lampe actuator 2000 bremen p52

8/3/2019 Lampe Actuator 2000 Bremen p52

1/4

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D. Lampe, R. GrundmannDresden University of Technology, Dresden, Germany

Abstract:Magnetorheological fluids can change their state from solid to liquid and vice versa. Hence, MRF-clutches areable to transmit torque either in a slipping or in a rigid mode. The first part of this paper presents experimentalresults concerning the yielding and engaging process. A criterion which denotes the demarcation between solidand liquid mode was to be derived. Experimental data for T max-stat and T min-dyn were obtained as function of themagnetic field strength and it was shown that their values do not depend on the speed of change of the appliedtorque. From these results, values for the static and dynamic yield stresses were computed, confirming the as-sumption that the static yield stress is larger than the dynamic yield stress. The second part of this paper describesthe torsion response of a MRF-clutch resulting from varying torque under different magnetic fields. Investigatedquestions are: Can MRF in solid mode sustain a load without preceding creep? Is there a constant shear modulus?Does it depend on the magnetic field strength? Experiments showed a nonlinear behaviour and that a permanent

deformation of the MRF has to be taken into account after release of a load.

Introduction

Magnetorheological clutches are distinguished byvery good controllability of transmitted torque, veryshort reaction times and little wearout. The funda-mental advantage over traditional clutches consistsin their ability to process electric control informationdirectly, i.e. without any mechanical links. Next totheir practical advantages, a wealth of informationconcerning general properties of MRF can be ob-tained from experiments with MRF-clutches.

Transitional Behaviour of MRF

Till today only little is known about the transitionalbehaviour of MRF. Nevertheless, for various appli-cation it is vital to prevent a drop of transmittedtorque while transitioning from solid to slippingtransmission.The conducted experiments aim at measuring themaximum static torque Tmax-stat (the maximum inrigid mode transmittable torque) and the minimumdynamic torque Tmin-dyn (e.g. further reduction of torque below T

min-dynleads to engaging of the

clutch). These values are to be determined as func-tion of the magnetic flux density B within the MRF.From the measured torques the dynamic yd and thestatic ys yield stress of the MRF shall be computed.

Experimental SetupThe experiments where made with the MRF-clutchshown in Fig.1. The MRF 132 LD of LORD Corp.was used. The thickness of the gap filled with MRFwas 1,75 mm on both sides. A controlled torque of up to 100 Nm was provided by a servo motor of Baumller GmbH. Electric coil current and torque

were controlled via PC.

Gap filled with MRF

Coil

Magnetic field

Rotating disc

F i x e

d s i

d e

cL

1 3 0 m m

Fig. 1: MRF-clutch used for the experiments

The experimental setup permitted to record time,coil current, torque and torsion angle (angle the discwas distorded from zero angle position) at a rate of 50 Hz simultaniously. The torsion of the shaft asfunction of the torque was computed separately andsubtracted from the measured torsion angle in orderto get the angle just the MRF was distorded.The magnetic flux density B within the MRF wascomputed by means of the FEM-program OPERA asa function of the coil current. These computationsshowed that B is almost independent of the radiusand a mean value of B as function of the coil currentcan be assumed.

Experimental ProcedureThe torque applied to the clutch by the servomotor isvarying with time like the dashed line in Fig.2. Thereason for choosing this function is such that theclutch shall start to rotate upon exceeding a certainabsolute value of the torque (T max-stat ) and that it shallengage, e.g. stop rotation, upon falling the absolutevalue of the torque below T min-dyn . This procedure

was repeated several times to ensure stable condi-


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tions. The rotational angle during such an experi-ment is also shown in Fig.2. Large slopes of thecurve indicate rotation of the clutch whereas constantvalues show the clutch to be engaged (note 360 are1 revolution).

-100

-75

-50

-25

0

25

50

75

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65Time [s]

T o r q u e

[ N m

]

-3000

-2000

-1000

0

1000

2000

3000

4000

T o r s

i o n

A n g

l e [ ]

Torsion Angle

Torque

Fig. 2: Torque and torsion angle during experiments

Printing torque vs. torsion angle for a procedure as

shown in Fig.2 gives Fig.3.

-100-80-60-40-20

020406080

100

-3000 -2000 -1000 0 1000 2000 3000 4000Torsion angle [ ]

T o r q u e

[ N m

]

B =247 mT

Fig. 3: Torque vs. measured torsion angle for one experimental procedure

Because the rotational speed of the clutch varies withtime, acceleration torques have to be considered.They were computed by multiplying the known mo-ment of inertia of the disc and the shaft with theangular acceleration obtained from central differ-ences of torsion angle over time.In order to proof that the frequency of the appliedtorque has no influence on the values obtained forTmax-stat and T min-dyn a preceding experiment wasmade. In this experiment torque vs. torsion anglecurves of the kind shown in Fig.3 were recorded for

various frequencies of the applied torque. The coilcurrent was kept constant. The single loops of thecurves varied only very little, allowing to show justexcerpts for transition from solid to liquid mode andvice versa. Fig.4 shows such curves of torque overtorsion angle. The torsion angle were corrected suchthat the solid mode of the MRF is at an angle of 0and acceleration torques were eliminated.The good agreement of the curves for various fre-quencies of the torque in Fig.4 proof the frequencyto have no influence on T min-dyn and T max-stat .

Torsion Angle [ ]

0

5

1015

20

25

30

35

40

45

50

-10 -8 -6 -4 -2 0 2

T o r q u e

[ N m

]

0 2 4 6 8 10Torsion Angle []

0

5

1015

20

25

30

35

40

45

50

T o r q u e

[ N m

]

B = 173 mT

Frequency oftorque:

0.4 Hz0.2 Hz0.1 Hz0.05 Hz0.025 Hz

Transitionliquid to solid

Transitionsolid to liquid

Fig. 4: Torque vs. torsion angle

Yield CriterionIn order to obtain values for T min-dyn and T max-stat acriterion for the torsion angle denoting the yieldingof the MRF has to be defined. Simply spoken atwhich torsion angle occur just T min-dyn and T max-stat ?This derivation starts from the relation between shear

angle and shear force [1], assumes solid mode, andresults in an value for the angle of torsion G for theclutch as a whole. Increasing the torsion of the clutchabove G would result in a drop of torque transmitta-ble in solid mode, thus leading to a break of particlechains and transition to liquid mode.

F rH

b

Particle

i

Fig. 5: Restoring force F r induced by mag-netic field H (after [1])With: b - distance between particles

i - internal permeability of particles - permeability of suspension

[1] gives the following expression for F r :Fr = 3a2H22f (1)

with: - depending on and i

( )[ ] 32||4

sincossin22 +

= f f f ba

f

1|| === f f f (according to [1])a particle radius

For determining G not the absolute value of F r , butonly its dependency on is of interest. This leads to:

( )4

32 sincossin4~

K F r

(2)

with: K length of particle chain (distance b multi-plied by number of particles in a chain)

The following Fig.6 shows the relation between theshear angle and the torsion angle of the clutch.The torque transmitted by the MRF computes as:

=

outer

inner

R

R

r dr r F T ),()( (3)


3/4

S

K

r

Particles

Fig. 6: Relation between shear angle and thetorsion angle of the clutch

(only one gap filled with MRF shown)

From Fig.6 one can find for and K: 2222 sin ; sinarctan r SK

Sr +=

= (4)

Introducing equations (4) and (2) into equation (3),integrating from the inner to the outer radius of theclutch, using Simpsons rule, results in Fig.7. Nor-

malizing the maximum torque to 1 eliminates theneed for knowing absolute values of F r.

R-outer = 130 mmR-inner = 55 mmgap size S = 1,75 mm

0,0

0,2

0,4

0,6

0,8

1,0

0 0,5 1 1,5 2 2,5 3Torsion ang le []

N o r m a

l i z e

d t o r q u e

[ / ]

G

Fig. 7: Computed normalized torque vs. torsionangle of the clutch

Fig.7 proofes the torque transmitted in solid MRFmode to have a maximum value at a certain angleG . Exceeding this angle results in a decrease of transmittable torque, hence the MRF yields andchanges to liquid mode. From Fig.7 one can read:

G = 0.85

Experimental ResultsFrom Fig.8, showing experimental results obtainedfor various magnetic flux densities, one can read

Tmin-dyn and T max-stat (see Fig.9). These are the torquesoccuring at G.Using the equations for T min-dyn and T max-stat derivedin [2], the yield stresses of the MRF can be com-puted from the geometry of the clutch and the tor-ques shown in Fig.9. They are depicted in Fig.10.Comparing Fig.9 with Fig.10, it is remarkable, thatTmax-stat < T min-dyn despite ys > yd . This apparentlycontroverse observation is only possible because theradial shear stress distribution in solid state (linearlyincreasing with radius) is different from the distribu-tion in liquid state (constant over radius) (see [2]).This is surprising in the first view, but confirms thefollowing observation.

During further experiments a torque was applied tothe clutch by lever and weight. It was possible toapply such a load, depending on the coil current, thatthe clutch started to rotate in order to come to restafter a few degrees of rotation. This procedure wasself repeating until the lever had rotated far enough

to decrease the applied torque considerably. Thisphenomena of successive yielding and engaging canonly be explained by T max-stat to be smaller thanTmin-dyn , e.g. the clutch yields at T max-stat and becauseTmin-dyn is smaller, it comes to rest again.

0 1 2 3 4 5 6 7 8 9 10Torsion angle [ ]

0 1

B =37 mT

B =105 mT

B = 157 mT

B =205 mT

B =247 mT

B =37 mT

B =105 mT

B = 157 mT

B =205 mT

B =247 mT

Torsion angle [ ]

T o r q u e

[ N m

]

0

10

20

30

40

50

60

70

Transitionliquid to solid

Transitionsolid to liquid

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

G = 0,85

G = 0,85

Fig. 8: Torque vs. torsion angle for transition fromsolid to liquid and vice versa

0

10

20

30

40

50

60

70

0 50 100 150 200 250

B [mT]

T o r q u e

[ N m

]

T min-dynT max-stat

Fig. 9: Maximum static torque T max-stat and minimumdynamic torque T min-dyn vs. magnetic flux density

0

1

2

3

45

6

7

8

9

10

0 50 100 150 200 250

B [mT]

Y i e l d s t r e s s

[ k P a

]

y-dynamic

y-static

Fig. 10: Static and dynamic yield stresses of the MRF 132 LD vs. magnetic flux density

Using the data obtained for ys and yd (Fig.10) andthe torque equations in [2], it is now possible todesign a clutch with zero torque jump while transi-tioning between solid an liquid mode.


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Torsion Response of a MRF-Clutch

This part of the paper is dealing with the solid modeof MRF. Experiments were made also with the clutchshown in Fig.1, but now the applied torque did notexceed the magnitude necessary to make the clutch

yielding, e.g. the MRF was all the time in solidmode. The first question to be answered was: CanMRF in solid mode sustain a load without precedingcreep? Therefore a constant torque was applied tothe clutch over a period of 48 hours, keeping the coilcurrent constant. The torsion angle was recordedduring this period of time and results showed nomeasurable creep.For the next experiment, a sinusoidal torque asshown in the inner picture in Fig.11 was applied tothe clutch.

0 10 20 30 40 50 60 70 80 90Torque [Nm]

F r e s h c

u r v e

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

T o r s

i o n a n g

l e [ ]

many cycles agree very well

020406080

100

0 20 40 60Time [s]

T o r q u e

[ N m

]

B = 419 mT

Fig. 11: Torsion angle vs. torque for sinusoidaltorque of constant amplitude

From the curve shown in Fig.11, for other magneticflux densities analog curves were obtained, the fol-lowing conclusions have to be drawn:1. The maximum torsion angle caused by a timevarying torque as well as the remanence torsionangle remaining after reducing the torque to zerodepends only on the magnitude of the maximumtorque.2. Because on one hand the fresh curve is nonlinearand on the other hand always a remanence torsionexists, MRF in solid mode can not assumed to belinear elastic bodies.

In order to permit a quantitative statement about thedeformation of the clutch, a sinusoidal torque withvarying amplitude was applied to the clutch. Fig.12shows the result for such a procedure. It has to beinterpreted in such a way that the torsion angle wenttrough the loops in sequence of the numbers 1 to6. In Fig.13 and 14 the maximum torsion angle(points B in Fig.12) and the remanence torsionangle (points A in Fig.12) are drawn against themaximum torque reached before reducing the torque.From Fig.13 and Fig.14 one has to conclude that theremanence torsion angle as well as the maximumtorsion angle increase stronger than linearly withgetting closer to the yielding torque T max-stat . For in

relation to T max-stat small torques the remanence andthe maximum torsion angle become independent of the magnetic flux density.

0 10 20 30 40 50 60 70 80 90 100Torque [Nm]

B = 419 mT

0

0.2

0.4

0.6

0.8

1

1.2

T o r s

i o n a n g

l e [ ]

6

43

2 5

1

AB

020406080

100

0 20 40 60Time [s]

T o r q u e

[ N m

]

Fig. 12: Torsion angle vs. torque for sinusoidaltorque of increasing amplitude

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80 90 100Maximalum torque [Nm]

M a x i m a u m

t o r s

i o n a n g

l e [ ]

B = 220 mT 263 mT306 mT

346 mT 385 m T409 mT

434 mT505 mT

519 mT

Fig. 13: Maximum torsion angle vs. maximumtorque (according to point B in Fig.12)

0 10 20 30 40 50 60 70 80 90 100Maximum torque [Nm]

B = 220 mT 263 mT306 mT

346 mT

385 mT

409 mT434 mT505 mT519 mT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.80.9

1

R e m a n e n c e

t o r s

i o n a n g

l e [ ]

Fig. 14: Remanence torsion angle vs. maximumtorque (according to point A in Fig.12)

References

[1] Bossis, G., Yield stresses in magnetic suspen-sions, Journal of Rheology, vol. 35, iss. 7, 1991

[2] Lampe, D., MRF-Clutch- Design Considerationsand Performance, ACTUATOR 98, Bremen,1998

[3] Gromann, K.; Grundmann, R.; Neundorf, H.,Intelligente Funktionsmodule der Maschinen-technik, Schlussbericht zum Landesinnovations-kolleg 1995 bis 1998, Schriftenreihe desLehrstuhls fr Werkzeugmaschinen der Technis-

chen Universitt Dresden, 1999

lampe actuator 2000 bremen p52

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