Paper No. 86
DEVELOPMENT OF TUNABLE VIBRATION ABSORBERS USING
MAGNETHORHEOLOGICAL ELASTOMERS WITH
BIMODAL PARTICLE DISTRIBUTIONS
By Paris R. von Lockette*
Jennifer Kadlowec
Rowan University
Glassboro, NJ
Jeong-Hoi Koo
Miami University
Oxford, OH
Presented at the Fall 168th Technical Meeting of the
Rubber Division, American Chemical Society
Pittsburgh, PA
November 1-3, 2005
ISSN: 1547-1977
*Speaker
i
ABSTRACT
Magnetorheological elastomers (MREs) are state-of-the-art elastomagnetic composites
comprised of magnetic particles embedded in an elastomer matrix. MREs offer enormous
flexibility given that elastomers are easily molded, provide good durability, exhibit hyperelastic
behavior, and can be tailored to provide desired mechanical and thermal characteristics. MRE
composites combine the capabilities of traditional magnetostrictive materials with the properties
of elastomers, creating a novel material capable of both highly responsive sensing and controlled
actuation in real-time.
Unwanted vibration in components or machinery can often be attenuated using vibration
absorbers which are tuned (fixed) to the frequency of the unwanted vibration. In a tunable
vibration absorber arrangement, the MRE acts a variable stiffness element with a natural
frequency governed by ωa = (k/m)½ . Application of the magnetic field produces a shift in the
material property-component of k, and thereby in ωa, which can account for drift in the frequency
of the unwanted vibration. This works seeks to develop a TVA apparatus using MRE elastomers
but goes further than previous works by beginning to examine the difference in behavior between
MRE samples with unimodal and bimodal particle distributions.
One set of samples used here contains 28.8% by volume of 40 micron particles whereas another
set of samples uses 24% by volume of 40 micron particles and 4.8% by volume of 10 micron
particles. The ratio of 40 to 10 micron particles is determined from analysis of the interstitial
positions in a BCC unit cell structure. These samples are tested in compression under an axial
magnetic field of B = 0.1T and with no field and results are compared. While the unimodal 40
micron sample shows increased stiffness in compression under a magnetic field as compared to
without the field, and initial strain softening in both cases, the bimodal specimen's behavior
differs. The bimodal samples are less stiff initially and show initial strain hardening under a
magnetic field (B = 0.1T) and higher stiffness and initial strain softening with no magnetic field.
Beyond a compressive stretch of λ = 0.95, however, both the unimodal and bimodal samples
behave qualitatively similarly. The shearing tests show an increase in the natural frequency of
the absorber mass in the TVA of approximately 8% under a B =0.1T field suggesting an increase
in
the
materials
stiffness
in
shear.
ii
DEVELOPMENT OF TUNABLE VIBRATION ABSORBERS USING
MAGNETORHEOLOGICAL ELASTOMERS WITH
BIMODAL PARTICLE DISTRIBUTIONS
I. INTRODUCTION
Magnetorheological elastomers (or MREs), solid analogs of MR fluids (MRFs), are state-of-theart elastomagnetic composites comprised of magnetic particles embedded in an elastomer matrix. A
recently published definition of this class of materials states that MREs have the following characteristics:
“…the particles have an asymmetric shape, preferably with a main
anisotropy axis; the particles are soft ferromagnetic or small permanent
magnets; and the composite has an elastic behavior, due to the matrix
properties, up to a relative deformation of 10-1.1
The study of MREs as a viable class of smart materials has gained increasing interest since they
have recently exhibited large magnetorheologcal (or MR) effects in sample materials.2 The MR
effect, ΔE, is measured as the relative change in a material’s complex modulus when placed
within a magnetic field, B, with respect to the modulus with no field present, e.g.
ΔE =
E B − E B =0
E B =0
(1)
The MR effect versus field strength has been reported for several elastomers with various
volume fractions of carbonyl iron1. The curves pass through linear regions before saturation.
Results are also reported for the shear modulus, G.
As a class of smart materials, MREs offer enormous flexibility given that elastomers themselves
are easily cast, provide good durability, exhibit hyperelastic behavior, and can be tailored to
provide desired stiffness, damping, environmental, and thermal characteristics. MRE composites
combine the capabilities of traditional magnetostrictive materials with the flexibility of
elastomers creating a novel material capable of both highly responsive sensing and carefully
controlled actuation in real-time.3,4 For example, as active elements in vibration absorbers the
variable stiffness of MREs enables them to shift the damped frequency under the application of a
magnetic field. Consequently, MREs have found use in a wide range of vibration attenuation and
control applications in the automotive and aerospace industries which has led to the current
emphasis on application-intensive research.5-8 However, since their behavior is governed by the
physics underlying both magnetic and elastomeric materials, the study of MREs must combine
knowledge of both subjects in order to better understand the science governing the composite
material’s behavior. This work begins an examination of the behavior of MREs as the
hyperelastic filled elastomers that they are. Specifically, this work addresses the filler
dependence of the magnetorheological response through dynamic shear and quasistatic
compression tests.
MREs are fabricated by combining usually asymmetric magnetic particles with an uncured
1
elastomer compound such as natural or silicone rubber. Effective particles sizes range from
naonparticles, ~40nm, to coarse iron filings, ~500 μm.1-11 The mixture is then cured either with
or without the presence of an applied magnetic field of 0.5 -1 Telsa (T) . While curing in a field,
particles may form lines collinear with field lines en masse. In addition, particles with a preferred
magnetization axis m tend to reorient with the external field B. Once cured, an external
magnetic field will induce a moment on the embedded particles in the matrix that is resisted by
torsional constant, K, see Figure 1. The summation of individual particle strains due to the
induced torques causes macroscopic strain in the bulk. In addition, applied mechanical strains
may induce a rotation with respect to the preferred axis as well. Together, these phenomenon
lead to the elastomagnetic constitutive equation of elastomagnetism for applied strain εz, field Bz,
remnant magnetization Mr, void permitivity μo, and volume of magnetic material, Vm 1:
θ=
− Kε z sin θ i cosθ i − M rVm μ 0 H z sin θ i
K + M rVm μ 0 H z cosθ i
.
(2)
A critical volume fraction of particles, often reported as roughly 30% - 40%, is needed to
maximize performance while still avoiding particle-particle interference.1,9,10 The maximum ΔE
for different combinations of matrix and filler materials varies considerably with roughly 60% at
approximately 0.8 T, the largest reported2,9; this would yield a linearized ΔE = 75%/T.
Recent theory states that this critical volume fraction maximizes the content of magnetic material
while allowing free action of the particles.1,9 These arguments elicit a notion of filler particle
packing wherein one attempts to maximize magnetic material density while retaining the elastic
behavior. Figure 2 shows a 2D schematic of such packing, but also clearly highlights the
availability of interstitial positions for particles with reduced dimensions which will enhance the
MR effect by increasing Vm in eq. (2).
Several other studies have also examined the effect of particle size on the maximum MR effect.
The largest ΔE values have been seen in materials with particles roughly 10-100 microns.11
Though particle size distributions are largely unreported, it can be assumed that the materials
have been made with particles of a nominally unimodal size distribution.
This work begins to examine the differing magnetorheological stress-stretch response between
MRE materials with unimodal versus bimodal particle distributions to loading in uniaxial
compression. Dynamic shearing tests are performed on MRE samples with bimodal particle
distributions to qualitatively compare the bimodal material's response in shear to that in
compression.
II. RESEARCH METHODS
The materials used in this work are all cast from using Dow Corning HS II RTV Silicone
Elastomer Compound as the matrix material. The compound is preheated in an oven to 60 C
before mixing to decrease viscosity. Once heated the desired amount of iron particles are added
and mixed thoroughly. The catalyst is added in a 15:1 compound:catalyst ratio in the final step.
Specimens were cast in cylindrical molds, 9.525 mm height by 19.05 mm diameter for
compression tests and rectangular prism molds 19.05 mm length by 12.7 mm width and 12.7 mm
2
height for the shearing specimens.
To investigate the role of particle distribution samples were made with the compositions in Table
1.
Table 1: MRE sample compositions
B
C
Volume Fraction[%]
Primary Secondary
28.8
0
24
4.8
Avg. Particle Size[μm]
Primary Secondary
None
40
40
10
Samples of type B and C used 40 and 10 micron particles to approach a total 30% volume
fraction, the critical volume concentration. Samples B and C moved from nominally unimodal to
nominally bimodal particle distributions in order to test the effects of particle distributions on the
MRE effect. As a starting point, the ratio of 40 to 10 micron particles was set at 1:12 by number
which follows the ratio of primary to interstitial locations in a body centered cubic unit cell
structure. The volumetric ratio is then calculated assuming a spherical particle shape of the
given particle diameter.
A schematic of the experimental setup for compression tests is shown in Figure 3. Tests were
performed using a MTS 831.10 servo-hydraulic frame and a permanent magnet 50.8 mm in
diameter to produce a uniform magnetic field through the specimen. The upper fixed platen was
machined from aluminum to avoid direct magnetic attraction between the magnet and the load
cell. A quasistatic strain rate of 0.1%/s was used to minimize magnetic eddy currents. The
specimens were stretched to λ = 0.7.
Dynamic tests were conducted using a shearing tunable vibration absorber (TVA) apparatus
designed for these experiments, see Figure 4. The TVA isolates the primary mass (the upper
mount, induction coil, and accelerometer) from the direct actuation of the hydraulic actuator
while allowing the primary and absorber mass (the upper accelerometer ) to respond to the input
together as a floating, base-excited two degree of freedom system. The TVA includes an
integrated induction coil capable of producing 0.1 T at 10 Amps across the gap where the PDMS
silicone elastomer MRE samples are suspended in shear.
In this system, as the primary mass vibrates a portion of that vibration is transferred to the
absorber mass (herein the upper accelerometer) which operates at a natural frequency, ωa. The
natural frequency of the absorber is governed by its mass and the stiffness of the two MRE
samples which suspend it; those samples vibrate in a shearing mode. By applying a magnetic
field through the MRE samples, their stiffness is altered which shifts the natural frequency of the
absorber. The actuator was driven over a frequency range of 10-100 Hz with uniform white
noise. Data was collected using a Bruel and Kaer PULSE data acquisition system with
accelerometers placed on the middle crossbeam (the input to the primary mass) and between the
two MRE samples (the output at the absorber mass).
III. EXPERIMENTAL RESULTS
3
Results of compressions tests on B type samples are given in Figure 5 which shows a Mooney
plot under no magnetic field and under an axial field of B = 0.1 T. The plot shows the expected
initial strain softening as the samples are compressed in both cases with an increase in stiffness at
higher compression ratios. Under the application of the magnetic field, however, the samples
show an increase in stiffness over the zero field case which is most apparent over the range
λ=0.98 – 0.8.
Figure 6 shows a Mooney plot for C-type samples with bimodal distributions of particles. With
no magnetic field, open circles, the samples show the expected initial strain softening however
with an applied magnetic field, triangles, the C-type samples show a strain hardening which
begins from a much weaker modulus. Previous analytical work has predicted a decrease in
modulus in compression for samples subjected to an axial magnetic field. After the in initial
decrease in stiffness with no field, or increase in stiffness under an applied field, the samples
recreate the trends seen in the B-type unimodal specimens where the application of the magnetic
field increases the stiffness over a limited compressive range.
Results of TVA testing are given in Figure 7 which shows a normalized frequency response plot
of the primary to absorber (input to output) behavior of the system. Each curve is normalized to
its maximum value which occurs at resonance. The materials used in the TVA were the bimodal
C-type specimens at a field strength of B = 0.1T. The graph clearly shows a shift in the natural
frequency of the absorber from approximately 49 to 53 Hz. when the magnetic field is applied.
IV. CONCLUSIONS
This work has shown some evidence that MRE materials with bimodal distribution of particles
may exhibit different characteristic behaviors than MRE materials with unimodal particle
distributions. The compressive graphs show the analytically predicted reduction of modulus
initially, in opposition the strain softening characteristic of elastomers, under a magnetic field in
compression for the bimodal samples but not for the unimodal samples. After λ = 0.9, however,
both samples behave similarly. The frequency response curves which are shearing tests show the
expected increase in natural frequency stemming from an increase in stiffness under the
influence of a magnetic field. This work has shown that the bimodal samples are capable of
reductions in stiffness in compression and increases in stiffness in shear whereas the unimodal
samples show increases in both shear and compression under a magnetic field.
In relative magnitude, the frequency response curves of the bimodal samples show a shift of
approximately 8% which is comparable to what has been shown in the literature for MREs with
unimodal particle distributions. The compressive tests on the unimodal (B) and bimodal (C)
samples show stiffness increases of approximately 7.5% at λ=0.9 which suggests a linearized
response of ΔE=75%/T (which would be saturation limited) which is also comparable to
published figures in the literature.
V. REFERENCES
4
1
L. Lanotte, G. Ausiano, C. Hison V. Iannotti, C. Luponio, and C. Luponio, Jr., JOURNAL OF
OPTOELECTRONICS AND ADVANCED MATERIALS, Vol. 6:2 (2004), 523-532.
2
G. Y. Zhou, SMART MATERIALS STRUCTURES 12, 139-146 (2003).
3
G. Y. Zhou, Q. Wang, “Field-dependant dynamic properties of magnetorheological elastomer
based sandwich beams,” manuscript from author.
4
G. Y. Zhou, Q. Wang, “Use of Magnetorheological Elastomer for Smart Piezoelectric Power
Actuator Design and Signal Processing,” manuscript from author.
5
T. Shiga, A. Okada, and T. Kurauchi, J. APPL. POLYM. SCI. 58, 787-792 (1995).
6
M.E. Nichols, J.M Ginder, J. L. Tardiff, and L.D. Elie, “The Dynamic mechanical behaviour of
magnetorheological elastomers”. in 156th ACS Rubber Division Meeting. 1999. Orlando,
Florida.
7
J. M. Ginder, M.E. Nichols, L.D. Elie, and J.L. Tardiff, SPIE 3675, 131-138 (1999).
8
J.M. Ginder, W.F. Schlotter, and M.E. Nichols., “Magnetorheological elastomers in tunable
vibration absorbers”, in Smart Materials and Structures 2001: Damping and Isolation, D. Inman
(Ed.) , Proc. of SPIE 4331, 103-110 (2001).
9
M. Lokander and B. Stenberg, POLYMER TESTING 22, 677-680 (2003).
10
M. Lokander and B. Stenberg, POLYMER TESTING 22, 245-251 (2003).
11
D. Szabó and M. Zrínyi, Int. J. MOD. PHYS. B 16 2616-2621(2002).
5
m
κ,θ i
P article
Matrix
z
y
Hz
Figure 1: Alignment and torque action due to external field acting on particle.
6
d2
d1
Figure 2: 2D schematic of available
interstitial positions.
7
Load cell
Aluminum Platen
δ
MRE sample
Magnet
Lower platen
Figure 3: Schematic of compression test setup
showing permanent magnet in load train.
8
B
Figure 4: Tunable vibration absorber experiment schematic.
9
1400
B=0T
B = 0.1T
1300
f*/(λ -1/λ 2 ) [Kpa]
1200
1100
1000
900
800
700
1
0.95
0.9
0.85
0.8
0.75
0.7
Stretch
Figure 5: Mooney plot of B-type unimodal sample in compression with and without
magnetic field where f* is the nominal stress.
10
1300
B = 0T
B = 0.1T
f*/(λ -1/λ 2 ) [Kpa]
1200
1100
1000
900
800
700
1
0.95
0.9
0.85
0.8
0.75
0.7
Stretch
Figure 6: Mooney plot of C-type bimodal sample with and without magnetic field where f*
is the nominal stress.
11
1.20
B = 0T
1.00
B = 0.1T
Normalized Frequency
Response
0.80
0.60
0.40
0.20
0.00
10
20
30
40
50
60
70
80
90
-0.20
-0.40
-0.60
Frequency (Hz)
Figure 7: Frequency response plot for C-type sample in TVA testing.
12
100
FIGURE CAPTIONS:
Figure 1: Alignment and torque action due to external field acting on particle.
Figure 2: 2D schematic of available interstitial positions.
Figure 3: Schematic of compression test setup showing permanent magnet in load train.
Figure 4: Tunable vibration absorber experiment schematic.
Figure 5: Mooney plot of B-type unimodal sample in compression with and without
magnetic field.
Figure 6: Mooney plot of C-type bimodal sample with and without magnetic field.
Figure 7: Frequency response plot for C-type sample in TVA testing.
13