Finite element design and analysis of adaptive base isolator utilizing laminated multiple magnetorheological elastomer layersYancheng Li and Jianchun Li

AbstractAvailable 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.

KeywordsMagnetorheological 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 load-carrying 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 weight-carrying 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

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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

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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 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. Finite element analysis

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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.

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Figure 4. H-B curve used in the analysis, tested using the equipment described in [25]

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(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.

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(b)Figure 6.Magnetic flux line when current I =3.0A: (a) 2D model; (b) 3D model

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.

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(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.

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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 magnetic field may be neglected for MRE device with single layer of MRE material and small motion.

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(c)Figure 9. Magnetic flux line for MRE base isolator: (a) 5mm deformation; (b)10mm deformation and (c) 15mm deformation

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.

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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.

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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.

ConclusionsIn 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.

AcknowledgementThe authors acknowledge the financial support by Discovery Grant (Grant No. DP150102636) from Australian Research Council.

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