Sensors and Actuators A 92 (2001) 318±325
Magnetorheologic ¯uids for actuators L. Zipser*, L. Richter, U. Lange HTW, University of Applied Sciences Dresden, Friedrich-List-Platz 1, D-01069 Dresden, Germany Accepted 28 December 2000
Abstract Magnetorheologic ¯uids (MRF) are suspensions consisting of a synthetic oil and very small soft-magnetic particles. In a magnetic ®eld, the particles are locked to long chains. In consequence of it, the viscosity and the ¯ow behaviour of the ¯uid are considerably changed. This reversible effect can be used in actuators, especially for controlled damping of shocks and vibrations, or in ¯uid devices for the electromagnetical in¯uencing of ¯ows. The paper describes the ¯ow behaviour of magnetorheologic ¯uids in narrow channels, in¯uenced by variable magnetic ®elds and temperature. Furthermore, possibilities and limits of applying magnetorheologic ¯uids in smart actuators are discussed. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetorheologic ¯uids; Smart actuators; Controlled dampers
1. Flow behaviour of magnetorheologic fluids Magnetorheologic ¯uids are suspensions of soft-magnetic particles of about 1±5 mm diameter in special oils [1]. The particles are covered with a thin non-magnetic ®lm which prevents agglomeration. The weight percentage of the particles in the suspension is about 80% at a total density of 3 g/cm3. An REM view of the particles is shown in Fig. 1. Without magnetic ®eld, the particles are statistically distributed. Under the in¯uence of a magnetic ®eld, the particles line up to chains. This behaviour is the ``magnetorheologic effect''. If an external force or pressure is applied, the chains are deformed according to Fig. 2. In the shear mode (a), the chains resist the displacement of the bordering plates. In the ¯ow mode (b), the chains are deformed and resist the applied pressure. In the squeeze mode (c), the chains prevent the draining off of the ¯uid. Most interesting fact of actuator applications is the ¯ow mode. In this case, under the in¯uence of a magnetic ®eld, the magnetorheologic ¯uid changes its ¯ow behaviour from Newtonian to Bingham characteristics. The Bingham ¯ow is described by [2] t
B; g_ ; Z tf
B ZB g_
(1)
with shearing stress t, magnetic flux density B, Bingham *
Corresponding author. Tel.: 49-351-462-2743; fax: 49-351-462-2193. E-mail address:
[email protected] (L. Zipser).
viscosity ZB and shearing rate g_ . A graphic presentation of (1) is given in Fig. 3. Without magnetic field, (i.e. B 0), the magnetorheologic fluid (MRF) is a conventional Newtonian fluid. For B > 0, the MRF is a Bingham ¯uid, with the result that a shearing stress t emerges. For values t < tf , the MRF behaves like a solid (area 1 in Fig. 4). Only at higher shearing stress t > tf , the MRF behaves like a ¯uid (area 2 in Fig. 4). This interesting viscoelastic behaviour can be used in actuators for the controlled damping of moving parts or for the control of ¯uid ¯ows in narrow channels. 2. Set-up for experimental investigation of MRF In the described experiments, the commercially available MRF type 132 LD from the LORD Corp., Cary, NC, USA was investigated. Other MRFs show a qualitatively similar behaviour. For a precise determination of the static rheologic parameters t, Z, and g_ of MRFs, an experimental apparatus was arranged (Fig. 5). The MRF is pressed through a narrow rectangular channel of 10 mm width, 120 mm length and variable height of 0.5, 1, or 2 mm. The active area AB, where the magnetic ®eld has an in¯uence on the streaming MRF is only 10 mm long. In the measurements, pressure difference Dp p1 p2 was measured with small sensors, arranged 30 mm before and behind the active area. The magnetic ¯ux density B was measured with a very small Hall sensor and
0924-4247/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 5 9 0 - 8
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Fig. 1. REM-view of the ferromagnetic particles of magnetorheologic fluids.
Fig. 2. Stress modes of magnetorheologic fluids. Fig. 4. Distributions of pressure p(y), shearing stress t(y), flow velocity v
y across a channel.
Fig. 3. Graphic presentation of the Bingham Eq. (1).
Fig. 5. Schematic experimental set-up.
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Fig. 6. Shift s(t) and pressures Dp2(t) and Dp1(t) for one measuring cycle.
the temperature W with Pt 100 elements. During one measurement cycle, the streaming MRF in the measuring channel is exposed to a magnetic ®eld of constant ¯ux density B in a de®ned active region AB. In this way, the ¯uid resistance and, in consequence, the pressure difference Dp p2 p1 across the region AB rises signi®cantly as a result of the magnetorheological effect. Before starting a measurement, the MRF element, the hydraulic pipes and cylinders are tempered to an equal temperature in a climatic chamber. Moreover, to avoid possible sedimentation, the MRF is repeatedly pressed through the measuring element. Fig. 6 shows the lapse of one measuring cycle for piston shift s(t) and measured pressures Dp2(t) and Dp1(t). The time variations of s(t), p1(t) and p2(t) are nearly constant within one measurement. Because of the unavoidable clearance of about 30 mm, the piston shift s(t) is not uniform at about t 1:3 s. This appears as a short-time decrease of the rise in the distance±time lapse. Only after that the piston of the hydraulic cylinder, and consequently, the MRF in the narrow channel are set in uniform motion. For the extraction of measuring values with the aid of evaluating programs, only this uniform part of the distance±time lapse is used. For constructive reasons, the measuring points for pressures p1 and p2 must be arranged in a certain distance from the active area AB (see Fig. 5). The resultant total pressure error D(Dp)) is corrected by a linear interpolation. Not until the measuring cycle of t 5:5 s is
®nished, the magnetic ®eld is switched off. Therefore, a pressure difference Dp 10 bar remains for t > 5:5 s. 3. Measuring results As examples, two sets of measuring results at the temperatures 20 and 808C are shown in Figs. 7 and 8. The dispersion of the measured values is probably due to local temperature effects resulting from the transformation of mechanical into thermal energy [3]. Such temperature effects have to be considered in designing magnetorheologic actuators. For small ¯ux densities B 3 mT, the MRF has to be considered as demagnetised and behaves like a Newtonian ¯uid. Stronger magnetic ®elds with B > 3 mT cause a shift of the Dp/V_ characteristic along the ordinate. For applications in actuators and dampers, the ¯ow resistance RMRF of an MRF-®lled channel in a magnetic ®eld is of interest. The measured characteristics in Figs. 7 and 8 represent the resistivity pro®le of such a resistor RMRF. At very high ¯ow velocities v of the MRF, the magnetorheologic effect could probably be reduced because there is not enough time for the formation of particle chains. In the actual experiments maximal velocities of v 7 m/s were reached. This corresponds to a dwell time as short as 1.5 ms in the active region AB. Despite this short time, the magnetorheologic effect becomes effective. Assumedly, such short dwell times are suf®cient in most actuator applications.
L. Zipser et al. / Sensors and Actuators A 92 (2001) 318±325
_ for the MRF at temperature W 208C and channel height h 1 mm. Fig. 7. Measured characteristics Dp Dp
V
_ for the MRF at temperature W 808C and channel height h 1 mm. Fig. 8. Measured characteristics Dp Dp
V
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Figs. 7 and 8 con®rm that the MRF under the in¯uence of a magnetic ®eld begins to ¯ow only if a minimal pressure difference Dpf is exceeded. This pressure difference is the yield point tf(B). 4. Characteristics of magnetorheologic fluids According to [4], under technically reasonable conditions, with the shearing stress g_
y
dv
y dy
(2)
from (1) follows the v-profile in area 2 of Fig. 4. Dp 2 tf h Dp h y v
t y tf : 2ZB l 2ZB 4l ZB
(3)
The maximum shearing stress before the MRF begins to flow, is the observed yield point tf
B
Dpf
B h : l 2
(4)
From the measured pressure difference Dp, volume flow V_ and the geometric parameters l, b, h of the channel, the resulting Bingham viscosity bh3 Dp3f ZB 2Dp 3Dpf 2 (5) _ Dp 24Vl
can be calculated. Finally, the shearing rate 1 Dp Dpf h y g_
y ZB l l 2
(6)
can be determined in an analogue way. Using Eqs. (3)±(6), from the measured values, the Bingham functions of the investigated MRF can be calculated. For the results of Figs. 7 and 8, the plots of the Bingham functions are shown in Fig. 9. For a flux density B > 0, a linear approximation of the Bingham function is permitted t
B; g_ tf
B ZB g_ a b_g
(7)
with the regression coefficients a and b, which depend on the flux density B. 4.1. Temperature dependence of MRF A comparison of Figs. 7 and 8 shows that the properties of MRFs strongly depend on the temperature T. For investigating the temperature dependence of the yield point tf(B), the different regression coef®cients a(B, T) in (7) are plotted in Fig. 10 as functions of the absolute temperature T. Flux density B is a parameter. The yield point tf(B) decreases proportionally to the absolute temperature T in the investigated interval of the ¯ux density B. This correlation can be described by a regression line tf
B cB dBT with coefficients c 145 N/V s and d
Fig. 9. Approximated Bingham functions of the MRF.
(8) 30:4 N/V s K.
L. Zipser et al. / Sensors and Actuators A 92 (2001) 318±325
Fig. 10. Yield point tf(B) in dependence of absolute temperature T for MRF.
Fig. 11. Newtonian viscosity ZN of the MRF.
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Fig. 12. Prototype of a miniaturised MRF-damper.
An MRF without magnetic ®eld behaves like an ordinary Newtonian ¯uid. Its temperature dependence can be described by the Vogel equation [1] (see Fig. 11). For designing magnetorheologic actuators the strong temperature dependence of the viscosity h, especially at low temperatures, has to be considered. 5. Design of magnetorheologic dampers For the design and experimental investigation of miniaturised magnetorheologically controlled dampers, a proto-
type according to Fig. 12 was used. A small cylinder, ®lled with an MRF, is covered with rubber membranes on both sides. The cylinder is divided into two equal parts by a brass disk with a central hole of 1 mm diameter. The two rodshaped poles of the electromagnet reach up to the inner hole. If a mechanical force is applied to one of the membranes, the MRF ¯ows through the hole and can be in¯uenced by an applied magnetic ®eld. This ®eld is produced by an electromagnet, consisting of two coils with 1200 windings each. This ®eld increases the ¯uid resistance RMRF of the hole, reducing the ¯uid ¯ow and damping the velocity v
s of the external mass. Fig. 13 shows the damping characteristics s s
t of the miniaturised MRF-damper for different small supply currents i 0 to i 50 mA. The external gravitation force of the mass is 3.2 N. Obviously, already with small control energy, it is possible to in¯uence signi®cantly the viscosity Z of the MRF and, in consequence, the damping characteristic of the damper. For small forces F < 2 N and currents i > 20 mA a hysteresis can be observed, i.e. the full elongation s 0:4 mm will not be reached. This shows limits in the application of magnetorheologic ¯uids for miniaturised dampers. 6. Conclusions Magnetorheologic ¯uids change their viscosity and, in consequence, their ¯uidic resistivity by more than one order of magnitude under the in¯uence of an applied magnetic ®eld. This opens a wide area of applications in controlled actuators, ¯uid devices and especially in miniaturised
Fig. 13. Damping characteristic of the miniaturised MRF-damper for F 3:2 N.
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dampers. Corresponding experiments of the authors show encouraging results. References [1] W. Kordonsky, Elements and devices based on magneto-rheological effect, J. Intelligent Mater. Syst. Structures 4 (1) (1993) 65±69. [2] W.M. Kulicke, Flieûverhalten von Stoffen und Stoffgemischen, HuÈthig±Verlag, Basel, 1998. [3] L. Richter, U. Lange, L. Zipser, Zur Ermittlung des Temperaturverhaltens magnetorheologischer Fluide, Wiss. Zeitschr. HTW Dresden 8 (1) (2000) 70±78. [4] U. Lange, L. Richter, L. Zipser, Zum StroÈmungsverhalten magnetorheologischer Fluide, Wiss. Zeitschr. HTW Dresden 8 (1) (2000) 79±82.
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Biographies Lothar Zipser studied Elekrotechnics at the Technical University Dresden. He received his PhD degree in information theory in 1976 and his Habilitation in fluid acoustics in 1986. Since 1993 he has been working as a professor at the HTW University of Applied Sciences in Dresden, where he heads a research group in the field of measurement technique. Lutz Richter studied automatic control engineering at the HTW University of Applied Sciences, Dresden. Since 1997 he has been involved in a project concerning industrial application of magnetorheologic fluids. Ulrich Lange studied automatic control engineering at the Technical University Hamburg Harburg. Since 1997 he has been involved in a project concerning industrial application of magnetorheologic fluids.