Research Article Analysis and Testing of Chain ...downloads.hindawi.com/journals/amse/2013/290691.pdfResearch Article Analysis and Testing of Chain Characteristics and Rheological

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2013 Article ID 290691 6 pageshttpdxdoiorg1011552013290691

Research ArticleAnalysis and Testing of Chain Characteristics andRheological Properties for Magnetorheological Fluid

Song Chen12 Jin Huang2 Hongyu Shu1 Tiger Sun1 and Kailin Jian1

1 College of Resources and Environmental Chongqing University Chongqing 400044 China2 College of Mechanical Engineering Chongqing University of Technology Chongqing 400054 China

Correspondence should be addressed to Jin Huang jhuangcqsohucom

Received 16 July 2013 Accepted 9 October 2013

Academic Editor Xing Chen

Copyright copy 2013 Song Chen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Digital holographic microscopy is presented in this study which can measure the magnetorheological (MR) fluid in differentvolume fractions of particles and different magnetic field strengths Based on the chain structure of magnetic particle under appliedmagnetic field the relationships between shear yield stress magnetic field size and volume fraction of MR fluid in two paralleldiscs are established In this experiment we choose three MR fluid samples to check the rheological properties of MR fluid and toobtain the material parameters with the test equipment of MR fluid the conclusion is effective

1 Introduction

Magnetorheological (MR) fluids are suspensions of micron-sized magnetizable particles in a carrier fluid such as syn-thetic oil and silicone oil which are regarded as the intelligentmaterials that respond to an applied magnetic field with achange in their rheological properties In the absence of anapplied magnetic field MR fluids exhibit Newtonian fluid-like behavior Upon application of a magnetic field the polar-ization between two induced dipoles causes the suspendedparticles in theMR fluids to form a chain-like microstructurealigned with the direction of applied magnetic field Themagnetic chain structure changes the rheological propertiesof the suspension Altering the strength of the appliedmagnetic field precisely and proportionally controls the shearyield strength of the fluids [1 2] Based on the mechanicalcharacteristics the fluids can be used in the controllableenergy-dissipating applications such as dampers [3 4] valves[5 6] and clutches and brakes [7 8]

Experiments showed that many other factors affect themacroscopic properties of an MR fluid It mainly includesthe applied magnetic field strength the size and gradationand the property and volume fraction of the particles theproperty of the carrier fluid and the additives Noma et al[9] found that Fe nanoparticles synthesized by the arc plasma

method exhibited a high saturation magnetization and maybe useful for MR fluids Ekwebelam and See [10] exploredthe yielding behavior and enhanced stress response exhibitedby bidisperseMR fluid over monodisperse systems He foundthat the stress enhancement in bidisperse suspensions is likelyto be due to the population and orientation of interactinglarge particles in the bidisperse suspensions Jang et al [11]studied the behavioral model for magnetorheological fluidunder a magnetic field using Lekner summation methodPacull et al [12] studied the effect of polar interactions onthe magnetorheology of silica-coated magnetite suspensionsin oil media reported He suggested that the nonnegligibleinterfacial interactions are responsible for both the absenceof MR effect in hydrophobic samples and the low yield stressin hydrophilic suspensions To resolve the sedimentationof carbonyl iron (CI) based MR fluid Fang et al [13]introduced fibrous single-walled carbon nanotube (SWNT)into carbonyl iron (CI) suspension as additives

2 Chain Characteristics of MR Fluid

21 Chain Process When a magnetic field is applied themagnetic particles inMR fluid aremoving orderly that causesthe suspended particles to attract each other under the action

2 Advances in Materials Science and Engineering

(a)

H

(b)

H

(c) (d)

Figure 1 The chain process of MR fluid

Figure 2The experimental device of measurement of MR fluids bydigital microholography

of magnetic force to form a chain-like microstructure alongthe field direction meanwhile the chain process of MR fluidoccurrs as shown in Figure 1 The distribution of particles inMR fluid without the magnetic field is shown in Figure 1(a)the dynamic yield stress is zero in this case The chainstructure of particles in MR fluid under the magnetic fieldis shown in Figure 1(b) Figure 1(c) shows that the numberand diameter of chain will increase with the appliedmagneticfield and the dynamic yield stress and apparent viscosity ofMR fluid also increase Figure 1(d) shows that the MR fluidrecovers rapidly and response time is only few millisecondswhen the applied magnetic field disappeared

Figure 2 shows the experimental device for recordingholograms of MR fluid The experimental conditions are asfollows the pixel number 119873 = 1024 the pixel size of thecharge coupled device (CCD) camera Δ119909 = 52 120583m thewavelength 120582 = 6328 nm the magnification of objective119872 = 40

The hologram and reconstruction images of calibrationtarget are shown in Figure 3 From Figure 3(b) we can easilyobtain the length between two graduation lines based oncounting the pixel numbers Because the actual scale ofcalibration target is 50 120583m1198721015840 and actual 119889 can be calculated[13]

After a strong magnetic field is applied to MR fluids themicroparticles will be polarized and aligned like chains alongthe direction of magnetic field The continuous holograms ofMR fluids under an applied magnetic field were encoded byCCD and the construction images of the chain configurationare shown in Figure 4The figures also indicate the transformprocess from micro-particles to chains in a magnetic field

The chaining process along the direction of magnetic fieldthat is the responding speed of MR fluids for magnetic fieldis easily calculated

22 Shear Yield Stress In order to analyze the relationshipbetween the shear yield stress and the magnetic field thesize the volume percentage of MR fluidThe assumptions forchain model of dipole are as follows

(1) The ordered arrangement of particles after magneticpolarization and the chain structure is steady All ofthe particles occupy a fixed position in the stablechain

(2) The single chain formed by particles is along with thedirection of magnetic field The chain is parallel tomagnetic field direction and its length is equal to thedistance between two plates All of the chains are thesame in geometry so the analysis results of arbitrarychain can be representative of the others

(3) The acting force between adjacent particles in thechains is equal which presents the tensile strength ofchains

(4) The adjacent particles are magnetized and turn intodipoles The direction of the centerline of particles isparallel to the magnetic field

(5) The interaction force in particles decides the strengthof chains When applied force is greater than theinteraction force between particles the chain will bepulled off When the shear stress is perpendicularto the direction of magnetic field the chain will beelongated and snapped

(6) The particles are supposed to be spherosome anduniform

The analysis mode of shear yield stress in MR fluid isshown in Figure 5 where ℎ represents the distance betweentwo parallel plates and 119865

119886is the external force [14] The

bottom plate is fixed and external force is applied to upperplateWhen the shear stress is perpendicular tomagnetic fielddirection the chain will deform and break The 120591

119910(119867) repre-

sents the shear yield stress under unit area The relationshipbetween 120591

119910(119867) and 119865

119886is indicated by 120591

119910(119867) = 119865

119886sin 120579 where

120579 represents the angle between the centerline of chain andmagnetic field direction as shown in Figure 5

Advances in Materials Science and Engineering 3

(a) Hologram (b) Reconstruction image

Figure 3 Hologram and reconstruction images of calibration target

1st 2nd 3rd 4th 5th

Figure 4 Reconstruction images (MR fluids under a magnetic field in different times)

FH

h 120579

Fa

Figure 5 The analysis mode of shear yield stress

With the applied magnetic field the single magneticparticle is magnetized and forms dipoles in theMR fluidThe119869 represents the dipole moment which can be expressed asfollows [15]

119869 = 12058301198811119872 (1)

where 1205830is the permeability of vacuum 119881

1is the average

volume of magnetic particles 1198811

= 412058711990333 and 119872 is

magnetization intensity

119872 = 120594119867 (2)

where 120594 is the magnetic susceptibility and119867 is the magneticfield strength

Themagnetic pole strength of the dipole can be expressedas follows

119898 =119869

2119903 (3)

The distance of dipoles which is formed by any twomagnetic particles in the same chain is

119889 =119899 (2119903 + 120575)

cos 120579 (4)

where 120575 is the average value of the gap between two adjacentparticles in the chain

The average value of acting force in particles in the samechain can be expressed as follows

119865 =1

41205871205830

1198982

1198892 (5)

The shear yield stress of MR fluid under magnetic field is

120591119910(119867) =

119873119865 sin 120579119860

(6)

where 119860 represents the area of the flat plateThe number of chains in the unit area can be expressed as

follows

119873 =(120601119860ℎ119881

1)

(ℎ119877) (7)

where 120601 is the volume fraction of magnetic particles in MRfluid and 119877 = 2119903 + 120575

Combining (1) (3) (4) and (6) the shear yield stress ofMR fluid under magnetic fieldis is expressed as follows

120591119910(119867) =

119896

sum

119899=1

1205830

121198992

119903120601(120583119903minus 1)2

1198672

(2119903 + 120575)sin 120579cos2120579 (8)


0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350

Experimental valueTheoretical value

120591 y(H

)(k

Pa)

H (kAmpm)

Figure 6 The yield stress versus applied magnetic field strength

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

120583r

H (kAmpm)

Figure 7 The relative magnetic permeability versus applied mag-netic field strength

where 120583119903represents the relative magnetic permeability ofMR

fluid 120583119903= 1+120594 119896 represents the average number of particles

in each chain and 119896 = 119860ℎ1198811119873

The theoretical value and experimental value of yieldstress versus applied magnetic field strength are shown inFigure 6Themagnetic particle is uniform spherosome in theMR fluid Assume that 120579 = 30

∘ 120575 = 0 1205830= 4120587 times 10

minus7 TmAand 120601 = 37The relationship between the relative magneticpermeability and the applied magnetic field strength canbe drawn as shown in Figure 7 As shown in Figure 6 thetheoretical value is satisfied with the experimental value theyield stress ofMRfluid is increasedwith the appliedmagneticfield and its value can be controlled by appliedmagnetic field

3 Rheological Properties of MR Fluid

31 Test Equipment The performance experimental devicefor rheological properties of MR fluid between two discs isshown in Figure 8 Based on this test system the transmissiontorques of MR fluids between two discs under zero magnetic

field and different applied magnetic fields are analyzedThe shearing rate of MR fluids between two discs can beadjusted by motor in the test system The applied magneticfield strength can be controlled by electric current in coilAll parameters in system are measured in real time bygaussmeter speed and torque sensors

32 Test Principle For the properties of experimental systemofMRfluid between two parallel disks shown in Figure 8 thefollowing assumptions are given the fluid is incompressibleThere is no flow in radial direction and axial directionbut only tangential flow The flow velocity of MR fluid is afunction of radius The pressure in the thickness direction ofMR fluid is constant The strength of magnetic field in thegap of the activation region is well distributed In cylindricalcoordinates (119903 120579 119911) the distribution of the flow velocity is

119881119903= 0 119881

120579= 119903120596 (119911) 119881

119911= 0 (9)

where119881119903119881120579 and119881

119911are the flow velocity of the fluid in the 119903-

direction the 120579-direction and 119911-direction respectively 120596(119911)is the rotation angular velocity of the fluid in the 120579-directionThe angular velocity 120596(119911) is the function of 119911-coordinate

The fluid shear strain rate may be approximated asfollows

120574 = 1205960

119903

ℎ (10)

where 1205960is speed of rotating disk The torque transmitted

by the MR fluid between two parallel disks is calculated byintegrating the shear stress of the MR fluid as follows

119879 = 2120587int

1198772

1198771

1205911199032d119903 (11)

where 1198771and 119877

2are the effective inner and outer radius of

the rotor-disc in the MR fluid exposed to the magnetic fieldrespectively Based on themean value theoremof integral thetorque 119879 in (11) can be expressed as follows

119879 =2120587

3120591lowast(1198773

2minus 1198773

1) (12)

where 120591lowast is the shear stress of the sample When (1198772minus 1198771) ≪

1198770 the 120591lowast is equal to the stress located at 119877

0= (1198772minus 1198771)2

approximately Using (10) and (12) the relationship between120591 and 120574 can be obtained by themeasuring torque119879 and speed1205960

33 Test Results In this experiment we choose MR fluidsamples MRM1 MRM2 and MRM3 to check the theoryas shown in Table 1 Then we make a comparison with theresults

When the magnetic displacement is small shown inFigure 9 magnetic particle is far from reaching a magneticsaturation and the shear stress quickly increases Withthe increase of the magnetic induction intensity curvesgradually become slow This is mainly because of differentmagnetisability of the solid ferromagnetism particles We


Motor controller

Motor

Coupling

Speed reducer

Speed sensor

Coil assembly

Magnetic field control device

Magnetic field measuring device

Torque sensor

Rotating disk

Fixed disk

MRF

(a) (b)

Figure 8 The performance experimental device for MR fluid rheological properties

01020304050607080

0 1 2 3 4 5 6 7 8 9

MRM1MRM2MRM3

120591(k

Pa)

B (kGs)

Figure 9 The shear stress of the different magnetic inductionintensities

Table 1 The MR fluid samples on different particle volume frac-tions

List Particle volumefraction

Zero fieldviscosity(Pasdots)

MRM1 5 01MRM2 15 02MRM3 35 11

must increase the applied magnetic field strength in order toobtain a greater shear stress If the magnetic induction inten-sity is large enough the particles gradually reach magneticsaturation particle interaction reaches the extreme value andthe shear stress at this timewill not increasewith themagneticinduction intensity and tends to a stable value

0

10

20

30

40

50

60

70

80

15 20 25 30

Volume fraction ()2 kGs4 kGs

6 kGs8 kGs

120591(k

Pa)

Figure 10The shear stress of the different particle volume fractions

The particles volume percentage refers to the percentageof the volume occupied by the dispersed phase of solidparticles in the MR fluid As Figure 10 shows the shear stressalso increases when the particle volume fraction increasesIn the case of not very high magnetic field strength bothare rendering the approximate linear relationship This canbe explained by MR fluid microscopic mechanism The solidparticulate magnetic becomes dipole under the action of themagnetic field Dipole of interaction form magnetic chainbetween the two plates When the volume percentage is lowthe number of solid particle is limited In a magnetic fielda few of magnetic chains are formed and the shear stress issmall When the volume percentage is high the number ofmagnetic chain increases and even forms column or meshstructure and the shear stress ensues to increase


01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)

Figure 11 The relationship between viscosity and shear stress rate

The apparent viscosity of MR fluid is the measure shearstress 120591 under certain conditions divided by the shear strainrate 120574 Obviously for a Newtonian fluid the apparent viscos-ity is the dynamic viscosity and the value of viscosity is a con-stant independent of the shear strain rate But for MR fluidit is not so As Figure 11 shows the apparent viscosity of MRfluid changes with shear strain rate under different magneticinduction intensity The apparent viscosity decreases withincreasing shear strain rate and in the beginning it decreasedrapidly and then leveled off

4 Conclusion

In order to predict the mechanical property of MR fluidunder magnetic field and shear strain the microstructuresof chain at different magnetic fields strength were measuredThe chain model of dipole interaction for MR fluid wasestablishedThe prediction model of yield stress for MR fluidis obtained The influence of yield stress by magnetizationintensity of magnetic particle and magnetic field strengthwere analyzed respectively In this experiment we obtain therelationship between the shear stress andmagnetic inductionand particle volume fraction

Acknowledgments

This work was financially supported by the National NaturalScience Foundation of China (Grant no 51175532) theNatural Science FoundationKeyProject ofChongqing (Grantno CSTC 2011ba4028) Key Program of the FundamentalResearch Funds for the Central Universities (Grant noCDJXS10242206)

References

[1] G L Gulley and R Tao ldquoStructures of a magnetorheologicalfluidrdquo International Journal of Modern Physics B vol 15 no 6-7pp 851ndash858 2001

[2] K H Song B J Park and H J Choi ldquoEffect of magneticnanoparticle additive on characteristics of magnetorheological

fluidrdquo IEEE Transactions onMagnetics vol 45 no 10 pp 4045ndash4048 2009

[3] J Huang P Wang and G Wang ldquoSqueezing force of themagnetorheological fluid isolating damper for centrifugal fanin nuclear power plantrdquo Science and Technology of NuclearInstallations vol 2012 Article ID 175703 6 pages 2012

[4] E Dragasius V Grigas D Mazeika and A Sulginas ldquoEvalua-tion of the resistance force ofmagnetorheological fluid damperrdquoJournal of Vibroengineering vol 14 no 1 pp 1ndash6 2012

[5] J Huang J M He and J Q Zhang ldquoViscoplastic flow of theMR fluid in a cylindrical valverdquo Key Engineering Materials vol274ndash276 no 1 pp 969ndash974 2004

[6] A M Afonso M A Alves and F T Pinho ldquoAnalyticalsolution of mixed electro-osmoticpressure driven flows ofviscoelastic fluids inmicrochannelsrdquo Journal of Non-NewtonianFluid Mechanics vol 159 no 1ndash3 pp 50ndash63 2009

[7] P Kielan P Kowol and Z Pilch ldquoConception of the electroniccontrolled magnetorheological clutchrdquo Przeglad Elektrotech-niczny vol 87 no 3 pp 93ndash95 2011

[8] J Huang J Q Zhang Y Yang and Y Q Wei ldquoAnalysis anddesign of a cylindricalmagneto-rheological fluid brakerdquo JournalofMaterials Processing Technology vol 129 no 1ndash3 pp 559ndash5622002

[9] J Noma H Abe T Kikuchi J Furusho andM Naito ldquoMagne-torheology of colloidal dispersion containing Fe nanoparticlessynthesized by the arc-plasma methodrdquo Journal of Magnetismand Magnetic Materials vol 322 no 13 pp 1868ndash1871 2010

[10] C Ekwebelam and H See ldquoMicrostructural investigations ofthe yielding behaviour of bidispersemagnetorheological fluidsrdquoRheologica Acta vol 48 no 1 pp 19ndash32 2009

[11] K I Jang J Seok B K Min and S J Lee ldquoBehavioralmodel for magnetorheological fluid under a magnetic fieldusing Lekner summation methodrdquo Journal of Magnetism andMagnetic Materials vol 321 no 9 pp 1167ndash1176 2009

[12] J Pacull S Goncalves A V Delgado J D G Duran and M LJimenez ldquoEffect of polar interactions on the magnetorheologyof silica-coated magnetite suspensions in oil mediardquo Journal ofColloid and Interface Science vol 337 no 1 pp 254ndash259 2009

[13] F F Fang H J Choi and M S Jhon ldquoMagnetorheology of softmagnetic carbonyl iron suspension with single-walled carbonnanotube additive and its yield stress scaling functionrdquo Colloidsand Surfaces A vol 351 no 1ndash3 pp 46ndash51 2009

[14] S Chen K Jian and X Peng ldquoCylindrical magnetorheologicalfluid variable transmission controlled by shape-memory alloyrdquoScience and Technology of Nuclear Installations vol 2012 ArticleID 856082 6 pages 2012

[15] X Z Zhang X L Gong P Q Zhang and Q M WangldquoStudy on the mechanism of the squeeze-strengthen effect inmagnetorheological fluidsrdquo Journal of Applied Physics vol 96no 4 pp 2359ndash2364 2004

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


(a)

H

(b)

H

(c) (d)

Figure 1 The chain process of MR fluid

Figure 2The experimental device of measurement of MR fluids bydigital microholography

of magnetic force to form a chain-like microstructure alongthe field direction meanwhile the chain process of MR fluidoccurrs as shown in Figure 1 The distribution of particles inMR fluid without the magnetic field is shown in Figure 1(a)the dynamic yield stress is zero in this case The chainstructure of particles in MR fluid under the magnetic fieldis shown in Figure 1(b) Figure 1(c) shows that the numberand diameter of chain will increase with the appliedmagneticfield and the dynamic yield stress and apparent viscosity ofMR fluid also increase Figure 1(d) shows that the MR fluidrecovers rapidly and response time is only few millisecondswhen the applied magnetic field disappeared

Figure 2 shows the experimental device for recordingholograms of MR fluid The experimental conditions are asfollows the pixel number 119873 = 1024 the pixel size of thecharge coupled device (CCD) camera Δ119909 = 52 120583m thewavelength 120582 = 6328 nm the magnification of objective119872 = 40

The hologram and reconstruction images of calibrationtarget are shown in Figure 3 From Figure 3(b) we can easilyobtain the length between two graduation lines based oncounting the pixel numbers Because the actual scale ofcalibration target is 50 120583m1198721015840 and actual 119889 can be calculated[13]

After a strong magnetic field is applied to MR fluids themicroparticles will be polarized and aligned like chains alongthe direction of magnetic field The continuous holograms ofMR fluids under an applied magnetic field were encoded byCCD and the construction images of the chain configurationare shown in Figure 4The figures also indicate the transformprocess from micro-particles to chains in a magnetic field

The chaining process along the direction of magnetic fieldthat is the responding speed of MR fluids for magnetic fieldis easily calculated

22 Shear Yield Stress In order to analyze the relationshipbetween the shear yield stress and the magnetic field thesize the volume percentage of MR fluidThe assumptions forchain model of dipole are as follows

(1) The ordered arrangement of particles after magneticpolarization and the chain structure is steady All ofthe particles occupy a fixed position in the stablechain

(2) The single chain formed by particles is along with thedirection of magnetic field The chain is parallel tomagnetic field direction and its length is equal to thedistance between two plates All of the chains are thesame in geometry so the analysis results of arbitrarychain can be representative of the others

(3) The acting force between adjacent particles in thechains is equal which presents the tensile strength ofchains

(4) The adjacent particles are magnetized and turn intodipoles The direction of the centerline of particles isparallel to the magnetic field

(5) The interaction force in particles decides the strengthof chains When applied force is greater than theinteraction force between particles the chain will bepulled off When the shear stress is perpendicularto the direction of magnetic field the chain will beelongated and snapped

(6) The particles are supposed to be spherosome anduniform

The analysis mode of shear yield stress in MR fluid isshown in Figure 5 where ℎ represents the distance betweentwo parallel plates and 119865

119886is the external force [14] The

bottom plate is fixed and external force is applied to upperplateWhen the shear stress is perpendicular tomagnetic fielddirection the chain will deform and break The 120591

119910(119867) repre-

sents the shear yield stress under unit area The relationshipbetween 120591

119910(119867) and 119865

119886is indicated by 120591

119910(119867) = 119865

119886sin 120579 where

120579 represents the angle between the centerline of chain andmagnetic field direction as shown in Figure 5




1st 2nd 3rd 4th 5th


FH

h 120579

Fa



119869 = 12058301198811119872 (1)


1is the average


= 412058711990333 and 119872 is


119872 = 120594119867 (2)



119898 =119869

2119903 (3)


119889 =119899 (2119903 + 120575)

cos 120579 (4)



119865 =1

41205871205830

1198982

1198892 (5)


120591119910(119867) =

119873119865 sin 120579119860

(6)


follows

119873 =(120601119860ℎ119881

1)

(ℎ119877) (7)



120591119910(119867) =

119896

sum

119899=1

1205830

121198992

119903120601(120583119903minus 1)2

1198672

(2119903 + 120575)sin 120579cos2120579 (8)


0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350


120591 y(H

)(k

Pa)

H (kAmpm)


0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

120583r

H (kAmpm)






∘ 120575 = 0 1205830= 4120587 times 10






119881119903= 0 119881

120579= 119903120596 (119911) 119881

119911= 0 (9)

where119881119903119881120579 and119881




120574 = 1205960

119903

ℎ (10)



119879 = 2120587int

1198772

1198771

1205911199032d119903 (11)

where 1198771and 119877



119879 =2120587

3120591lowast(1198773

2minus 1198773

1) (12)



0= (1198772minus 1198771)2





Motor controller

Motor

Coupling

Speed reducer

Speed sensor

Coil assembly



Torque sensor

Rotating disk

Fixed disk

MRF

(a) (b)


01020304050607080

0 1 2 3 4 5 6 7 8 9

MRM1MRM2MRM3

120591(k

Pa)

B (kGs)





MRM1 5 01MRM2 15 02MRM3 35 11


0

10

20

30

40

50

60

70

80

15 20 25 30


6 kGs8 kGs

120591(k

Pa)




01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)



4 Conclusion


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






1st 2nd 3rd 4th 5th


FH

h 120579

Fa



119869 = 12058301198811119872 (1)


1is the average


= 412058711990333 and 119872 is


119872 = 120594119867 (2)



119898 =119869

2119903 (3)


119889 =119899 (2119903 + 120575)

cos 120579 (4)



119865 =1

41205871205830

1198982

1198892 (5)


120591119910(119867) =

119873119865 sin 120579119860

(6)


follows

119873 =(120601119860ℎ119881

1)

(ℎ119877) (7)



120591119910(119867) =

119896

sum

119899=1

1205830

121198992

119903120601(120583119903minus 1)2

1198672

(2119903 + 120575)sin 120579cos2120579 (8)


0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350


120591 y(H

)(k

Pa)

H (kAmpm)


0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

120583r

H (kAmpm)






∘ 120575 = 0 1205830= 4120587 times 10






119881119903= 0 119881

120579= 119903120596 (119911) 119881

119911= 0 (9)

where119881119903119881120579 and119881




120574 = 1205960

119903

ℎ (10)



119879 = 2120587int

1198772

1198771

1205911199032d119903 (11)

where 1198771and 119877



119879 =2120587

3120591lowast(1198773

2minus 1198773

1) (12)



0= (1198772minus 1198771)2





Motor controller

Motor

Coupling

Speed reducer

Speed sensor

Coil assembly



Torque sensor

Rotating disk

Fixed disk

MRF

(a) (b)


01020304050607080

0 1 2 3 4 5 6 7 8 9

MRM1MRM2MRM3

120591(k

Pa)

B (kGs)





MRM1 5 01MRM2 15 02MRM3 35 11


0

10

20

30

40

50

60

70

80

15 20 25 30


6 kGs8 kGs

120591(k

Pa)




01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)



4 Conclusion


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350


120591 y(H

)(k

Pa)

H (kAmpm)


0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

120583r

H (kAmpm)






∘ 120575 = 0 1205830= 4120587 times 10






119881119903= 0 119881

120579= 119903120596 (119911) 119881

119911= 0 (9)

where119881119903119881120579 and119881




120574 = 1205960

119903

ℎ (10)



119879 = 2120587int

1198772

1198771

1205911199032d119903 (11)

where 1198771and 119877



119879 =2120587

3120591lowast(1198773

2minus 1198773

1) (12)



0= (1198772minus 1198771)2





Motor controller

Motor

Coupling

Speed reducer

Speed sensor

Coil assembly



Torque sensor

Rotating disk

Fixed disk

MRF

(a) (b)


01020304050607080

0 1 2 3 4 5 6 7 8 9

MRM1MRM2MRM3

120591(k

Pa)

B (kGs)





MRM1 5 01MRM2 15 02MRM3 35 11


0

10

20

30

40

50

60

70

80

15 20 25 30


6 kGs8 kGs

120591(k

Pa)




01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)



4 Conclusion


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Motor controller

Motor

Coupling

Speed reducer

Speed sensor

Coil assembly



Torque sensor

Rotating disk

Fixed disk

MRF

(a) (b)


01020304050607080

0 1 2 3 4 5 6 7 8 9

MRM1MRM2MRM3

120591(k

Pa)

B (kGs)





MRM1 5 01MRM2 15 02MRM3 35 11


0

10

20

30

40

50

60

70

80

15 20 25 30


6 kGs8 kGs

120591(k

Pa)




01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)



4 Conclusion


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




01020304050607080

0 100 150 200 250 300 350

1 kGs2 kGs

3 kGs4 kGs

120578(P

amiddots)

120574 (sminus1)



4 Conclusion


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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