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Finite element design and analysis of adaptive base isolator
utilizing laminated multiple magnetorheological elastomer
layers
Yancheng Li and Jianchun Li
Abstract
Available magnetorheological elastomer (MRE) devices normally consists 1-2 layer of small-size MRE materials. To be
used in large-scale structures, MRE devices with multiple larger MRE materials are expected. This paper addresses the
critical issue in designing a large scale device with multiple layers of low magnetic conductive MRE materials, i.e.
magnetic circuit design. The primary target in magnetic circuit design for MRE devices is to provide sufficient and
uniform magnetic field to all MRE layers in the device. In this paper, finite element investigations are conducted. An
innovative magnetic circuit design is proposed for MRE base isolator with multi-layer of MRE materials. In the design,
laminated MRE and steel structure is adopted as part of the magnetic core together with two steel blocks. Cylindrical steel
tube is used as the yoke of the magnetic circuit. Two plates are places on the top and bottom the device to form enclosed
magnetic path in the device. Finite element results showed that such innovative magnetic design is able to provide
sufficient and uniform magnetic field to all MRE layers, i.e. 25 MRE layers with thickness of 1mm and diameter of
120mm in this case. Finally, the influence of lateral deformation of the MRE base isolator on the magnetic field is
investigated. It is found that the magnetic field in MRE materials deteriorates when the deformation of the device increases.
Keywords
Magnetorheological elastomer; laminated; finite element analysis; adaptive base isolator;
Introduction
In recent years, a new class of materials in
magnetorheological (MR) family, magnetorheological
elastomer (MRE), has attracted a great deal of attentions
from researchers around world (Popp et al., 2010). The
functionality of MREs is based on magnetic interaction of
particles when subjected to an external magnetic field.
Similarly as MR fluids, the iron particles dispersed in the
rubber matrix arrange themselves in the direction of
magnetic field when energized. An iron particle network
thus forms with existence of magnetic field and the iron
particles will have local motion constrained by the rubber
matrix. Connection between iron particles is dependent on
the degree of the magnetic field applied. Once removing
the magnetic field, the material instantly recovers its
original status.
The most important feature of MRE material is its
controllable shear modulus. It is found that maximum
changes of the shear modulus of a MRE material varies
from about 50% (stiffer rubber matrix) to over 1000% (soft
rubber matrix, e.g. silicone gel) when it is subjected to
external magnetic field (Li et al., 2006). MRE material,
with stable mixture of the particles and the rubber matrix,
can overcome some major problems associated with MR
fluids and gels, such as particle settling and sealing (Li et
al., 2010). Such controllable MR elastomer materials
project great potentials for critical functionality comparing
to conventional elastomers and open a door for
development of stiffness-variable devices, and therefore
could be a link that bridges the real world applications and
modern control technologies with smart materials
(Abramchuk et al., 2006).
Field-dependent modulus and damping of MRE
material offers enormous potentials to develop vibration
reduction and mitigation devices. Traditional rubber
devices, such as vibration absorbers and vibration isolators,
become natural choices to engage MRE materials for
adaptive performances (Ginder et al., 2001; Lerner and
Cunefare, 2008; Deng and Gong, 2008; Ni et al., 2009;
Hoang et al., 2009; Opie and Yim, 2009; Liao et al., 2011;
Behrooz et al., 2014). Ginder et al. (Ginder et al., 2001)
prototyped an adaptive tuned vibration absorber using
MRE material as variable spring element. Lerner and
Cunefare (Lerner and Cunefare, 2008) designed three
MRE-based vibration absorbers working in shear,
compression and squeeze modes, respectively. Deng and
Gong (Deng and Gong, 2008) developed an adaptive tuned
vibration absorber with tuned natural frequency shifting
from 27.5Hz to 40Hz. Behrooz et al (Behrooz et al., 2014)
proposed a variable stiffness and damping isolator (VSDI),
to be used in vibration mitigation of structures. A
comprehensive review on MRE devices can be found in Li
et al (2014). Despite the innovative designs presented,
aforementioned MRE devices contain very few layers of
MRE materials and most of the devices have limited loadcarrying capacity which makes them vulnerable for
applications with such requirement. In addition, most of the
devices only contain small size MRE material. This is
mainly due to the difficulty in providing sufficient
magnetic field for low conductive MRE materials. To date,
designing large-scale MRE device still remains a challenge.
MRE material has been proposed to be used in new
base isolation system (Hwang et al., 2006; Jung et al., 2011)
to overcome the drawbacks of traditional base isolation
system. Jung et al (2011) numerically explored the
feasibility of MRE material for the development of a smart
base isolation system its field dependent property. A
simple shake table test on a single storey building proves
that the utilization of MRE material in the system greatly
improves the performance of the base isolation system in
term of seismic protection. As a typical large-scale device,
its design imposes great challenge. In addition, there are
also other requirements which need to be addressed. Base
isolators in the system, mainly elastomeric bearings, are
installed underneath the buildings and therefore should be
able to support large vertical loading. On the other hand,
low lateral stiffness is required to effectively decouple
earthquake motions. Therefore, on top of meeting
requirements on device performance, an innovative design
on the magnetic circuit should be explored to energize the
field-sensitive while low conductive materials.
This paper features an important aspect in designing
large scale MRE devices, i.e. magnetic circuit design, using
MRE base isolator as example. An innovative laminated
MRE structure is proposed to fulfill the demand for weightcarrying capacity in engineering application. Finite
element analysis is used to illustrate the effectiveness of
this design. Finally, variation of magnetic field due to
lateral deformation of MRE base isolator is discussed in the
last session.
Design of the MRE base isolator
Laminated structure for large-capacity MRE device
(a)
(b)
Figure 1. Rubber under compressive loading: (1) thick
rubber block; (2) laminated rubber layers
Rubber is an important engineering material and can be
used in versatile engineering applications. It is one of the
most important materials in vibration isolation and
reduction. In applications with heavy duty environment,
laminated structure (figure 1) with alternative rubber and
steel layers is adopted for following reasons: (1) providing
enhanced loading-carrying capacity (2) preventing bulging
of the rubber under compressive loading and (3) achieving
low lateral stiffness. Similar principles apply to MRE
material if it is used for designing large-capacity devices,
such as vibration isolator for machinery and base isolator
for civil structures. However, this creates a great challenge
due to the low magnetic conductivity of MRE material and
the demand for sufficient magnetic field to activate and
utilize MR effect.
Proposed MRE base isolator design
Top plate
Gap
Laminated
MRE and
steel layers
Coil
Steel
Yoke
Steel
block
(a)
(b)
Figure 2. Proposed MRE base isolator with laminated
MRE structure (dash line indicates magnetic path): (a)
cross section; (b) 3-D model
Figure 2 shows the sketch of the proposed MRE base
isolator and 3-D view of the device. Unlike the designs of
other MRE devices, in this design the MRE materials are
placed inside the coil. According to the principle of
magnetics, all the magnetic lines that enter any region must
also leave that region. In a magnetic circuit, the area inside
the coil is the region that all magnetic lines must pass
through. Therefore, this placement guarantee uniform and
strongest magnetic field given sufficient magnetic flux is
provided. Laminated MRE structure with steel layer
embedded serves as part of the magnetic core. The
magnetic conductivity of the MRE material is fairly low
due to the large volume fraction of rubber matrix and hence
to achieve saturated magnetic field for MRE material
considerable power consumption is expected. Laminated
structure with high magnetic conductive steel layers
between MRE layers improves its overall magnetic
conductivity. Two solid steel blocks are added on the top
and bottom of the laminated structure to further improve
the permeability of the magnetic core. To form an enclosed
path for the magnetic flux, two steel plates, one on the top
and the other on the bottom, are designed to perform two
roles as: 1) creating paths for magnetic field and 2) being
fixture to connect the device to the ground and the
superstructure above (Li et al., 2013a). In addition, an
annular steel yoke is attached to the coil to complete the
Finite element analysis
1.40
1.20
1.00
B (T)
magnetic flux path. Gap between the top connection plate
and the steel yoke allows lateral deformation of base
isolator. Size of the gap is determined by considering the
compression of MRE layers under maximum designated
compressive loading and stability under maximum lateral
deformation.
0.80
0.60
0.40
0.20
0.00
0
5000
10000
H (kA/m)
15000
Figure 4. H-B curve used in the analysis, tested using the
equipment described in [25]
(a)
(a)
(b)
(c)
Figure 3. FE model with meshing built in ANSYS
Maxwell: (a) base isolator with hiding coil and yoke; (b)
magnetic core: laminated structure and two steel blocks; (c)
laminated structure containing 25 layers of MRE and 24
layers of steel sheets
Finite element analysis was conducted using ANSYS
Maxwell software. Figure 3 shows the FE model of
laminated structure used in the analysis. MRE material
used in the device is composed of iron particles, silicon oil
and silicon rubber with mass ratio of 70g: 15g: 15g.
Thickness of the MRE sheet is 1 mm and there are 25 MRE
layers used in the devices. 24 steel sheets bonded with
MRE layers are have same diameter of 120mm but a
thickness of 0.92mm. The annular yoke has a height of
144mm and diameters of 200 mm and 220 mm. The coil
attaches the inside of the yoke and has thickness of 25mm.
The coil has 2900 turns and is made of electromagnetic
wire with diameter of 1.0mm. The coil has electric
resistance of 42.3 Ω. Length of the steel block is chosen to
be optimum of 50 mm each to maintain the strong and
uniform magnetic field in the MRE material. Two
connecting plate has thickness of 12mm. Gap between the
top plate and the yoke is 5mm. Magnetic property of the
MRE material was obtained from the testing setup used in
(Zeng et al., 2013). H-B curve of the material is shown in
Figure 4. Other parts of the device, including annular yoke,
steel plates, steel sheets and steel blocks, are all made of
steel 1008. The magnetic property of the steel can be found
in the software.
(b)
Figure 5. Magnetic flux density when current I =3.0A: (a)
2D model; (b) 3D model
Figure 5 shows the magnetic flux density inside of the
device when applied current is 2.0A. It can be observed that
the magnetic field inside of the MRE material is around 0.9
T and the distribution is uniform for all MRE materials. Gu
and Li (2013) has demonstrated that the magnetic field in
a solenoid reaches highest in the center, while it gradually
weakens when leaving the center due to the dispersion of
the field. Built on this, the laminated MRE and steel
structure was designed in the center of the magnetic core,
while high permeable steel blocks was attached to the
laminated structure. This arrangement can shift the
weakening magnetic field away from the MRE materials.
Due to the better conductivity, the magnetic field inside
other narrow magnetic paths, i.e. connecting plates and
yoke, is much stronger than that in MRE material. This is
not a surprise since the magnetic conductivity of MRE
material is much lower than steel. However, laminated
structure with alternative steel sheets and MRE sheets
greatly improves the magnetic permeability of the structure
as a whole. Magnetic flux densities inside each MRE layer
are plotted in figure 7. It is observed that the magnetic
fields in the MRE layers are evenly distributed except the
edge. Considerable leaking occurs around the edge of MRE
layers due to field dispersion. All the MRE layers have the
same magnetic field level.
Magnetic field distribution in 7th MRE layer
1.5
B field T
1
0.5
0
50
50
0
0
-50
-50
Y mm
X mm
(b)
Magnetic field distribution in 13th MRE layer
(a)
1.5
B field T
1
0.5
0
50
50
0
0
-50
-50
Y mm
(b)
Figure 6.Magnetic flux line when current I =3.0A: (a) 2D
model; (b) 3D model
(c)
Magnetic field distribution in 18th MRE layer
1.5
1
B field T
The most important issue in designing the magnetic
circuit of the MRE device is to form an enclosed magnetic
path with highly permeable material. Only though this, the
energy loss in the air can be reduced to minimal and thus
maintain efficiency of the magnetic circuit design. In this
device, two connecting plates, yoke, two steel blocks and
the laminated structure form an enclosed magnetic path.
X mm
0.5
0
50
Magnetic field distribution in 1st MRE layer
50
0
0
-50
X mm
(d)
1
Magnetic field distribution in 25th MRE layer
0.5
1.5
0
50
1
50
0
0
-50
-50
Y mm
B field T
B field T
-50
Y mm
1.5
0.5
X mm
(a)
0
50
50
0
0
-50
Y mm
-50
X mm
(e)
Figure 7. Magnetic flux density in MRE layers: (a) 1st
layer; (b) 7th layer; (c) 13th layer; (d) 18th layer; (e) 25th
layer; MRE layers are numbered from bottom to top.
To investigate the importance of the each part of
magnetic path, comparative studies on several models are
explored and presented in figure 8. Design 1 is the
complete device while designs 2-4 are incomplete designs
with one part of the device missing, i.e. steel blocks,
connecting plates and yoke, respectively. Magnetic field in
each layer is the average magnetic flux density. As can be
seen, each part of the magnetic path is equally important
which indicated the necessity of enclosed magnetic path.
For incomplete design, the maximum magnetic field
achieved is 0.2 T while the field level for complete design
is around 0.9 T. It is also observed that the magnetic field
decreases from layer 1 to layer 25. This is due to the
existence of the 5mm gap between the top plate and the
yoke, which induces great energy loss in the air.
It is worthwhile to note that magnetic field obtained in
the finite element analysis is far above the real magnetic
field achieved in the device during experimental testing. In
the testing, the magnetic field achieved is around 0.4 T
when applied current is 2.0 A, which is around 50% in the
numerical simulation. The reason for the difference is
because of the un-tight bonding between the MRE layers
and steel layers. Detailed discussion can be found in (Li et
al., 2013a). It needs to address here that the bonding of the
device in (Li et al., 2013b) which is also used in this work
has been improved compared with the design in (Li et al.,
2013a). The magnetic field achieved in the device (Li et al.,
2013a) is only 33% of that from the finite element analysis.
Special consideration on improving the bonding needs to
undertake when fabricates the laminated structure.
magnetic field may be neglected for MRE device with
single layer of MRE material and small motion.
(a)
(b)
1
0.9
0.8
B field T
0.7
Design 1: full design
0.6
Design 2: w/o blocks
0.5
(c)
Figure 9. Magnetic flux line for MRE base isolator: (a)
5mm deformation; (b)10mm deformation and (c) 15mm
deformation
Design 3: w/o plates
0.4
Design 4: w/o yoke
0.3
0.2
0.1
0
1
5
9
13
17
No. of MRE layers
21
25
Figure 8. Comparative analysis on magnetic field
distribution of each design
Magnetic field under shear deformation
Magnetic field is very sensitive to any change in the
magnetic path. Under external loadings, i.e. shear or
compressive loading, shape of MRE layers change.
Therefore, the magnetic path will also be slightly displaced.
It is expected that the magnetic field will also be affected
due to motion of the MRE device. The variation of
Under the action of external loadings, MRE base
isolator undergoes shear deformation. To analyze the
magnetic field inside the device when it is subjected to
shear deformations, finite element models of MRE base
isolator under deformations of 5mm, 10mm and 15mm
have been constructed in ANSYS Maxwell. Figure 9
presents the magnetic flux line inside the MRE base
isolator with various deformations. It is shown that the
magnetic flux lines close to the top and bottom MRE layers
tend to follow the deformation direction while the flux
lines in the middle still maintain the vertical direction.
Field distributions inside layer 18 for different shear
deformations are plotted in figure 10. In this figure, the
MRE base isolator deforms along x axis. Magnetic field is
almost evenly scattered in the MRE layer for no
deformation case. However, the right side of the MRE
layer has gradually decreasing magnetic field when
deformation increases. It means that the magnetic field
leaking in the edge of the layer becomes more obvious
along direction of the deformation. For larger deformation,
the magnetic field becomes more dispersive. To
demonstrate the impact of deformation on magnetic field,
Figure 11 plots the average magnetic field in MRE layers
for various deformations, i.e. 0mm, 5mm, 10mm and
15mm, respectively. It can be observed that the magnetic
field decreases along increase of deformation. For an
applied current of 1.0 A, the magnetic field in layer 1
decreases from 0.58 T at 0 mm deformation to 0.56 T at
15mm deformation. While, for MRE layer 25, the magnetic
field drops from 0.55 T at 0 mm deformation to 0.5 T at 15
mm deformation (9% decrease). Magnetic field flux
densities in MRE layer 1 for all deformed cases are quite
close, which is due to that for all cases local deformation
in this layer is quite minimal. Field drops for these cases in
layer 1 are mainly because of the change of the magnetic
path, i.e. top plate and top steel block. For MRE layer 25,
the field drop for all deformed cases are not so close due to
that maximum deformation happens at this layer.
Magnetic field distribution in 18th MRE layer-10mm deformation
1.5
B field T
1
0.5
0
50
50
0
0
-50
-50
Y mm
X mm
(c)
Magnetic field distribution in 18th MRE layer-15mm deformation
1.5
B field T
1
0.5
Magnetic field distribution in 18th MRE layer-no deformation
0
50
1.5
50
0
-50
1
B field T
0
-50
Y mm
0.5
(d)
Figure 10. Distributions of magnetic flux density in layer
18 (I=0.5A): (a) no deformation; (b) 5mm deformation;
(c) 10mm deformation; and (d) 15 mm deformation. Note:
deformation all happens in x direction and is to the right.
0
50
50
0
0
-50
-50
Y mm
X mm
X mm
Average magnetic field distribution MRE layers
(a)
0.8
Deformation=0mm
Deformation=5mm
Deformation=10mm
Deformation=15mm
Magnetic field distribution in 18th MRE layer-5mm deformation
0.7
1.5
0.6
B field T
B field T
1
0.5
0.5
0.4
0
0.3
50
50
0
0
-50
0.2
-50
Y mm
X mm
(b)
5
10
15
20
25
Layer No.
Figure 11. Average magnetic field in MRE layers for
various deformation (I=1.0 A)
Different from MR fluid devices where the magnetic
field can be maintained constant level during operation,
magnetic field inside MRE device will rely on its motion.
This is the main discovery from the finite element analysis
in this paper. Due to the independence of magnetic field
with motion, magnetic field in MR fluid devices is
considered only related to applied current during modeling.
However, for MRE devices, it may not be the case.
Therefore, finite element analysis should be undertaken
before the modeling taking place for MRE devices. If the
field difference is enough to change the performance of the
device, another parameter related to deformation or motion
should be introduced into the model of MRE devices.
Conclusions
In this paper, finite element analysis was conducted for
MRE base isolator to gain understanding on the magnetic
field distribution. Innovative magnetic design was present
for the device in which laminated MRE and steel structure
serves as the magnetic core together with two steel blocks.
Impact of each part of the magnetic circuit was investigated.
In particular, variation of magnetic field due to the motion
of the device has been discovered. It is found that the
motion of MRE device may cause change of the magnetic
field. This should be considered during the modeling of its
nonlinear behaviors.
Acknowledgement
The authors acknowledge the financial support by
Discovery Grant (Grant No. DP150102636) from
Australian Research Council.
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