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Development of a multi-pole magnetorheological brake

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2013 Smart Mater. Struct. 22 065008

(http://iopscience.iop.org/0964-1726/22/6/065008)

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IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 22 (2013) 065008 (13pp) doi:10.1088/0964-1726/22/6/065008

Development of a multi-polemagnetorheological brake

Yaojung Shiao1 and Quang-Anh Nguyen

Department of Vehicle Engineering, National Taipei University of Technology, Taipei, Taiwan

E-mail: yshiao@ntut.edu.tw

Received 24 January 2013, in final form 8 April 2013Published 26 April 2013Online at stacks.iop.org/SMS/22/065008

AbstractThis paper presents a new approach in the design and optimization of a novel multi-polemagnetorheological (MR) brake that employs magnetic flux more effectively on the surface ofthe rotor. MR brakes with conventional single ring-type electromagnetic poles have reachedthe limits of torque enhancement. One major reason is the limitation of the magnetic fieldstrength within the active area of the MR fluid due to the geometric constraints of the coil. Themulti-pole MR brake design features multiple electromagnetic poles surrounded by severalcoils. As a result, the active chaining areas for the MR fluid are greatly increased, andsignificant brake torque improvement is achieved. The coil structure, as a part of the stator,becomes flexible and customizable in terms of space usage for the winding and bobbin design.In addition, this brake offers extra options in its dimensions for torque enhancement becauseeither the radial or the axial dimensions of the rotor can be increased.

Magnetic circuit analysis was conducted to analyze the effects of the design parameterson the field torque. After that, simulations were done to find the optimal design under allmajor geometric constraints with a given power supply. The results show that the multi-poleMR brake provides a considerable braking torque increase while maintaining a compact andsolid design. This is confirmation of its feasibility in actual braking applications.

(Some figures may appear in colour only in the online journal)

1. Introduction

MR fluid research was initially started by Rabinow in1948 [1]. The fluid consists of micrometer-scale magneticparticles in a carrier fluid. The yield stress of the fluid in theactive state can be controlled accurately by an input current,providing reversible, quiet, rapid response interfaces betweenthe electronic controls and mechanical systems [2, 3]. In theMR brake, the fluid is under direct-shear mode operation,as seen in figure 1. The fluid with thickness g is betweenrotating and static plates of length L and width w. Underan applied field that is perpendicular to the flow direction,magnetic particles form many parallel chains across the flow.These chains restrict the movement of the fluid, which createsfrictional force or torque. However, this mode contains a

1 Address for correspondence: Department of Vehicle Engineering, NationalTaipei University of Technology, No. 1, Section 3, Chung-Hsiao E. Road,Daan District, Taipei City 106, Taiwan.

weak connection between magnetic particles under the strainof external forces on their chains. This causes the chain tobe broken at some points and reconnected to the next one,resulting in the limitation of torque under a specific yieldstress. To enhance the torque, there are several directions thatcan be followed, such as:

• Using an MR fluid with better yield characteristics.

• Reducing the fluid gap g.

• Extending the active area of the fluid (for example,modifying the geometric dimensions L or w).

• Increasing the applied field strength while avoidingmagnetic saturation.

Torque enhancement has been widely investigated inconventional MR brakes, which consist of a round housing(stator) and a disc (rotor) inside. The first two directionsshown above are the easiest to apply to any MR brake

10964-1726/13/065008+13$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA

Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 1. The direct-shear mode of the MR fluid.

device [4, 5]. However, the torque improvement by changingto an MR fluid with a higher yield stress is not great. Inaddition, the fluid gap in an MR brake cannot be reduced bymuch because of limitations in manufacturing.

The third method has been used since the earliest MRbrake designs. Simple solutions include adding an extrarotating disc [6, 7] or using additional coils [8]. The rotor’sradial [9] (in the disc-type MR brake) or axial (in thedrum-type MR brake) dimensions [10] can also be extendedto generate a greater active area of the fluid, thus producinga higher shear stress and, consequently, a higher brakingtorque. Nguyen et al [11] have discussed details of theoptimal value of significant geometric dimensions in anMR brake to produce a maximum torque. In their study,hybrid and T-shaped types were taken into account. Anotheradvanced solution focuses on the modification of the rotorboundary itself. Tran et al [12] studied a rotor with awaveform boundary to create a resistance force based on thematerial deformation process. The results showed a significantimprovement of torque. However, the total contact areabetween the MR fluid and the rotor and stator was increased,resulting in a higher viscosity torque in the inactive state ofthe brake. This consumes more driving power from the drivesource. In addition, the weight and size of the MR brake werealso increased.

In the fourth method, by increasing the number of wireturns as well as the input current, the yield stress cantheoretically be enhanced. However, due to the operatingconcept and structure of conventional MR brake design,magnetic saturation and space limitations place restrictionson the improvement of the magnetic field strength and thecorresponding braking torque.

As a result, this paper addresses a new MR brakedesign to provide a solid structure and flexibly enhancethe magnetic field as well as the braking torque. Theoriginal concept of the multi-pole MR brake was firstintroduced by Shiao [13]. However, its complex structureand the need for performance improvements required it tobe redesigned. In the following sections, the design andoptimization of a multi-pole MR brake are presented. The newoperating concept intends to overcome those disadvantagesof the conventional design while providing features for moreeffective torque enhancement.

2. Operating concept

The brake consists of a solid and magnetically permeablehousing stator with a multi-pole and a rotor, as shown in

figure 2. The poles create a cylindrical space within whichthe rotor is placed. Magnetic flux travels, following the pathof the red lines. The direction of magnetic flux in each poleis opposite to that of its two adjacent magnetic poles. As aresult, the flux will travel in a closed loop, from one pole,through the MR fluid gap, into the rotor, back to the MRgap and into the two adjacent poles. By such a novel design,the produced magnetic flux will orthogonally penetrate allthe MR fluid in the channel between the cylindrical surfaceof the rotor and the stator. The result is such that a yieldresistance is produced, thus creating a field torque for thebrake. From the operating concept, the head area of each polewill be affected to activate the MR fluid area in the channel.Depending on the size of rotor, winding and manufactureabilities, different arrangements and numbers of poles can bechosen, from simple four- or six-pole brakes to more complexsystems with eight, ten, or even twelve poles. In this study,the performance of a six-pole MR brake has been analyzedand verified due to its balance between size constraints andbraking performance in our future applications. The magneticfield strength in the MR fluid can be enhanced by adjusting thepole configuration and the rotor’s radial and axial dimensions.Finally, the corresponding shear stress on the cylindricalsurface is increased significantly, which helps to increase thebraking torque.

Although the pole structure of the new multi-pole MRbrake is similar to that of an electric motor, the designconsideration and operating concept are quite different. Forease of comparison, the concept of a brushless direct current(BLDC) motor was chosen, as shown in figure 2. The majordifference is the magnetic permeability of the material filledbetween the housing stator and the rotor. In the BLDC motorit is air, whereas in this new MR brake it is an MR fluid.Air is not magnetically permeable and has a high magneticreluctance. In contrast, the MR fluid becomes magneticallypermeable after applying a current to the coils, and the chainof MR particles forms a route for magnetic flux to passthrough. The MR fluid filled between the housing statorand the rotor functions as a resistance source for the brake.The other difference is that the rotor of the BLDC motor isequipped with a permanent magnet while that of the MR brakeis just made of metal. With a flexible geometric configurationof the brake, it increases the magnetic field strength in theactive area of the MR fluid to generate a field torque and resistthe rotation of the rotor. Whereas in the motor, the magneticfield is employed to generate and maintain rotor rotation.

3. Design configuration

3.1. Material selection

3.1.1. MR fluid. The most suitable fluid for braking purposesmust meet multiple requirements, such as its viscosity withouta magnetic field, operating temperature, shear stress gradientwith respect to the applied magnetic field strength, thermalconductivity and coefficient of thermal expansion. Comparingseveral types of MR fluid, as seen in table 1 (data was referredfrom Lord technical papers [14–17]), Lord MRF-140CG was

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 2. Operating concept of (a) the BLDC motor and (b) the multi-pole MR brake.

Table 1. Properties of current commercial MR fluids.

Property MRF-122-EG MRF-132DG MRF-140CG

Carrier liquid Hydrocarbon Hydrocarbon HydrocarbonDensity (g cm−3) 2.28 3.09 3.64Yield strength (kPa) at 100 kA m−1 23 23 38Yield strength (kPa) at 200 kA m−1 32 42 57Plastic viscosity (mPa s) at 40 ◦C, γ > 500 s−1 42 112 280Operating temperature (◦C) −40 to +130 −40 to +130 −40 to +130Thermal conductivitya (W m−1 ◦C−1) at 25 ◦C 0.21–0.81 0.25–1.06 0.28–1.28Coefficient of thermal expansion 0–50 ◦C 6.5× 10−4 5.5× 10−4 5.0× 10−4

a Values were calculated with and without magnetic field applied.

Figure 3. Yield stress versus magnetic field strength of LordMRF-140CG fluid [18].

selected due to its higher yield stress gradient compared tothe others, while its viscosity and other properties are in thenormal range. Figure 3 shows the detailed yield stress versusmagnetic field strength of MRF-140CG.

3.1.2. Materials for MR brake hardware. The materialsused in the brake have a critical influence on the magneticfield as well as the structural and thermal characteristics.Based on the magnetic properties, the major focus on materialselection was ferromagnetic materials. Considering the cost,permeability and availability, AISI 1018 steel could be used

Figure 4. The B–H curve of AISI 1018 steel.

as the magnetic material in the MR brake [7]. Its magneticproperties are shown in figure 4. Aluminum was used as thenon-ferromagnetic material to make the shaft and the MRbrake covers. AWG-21 copper wire was used for the coils.

3.2. Design parameters

Based on the operational concept above, the generaldimensions and parameters of the brake are listed in table 2.

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Table 2. Design dimension of the multi-pole MR brake.

Parameters Definition

Rotor-ring thickness tr = R2 − R1

Rotor radius Rr = R2

Stator-ring thickness ts = R6 − R5

Stator radius Rs = R6

MR fluid gap g = R3 − R2

Slot s

Core thickness c

Rotor/stator axial width z

These parameters were later used in magnetic circuit analysis,modeling and optimization of the MR brake. Since themagnetic flux orthogonally penetrates the cylindrical surface,to employ that flux effectively, the axial widths of the rotor andstator were made the same. Moreover, to reduce the weight ofthe rotor, it was designed as hollow with an I-shaped crosssection.

4. Analytical modeling of the multi-pole MR brake

The behavior of the MR fluid can be described effectively byusing the Bingham plastic model [19, 20]. According to themodel, the total shear stress in the MR fluid under an appliedmagnetic field is given by

τ = τy + ηγ (1)

where τ is the total shear stress, τy is the yield stress developedin response to the applied magnetic field and depends on themagnetic field strength in the fluid HMR, η is the viscosity ofthe MR fluid with no applied magnetic field, and γ is the shearrate of the MR brake in the direct-shear mode. From the rightside of the equation, the first term is a ‘magnetic term’ relatedto the applied magnetic field strength whereas the second termis a ‘viscous term’ related to the viscosity of the MR fluids.

To simplify the torque analysis, the flow characteristicsof the MR fluid are assumed as: incompressible flow, laminarsteady motion, linear fluid velocity distribution across the gap,no effects of gravity and centrifugal force, no slip condition,and a very small gap (i.e. gap thickness � rotor radius).Taking the above assumptions into account, the shear rate inthe gap can be obtained by using [6]:

γ =rω

g(2)

Figure 5. The cylindrical coordinate system applied to the rotor.

where r is the relevant radius, ω is the angular velocity of thedisc and g is the thickness of the MR fluid gap.

In this study, the Lord MRF-140CG fluid was used. Theyield stress τy in equation (1) can be approximated in termsof a function of the magnetic field strength applied to the fluidby using a curve-fitting method from figure 3.

τy = k5H5MR + k4H4

MR + k3H3MR

+ k2H2MR + k1H1

MR + k0 (3)

where

k =[−2E − 10 9E − 08 −2E − 05 −0.0002 0.5324 1.0303

].

It is noted that the value of magnetic field strength HMR isvariable and depends on θ and z of the cylindrical coordinatesystem of the rotor, as shown in figure 5.

By substituting equation (2) into (1), the total shear stresscan be written as

τ = τy + ηrω

g. (4)

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Using equation (1) and applying it to the brake geometry,the braking forces developed by a direct-shear devicecan be determined by integrating the shear forces on thecorresponding surface

dF = dFMR + dFfr (5)

in which the force from the MR fluid is dFMR = τdAw, whereAw is the working area, which is the cylindrical surface of therotor where the fluid is activated by the applied magnetic field.dFfr is the friction force due to the bearing sealing parts.

The torque generated by the brake can be calculated byusing

dT = dTMR + dTfr (6)

where dTMR is the torque from the MR fluid and dTfr is thefriction torque.

TMR for the cylindrical surface of the rotor can becalculated from surface integration of the total shear stress onthat surface.

TMR =

∫Aw

rτ dAw = Rr

∫ z

0

∫ 2π

0Rrτ dθ dz (7)

where the length of the moment arm is the rotor radius Rr.Then, substituting equation (4) into (7), the torque

function becomes

TMR = Rr

∫ z

0

∫ 2π

0Rr

(τy + η

Rrω

g

)dθ dz

= R2r

∫ z

0

∫ 2π

0τy dθ dz+

2πηωg

R3r z. (8)

The right hand side of equation (8) can be divided intotwo parts

Tf = R2r

∫ z

0

∫ 2π

0τy dθ dz (9)

Tv =2πηω

gR3

r z (10)

where Tf and Tv are the field torque component and theviscous torque component, respectively. Generally, in theanalytical model of a conventional MR brake, the yield stressis presented by its mean value rather than the dependence onthe field strength. However, in this proposed MR brake, τy,which is given by equation (3), is estimated accurately by thevariation of magnetic field strength on the working area. Sinceτy is nonlinear, Tf can be found by the finite element method(FEM). Finally, the total braking torque produced by the MRbrake is

T = R2r

∫ z

0

∫ 2π

0τy dθ dz+

2πηωg

R3r z+ Tfr. (11)

From equation (11), the total torque generated by themulti-pole MR brake contains three components: the fieldtorque, the viscous torque and the friction torque. Thecontrollability of the MR brake has a strong dependenceon the field torque. The field torque depends on the yieldcharacteristics of the active MR fluid and the rotor structure(Rr, z). The viscous torque also has close relationships to the

brake structure, fluid viscosity and rotational speed. Frictiontorque is always present whenever the brake is rotated. Itis apparent from equation (11) that torque enhancement iseffectively influenced by the extension of rotor radius Rras well as its axial width z. This is the advantage of themulti-pole MR brake compared to the conventional design.These extra options for torque improvement are useful inspecific applications where only these two parameters can beextended. For example, if the rotor radius is limited by the rimwhere the MR brake assembly is inserted within the wheel, thenew MR brake can extend in the axial dimension to increasethe brake torque. Another option is to enhance the yield stressτy developed in the MR fluid. This stress is influenced bythe input power and other geometric parameters, as will bediscussed in the magnetic circuit analysis.

5. Magnetic circuit analysis

The initial step toward optimization is to model the magneticcircuit associated with the multi-pole MR brake. It was statedearlier that the operational concept of the new MR brakeproposed here is different from the conventional design. Themechanical part of the brake modeled in section 4 is based onBingham’s equation. In this section, the magnetic circuit ofthe MR brake is proposed and analyzed based on Ampere’slaw and Gauss’s law. As mentioned in the study of Nguyenet al [21], the purpose of magnetic circuit analysis is toapproximate the effects of the structure parameters and inputpower on the magnetic field strength within the MR fluid,from which the field braking torque can be computed. Theanalysis results can support the optimization process of torqueenhancement being effectively conducted.

Since the multi-pole MR brake is symmetrical in structureand uses the same material for each magnetically permeablecomponent, it is convenient to model the magnetic circuitof one-sixth of the 6-pole brake, as seen in figure 6. Thecomponents in the magnetic circuit of the first and second poleare divided into sections and connected at nodes. The sectionnames are listed as follows.

• Stator ring: a1a2.

• Coil: a1b1; a2b2.

• Pole head: b1c1; b2c2.

• MR fluid gap: c1d1; c2d2.

• Rotor ring: d1d2.

Figure 7 shows the magnetic circuit of one-sixth of theMR brake. Following a closed loop of the magnetic flux,the MR brake mechanical elements have been convertedto equivalent magnetic properties. Rc;Rp;RMR are themagnetic reluctance of the core, pole head and MR fluidgap respectively. Note that the serial connection of magneticreluctance Rc;Rp;RMR is based on the operating principle toprevent the magnetic flux from directly flowing from one poleto the others. To achieve this requirement, further analysisof the slot dimension s is discussed in section 6. The circuitcomponents are listed in table 3.

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

d1d2

Figure 6. Node configuration of one-sixth of the multi-pole MRbrake.

Figure 7. Magnetic circuit of one-sixth of the multi-pole MR brake.

Table 3. Parameters of the magnetic circuit of the multi-pole MRbrake.

Term Parameter

Reluctance of the stator ring RsReluctance of the coil RcReluctance of the pole head RpReluctance of the MR RMRReluctance of the rotor ring RrMagnetic flux of coil 8cMagnetomotive force FPermeability of AISI 1018 steel µsteelPermeability of the MR fluid µMR

To simplify the circuit, the corresponding magneticreluctance R was used, as seen in figure 8.

R = Rc +Rp +RMR. (12)

Since the circuit presents only one-sixth of the completeMR brake, an additional magnetic flux at each node wasadded to provide the relationship with the remaining part ofthe brake. 8a16,8a12 and 8a32 are the magnetic flux on thestator-ring area from pole 1 to 6, pole 1 to 2, and pole 3 to2, respectively. 8d61,8d21 and 8d23 are the magnetic flux on

s

Figure 8. Simplified magnetic circuit of one-sixth of the multi-poleMR brake.

the rotor-ring area from pole 6 to 1, pole 2 to 1, and pole 2 to3, respectively.

Based on the same structure and current input, themagnitude of the magnetic flux through the two coils and themagnetomotive forces are identical

81 = 82 = 8c (13)

F1 = F2 = Ni (14)

where N is the number of turns for each coil and i is the inputcurrent.

Applying Gauss’s law to node a1 and a2

−81 +8a16 +8a12 = 0 (15)

82 −8a32 −8a12 = 0. (16)

The minus signal means the magnetic flux points towardthe node. From equations (15) to (16)

8a32 = 8a16. (17)

Due to the symmetry of the MR brake structure, at nodea1:

8a12 = 8a16 =8c

2. (18)

Taking the same process with node d1 and d2:

8d23 = 8d61

8d21 = 8d61 = −8c

2.

(19)

Applying Ampere’s circuit law to the loop

81R− F1 +8a12Rs − F2 +82R+8d21Rr = 0. (20)

Substituting equations (13), (14), (18) and (19) into (20)then

− 2Ni+ 28cR+8c

2(Rs −Rr) = 0. (21)

From equation (21) the magnetic flux in the core is

8c =4Ni

4R+Rs −Rr. (22)

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 9. Fringing of the magnetic flux in the magnetic circuit.

The fringing effect in the area between the MR fluid(RMR) and the pole head (Rp) is also considered, as shownin figure 9. To find the relationship between the magnetic fieldstrength within the MR fluid HMR to that created by the coil,it is necessary to investigate the total magnetic flux in the MRfluid [22], which is given by

8MR = BMRAMR = µMRHMRAMR (23)

where AMR is the effective pole area due to fringing, as seenin figure 9.

Using the principle of continuity of the magnetic fluxbetween the fluid and the coil

8MR = 8c. (24)

The magnetic reluctance of different sections can becalculated as

Rs =ls

µsteelAs; Rr =

lrµsteelAr

R = RMR +Rp +Rc

=HMRg

8MR+

lpµsteelAp

+lc

µsteelAc

(25)

where ls = a1a2; lc = a1b1; lp = b1c1; lr = d1d2, as seen infigure 4. As,Ar,Ap,Ac are the cross-sectional areas of thestator ring, rotor ring, pole head and core, respectively.

Substituting equations (24) and (25) into (22) then

8MR

=4Ni

4(HMRg8MR+

lpµsteelAp

+lc

µsteelAc)+ ls

µsteelAs−

lrµsteelAr

. (26)

After substituting equation (24) into (26), the magneticfield strength of the MR fluid is given by

HMR =4Ni

4(g+ lpµsteelApµMRAMR

+lc

µsteelAcµMRAMR

)+ lsµsteelAs

−lr

µsteelAr

. (27)

Note that AMR ≈ Ap ≈ Ac, which is the area of the polehead. Moreover, µsteel ≈ 1000µMR and lp, lc are not too large.Hence equation (27) can be simplified to

HMR =4Ni

4g+ lsµsteelAs

−lr

µsteelAr

. (28)

Substituting the parameters in table 2 into equation (30)then

HMR =4Ni

4g+ lsµsteel(tsz) −

lrµsteel(trz)

. (29)

The values of ls and lr can be calculated as

ls = Rs −ts2≈ Rs; lr = Rr −

ts2≈ Rr. (30)

Substituting equation (30) into (29) then

HMR =4Ni

4g+ 1zµsteel

(Rsts−

Rrtr). (31)

It is obvious from equation (31) that the value of HMR canbe affected by the MR brake configuration (MR fluid gap g,axial width of rotor z, radii Rr,Rs and thicknesses tr, ts of rotorand stator) and the magnetic permeability of the material µsas well as input power Ni. As a result, the new design offersflexible options for field torque enhancement compared to theconventional design.

6. Design optimization

In this section, the optimization of the multi-pole MR brakehas been conducted with the objective of maximizing thebraking torque. Other significant factors such as weightand thermo-dependent nonlinear magnetic characteristics areneglected. The cost function of field torque in equation (11)is correlated to the yield stress in equation (3), whichdepends on the magnetic field strength in equation (31).The maximization of field torque is associated with themaximization of HMR. In this specific design, the outer sizesof the rotor Rr and the stator Rs and its axial width z arefixed because of the application constraints. Ni, which isbased on the input power supply, is also fixed. Referring toequation (31), note that to maximize HMR, the MR fluid gapg should be minimized but not be smaller than a limitingvalue [12]. The details of the fixed input parameters used foroptimization are listed in table 4.

Considering the values of ts and tr to maximize HMR,note that ts should be increased while tr should be decreased,while ensuring that saturation is avoided. The results ofthe optimization process later agree with this statement. Forfeasibility of manufacture, the value of ts and tr should be keptsomewhere in the ranges 2–8 mm and 2–10 mm, respectively.Since Ni and the axial width z are fixed, it is necessary to

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Table 4. Fixed parameters used in optimization process.

Fixed parameter Value

Magnetomotive force Ni (Ampere-turn) 400Rotor radius Rr (mm) 44.5Stator radius Rs (mm) 70Rotor/stator axial width z (mm) 75MR fluid gap g (mm) 0.5

optimize the core thickness c to avoid magnetic saturationwhile maintaining a light structure. Based on available space,the domain for c is set from 10 to 16 mm.

In addition, if magnetic flux can flow directly fromone pole through the MR gap to other adjacent poles, theorthogonal magnetic flux to penetrate to rotor cylindricalsurface is decreased. This reduces the yield stress between theMR fluid and the rotor surface, resulting in a reduced fieldtorque. To prevent this, the slot s has to be taken into accountduring the optimization. With the optimal value of s, all themagnetic flux is forced to follow a closed loop, as mentionedin the magnetic circuit analysis. Based on winding capability,the domain for s is set from 3 to 19 mm. Then the optimizationproblem is expressed as follows

* Maximize the field torque Tf of the multi-pole MR brake

* Subject to:

min DV ≤ DVi ≤ max DV (32)

where

min DV = [ts min tr min smin cmin] = [2 2 3 10]

max DV = [ts max tr max smax cmax] = [8 10 19 16]

i = 1: n, n is the number of iterations.

Magnetic analysis software has been employed to solvethe optimization problem above. A 3D simulation model ofthe multi-pole MR brake has been built. The model containscompleted components of the brake embedded with materialproperties. The field torque performance was simulated byadding the field torque equations to a specific rotor surfaceand controlled by input currents. The saturation status ofcomponents is easily observed from the simulation results.

The built-in FEM-approximation Sequential NonlinearProgramming (SNLP) optimizer was employed for optimiza-tion [23]. With the simple evaluation of the cost function,the SNLP optimizer gives a good approximation of the costfunction in terms of the optimization variables. The SNLPoptimizer creates a response surface using a Taylor seriesapproximation from the FEM simulation results availablefrom past solutions. Therefore, an optimetric process, whichis also a built-in function, should be done in advanceto determine the optimum search domain for the designvariables. It is called the focus box, as shown in figure 10.

The response surface is used in the optimization loopto determine the gradients and calculate the direction anddistance for the next step. It helps to reduce the number ofFEM simulations and greatly speeds up solving the problem.

Figure 10. The initial focus box for SNLP.

<_

Figure 11. Optimization flowchart for optimal design of themulti-pole MR brake.

Convergence is improved as more FEM solutions are createdand the response surface approximation is improved. Theoptimization procedure is explained in the flowchart shownin figure 11.

7. Result and discussion

7.1. Optimization results

Figures 12 and 13 present the optimization results using theSNLP optimizer as discussed above. From figure 12, onecan see that ts and c converge quickly to optimal values ofapproximately 7.5 mm and 16 mm, respectively. This is dueto the small range of these design variables made available tothe optimizer during the selection of candidates. tr convergesslowly due to the optimizer needing to search under twoconditions: a smaller value of ts while avoiding saturationin rotor ring. The convergence of ts to bigger values and trto smaller values in their ranges agrees with equation (31).At this point, the magnetic field strength in the MR fluidreaches its maximum value. The optimal value of the slot s

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Table 5. Optimal solution for the multi-pole MR brake.

Parameter Optimal value Manufactured value

Stator-ring thickness ts (mm) 7.555 7.5Rotor-ring thickness tr (mm) 6.138 6Core thickness c (mm) 15.974 16Slot s (mm) 11.010 11

Figure 12. Solution for the design variables of the optimizationproblem.

Figure 13. Solution for the cost function of the optimizationproblem.

is approximately 11 mm. Its large variable range requires theoptimizer to take more tries to reach the convergence value.This emphasizes the importance of the focus box for designvariables with a large range. Convergence of the cost functionin figure 13 is achieved at the 27th iteration. The maximumfield torque is 25.14 N m.

Since the optimizer chooses the next candidate forverification based on a Taylor series approximation, the levelof convergence is not the same for each time run. However,the optimal solution always converges to a unique value. Theresults confirm the accuracy of the optimization procedure andvalidate the prior analysis of the magnetic circuit of the MRbrake.

Table 5 presents the details of the optimal design. Thesevalues have been rounded for ease of manufacture.

7.2. Magnetic analysis of the multi-pole MR brake

Figure 14 shows the direction of the magnetic flux in thecross-section of the MR brake. Its flow direction is noticeableas a loop from one pole through the MR gap to the rotor,then back through the MR gap again to the adjacent poles.More detail is shown in figure 15. Magnetic particles in theMR fluid form up to become many chains as the magnetic

Figure 14. Flow direction of the magnetic flux in the multi-poleMR brake.

Figure 15. Detailed illustration of the magnetic flux between twoadjacent poles.

flux orthogonally penetrates the fluid. The results confirm thefeasibility of the operating concept of the brake.

In figure 16, the magnitude of the magnetic field strengthin the middle cross-section of the MR brake is shown. Themaximum magnetic field strength occurs across the MR fluidgap under the pole-head area (around 280.5 kA m−1). Theseareas are the sources of high-yield stress, which help to slowthe motion of the rotor. Figure 17 gives the details of themagnetic field strength between two adjacent poles. Note thatthe field strength in the MR fluid gap between the two polesis around 5 kA m−1, which is very low. The results showthe importance of slot s. With its optimal value, almost all of

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 16. Magnetic field strength of the cross-section of themulti-pole MR brake.

Figure 17. Expanded view of the magnetic field strength betweentwo adjacent poles.

the flux follows the loop mentioned above rather than directlyflowing from one pole through the MR gap to other poles.

The multi-pole design shows an advantage not only in theextension of the active chaining area of the MR fluid but alsoby making it a high-yield area, as seen in figure 18. Almost allthe MR fluid covering the cylindrical surface of rotor has beenactivated. Created by the poles, magnetic flux was employedeffectively to increase the magnetic field strength within thefluid, especially in the core area. The field strength can beadjusted flexibly using the specification of the poles and inputcurrent. Torque enhancement can be achieved in two ways,both of which increase the active MR fluid area:

• Increase the rotor radius and add more poles to activate thewhole MR fluid in the cylindrical surface of the rotor.

• Keep the radius constant and increase the axial width of therotor.

Details of the magnetic field strength on the rotor areshown in figure 19. On the rotor-ring area, the green patternis interspersed by yellow-green areas, which are the areasbetween two poles. In this area, due to the rib in the middlepart of the rotor, the magnetic field strength in the rib area was

Figure 18. Magnetic flux density in the MR fluid gap.

Figure 19. Magnetic flux density in the rotor.

smaller. The arrangement confirms that most of the flux afterflowing through the MR fluid will go to the rotor via theseyellow-green areas.

Analysis of the magnetic flux density was done to preventthe occurrence of magnetic saturation, as shown in figure 20.The AISI 1018 steel becomes saturated at around 2.3 T whenthe magnetic field strength is greater than 100 kA m−1, asshown in figure 4. In the stator, the maximum magnetic fluxdensity (around 2.0 T) occurred in pole-head area due to itsthinness. At the green area where the cores are located onthe stator ring, it is suitable to assemble three edges of thestator with the outer ring. The optimal thickness of stator ringts and the core c maintains the flux density in these areasbelow 1.75 T. For weight reduction, it is important to reducethe thickness tr while avoiding saturation in the rotor-ringarea where the highest magnetic flux density occurs. The fluxdensity in the hollow structure is still around 1.5 T. This resultconfirms that magnetic saturation is avoided throughout thestructure of the manufactured prototype.

The generated field torque basically depends on themagnitude of magnetic field strength. Its level on thecylindrical surface of the rotor was investigated. A probe line

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 20. Magnetic flux density in the cross-section of themulti-pole MR brake.

Figure 21. Magnetic field strength on the middle of the cylindricalsurface of the rotor.

was drawn along the circumference and in the middle of thissurface. Figure 21 shows the magnetic field strength alongthis probe line for different input currents. The positions ofthe six poles around the rotor are indicated by the six peaksin the figure. In the space between poles, the field strengthis nearly zero, which means the slot has almost isolated theflux from going directly from one pole via the MR fluid to

the other poles. The variation of the field strength across thecircumference direction corresponds to the uniformity of yieldstress on the surface, which affects the field torque. With aninput current of 0.4 A, the variation of field strength is smalland indicated by the six low peaks. However, the higher theinput currents are, the bigger the variation of field strengththat occurs. At 2 A input current, the results of the fieldstrength at each pole have a small variation. This is due to theinconsistent meshing process at each pole and noise duringthe 3D magneto-static simulation.

7.3. Details of prototype for manufacture

Figure 22 presents the prototype details for manufacture.One major issue was the prevention of MR fluid leakage.Aluminum plates were inserted between the poles and sealedwith a special gel. Two O-rings were located between thecover and stator assembly. Rubber gaskets were used toprevent leakage around the ball-bearing location. Other MRcontacted surfaces were sealed by gel. The hollowed rotorwas covered by two aluminum plates. The stator assembly waskept firmly in place by the outer ring and both side covers.

Compared to the conventional MR brake, the multi-poleMR brake uses the same materials. Its structure lookscomplicated but the manufacture is not so complicated. Basedon our experience in machining this type of MR brake forindustrial applications and the evaluation for mass production,it is noted that although the production cost of a singleprototype is a little high, the cost of the brake under massproduction can be cut down. The winding can also be doneby automatic machine for mass production.

7.4. Experimental setup

The multi-pole MR brake is manufactured based on the abovecalculation. Details of the test layout are shown in figure 23.The MR brake is connected to a torque sensor and driven bya servo motor. The NI USB-6211 card is used to acquire thesignal from the speed sensor and torque sensor. This card is

Figure 22. Exploded view of the prototype of the multi-pole MR brake.

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Figure 23. Experiment layout of the multi-pole MR brake.

Figure 24. The test bed of the multi-pole MR brake .

also used as the intermediate interface to get the commandfrom the computer to control the rotational speed of the servomotor and input the current to the MR brake. The LORDWonder BoxTM Device Controller Kit is used as a currentamplifier to supply the exact current to the brake. Figure 24shows the test bed of the multi-pole MR brake.

7.5. Torque analysis in the multi-pole MR brake

Figure 25 shows the details of the torque results at differentinput currents from simulation and experiment. Like theconventional MR brake, the torque in the multi-pole MR brakeis linear with respect to the input current for currents smallerthan 1 A. The torque level can be accurately controlled bythe input current. With steps of 0.2 A, the torque increment issignificant. The maximum simulated torque is 22.4 N m, whileit is 19.9 N m for the experimental torque, all at 1 A inputcurrent. The difference between simulated and experimentaltorque is due to the viscosity torque as well as the frictiontorque, which is not accurately accounted for in the simulationmodel.

To compare the performance of the proposed MR brakewith the conventional one, the torque to volume ratioRTV [24], which is defined by the ratio of maximum braketorque divided by the overall geometric volume of the brake,is used. The device with a higher value of RTV has betterperformance in torque generation given the restriction of itsgeometric volume. In our study, three conventional MR brakedesigns (two disc-types [7, 25] and one drum-type [24]) wereselected as candidates for comparison. Figure 26 shows theresults of RTV for those designs. RTV of the proposed MR

Figure 25. The brake torque of the multi-pole MR brake .

Figure 26. Comparison of the torque to volume ratio for differentMR brake designs.

brake performs much better than the one in the Karakoc studyand better than the commercial MR brake from LORD. It isslightly smaller than that of the Erol study. We conclude thatthe multi-pole MR brake can generate a high braking torquewhile maintaining a compact design and a low input current.

Furthermore, the multi-pole MR brake also gives betterperformance than one of the previous prototypes which hadthe same operating concept [13]. This is due to the solidstator structure, which reduces the magnetic reluctance causedby air gaps between components. The design with optimalparameters also contributes to the better result.

8. Conclusion

This paper proposes the complete procedure for the design andoptimization of a multi-pole MR brake. First, the operatingconcept and material selection were introduced. Next, ananalytical model of the brake was built to understand thetheory of braking torque generation. Based on this model,magnetic circuit analysis was done to clarify the parametersthat affect the torque enhancement of the multi-pole MRbrake. Finally, the optimization problem to maximize thefield torque was solved by FEM using the SNLP optimizer.

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Smart Mater. Struct. 22 (2013) 065008 Y Shiao and Q-A Nguyen

Simulation results confirm that the new design is feasiblefor actual application. With its distinct operational conceptcompared to the conventional design, the multi-pole MR brakeperforms with significant advantages as follows:

• A unique solid structure that employs a multi-pole designto generate torque.• A lightweight rotor with a hollow structure was designed

and optimized.• The MR fluid chaining area was extended. Almost

all of the cylindrical surface of the rotor has beenorthogonally penetrated by magnetic flux lines, resultingin an enhancement of the brake torque.• Flexible options for torque enhancement by increasing

either the axial or the radial dimensions of the rotor.• Capability to produce a very large brake torque while

maintaining a compact design and a low input current.

Future work should focus on experiments and controlof a manufactured prototype. Other factors that need to beinvestigated include hysteresis effects, thermal characteristicsand cooling management. With its described performance,the multi-pole MR brake shows excellent promise for variousapplications.

Acknowledgment

This study has been sponsored by the National ScienceCouncil—Taiwan (NSC project no.: NSC 101-2221-E-027-033).

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