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Article Type: Research Article

Authors: Olaru , R. | Petrescu , C. | Hertanu , R.

Affiliations: "Ghe. Asachi" Technical University of Iasi, Faculty of Electrical Engineering, 67 Prof.

Dimitrie Mangeron Street, 700050 Iasi, Romania

Abstract: The paper studies an actuator based on magnetofluidic forces acting on a non-magnetic disc

plunged into a ferrofluid that is exposed to a non-uniform magnetic field generated by magnetic

inductor(s). The input output equations (force – current and displacement – current) that describe the

behaviour of two types of actuators are established. The expression of the force generated on the

nonmagnetic disc is determined analytically for the particular conditions imposed by the two actuator

configurations: a) simple, with one magnetic inductor; b) differential, with two inductors. The derived

relations enable a comparative study of the two types of actuators. The results show the superior

performance of the differential actuator. The latter was tested as a current to displacement transducer in an

electropneumatic converter.

Keywords: Magnetic actuator ferrofluidic actuator magnetic force ferrofluid magnetic fluid

DOI: 10.3233/JAE-2010-1083

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 32, no. 4, pp. 267-274,

2010

30 April 2010

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Accepted 30 April 2010

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Published 2010

Magnetic actuator with ferrofluid and non-magnetic disc

R. Olaru1, C. Petrescu1, R. Hertanu1

1 Ghe. Asachi Technical University of Iasi, Faculty of Electrical Engineering, 67 Dimitrie

Mangeron Street, 700050 Iasi, Romania

Corresponding author : R. Olaru,

Phone : + (40) 232 27 86 83

Fax : +(40) 232 23 76 27

E-mail : rolaru@ee.tuiasi.ro

Abstract

The paper studies an actuator based on magnetofluidic forces acting on a non-magnetic disc

plunged into a ferrofluid, caused by the effect of a magnetic field gradient generated by

magnetic inductor(s). The behavior of the two types of actuators is described by the input –

output equations (force-current and displacement-current), established in this paper. The

expression of the force generated on the nonmagnetic disc is determined analytically for the

particular conditions imposed by the two actuator configurations: a) simple, with one

magnetic inductor; b) differential, with two inductors. The derived relations enable a

comparative study of the two types of actuators. The results show the superior performance of

the differential actuator. The latter was tested as current to displacement transducer into an

electropneumatic converter.

Key words: Magnetic actuator, Ferrofluidic actuator, Magnetic force, Ferrofluid, Magnetic

fluid.

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1. Introduction

Magnetic actuators have important advantages over conventional mechanical drives:

simplicity, flexibility and reliability. Most of the magnetic field driven actuators belong to the

electromagnetic, electrodynamic, magnetostrictive, magnetorheologic or ferrofluidic types.

While the first three mentioned categories have been known for a long time and are widely

used, the actuators of the latter two groups have been gaining importance only in the last few

years. Thus, the first notable researches about actuators based on ferrofluids have been

reported only ten years ago.

One principle used for generating mechanical actions with a ferrofluid, is the change in

position of a nonmagnetic body in a ferrofluid, due to the effect of levitation of non-magnetic

bodies in a ferrofluid exposed to a field gradient [1]. One application of the phenomenon of

levitation is its use in micro positioning systems [2]. In such systems levitation occurs due to

the combined action of an electromagnetically controlled field and gravity [3, 4].

In some of our papers a new type of actuator which generates mechanical actions due to

the magnetic forces exerted on a non-magnetic disc within the ferrofluid was described [5, 6].

The actuator can be simple (with one magnetic inductor) or differential (with two inductors).

In this paper an analytical method for the determination of the input-output

characteristic equations of the two actuators is presented. The differential actuator was

experimental investigated as current to displacement transducer into an electro pneumatic

converter.

2. Functional equations for the simple actuator (with one inductor)

The electromagnetic actuator is shown in Fig. 1. This simple one-directional actuator

consists of a chamber filled with ferrofluid, a magnetic field inductor and a lever used to

transmit the actuator active force. The lever is composed of a rod and a non-magnetic disc

attached to its bottom; the rod is tied to the actuator shell by means of an elastic membrane or

a goffered tube.

As shown in [7], the magnetic field in the ferrofluid may be considered to be linear,

according to the following relation:

0,0,10 xaxaHH (1)

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where 0H is the magnetic field in the ferrofluid, in the centre of the core base, and the

coefficient a is a dimensional constant [a]=mm-1. 0H has the expression

22

11

22

22

2

0

2

11

2

0

2

22

0

rF12

00 lnln)(2

N),(

lrr

lrrl

xrr

xrrx

rrL

iixH rM

, (2)

where L is the length of the coil having an interior magnetic core with the length L+l=

0x (Fig. 2), N is the number of coil turns, 1r and 2r are the minimum and maximum coil

radius, respectively, rM and rF are the relative permeability of the magnetic core and of the

ferrofluid, respectively.

With a dc field of moderate amplitude, the magnetization M is approximately a linear

function of the field H, M=χH, where χ is the magnetic susceptibility of the ferrofluid in weak

fields. Consequently, the repellent force, acting in the positive x direction on a disc with the

cross-section S, is [7]:

2

2

2

1

0)+(

)(0

2

S)d(

d2

d1

HHHxHSFdxH

xH

, (3)

where )(11 dxHH and )(22 dxHH d have the expressions given by (1).

After some algebraic calculus in Eq. (3), the expression of the simple actuator force

exerted on the magnetic disc in magnetic fields of moderate amplitude becomes [7]:

22

2

2

0)1(

)2/(1()( ikdxaSdaxF drMds

, (4)

where k is a constructive coefficient of the inductor, having the expression:

22

11

22

22

2

0

2

11

2

0

2

22

0

12

lnln)(2

N

lrr

lrrl

xrr

xrrx

rrLk

(5)

The displacement Δx obtained for a command current i has the expression [7]:

rrM

ds

kikSda

xFx

22

2

22

01

, (6)

where rk represents a constant of the equivalent elastic resistance force, depending on the

elastic moment of the lever articulation and on the weight of the lever-disc system.

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3. Establishing functional equations for the actuator with two inductors

In establishing the functional equations for the differential actuator, with two inductors,

(same as in Fig.1, but with a second identical inductor, placed symmetrically on the right

side), the linearised field curves in Fig. 3 are considered.

The current, i, in the left and right magnetic field inductors, has directions so as to

create magnetic fields in opposite directions on the Ox axis, lH and Hr , respectively, with

expressions exhibiting the linear dependence on the variable x:

),( ixH l =k’ i(1-ax) (7)

),( ixH r = -k’ i[1-a( mx -x)] (8)

In relation (8) mx = dxd 2 is the distance between the two magnetic cores and the constant

'k has the expression:

kkrF

rM

' (9)

The resulting magnetic field in a point x on the inductors axis is the sum of the

expressions (7) and (8):

ixxakixH ms )2('),( (10)

For current variations in opposite directions in the two coils, ±Δi, the magnetic fields in

a neighbouring point, x+x, have the expressions determined with the help of eqs. (7) and (8):

),( iixxH l = k’(i+i) [1-a(x+x)] (11)

),( iixxH r = - k’ (i-Δi) [1-a( mx -x-x)]. (12)

Using expression (13) of the resulting field

mms axixxxaikiixxH 22'),( (13)

the magnetic field intensity in the vicinity of the two disc faces, in the points dx and dxd ,

is determined:

iaxixdakiixxH mds 22'),(1 (14)

iaxixdakiixdxH mds 22'),(2 . (15)

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Introducing (14) and (15) in (3), the general equation of the force exerted by the

differential actuator, by means of the non-magnetic disc situated at a distance dx +x from the

left inductor, obtained for a constant premagnetization current 0i , is:

0

2

20

2

0)1(2

14 ikix

axiaSdaF m

rMd

(16)

In the particular case x=0 the force exerted upon the disc actuator, in the initial,

symmetric position, is:

iikx

aSdaxF m

rMdd

0

2

2

2

0)1(2

14)( (17)

The force given by eqn. (17) is in fact the magnetofluidic force exerted on the disc in

the moment immediately following the action of the initial force and producing a

displacement x, until it is balanced by a resistant, elastic force, characterized by the constant

rk . The expression of the disc displacement in the case of the differential actuator is:

rrM

dd

kikSda

xFx

2

0

2

2

22

01

4

(18)

4. Experimental results

A ferrofluid differential actuator for electropneumatic converters, as shown in Fig. 4,

includes a cilindrical recipient filled with ferrofluid, two magnetic cores, two coils, driving

rod, lower diving disc, upper driving disc, goffered membrane and foot plate.

To begin with the driving rod has been non-elastic suspended by a rotational axle and it

determinate the force moment in the equilibrium position (Fig. 5), with and without pre-

magnetising of the cores with permanent magnets placed on the external edges of its.

Figure 6 shows the displacement versus differential current characteristic of the actuator from

Figure 4, but having pre-magnetizing magnets. The hysteresis is the effect of the viscous

forces into ferrofluid.

The experimental set-up scheme shown in Figure 7 includes the differential actuator

with pre-magnetising magnets, pneumatic amplifier of a flapper-nozzle type and power

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pneumatic amplifier. The dependence of power amplifier output pressure on the actuator

command current is illustrated in Figure 8, for two polarisation currents 0I .

5. Conclusions

The behavior of a magnetic actuator with a non-magnetic disc immersed in the

ferrofluid was analyzed by means of the analytical expressions established for the force and

disc displacement in two cases: simple (with one inductor) and differential (with two

inductors). The relations obtained indicate the factors that influence the actuator performance.

The analysis of the current-force functional equations for the two actuators shows that

the force transfer factor of the differential actuator is twice the one of the simple actuator and

is constant for command current variations. Some more observations can be made:

both the force-current equations, (4), (17), and the displacement-current relations, (6),

(18), display the same structural forms for the two actuators, only the current

dependence is different : in the case of the simple actuator the dependence of the

command current is quadratic, while in the case of the differential actuator the output

characteristic depends linearly on the command current; in the latter case a

premagnetization current can be used;

the previous considerations lead to the conclusion that the differential actuator has a

linear characteristic and presents the advantage of a bidirectional displacement.

Expressions (4), (6), (17) and (18) are useful in the analysis and design of such a

ferrofluid actuator and form the basis for the analysis of other ferrofluid devices based on the

levitation of non-magnetic bodies.

Trough the comparison study between the theoretical analyses and the experimental

results, the applicability of the proposed ferrofluid actuator to an electro pneumatic converter

was verified.

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References

[1] R. Olaru, Actuators based on ferrofluids, Buletin I.P.Iaşi., Tomul LII (LVI), Fasc. 5C,

Sectia Electrotehnica, Energetica, Electronica (2006), 1083-1088.

[2] S. Odenbach, Ferofluids, in: Handbook of Magnetic Materials, Vol. 16, edited by K. H.

J. Buschow, Elsevier B.V., 2006, pp. 156.

[3] E. Uhlmann, N. Bayat, Positioning systems with magnetic fluids, ZWF Zeitschrift fur

Wirtschaftlichen Fabrikbetrieb, 100, 10 (2005), 573-576, in German.

[4] E. Uhlmann, N. Bayat, High precision positioning with ferrofluids, CIRP Annals –

Manufacturing Technology, 55, 1 (2006), 415-418.

[5] Camelia Petrescu, R. Olaru, Numerical determination of magnetic forces in ferrofluids,

Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 44, 2 (1999), 135–141.

[6] R. Olaru, A. Sălceanu, D. Călăraşu, C Cotae, Magnetic Fluid Actuator, Sensors and

Actuators A Physical, 81 (2000), 290-293. [7] R. Olaru, Camelia Petrescu, Simplified approach for calculating the force of a

ferrofluidic actuator, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 53, 4 (2008),

435-443.

Figure captions

Figure 1, Ferrofluid actuator with one magnetic inductor.

Figure 2, Magnetic inductor and disc positioning.

Figure 3, Linearizing curves of magnetic field.

Figure 4, Schematic configuration of the ferrofluid differential actuator.

Figure 5, Force moment vs. differential current: without ( 0I =100 mA-bottom in first

dial and 0I = 120 mA-midle) and with premagnetizing ( 0I =100 mA-up).

Figure 6, Displacement vs. differential current for the differential actuator having

premagnetizing magnets ( 0I =100 mA).

Figure 7, Scheme of experimental set-up for a current to pressure converter with

ferrofluidic actuator.

Figure 8, Output pressure vs. command current of the actuator: 0I = 50 mA (left curve)

and 0I = 90 mA.

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Figure 3

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Figure 4

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Figure 5

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1

-500

-400

-300

-200

-100

0

100

200

300

400

500

-300 -200 -100 0 100 200 300

Differential current (mA)

Dis

pla

ce

me

nt

[x1

0 e

xp

-6]

(m)

Figure 6

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Figure 7

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Figure 8

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