Magnetorheological Fluid Based Braking System using L-shaped Disks

Mohammadhossein Hajiyan, Shohel Mahmud, and Hussein A. Abdullah

School of Engineering, University of Guelph, 50 Stone Road East,Guelph, Ontario, Canada, N1G 2W1

For correspondence: mhajiyan@uoguelph.ca, Tel: +1(226) 500-0211

Abstract: This paper presents a novel designof multi-disks Magnetorheological brakingsystem (MR brake) for automotive applica-tion. Magnetic saturation in both electromag-netic core and MR fluid is considered in thispaper. The electromagnetic analysis of theproposed configuration is carried out usingFinite Element based COMSOL multiphysicssoftware (AC/DC module). The system ge-ometry, created using AutoCAD software, isdiscretized using a finite number of triangu-lar elements with a higher concentration ofelements near the internal boundaries. Postprocessing option of COMSOL multiphysicssoftware is utilized to calculate the magneticfield distribution and magnetic flux densityinside the MR fluid and electromagnetic core.A one dimensional analytical model is de-veloped to calculate the braking torque ofthe proposed system. The performance ofthe proposed design shows improvement overthe designs available in the existing literatureconsidering the same dimensional restrictions.

Keywords: Magnetorheological fluid, Brak-ing torque, Finite Element Analysis, BinghamModel.

1. Introduction

Magnetorheological fluids (MR fluid) area class of smart fluids which are composedof liquids (basically oils) and varying percent-ages of iron particles. MR fluids are widelybeing used in applications where controlla-bility and flexibility are important. For in-stance, in large-scale damper to protect struc-

tures [1], damping system for small and midsize applications [2][3][4], Braking systems[5][6][7], portable rehabilitation devices andprosthetic joints [8][9], and body fitness equip-ment [10]. The two important characteristicsof MR fluid are: variable viscosity and fast re-sponse. The former characteristic feature de-pends on the magnitude of the applied mag-netic field and the latter can provide semi-solid material within a millisecond as soon asthe magnetic field is applied to the MR fluid.Figure 1 will clearly explain the arrangementof iron particles in MR fluid without and withthe imposed magnetic field.

Figure 1: Arrangement of iron particles inside theMR fluid in the absence (A) and presence (B) ofmagnetic field [11].

2. Related Works

In recent days, MR braking systems havereceived considerable attention in the auto-motive industries. However, automotive in-dustries are paying special focus on the gener-ation of higher braking torque using MR brak-ing systems. One of the limitations of MRfluid is its low magnetic permeability com-

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pared to the iron core used in MR brakingsystem. Directing an increasing amount ofmagnetic flux through the MR fluid can pro-vide higher braking torques, which remainsas one of the challenging factors during de-sign. For example, Nguyen and Choi [12] pro-posed braking systems with disk type, drumtype, and T-shaped disks. Kwan et al. [13]proposed a new design of MR braking systemwith small steel roller.

In this paper, we propose a new disk geom-etry which can direct more magnetic flux intoMR fluid compared to the configurations re-ported in the current literature. The proposedconfiguration shows the potential to improvethe torque produced by the MR brake. There-fore, the major contribution of this paper canbe summarized as:

• development of a mathematical modelfor the proposed design that utilizesBingham model to calculate the brak-ing torque.

• simulation of the MR brake system us-ing COMSOL multiphysics software.

3. The Proposed Design

This section presents a brief descriptionof the proposed MR braking system. Figure2 shows the three dimensional CAD drawingof the braking system with its important com-ponents. The major components are shown inFigure 3 are : (a) straight and L-shaped disks,(b) cavities filled with MR fluid, (c) back iron,(d) shaft, and (e) copper coil. The flanges ontwo L-shaped side disks are designed to directthe magnetic field into the MR fluid and con-sequently increase magnetic field inside theMR fluid. Figure 3 presents the location ofthe major components of the proposed design.The rational behind selecting the current ge-ometry is to obtain

• maximum possible magnetic field inten-sity inside the MR fluid within its satu-ration limit

• higher braking torque

Figure 2: CAD model of the proposed design

dr

hrhl

t

di

Non-magnetic Parts

Coil

MR fluid

Magnetic Part

Figure 3: Parameters of the proposed MR brakingsystem.

In this study, some dimensional limitationshave been considered to simulate a feasibleMR braking system for automotive applica-tions. Table 1 provides some important di-mensions to simulate the proposed design inCOMSOL software environment.

Table 1: Dimensional limitations of the MR brake.

Parameters Upper boundary

MR brake diameter 260 mmMR brake width 60 mm

Assembly clearance 2 mmDisks thickness 5 mmMR fluid gap 1 mm

3.1. Material

Table 2 provides the list of materials usedfor different parts to simulate the MR brake.Note that sealing accessories, such as, screws,

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nuts, o-rings, and rotary sealing are disre-garded.

Table 2: Material description for the MR brakesimulation.

Parts Material description

Magnetic AISI-1010Non-magnetic AISI-4340

MR fluid MRF-132DGCoil Copper AWG-24

3.2. Torque Equation

This section will present the equations tocalculate the output torque of the proposedsystem. A prior calculation of the magneticfield intensity and identification of the satura-tion point in different parts of the MR brak-ing system are required for torque calculation.However, the functional relationship betweenthe magnetic flux density (B) and the mag-netic field intensity (H) is highly non-linear formost of the magnetic materials which posessome complexity while calculating torque fora particular system. To elaborate on the non-linear magnetic material behaviour, Figure 5illustrates graphically the functional relation-ship between B and H of AISI 1010 steel whichis the magnetic material selected for the newproposed design. In order to complete thetorque model of proposed system MR fluid istreated as a non-Newtonian fluid which obeysBingham model. For single disk the brakingtorque is given by

Tb = 2πN

∫ ro

ri

(µprω

h+KHβ)r2dr (1)

where N is the number of disks contacting theMR fluid, ω is the angular velocity of the diskand h is the MR fluid gap, K and β are con-stant parameters and depends on the specificfluid, and ri and ro are the inner and the outerradius of brake disks, respectively.

Figure 4: Annular MR fluid in the gap.

0 0.5 1 1.5 2 2.5 3 3.5

x 105

0

0.5

1

1.5

2

2.5AISI 1010 Carbon Steel

H[Amp/m]

B[T

]Figure 5: B-H curve for AISI 1010 [7].

Readers are referred to Figure 2 to Figure4 for the explanation of different dimensionsin the torque equation. Now, the generatedbraking torque for the entire system, as shownin Figure 3, can be calculated from the follow-ing equations:

Tb = π

∫ dr

0

r2τdr + πr2∫ hl

0

τdr (2)

+π

∫ t

0

r2τdr + πr2∫ hl−t

0

τdr

+π

∫ dr−t

0

r2τdr + 2π

∫ dr

0

r2τdr + πr2∫ t

0

τdr

+π

∫ dr

0

r2τdr + πr2∫ hr

0

τdr

+π

∫ t

0

r2τdr + πr2∫ hr−t

0

τdr + π

∫ dr−t

0

r2τdr

The final torque equation can be obtainedafter all integrations are performed:

Tb =πτHd

3r

3+πωµpd

4r

4g+ πd2rτHhl (3)

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+πd2rωµph

2l

2g+πτHt

3

3+µpωµpt

4

4g

+π(dr − t)2τH(hl − t) +π(dr − t)2ωµp(hl − t)2

2g

+πτH(dr − t)3

3+πωµp(dr − t)4

4g+

2πτHd3r

3

+πτHd

3r

3+πωµpd

4r

2g+ πd2rtτH +

πd2rµpωt2

2g

+πωµpd

4r

4g+ πd2rτHhl + π(dr − t)2τH(hl − t)

+πd2rωµph

2l

2g+πτHt

3

3+πωµp(dr − t)4

4g

+π(dr − t)2ωµp(hl − t)2

2g+πτH(dr − t)3

3+µpωµpt

4

4g

It is important to note that Tb(Eq. 3) is afunction of τ which can be obtained from therelationship between the yield stress and mag-netic field intensity as presented in Figure 6.

0 50 100 150 200 250 3000

5

10

15

20

25

30

35

40

45

50MRF−132DG

Magnetic Field Strength[kA/m]

Yie

ld S

tres

s[kP

a]

Figure 6: Magnetic field vs. Yield stress [14].

4. Numerical simulations

Magnetic Field module (mf ) of COM-SOL software (AC/DC module) is selectedto simulate the proposed system. In orderto reduce computational time, only a 2D ax-isymmetric section is used for the simula-tion. To calculate the magnetic field inten-sity (H) across the shear surfaces, the lineand area integrations available in the post-processor of AC/DC module is utilized. Fig-

ure 7 presents the mesh used for COMSOLsimulation. Mesh size is selected using theCOMSOL’s automatic mesh generator with”Extra fine” element option. Approximately8900 triangular elements are used to solve thefollowing electromagnetic equations:

Je = 5× H (4)

5 ·B = 0 (5)

The solver was stationary and non-linear inthis study. Non-linear material properties areconsidered for both the MR fluid and mag-netic steels. Air boundary around the wholesystem is selected.

Figure 7: Mesh used for the proposed system us-ing small size triangular element.

5. Result and Discussion

In this section, some simulation resultsare presented. Figure 8 provides the quali-tative surface plot of magnetic flux densityin MR brake for applied current density of10E5 [A/m2]. The magnetic field concentra-tions around the corners are notable in Fig-ure 8. Magnetic flux leakage in the systemincreases when higher current density is ap-plied. Therefore, round edges are highly rec-ommended to design the prototype to reducethe magnetic leakage.

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Figure 8: Magnetic flux density of MR brake whencurrent density is J ≈ 20E5 [A/m2].

Figure 9 shows the corresponding mag-netic vector potential contours inside thebraking system. It is observed clearly fromthe magnetic potential plot in Figure 9 thatflanges of side disks direct the magnetic fieldto MR fluid efficiently. In this design, thegenerated magnetic flux is higher when theapplied current density was lower comparedto [15] (Figure 10).

Figure 9: Magnetic vector potential of MR brakewhen current density is J ≈ 20E5 [A/m2].

It is observed from Figure 6 that the yieldstress in MR fluid increases with increasingmagnetic field. This trend can result in ahigher braking torque in the proposed sys-tem. However, magnetic saturation in MRfluid has to be taken into account. Figure 10

illustrates the magnetic flux distribution onboth the mid and side disks. In Figure 10, asignificant difference is observed between theflux around the tip of the disks compared tothe root of the disks. It is important to men-tion that the design considered in this paper isbased on ease of manufacturing and machin-ing feasibility.

Figure 10: Magnetic flux on disks when currentdensity is J ≈ 20E5 [A/m2].

Figure 11 shows the magnetic field inten-sity distribution in MR fluid. The yield stresscan be computed using this distribution andFigure 6. As can be seen from this figure thatthe maximum magnetic field in the MR brak-ing system is approximately 8E4 A/m.

Figure 11: Magnetic field intensity distributionin MR fluid when current density is J ≈ 20E5[A/m2].

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10

15

20

25

30

35

5 10 15 20

Bra

kin

g T

orq

ue

[N.m

]

Current Density × E5 [A/m2]

Braking Torque Vs. Current Density

2mm

1mm

0.5mm

Figure 12: Braking torque vs. Current density with different MR fluid gap.

Figure 12 provides braking torque of thesystem when different current densities areapplied. Three different values of MR fluidgap (i.e., 0.5 mm, 1.0 mm, and 2 mm) areused in Figure 12. It is observed from thefigure that a braking system with 2 mm MRfluid gap can generate highest braking torquewhen the maximum possible current density isapproximately 20×105A/m2. Applying a cur-rent density beyond this point may cause un-wanted heat generation by the coil which re-sults in greater loss throughout the MR brak-ing system.

Finally, the torque generation perfor-mance of the proposed system is comparedwith the performance results presented byBenetti and Dragoni [15]. Note that the sys-tem of Benetti and Dragoni [15] consists of 6rotary and 6 stationary straight disks. Au-thors obtained an average torque of 8.5 N.mfor each discs with an applied current densityof 2.5 A/mm2. In contrast, our 3-disk sys-tem can produce total 33 N.m (11 N.m/disc)for the same current density input within thesame geometric dimensional restrictions.

6. Conclusion

In this paper, a new geometry of disks inMagnetorheological brake is presented. Ana-lytical models of the system that utilize Bing-ham model are provided to calculate the brak-

ing torque for an applied magnetic field. Fur-thermore, magnetic field intensity and themagnetic flux density are calculated using fi-nite element based COMSOL software. Non-linear relationship between magnetic field andmagnetic flux for commercially available MRfluid is applied during current simulation.The proposed design shows improvement overthe designs available in the current literaturewith the same limitations.

Remarks on COMSOL

One of the advantages of COMSOL is theuse of ”material definition” which gives usflexibility to define non-linear relationship be-tween Magnetic flux and Magnetic field. Sur-face integration tool helps us to compute themagnetic flux on the internal surfaces. Gener-ation of 2D graph in the post-processing modeto illustrate magnetic flux density on the disksis very user friendly. Another advantage ofusing COMSOL is the easy selection of meshtype, mesh size, and mesh control near cornersand interfaces. Finally, COMSOL LiveLinkfor AutoCad allows us updating the model onCOMSOL and re-simulate the system.

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References[1] G. Yang, B. S. Jr., J. D. Carlson, and M. K. Sain,

“Large-scale mr fuid dampers: modeling and dynamicperformance considerations,” Engineering Structures,vol. 24 no. 3, pp. 309–323, 2002.

[2] I. Iryani, M. Yazid, S. A. Mazlan, T. Kikuchi, H. Za-mzuri, and F. Imaduddin, “Design of magnetorheolog-ical damper with a combination of shear and squeezemodes,” Materials and Design, vol. 54, pp. 87–95,2014.

[3] D. Ghorbany, “Magnetorehological damper hystere-sis characterization for the semi-active suspension sys-tem,” Master’s thesis, University of Agder, 2011.

[4] J. W. Gravatt, “Magneto-rheological dampers forsuper-sport motorcycle applications,” Master’s thesis,Virginia Polytechnic Institute and State University,2003.

[5] C. Sarkar and H. Hirani, “Design of a squeeze filmmagnetorheological brake considering compression en-hanced shear yield stress of magnetorheological fluid,”Electrorheological Fluids and Magnetorheological Sus-pensions, vol. 412, p. conference 1, 2012.

[6] O. Erol and H. Gurocak, “Interactive design optimiza-tion of magnetorheological-brake actuators using thetaguchi method,” Smart Materials and Structures,vol. 20 no. 10, p. ., 2011.

[7] K. Karakoc, E. J. Park, and A. Suleman, “Designconsiderations for an automotive magnetorheologicalbrake,” Mechatronics, vol. 18 no.8, pp. 434–447, 2008.

[8] M. Avraam, M. Horodinca, P. Letier, andA. Preumont, “Portable smart wrist rehabilita-tion device driven by rotational mr-fluid brakeactuator for telemedecine applications,” in Interna-tional Conference on Intelligent Robots and Systems,2008.

[9] F. Jonsdottir, E. T. Thorarinsson, H. Palsson, andK. H. Gudmundsson, “Influence of parameter vari-ations on the braking torque of a magnetorheologi-cal prosthetic knee,” Intelligent Material Systems andStructures, vol. 20, pp. 659–667, 2009.

[10] W. K. Sum, Liao, and W. Hsin, “Adaptive body fit-ness equipment using magnetorheological fluids,” inROBIO, pp. 432–437, IEEE, 2005.

[11] http://science.howstuffworks.com/.

[12] Q. H. Nguyen and S. B. Choi, “Selection of magne-torheological brake types via optimal design consider-ing maximum torque and constrained volume,” SmartMaterials and Structures, vol. 21 no. 1, pp. 12–20,2012.

[13] A. K. Kwan, T. H. Nam, and Y. Young, “New ap-proach to design mr brake using a small steel roller asa large size magnetic particle,” in International Con-ference on Control, Automation and Systems, 2008.

[14] http://www.lord.com/.

[15] M. Benetti and E. Dragoni, “Nonlinear magneticanalysis of multi-plate magnetorheological brakes andclutches,” in COMSOL Users Conference 2006 Mi-lano, 2006.

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