# Investigation on variable shear modulus of magnetorheological elastomer based on natural rubber due to change of fabrication design.

A magnetorheological elastomer (MRE) is a smart material that has a reversible and variable modulus in a magnetic field. Natural rubber (NR), which has better mechanical properties than other rubbers, was used as the matrix. Carbonyl iron powder (CIP) was selected for the generation of a magnetic field-dependent modulus in the MREs. The MRE specimens were cured in an anisotropic mold, which was used to induce a magnetic field. SEM images validated the CIP orientation. The shear modulus of the MREs was evaluated under a magnetic field induced by a magnetic flux generator (MFG). An evaluation system was designed that includes an MFG, which is a device that generates a magnetic field via a continuously variable-induced current to determine the magnetic field-dependent shear modulus. The variations of the shear modulus were observed with increasing CIP volume fraction and induced current. The experimental results revealed that the maximum variation rate of the shear modulus was 76.3% for 40 vol% of CIP and an induced current of 4 A. Using these results, the appropriate CIP volume fraction and induced current can be proposed as the guidelines in fabrication design of MREs based on NR. POLYM. ENG. SCI., 53:992-1000, 2013. [C] 2012 Society of Plastics EngineersINTRODUCTION

Materials with rheological properties that can be varied by the application of magnetic fields belong to a specific class of smart materials, which respond to changes in their environments via solid-state electronics and modern control algorithms (1). These materials are composed of iron particles and a low-permeability carrier. Then, by generating an external magnetic field via induction, chain-like structure of iron particles will form inside the material, or the strength of the structure already embedded in the material, such as in a magnetorheological elastomer (MRE), will change (2). Thus, the mechanical properties of the material will also change.

The magnetorheological (MR) effect of MRE is optimized by choosing an iron particle with a high-magnetic saturation and aligning by an applied magnetic field before curing the matrix. Carbonyl iron, spherical iron particles with a diameter of some micrometers, has been widely used for manufacturing MREs.

MRE materials operate within the preyield regime, and the magnetic field-dependent modulus can be used to design devices. Therefore, MRE devices are used in structures to adjust their natural frequency, which is affected by the equivalent stiffness of the structure. In other words, to change the natural frequency of a device, one can prevent the system from attaining resonance or coupling with other frequencies (3).

This type of material was first investigated experimentally by Jolly et al. (2). They built double-lap shear specimens, and shearing the outer and inner board under different frequencies. they demonstrated that the MREs were dependent on the magnetic field. In particular, they used the point-dipole model to calculate the shear modulus. Ginder et al. (4) adopted the same experimental method to study the field-dependent mechanical properties of MRF, hut they used column-like shear equipment. Davis (5) used the finite element (FE) method to analyze the dependence of the effective shear storage modulus of an MRE on interparticle magnetic forces.

In most of the previous studies, there were three limitations. First, silicone rubber was used as the matrix, because it can be vulcanized at room temperature and can be fabricated into complicated geometries, as is the case for liquid silicone rubber (6-9). However, MREs based on natural rubber (NR) generally perform better in terms of their mechanical properties and heat resistance than MREs based on silicone rubber and other rubber matrices. For instance, the tensile and tear strength of MREs based on NR are almost 10 times those of MREs based on silicone (10).

Second, the shear moduli of MREs were investigated as a function of only the magnetic flux density (11), (12). However, because the magnetic flux density is sensitive to the geometry of the magnetic conductor, it is not uniformly distributed within the cross-sectional area of the magnetic conductor, making it difficult to accurately measure using a Tesla meter. Moreover, it is difficult to express the experimental results on a linear scale of independent variables, such as the magnetic flux density. Thus, to confirm the equivalent magnetic flux density inside MREs, it is necessary to define the results by other independent variables, such as the variable-induced current. In particular, mechanical systems using MREs, such as tunable vibration absorber, need to know the shear modulus as a function of the variable-induced current in order to regulate their semiactive vibration control. For example, because vehicles generally possess a maximum battery voltage of 12 V. it is important to evaluate the modulus due to the continuously variable-induced current and to decrease the resistance of the magnetic flux generator (MFG), which generates the magnetic field inside MREs.

Third, the evaluation mechanism of the shear modulus was largely insufficient. Most of the previous studies used the relationship between the known sinusoidal frequency of excitation and its responses to evaluate the shear modulus of MREs; however, it is difficult to excite MREs over the 100 Hz, because fixing MRE specimens with a high-excitation frequency causes them to lose their viscoelasticity.

Thus, this study aims to fabricate anisotropic MREs based on NR using an anisotropic mold, which produce a more advanced MR effect than isotropic MREs. In addition, it will evaluate the shear modulus variations of the MREs due to continuously variable induced current and validate the performance of the carbonyl iron powder (CIP) orientation in each MRE specimen via SEM images.

Using this evaluation system, this study identifies the variation characteristics and the maximum variation rate of the shear modulus of MREs for six different volume fractions of CIP and for a continuously variable induced current. The effective range for inducing currents also investigated. Finally, appropriate conditions for the fabrication design of MREs, such as the CIP volume fraction and induced current with respect to the desired shear modulus variation rate for MREs based on NR, are proposed as guidelines.

FABRICATION OF MRE MATERIALS AND EXPERIMENTAL

Composition and Fabrication Method of MRE Materials

Most of the previous studies used silicone rubber as a matrix, because liquid silicone rubber can be vulcanized at room temperature and can occasionally be fabricated into complicated geometries. However, MREs based on NR generally perform better in terms of their mechanical properties and heat resistance than MREs based on silicone rubber and other matrices. Thus, MREs based on NR are often applied to various mechanical systems.

Hence, in this study, the MRE materials consist of a matrix of NR, CIP (International Specialty Products s1641 grade). ZnO, stearic acid, sulfenamide (CZ), and sulfur as a curing agent (Table 1).

TABLE 1. Composition of MRE materials. Common components NR (matrix) 100 ZnO (activator) 5 phr Stearic acid (activator) 2 phr CZ (accelerator) 0.8 phr Sulfur (crosslinking agent) 2.5 phr Magnetic reactive powder Natural rubber (CIP 0 vol%) Carbonyl iron powder 10 vol% Carbonyl iron powder 20 vol% Carbonyl iron powder 30 vol% Carbonyl iron powder 40 vol% Carbonyl iron powder 50 vol%

In the first step of the fabrication process, all the ingredients were thoroughly blended on a roll mill. The compounded mixtures were then stored at room temperature for 24 hr in order to stabilize. The cured characteristics of the compound were measured using a rubber rheometer (Daekyung DRM-100, Korea), and then they were vulcanized with a hydraulic hot press at 160[degrees]C.

In this study, an anisotropic mold (Fig. la) that used both neodymium magnets and a specially designed aluminum frame was developed to generate a chain-like formation of CIP in the NR matrix. The anisotropic mold consisted of an aluminum body, which prevented the formation of defects from the pressure during the vulcanization process and two neodymium magnets (Fig. lb) with a surface magnetic flux density of 0.3 T. This mold was used to orient the CIP in the NR matrix during vulcanization while simultaneously fabricating specimens that could undergo tensile testing. In addition, it minimized the generated vapor with constant temperature and pressure. Six oriented specimens containing 0, 10, 20, 30, 40, and 50 vol% CIP were fabricated using this anisotropic mold. The size of each specimen was 20 mm (length) x 20 mm (width) X 2 mm (thickness).

Experimental Procedure to Evaluate the Shear Modulus Characteristics of MREs

The experimental setup used to evaluate the variation in the shear modulus of the MREs due to a continuously variable induced current is presented in Fig. 2. The shaker (B&K Type4810) beneath the center of the fixed--fixed end beam was operated by a power amplifier (Inkel MA-320) and a noise generator (Seintek G5100). The signal of the excitation was white noise--that is, a random signal with statistically the same magnitude across the whole frequency domain--because it was necessary to identify the oscillator's natural frequency of free vibration due to the variable-induced current. When the entire evaluation system was excited by the shaker, the MRE specimens were deformed in the shear direction by the inertial force of the oscillator. Then the transfer function, which is the relation between the input force signal of the force transducer (Endevco 2311-100) and the response signal of the accelerometer (Endevco 27AM1-100), was experimentally measured by an FFT analyzer (B&K Pulse 3560-B-040). At the same time, a DC power supply (Unicorn UP-3003T) powered the variable-induced current through a coil to generate a magnetic field in the MRE materials, which were fixed at the upper gap of the MFG. Then the natural frequency of the oscillator was identified via the measured experimental transfer function and was inserted into the frequency-shear modulus equation (Eq. 3) to determine the shear modulus of the MREs due to the variable-induced current.

The variations in the shear modulus of the MREs due to this current were experimentally assessed by a single degree-of-freedom evaluation system that generated a magnetic field by means of the variable-induced current. A schematic diagram of the evaluation system is shown in Fig. 3.

Because the conventional evaluation device, a dynamic mechanical analyzer, is not able to generate the magnetic field in MREs, the design of an evaluation system involving an MFG, which can generate a magnetic field in MREs using a continuously variable induced current, is essential.

Before the optimization was implemented, the magnetic flux density of the MFG was measured, and a validated FE model with errors within 1% was obtained. Then the optimized level was determined by design of experiments (DoE) for the validated FE model.

Consequently, the result--a reliable electromagnetic FE model of the MFG--is shown in Fig. 4. In addition, the measured magnetic flux densities and those found via the electromagnetic FEM are shown in Table 2.

TABLE 2. Results of electromagnetic FEM and measurement. Magnetic flux density (T) Error (%) Measurement 0.278 -- Electromagnetic FEM 0.280 0.72

Using the commercial statistical program MiniTab (13), DoE was performed to optimize the dimensions of the obtained FE model in order to determine the best MFG magnetic flux density. Likewise, DoE was used to determine the factors affecting the magnetic flux density of the MFG and their corresponding levels: these factors were the height (L), the cross sectional area (A), and the number of coil turns (N) of the validated FE model (Fig. 5 and Table 3). Note that, in MiniTab, the number of experiments is determined by [K.sup.n]. where K is the number of levels and ii is the number of factors, and so the orthogonal array for the levels and factors is denoted by [L.sub.9]([3.sup.3]) when there are three levels and three factors (Table 4).

TABLE 3. List of factors and levels for DoE. Factors Levels Boundary conditions L (height) 8 cm (three factors, 9 cm three levels) 10 cm A (area) 1.5 x 1.5 [cm.sup.2] 2.0 x 2.0 [cm.sup.2] 2.5 x 2.5 [cm.sup.2] N (turns) 800 turns 1000 turns 1200 turns TABLE 4. Experimental layout using array [L.sub.9] Assignment and levels and factors Control factors Characteristic value [magnetic Expt. No. L (cm) A ([cm.sup.2]) N (turns) flux density (T)] 1 8 [1.5.sup2] 800 0.227 2 8 [2.0.sup.2] 1000 0.294 3 8 [2.5.sup.2] 1200 0.363 4 9 [1.5.sup.2] 1000 0.234 5 9 [2.0.sup.2] 1200 0.293 6 9 [2.5.sup.2] 800 0.344 7 10 [1.5.sup.2] 1200 0.241 8 10 [2.0.sup.2] 800 0.280 9 10 [2.5.sup.2] 1000 0.356

Finally, the optimal levels (L, 8 cm; A, [2.5.sup.2] [cm.sup.2]; N, 1200) for each factor were obtained for the maximum characteristic value. The results of the main effect analysis were plotted in Fig. 6.

According to the results of the main effect analysis, the variation in height (L) did not significantly influence the magnetic flux density, while the cross-sectional area (A) was the most effective factor at controlling the magnetic flux density in the air gap of the MFG. Thus, in the MFG design, the height was .considered only in terms of kinematic geometry, while the cross-sectional area was increased to maximize the magnetic field strength.

The inducing current in the optimized MFG causes a natural frequency shift in the oscillator as the shear stiffness of the MRE changed. The accelerometer and the force transducer were placed on the oscillator and beneath the fixed--fixed end beam to measure their responses. respectively. The measured signals were then sent to the FFT analyzer, where the transfer function was obtained by FFT analysis. After the natural frequency of the oscillator was identified in the transfer function, it was substituted into Eq. 3. which represents the relationship between the shear modulus and natural frequency.

Thus, the frequency-shear modulus equation was derived from a mathematical model of the MREs and the oscillator, as shown in Fig. 7. This model, which has only one degree-of-freedom, consists of a mass (oscillator) and two springs (MREs). Hence, once the natural frequency of the oscillator is measured experimentally, the shear stiffness and modulus of the MREs can be obtained using Eqs. 1,3.

Accordingly, the relationship between the natural frequency of the oscillator and the stiffness of the MREs can be given by

[k.sub.t] = 2[[pi].sup.2][f.sup.2]m (1)

where f is the natural frequency of the oscillator, [k.sub.t] is the stiffness of the MREs in the shear direction, and m is the mass of the oscillator.

In Eq. 2, [G.sub.MRE] is the shear modulus of the MRE, A is the cross sectional area of the MREs in the shear direction, and t is the thickness of the MRE.

Assuming that the forces in the shear direction, [G.sub.MRE], A, and [k.sub.t] * t, are the same, we can derive the shear modulus, such that

[G.sub.MRE] = [k.sub.t]t/A (2)

Then, by substituting Eq. 1 into Eq. 2, the shear modulus of the MREs can be written as

[G.sub.MRE] = 2[[pi].sup.2][f.sup.2]mt/A (3)

Hence, by substituting the natural frequency of the oscillator into the frequency-shear modulus equation (Eq. 3), we were able to determine the shear modulus of the MREs due to the variable-induced current. Moreover, this evaluation mechanism, which used the single degree-of-freedom vibration method, was validated by the measured experimental transfer function.

RESULT AND DISCUSSION

SEM Validation of CIP Orientation in the Anisotropic MREs

Carbonyl iron powder (CIP), a magnetic reactive powder, is spherical particle with an average diameter of 4-6 [micro]m. Each particle has a silica coating to prevent oxidation and is an s-1641 grade product, which exhibits little deformation despite vulcanization at high pressures (14).

In fact, analysis of the SEM images revealed that the CIP particles remained spherical despite the compression process and that the diameter of almost all the particles was less than 10 [micro]m.

It is necessary to confirm the presence of defects and vapor, because this can degrade the mechanical properties of the MREs. However, defects and vapor were not found in the anisotropic MREs that were fabricated using an anisotropic mold, because the bumping process could be applied during curing process. The surface of anisotropic MRE was confirmed by SEM.

Anisotropic MREs have a higher shear modulus variation, because the CIP, which is oriented by an external strong magnetic field during the fabrication process, can easily be arranged into a chain-like structure. These findings indicate that the CIP orientation is a key factor in determining the MR effects of an MRE. In this study, the orientation of the CIP in the MRE matrix was validated by SEM images and compared to that of isotropic MREs, which were cured without the CIP orientation process after compounding. Cross-sectional SEM images of isotropic MREs are shown at 400X magnification in Fig. 8.

In particular, orientation of the CIPs was not detected in these images, regardless of the volume fraction of CIP.

In contrast, orientation of the CIP in the anisotropic MREs fabricated using an anisotropic mold was observed as shown in Fig. 9. The CIP in these MREs was distinctly oriented in the specimens containing 30 and 40 vol%. Yet, despite the increased loading volume fraction of the 50 vol% CIP, the orientation of the CIP in that specimen was not clearly visible. Accordingly, the critical volume fraction where the NR matrix, instead of the air, filled the space between the CIP under normal temperature, and pressure was identified as between 30 and 40 vol%.

Hence, one of the anisotropic MREs possessing 30 or 40 vol% of CIP was expected to have the highest shear modulus variation as a function of the variable-induced current.

Characteristics of the Shear Modulus of MREs Oriented by Various Fabrication Molds

Figure 10 compares the shear moduli of CIP with 30 and 40 vol% due to a continuously variable induced current from 0 to 3 A for an isotropic MRE, an anisotropic MRE oriented by neodymium magnets only, and an isotropic MRE oriented by an anisotropic mold.

These data indicate that the anisotropic MRE had a higher variation of its shear modulus than the isotropic MRE. It also verifies that the CIP orientation in MREs significantly influences the shear modulus variation. Furthermore, the anisotropic MRE oriented by the anisotropic mold had a much higher magnetic reactivity and shear modulus value than the anisotropic MRE oriented by neodymium only, even with the same CIP volume fraction. Because vapor was generated when the specimen was separated from the neodymium magnets, the shear modulus and magnetic reactivity decreased.

Variation Rate for the Shear Modulus of Anisotropic MREs due to CIP Volume Fraction and Induced Current

The six specimens of anisotropic MREs with 0, 10, 20, 30, 40, and 50 vol% carbonyl iron powder (C1P) were evaluated relative to the continuously variable-induced current from 0 to 5 A using the new evaluation system described in the previous sections. The natural frequency of the oscillator was identified through the experimental transfer function between the input signal of the force transducer and the response signal of the accelerometer. The identified frequency was then inserted into Eq. 3 to determine the shear modulus of the MREs due to the continuously variable-induced current.

As shown in Fig. 11, the variation rate for the shear modulus increased with increasing variable-induced current, except for the 30 vol% CIP specimen from 4 to 5 A. Because NR is a temperature-dependent viscoelastic material, it behaves like an elastomer at room temperature but turns into a soft viscoplastic or fluid when heated. This physical phenomenon results from inducing current over the magnetic saturation. Similarly, the variations in the shear modulus increased with increasing CIP volume fraction, except for CIP 50 vol%. This specimen likely did not exhibit an increase, because it had exceeded the critical volume fraction, leaving little space in the MRE material to accommodate the chain-like CIP orientation (15). Furthermore, the magnetic saturation point of CIP, which indicates the upper bound for the effective range of the induced current, was 4 A. Consequently, the shear modulus variation rate did not increase for induced currents greater than 4 A.

Determination for Fabrication Design of MREs with Respect to Variation of Shear Modulus

As shown in Fig. 12, the shear moduli linearly increased as a function of the volume fraction of CIP without inducing currents. Consequently, the appropriate volume fraction of CIP in MREs without inducing currents can be determined for any particular desired shear modulus. However, when the inducing current was nonzero, the shear modulus varied nonlinearly as a function of the volume fraction of CIP.

Accordingly, the experimental results indicated a maximum variation rate of the shear modulus at 76.3% with a 40 vol% of CIP and an induced current of 4 A in the effective range of the inducing current from 1 to 4 A (Fig. 13). However, the shear modulus variation rates with an induced current of 1 A were much lower than for any other induced currents, most likely because 1 A was insufficient to make the strong chain-like formation of CIP in the MREs. Consequently, it is necessary to have an induced current higher than 1 A to create the strong chain-like CIP formation in MREs.

Furthermore, the shear modulus variation rate of the 50 vol% CIP decreased more than that of the 40 vol% CIP (see Fig. 13), even though the shear modulus of the MRE with 50 vol% cm increased more than that with 40 vol% CIP (see Fig. 12) due to the increased concentration of CIP. In other words, the CIP with 50% volume fraction did not rearrange much within the chain-like formation during the orientation process, because the spaces where the particles of CIP could be oriented were insufficient in the NR matrix.

To quantitatively determine the volume fraction of CIP that would yield a rate of shear modulus variation greater than 50%, the value of the appropriate volume fraction was plotted in Fig. 13.

From this figure, it was possible to confirm the increase in the shear modulus variation due to the induced current. In addition, the CIP volume fraction achieving a variation rate greater than 50% was determined to be 34%, as shown in Eq. 4. Note that this result was obtained for an induced current of 4 A by linearly extrapolating from 30 to 40 vol%.

CIP(vol%) = 30 + [10 x (50 - 33.1)]/[76.3 - 33.1] = 34(vol%) (4)

Using this equation, the appropriate volume fraction of CIP in the MREs can be calculated to achieve a desired shear modulus variation rate. For example, if the desired shear modulus variation rate for the MREs is 50%, then the appropriate conditions for the fabrication design of the MREs based on NR include a CIP volume fraction of 34%, a CIP orientation formed using an anisotropic mold, which can generate a magnetic flux density of more than 0.6 T, and an induced current of 4 A. These conditions can further be used as guidelines for the fabrication design of MREs.

CONCLUSIONS

To improve the variation performance of the shear modulus for MREs due to a continuously variable-induced current, the following conclusions were obtained:

The orientations of anisotropic MREs for various CIP volume fractions were verified using SEM images. In particular, the critical CIF' volume fraction--that is, where the NR matrix filled in the space between the CIP instead of the air under normal temperature and pressure--was found to be between 30 and 40 vol% CIP.

Then the variation of the shear modulus was identified experimentally using a new evaluation system for MREs that were oriented by various fabrication molds, possessed a range of CIP volume fractions, and exhibited a continuously variable-induced current. The shear modulus variation of the anisotropic MREs oriented by anisotropic mold was investigated by the evaluation system for an induced current of 0 to 5 A and for various volume fractions of CIP. As a result, this study obtained a maximum shear modulus variation rate of 76.3% with CIP 40 vol% and an induced current of 4 A.

Moreover, the results of this study showed that it was possible to obtain the appropriate volume fraction of CIP and induced current for a desired shear modulus variation of an anisotropic MRE. Conversely, the volume fraction of CIP in MREs can be determined in advance according to the desired shear modulus and its variation range. Thus, appropriate CIP volume fractions and induced currents can be proposed as guidelines for the fabrication of MREs.

The proposed MREs in this study, with their variable shear moduli, are applicable to numerous mechanical system devices for semiactive vibration control.

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Ji-Hyun Yoon, (1) In-Hyung Yang, (1) Un-Chang Jeong, (1) Kyung-Ho Chung, (2) Jung-Youn Lee, (3) Jae-Eung Oh (4)

(1.) Graduate School of Mechanical Engineering, Hanyang University, Seoul, South Korea

(2.) School of Polymer Engineering, Suwon University, Hwaseong, Gyeonggi Province, South Korea

(3.) School of Mechanical System Design, Kyonggi University, South Korea

(4.) School of Mechanical Engineering, Hanyang University, Seoul, South Korea

Correspondence to: Jae-Eung Oh; e-mail: jeoh@hanyang.ac.kr

Contract grant sponsor: Ministry or Education, Science and Technology (Basic Science Research Program); contract grant number: 2011-0002879.

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

DOI 10.1002/pen.23349

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Author: | Yoon, Ji-Hyun; Yang, In-Hyung; Jeong, Un-Chang; Chung, Kyung-Ho; Lee, Jung-Youn; Oh, Jae-Eung |
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Publication: | Polymer Engineering and Science |

Article Type: | Report |

Geographic Code: | 9SOUT |

Date: | May 1, 2013 |

Words: | 4486 |

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