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MRE properties under shear and squeeze modes and applications MRE properties under shear and squeeze modes and applications
Kristin Popp
Institute of Machine Elements, Design and Production
Matthias Kroger
Institute of Machine Elements, Design and Production
Weihua Li
University of Wollongong
, weihuali@uow.edu.au
Xianzhou Zhang
University of Wollongong
, xianzhou@uow.edu.au
Prabuono B. Kosasih
University of Wollongong
, buyung@uow.edu.au
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Recommended Citation Recommended Citation
Popp, Kristin; Kroger, Matthias; Li, Weihua; Zhang, Xianzhou; and Kosasih, Prabuono B.: MRE properties
under shear and squeeze modes and applications 2009, 1-4.
https://ro.uow.edu.au/engpapers/4155
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MRE Properties under Shear and Squeeze
Modes and Applications
KRISTIN M. POPP,
1
MATTHIAS KRO
¨
GER,
1
WEIHUA LI,
2,
*XIANZHOU ZHANG
2
AND PRABUONO B. KOSASIH
2
1
TU Bergakademie Freiberg, Institute of Machine Elements, Design and Production, Agricolastrasse 1, 09596 Freiberg, Germany
2
University of Wollongong, School of Mechanical, Materials & Mechatronic Engineering, NSW 2522, Australia
ABSTRACT: Magnetorheological elastomers (MREs) are smart materials whose mechanical
properties, like their modulus and elasticity, can be controlled by an external magnetic
field. This feature has resulted in a number of novel applications, such as adaptive
tuned dynamic vibration absorbers for suppressing unwanted vibrations over a wide frequency
range. MRE-based devices operate in different modes, such as shear mode and squeeze
mode; however, the study of mechanical performances of MREs under squeeze mode is
very rare. This article aims to investigate MRE performances under both shear and
squeeze modes. Experimental studies and simulations were conducted to analyze the MR
effect in both modes. These studies indicate a different working frequency ranges for both
modes. In a case study, a MRE-based vibration absorber was built up in a simulation and
its mechanical performances were analyzed, which demonstrated good capabilities in
reducing vibrations.
Key Words: magnetorheological elastomers, shear and squeeze mode, adaptive tuned
dynamic vibration absorber.
INTRODUCTION
M
AGNETORHEOLOGICAL elastomers (MREs) are
composite materials of a rubber-like base,
micron-sized magnetizable particles, and additives
(Carlson and Jolly, 2000; Bellan and Bossis, 2002;
Lokander and Stenberg 2003; Chen et al., 2007;
Stepanov et al., 2007; Zhang et al., 2008). When individ-
ual particles are exposed to an applied magnetic field,
magnetic dipole moments pointing along the magnetic
field are induced in the particles. Pairs of particles then
form head-to-tail chains. After the matrix is cured, the
particles are locked into place and the chains are firmly
embedded in the matrix. The elastic modulus of MREs
increases steadily as the magnetic field increases. By
removing the magnetic field, MR elastomers immedi-
ately reverse to their initial status. A few groups made
use of such materials to develop novel adaptive tuned
dynamic vibration absorbers, as such MRE-based vibra-
tion absorbers are expected to have many advantages:
very fast response (less than a few milliseconds), simple
structure, easy implementation, good maintenance, high
stability, and effective control. Ginder et al. (2002) did a
pioneer work that utilized MREs as variable-spring-rate
elements to develop an adaptive tuned dynamic
vibration absorber (ADTVA). Their results indicated
that a natural frequency ranged from 580 to 710 Hz at
a magnetic field 0.56 T. However, the natural frequency
varying was only 22% from its center frequency. Deng et
al. (2006) developed MRE ATDVA whose natural fre-
quency can be tuned from 55 to 82 Hz. Its absorption
capacity was also experimentally justified. Similar MRE
vibration absorber was developed by Zhang and Li
(2009). Experimental results indicated that the absorber
can change its natural frequency from 35 to 90 Hz,
150% of its basic natural frequency. It is noted that
the abovementioned MRE dynamic vibration absorbers
do not have wide enough tuning frequency ranges. The
reason for this could be because the MRE materials
operate in a simple shear mode. In MR fluid research,
a few groups (Zhang et al., 2004; Tang et al., 2006; Li
and Zhang, 2008) demonstrated that MR fluid working
in a squeeze mode would greatly enhance their MR
effects. In this study, we would extend this idea to the
MR elastomer research. In other words, this study aims
to investigate the MR effect under squeeze mode and
compare it with that of shear mode. MRE samples
with different compositions were fabricated and tested
on a home-made test rig. The mechanical performances
under both shear mode and squeeze mode were used to
verify simulation analyses based on a one degree of free-
dom model. This study is expected to provide good guid-
ance to develop high-efficiency MRE-based devices.
*Author to whom correspondence should be addressed.
E-mail: weihuali@uow.edu.au
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 21—October 2010 1471
1045-389X/10/15 14717 $10.00/0 DOI: 10.1177/1045389X09355666
ß The Author(s), 2010. Reprints and permissions:
http://www.sagepub.co.uk/journalsPermissions.nav
FABRICATION AND CHARACTERIZATION OF
MR ELASTOMERS
Fabrication of MRE Samples
In this study, four MRE samples with different com-
positions were manufactured. Five components, includ-
ing two types of silicon rubber, a silicon oil, a curing
agent, and two types of iron particles, were used to fab-
ricate these MRE samples. The mass fractions are listed
in Table 1. The silicon rubber, PDMS 2025 (Dow
Corning Corporation, USA), was used for MRE 1 and
MRE 2, while a room temperature vulcanizing silicon
sealant (PERFIX, Selleys Pty Ltd, Australia) was used
for fabrication of MRE 3 and MRE 4. A silicon oil DC
200/200cs (Dow Corning Corporation, USA) was mixed
within the sample to change the ductility of the rubber
base. To this base two grades of iron powder were
added, one with 5 mm sized particles (Sigma-Aldrich
Chemie GmbH, Germany) and one with 100 mm
(M93-000-31 F14 Neosid Australia Pty Limited).
The mixture was filled in a mold and placed in a
strong magnetic field of 1 T generated by an electromag-
netism system (Peking EXCEEDLAN Inc., China). Ten
minutes later, the magnetic field was reduced to 0.5 T so
that the samples were cured for seven more hours. After
24 h the mixture was removed from the mold. Samples
with a diameter of 20 mm and a thickness of 6 mm were
cut out. With these, MRE tests were curried out and the
relative magnetorheological effects as well as the reso-
nance frequency were measured.
Experimental Characterization of MRE Performances
The experiments were conducted on a test rig with
two different setups, as shown in Figure 1(a) and (b),
where MREs work in squeeze mode and shear mode,
respectively.
The test rig was built up as a one degree of freedom
system with a mass, connected to the base via two pieces
of MREs, and moves independently to the base. In
squeeze mode, the MREs and mass were directly fixed
on the base by a double-sided adhesive tape. In shear
mode the mass was fixed by contact forces of two cylin-
ders which were tightened on the base. On the base two
coils were wound to generate a magnetic field which was
adjusted by a GW laboratory DC power supply (Type:
GPR-3030D, TECPEL CO., Ltd. Taiwan). The mag-
netic field strength up to 150 ± 17 mT can be obtained
when the coil current is 3 A. The base was forced to
vibrate by a vibration exciter (Type: JZK-5, Sinocera
Piezotronics, Inc. China), which was driven by a signal
source from a power amplifier (YE5871-100 W) and a
Data Acquisition (DAQ) board (Type: LabVIEW
PCI-6221, National Instruments Corporation. USA).
During the experiments a frequency range from 35 to
90 Hz was obtained, as shown in Figure 1(c).
Two acceleration sensors (Type: CA-YD-106) were
placed on the upper surface of the mass and the base
to measure the amplitude and the phase angle between
both parts. The tramsmissivity amplitude responses
of the tested MRE with variable magnetic field intensi-
ties are shown in Figure 1(c). The resonance frequency of
the mass was located at the maximal amplitude of the
oscillation and the relative MR effect was calculated by
the increase of the frequency at different magnetic field
strengths. The results of preliminary tests of the four
manufactured MREs in shear mode are listed in Table 2.
It can be seen from Table 2 that the resonance fre-
quencies increase steadily with the increment of mag-
netic field, which demonstrated the MR effects. It is
also noted that the relative MR effects for these four
MRE samples are very different. The MR effects of
samples 1 and 2 have a lower level, while samples 3
and 4 show a higher change in frequency. For example,
the MR effect of sample 4 is more than 15 times higher
than of sample 1. The major composition difference
between sample 1 and 2 against sample 3 and 4 is the
particle size. As shown in Table 1, for samples 1 and 2
the mixture with particles of 5 and 100 mm were used
while for samples 3 and 4 only particles of 5 mm were
added. Besides, the components used for the rubber
base, comparing MRE 1 and 2 against MRE 3 and 4,
also have an influence of the MR effect.
Similarly, the MRE performances under squeeze mode
were experimentally evaluated. For the MRE sample 3,
the performance comparison between shear mode and
squeeze mode is shown in Table 3. In addition, the com-
parison between experimental results and modeling pre-
dictions, which will be detailed in the section
‘Comparison between Theoretical Analysis and
Experimental Results’, are also listed in this table. As
can be found from this table, the overall difference
between the experimental results and modeling predic-
tions is about 12%. Further inspection of the two cases
of minimum and maximum magnetic fields indicates that
the difference is much small. For example, the natural
frequency at 0 mT has about 4% difference (2526 Hz)
while at 108 mT has less than 2% difference (5253 Hz).
The tests using MRE 3 in shear and squeeze
mode show different MR effects and a different
Table 1. Component weight ratio of manufactured
MREs.
MRE 1 MRE 2 MRE 3 MRE 4
Silicon rubber 20 wt% 16 wt%
Silicon sealant 20 wt% 24 wt%
Silicon oil 20 wt% 24 wt% 20 wt% 16 wt%
Iron particle (5 mm) 20 wt% 20 wt% 60 wt% 60 wt%
Iron particle (100 mm) 40 wt% 40 wt%
1472 K. M. POPP ET AL.
working frequency range. The initial resonance fre-
quency in squeeze mode without an applied magnetic
field is almost twice as high as in shear mode. Also the
absolute changing frequency increment is higher in
squeeze mode with 37 Hz than in shear mode with
28 Hz. This indicates that the MR effect is dependent
on the working mode of the MRE, which should be
considered in developing MRE-based devices.
Characterization of Material Properties using MR
Rheometer
The rheomoter Physica MCR301 (MEP instruments,
Anton Paar Germany GmbH), as shown in Figure 2,
with a parallel-plate configuration was used to measure
material properties of MR elastomers. The MRE sam-
ples were cut into standard ones with a diameter of
20 mm and a thickness of 1 mm. Each sample
was placed in between the plates, and the squeeze
force, ranging from 5 to 15 N, were placed to the
sample through the upper plate. After which, oscillatory
shear was applied to obtain dynamic performances of
the samples. In these tests, five strain amplitudes,
0.1%, 1%, 5%, 10%, and 15%, were selected to mea-
sure viscoelastic properties of these samples under vari-
ous magnetic fields.
Viscoelastic properties of MR materials are generally
characterized by using the amplitude sweep mode and/or
Sensor
Mass
MRE
Coil
Base
Shaker
(a) (b) (c)
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
050
T
f
0
100
Frequency (Hz)
150 200
0 kA/m
50 kA/m
100 kA/m
150 kA/m
200 kA/m
250 kA/m
300 kA/m
Transmissibility
Figure 1. Experimental setup for measurements in (a) squeeze mode, (b) shear mode, and (c) recorded frequency responses.
Table 2. Measured resonance frequency f
0
, amplitude T and MR effect for MREs in shear mode.
MRE 1 MRE 2 MRE 3 MRE 4
Current (A) B (mT) T
max
f
0
(Hz) B (mT) T
max
f
0
(Hz) B (mT) T
max
f
0
(Hz) B (mT) T
max
f
0
(Hz)
0 0 3.31 65 0 2.89 36 0 2.53 25 0 2.40 26
0.76 45 3.70 66 42 2.96 38 46 2.43 26 51 2.29 32
1.5 81 3.97 67 73 3.17 41 90 2.36 35 91 2.35 40
2.26 113 3.94 72 111 3.08 43 136 2.52 46 131 2.57 52
3 132 4.39 71 143 3.21 43 156 2.69 53 167 2.72 64
Increase 9.2% 19.4% 112.0% 146.2%
Table 3. Comparison of test data and calculated results for MREs in squeeze and shear mode.
Measurement Calculation
Squeeze mode Shear mode Squeeze mode Shear mode
Current
(A) B (mT) f
0
(Hz) T
max
B (mT) f
0
(Hz) T
max
f
0
(Hz) G
0
(f
0
) (Pa) T
max
f
0
(Hz) G
0
(f
0
) (Pa) T
max
Shear
strain (%)
0 0 48 2.68 0 25 2.53 47 60.1e3 2.13 26 56.3e3 2.31 10
0.76 46 53 2.77 32 26 2.43 50 66.1e3 2.10 27 61.8e3 2.27 10
1.5 90 63 3.26 49 35 2.36 60 95.7e3 2.27 34 90.2e3 2.49 5
2.26 136 76 3.66 76 46 2.52 73 143e3 2.50 41 136e3 2.71 2
3 155 85 3.66 108 53 2.69 83 186e3 2.52 52 216e3 3.04 0.1
37 Hz 28 Hz 36 Hz 26 Hz
Increase 77.1% 112.0% 76.6% 100.0%
MRE Properties under Shear and Squeeze Modes and Applications 1473
frequency sweep mode (Li et al., 1999). In this study, the
frequency sweep mode was used to study the effect of
strain amplitude and magnetic field on the viscoelastic
properties of MRE samples. At a constant magnetic
field of 409 mT, the storage modulus versus frequency
at various strain amplitudes was shown in Figure 3.
As can be seen from this figure, the storage modulus
initially shows an increasing trend over frequency up to a
maximum value. Then it decreases slightly with further
increasing frequency. Also, the storage modulus decreases
steadily with the increment of the strain amplitude. The
effect of magnetic field was measured and shown in
Figure 4. As common, the storage modulus increases
steadily with the increment of the magnetic field, which
demonstrates the MR effect. Again, there is an optimal fre-
quency, in which MRE has the highest storage modulus.
Besides, the frequency dependence of loss factor under
various strain amplitudes and magnetic fields are shown
in Figures 5 and 6, respectively. The results indicate that
the loss factor is indeed amplitude dependent. For strain
amplitudes less than 1%, the loss factor lies between 0.2
and 0.4, which agrees well with reports (Demchuk, 2002;
Kallio, 2005). However, for high strain ampltidue the
loss factor values can be up to 0.9, which demonstrates
that MRE have non-linear viscoelastic properties. This
behavior was also detected at MR fluids (Li et al., 2003)
and will be considered in future studies.
COMPARISON BETWEEN THEORETICAL
ANALYSIS AND EXPERIMENTAL RESULTS
Modeling Analysis
The model, to describe the elastomers mathematically,
is a one degree of freedom system as shown in Figure 7.
Here, k* is the complex stiffness of MR elastomers and
m is the weight of the mass. The weights of the MREs
are neglected.
The equation of motion of this system is defined by:
m
€
x
1
þ k
x
1
¼ k
^
x
e
sinð!tÞ, ð1Þ
with the variable excitation
^
x
e
sinð!tÞ of the shaker.
The stiffness of the MREs is substituted either by a
shear spring or a compression spring, according to the
used mode. The stiffness in shear mode is dependent on
the shear modulus G the square face A and the thickness
h of the MRE:
k
shear
¼
G A
h
: ð2Þ
Storage modulus (N/mm
2
)
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
0
0
20 40
Frequency (Hz)
60 80 100
0.1%
1%
2%
5%
10%
15%
Figure 3. Storage modulus dependent on shear strain at a current
intensity of 409 mT.
Rotator
Cove
r
MRE
Plate
Figure 2. Rheometer setup.
Storage modulus (N/mm
2
)
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
0
Frequency (Hz)
0 20406080100
0 mT
46 mT
90 mT
136 mT
155 mT
Figure 4. Storage modulus dependent on current intensity at a
shear strain value of 1%.
Frequency (Hz)
0
0
0.1
0.2
0.3
0.4
Loss factor
0.5
0.6
0.7
0.8
0.9
1
20 40 60 80 100
0.1%
1%
2%
5%
10%
15%
Figure 5. Loss factor dependent on shear strain at a current
intensity of 409 mT.
1474 K. M. POPP ET AL.
