengthofthepistonhead𝐿 𝐿 80 80
Thicknessofthedampercylinder 𝑅ℎ 8 8
4.1.PrototypingoftheDoubleCoilMRDamperandtheTest
RigSetup. Figure12istheprototypeoftheproposeddouble Lengthoftheendflange 𝐿1 10 11
coilMRdamper.Here,thedamperpistonwithsquareends Lengthofthemiddleflange 𝐿2 20 22
wasmanufacturedforthepistonhead.AndTable3listssome Lengthofthecoilwinding 𝐿𝑐 20 18
parametersofthedamper. Widthofthecoilwinding 𝑊𝑐 9 8
Figure13showsthetestrigforthedampingperformance
of the proposed double coil MR damper. The INSTRON
8801testmachinewasusedtosupplytheexternalfrequency
and displacement amplitude; and two power supplies were 4.2.DampingForceundertheSameDirectionCurrentsApplied
adoptedtosupplycurrentsoncoil1andcoil2,respectively; on the Double Coil. Figure 14 shows the damping force of
thecontrolmonitorwasusedtodisplayandsavethedataof thedoublecoilMRdamperunderthedifferentdisplacement
thedampingforces. amplitudes and different currents with the same direction.
8 ShockandVibration
0.6
0.5
0.4
T)
B ( 0.3
0.2
0.1
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 (a) Parts (b) Assembly
I (A)
Figure12:PrototypeoftheproposeddoublecoilMRdamper.
Optimal
Initial
Double coil
Figure 10: Comparison of magnetic flux density between initial
MR damper
designandoptimaldesign.
5
INSTRON machine
4
3 Power supply
N)
K
F (
2 Controller monitor
Figure13:ExperimentaltestrigforthedoublecoilMRdamper.
1
0.3
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
I (A) 0.2
Optimal
Initial 0.1
Figure11:Comparisonofdampingforcebetweeninitialdesignand N)
K 0.0
optimaldesign. F (
−0.1
Here,thetestmachinewassetatasinusoidalloadingwitha
−0.2
frequency of 0.5Hz and displacement amplitude of 2.5mm
and 5.0mm, respectively. It can be seen that the viscous
dampingforceequalsabout100Nwhentheappliedcurrents −0.3
−6 −4 −2 0 2 4 6
𝐼1 and 𝐼2 are zero, and the maximum damping force can S(mm)
reach220Nwhentheappliedcurrents𝐼1and𝐼2are0.25A.In
addition,thedampingforcewithdisplacementamplitudeof S=2.5mm,I1=I2=0A
5.0mmisgreaterthanthatof2.5mm,andthedampingforce S=2.5mm,I1=I2=0.25A
increases to 50N, which denotes that the viscous damping S=5.0mm,I1=I2=0A
forceisaffectedbythedisplacementamplitude. S=5.0mm,I1=I2=0.25A
Figure 15 shows the damping force of the double coil Figure 14: Damping force under different currents and different
MR damper under the different loading frequencies and displacements.
ShockandVibration 9
0.4 0.8
0.2 0.4
N) N)
K 0.0 K 0.0
F ( F (
−0.2 −0.4
−0.4 −0.8
−10 −8 −6 −4 −2 0 2 4 6 8 10 −10 −8 −6 −4 −2 0 2 4 6 8 10
S(mm) S(mm)
S=2.5mm,f=0.5Hz S=2.5mm,f=1.0Hz S=2.5mm S=7.5mm
S=5.0mm,f=0.5Hz S=5.0mm,f=1.0Hz S=5.0mm
S=7.5mm,f=0.5Hz S=7.5mm,f=1.0Hz
Figure16:Dampingforceunderdifferentdisplacements.
Figure15:Dampingforceunderdifferentfrequenciesanddifferent
displacements.
1.5
1.0
different displacement amplitudes. Here, the test machine
wassetatasinusoidalloadingwithafrequencyof0.5Hzand
0.5
1.0Hz,respectively;anddisplacementamplitudesof2.5mm,
5.0mm,and7.5mmwerealsoloadedseparately.Meanwhile, N)
tinhethapepslaiemdecudrirreecnttiso𝐼n1,aanndd𝐼t2hienvthaeludeoiusb0le.5cAoi.lAwsersehaopwpnlieind F (K 0.0
the figure, the greater the loading frequency is, the bigger −0.5
thedampingforceisunderthesamedisplacementamplitude.
Furthermore, the greater the displacement amplitude is, −1.0
the bigger the damping force is under the same loading
frequency. −1.5
−15 −10 −5 0 5 10 15
4.3. Damping Force under the Reverse Direction Currents S(mm)
Applied on the Double Coil. Figure 16 shows the damping 0.00A 0.75A
forceunderdifferentamplitudedisplacementsfrom2.5mm 0.25A 1.00A
to 7.5mm. Here, the test machine was set at a sinusoidal 0.50A
loadingwithafrequencyof1.0Hz,andtheappliedcurrents
Figure17:Dampingforceunderdifferentappliedcurrents.
𝐼1and𝐼2inthedoublecoilswereappliedthereversedirection
withavalueof0.7A.ObservingFigure16,thedampingforce
increasedwiththeincreasingofthedisplacementamplitude,
and the maximum damping force reaches 0.7KN at the big though the trend is the same. The reason may be the
displacementamplitudeof7.5mm. thickening effect of the used MR fluid, while the Bingham
Figure 17 shows the damping force under the applied fluid model used in the simulations did not consider this
current changed from 0A to 1.0A. Here, the test machine effect. Another possible reason may be the enhanced yield
wassetatasinusoidalloadingwithdisplacementamplitude stressphenomenonprocesswhichoccurswhenseveralsingle
of10mmandafrequencyof1.0Hz,whiletheappliedcurrents chainstructuresofmagneticparticlesjointogetherandform
𝐼1 and 𝐼2 in the double coils were applied in the reverse athickcolumn,whichmakethesaturatedyieldstressvalue
direction. As expected, the damping force increased from in the simulation bigger than the experimental conditions
0.33KN at 0A to 1.21KN at 1.0A, and the dynamic range [31,32].
nearlyequals4. Figure19showsthechangeinthedampingforceunder
Figure 18 shows the comparison of simulation results differentdisplacementamplitudesandappliedcurrentdirec-
andexperimentalresultsofthedampingforceattheapplied tions. Here, the test machine was set at sinusoidal loading
currentof1.0A.Itcanbeseenthatthemaximumsimulated with a frequency of 0.5Hz and displacement amplitude of
dampingforceisabout4.0KN,whilethemaximumexperi- 5.0mmand7.5mm,respectively.Theappliedcurrents𝐼1and
mentaldampingforceisonly1.21KN.Thedeviationisalittle 𝐼2inthedoublecoilsweresetto0.5Awiththesamedirection
10 ShockandVibration
5.0 1.0
2.5 0.5
N) N)
K 0.0 K 0.0
F ( F (
−2.5 −0.5
−5.0 −1.0
−15 −10 −5 0 5 10 15 −15 −10 −5 0 5 10 15
S(mm) S(mm)
Simulation I2=0.5A I2=0.8A
Experiment I2=0.6A I2=1.0A
Figure18:Comparisonofsimulateddampingforceandexperimen- Figure20:Dampingforceunderdifferentcurrentsinthedouble
taldampingforceattheappliedcurrentof1.0A. coil(𝐼1=0.5A).
0.6 1.0
0.4
0.5
0.2
N) N)
K 0.0 K 0.0
F ( F (
−0.2
−0.5
−0.4
−0.6−8 −6 −4 −2 0 2 4 6 8 −1.0−15 −10 −5 0 5 10 15
S(mm) S(mm)
S=5.0mm,I1=I2=0.5A I1=0.5A I1=0.8A
S=7.5mm,I1=I2=0.5A I1=0.6A I1=1.0A
S=5.0mm,I1=−I2=0.5A
S=7.5mm,I1=−I2=0.5A Figure21:Dampingforceunderdifferentcurrentsinthedoublecoil
(𝐼2 =0.5A).
Figure 19: Damping forces under different displacements and
differentcurrentdirections.
varied applied current 𝐼1 and the fixed applied current 𝐼2.
Here, the test machine was set at a sinusoidal loading with
and reverse direction, respectively. The figure shows that amplitudedisplacementof10mmandafrequencyof1.0Hz.
the damping forces with the currents in a reverse direction Asshowninbothfigures,thedampingforceincreasedwith
weremuchgreaterthanthosecurrentsinthesamedirection. the increase of the applied currents 𝐼1 and 𝐼2, respectively,
Moreover,thedampingforceincreasedasthedisplacement though the other exciting coil’s applied current was fixed.
amplitude increased because the increased velocity of the Furthermore, the damping force under the fixed current 𝐼1
damperledtoanincreaseintheviscousdampingforcein(2), equalsthatunderthefixedcurrent𝐼2whenthetotalapplied
sothedampingforcealsoincreasedtoo. currentisofthesamevalue.
4.4.DampingForceunderCurrentAppliedonOneoftheCoils. 5.Conclusions
Figure20showsthechangeofthedampingforceunderthe
variedappliedcurrent𝐼2andthefixedappliedcurrent𝐼1,and A double coil MR damper with annular gap was proposed;
Figure21showsthechangeofthedampingforceunderthe the damping force and dynamic range were also derived. A