Thermal effects on the laminated magnetorheological elastomer isolator

In this work, room temperature vulcanizing (RTV) silicon rubber (Model SC-2110, Beijing Sanchen Industrial New Material Co., Ltd, China) was chosen as the MRE matrix. Soft magnetic carbonyl iron particles (CIP, Model JCF2-2, d = 5 ∼ 8 $\mu {\rm{m}},$ Jilin Nichkel Industry Co., Ltd, China) were used as the filling particles, while silicone oil was used as the plasticizer. The mass fractions of CIP, RTV silicon rubber and silicon oil were 70%, 15% and 15%, respectively. After being stirred for 25 min, with the viscosity of reactants increasing obviously, the mixture of CIP, RTV silicon rubber and silicone oil was placed in a vacuum oven to remove air bubbles and then poured into aluminum molds. Eventually, after curing for 24 h under a constant magnetic field of 0.7 T, MRE samples used for the isolator were prepared completely.

The dynamic mechanical properties of the MRE samples with various temperatures (30 °C, 50 °C, 70 °C, 90 °C) and strain of 0.1% investigated using an advanced rheometer (Model MCR301, Anton Paar, Austria) are presented in figure 1. The testing frequency is 10 Hz and the magnetic flux densities increase from 0 to 0.85 T. Figure 1(a) gives the relationship between the shear storage modulus and the magnetic flux density, where the shear storage modulus increases nonlinearly with increasing magnetic flux densities and decreases with increasing temperature. The stable shear storage modulus with the temperature of 90 °C at 0.85 T is 1.01 MPa, which is attenuated by 28.37% compared with the modulus of 1.41 MPa for 30 °C. Moreover, figure 1(b) presents the shear loss modulus versus magnetic flux density under different temperatures, in which the maximum shear loss modulus is 0.1 MPa at 90 °C, a reduction of 33.70% compared with 30 °C. Accordingly, high temperature will reduce the shear storage modulus and shear loss modulus of RTV silicon rubber based MRE samples for the high temperature softening of the MRE matrix.

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Figure 2 gives the structural configuration diagram of the MRE isolator used for lateral vibration suppression of the bridge monitoring equipment; it is similar to the structure of traditional rubber bearings[40, 41], which can greatly enhance vertical bearing capacity. It consists of six layers of MREs with 2 mm thickness bonded to five layers of thin steel plate with 1 mm thickness by homemade silicone rubber adhesive. The laminated MREs are placed in the centre of an electromagnetic coil, which provides a uniform magnetic field when current is passed through it. The coil, whose electric resistance is 3 Ω, is made of copper with diameter of 0.8 mm and wound on a coil bobbin. The distance between the laminated MREs and the coil bobbin gives the MRE isolator a maximum deformation of 4 mm. In order to improve the stability of top cover and increase the vertical carrying capacity of the laminated MRE isolator, a small gap between the top cover and the steel sleeve is designed, where 80 steel balls are evenly distributed.

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The maximum power ${P}_{\max }$ of the coil under maximum operating current ${I}_{\max }$ of 3 A is represented by

$$\begin{eqnarray}&&{P}_{\max }={{I}_{\max }}^{2}R\end{eqnarray} \tag{ 1 }$$

where $R$ is the electric resistance of the coil. The maximum power ${P}_{\max }$ can reach 27 W, ignoring the impact of temperature on the electric resistance. As a result, the heating of the coil will be very significant with 3 A current for a long working time.

Figure 3 gives the magnetic flux density and magnetic flux path under the excitation current of 3 A by Ansoft Maxwell. The result of figure 3(a) indicates that the distribution of magnetic field is uniform under the working area of the laminated MREs with the magnetic flux density of 420 mT. Figure 3(b) shows that the magnetic lines of flux pass perpendicularly and uniformly through the cross-section of the laminated MREs, in order to ensure that the working area has the most effective magnetic field.

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The performance of MREs will change with the environmental temperature, which determines the stability of MRE isolators in different temperature environments. Nevertheless, the internal temperature of the MRE isolator will be increased due to the heating of the coil in the running process. Therefore, it is necessary for the MRE isolator to monitor its internal temperature and a temperature measurement system is set up as shown in figure 4(a) for this purpose. Three spherical temperature probes of a thermocouple thermometer (Model F-8855, Shenzhen Frank Electronic Co., Ltd, China) with diameters of 1 mm, shown in figure 4(b), are fixed between the MRE and the steel sheet. The specific arrangement of five measuring points is displayed in figure 5, where the temperature at each layer of the MRE is obtained by taking the mean value of points a,  b and c. During the experiment, a DC power (Model WYK-305B, EAST Electric Power System Technology Co., Ltd, China) is employed to supply 3 A current to the MRE isolator for 145 min and the data of temperature are recorded every 5 min.

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The temperature-time curves shown in figure 6 illustrate that the data from the five measuring points increases nonlinearly with the increase of time and decreases with increasing measuring point number. Because the metal has good thermal conductivity, the heat will be transferred through the backplane to the lowest MRE, which will cause the temperature of the lowest MRE to rise quickly. However, when the thermal equilibrium is reached, the temperature of each layer of MRE is basically the same. This non-uniform temperature distribution will make the performance of each layer of MRE different, thus temperature compensation is required in further study to provide the same working environment for laminated MREs. The average temperature of the laminated MREs is consistent with the data from measuring point 3 and also has an obvious rise with the continuous operation of the MRE isolator, 26.6 °C for 0 min and 85.1 °C for 145 min, which increases by 219.92%. The testing results show that heating of the coil has a great influence on the temperature of the isolator. The total energy produced by the coil can be calculated by:

$$\begin{eqnarray}&&W={I}^{2}Rt=mc(T-{T}_{0})\end{eqnarray} \tag{ 2 }$$

where $W$ is the total energy, $I$ is the current in the coil, $R$ is the coil resistance, $t$ is the running time, $m$ is the total mass of the MRE isolator, $c$ is its specific heat capacity, $T$ and ${T}_{0}$ are the current temperature and initial temperature respectively. Formula (2) indicates that there is a positive proportional function between current temperature and running time. However, due to the heat exchange between the surrounding air and the sleeve of the MRE isolator, this linear relationship is destroyed. With the increase of ambient air temperature, the heat exchange between the two parts becomes weaker, until a state of equilibrium is reached. At this moment, the internal average temperature will reach a stable value (about 85.1 °C for 145 min).

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Experimental results prove that the interior temperature of the MRE isolator will increase rapidly after a long period of work. In order to further understand the effect of temperature on characteristics of the isolator, a sine sweeping-frequency vibration method is adopted to evaluate its transmissibility at different temperatures. The resonant frequency, the stiffness and the damping of the prototype can be obtained to characterize its performance.

3.2.1. Experimental setup

Figure 7 gives the experimental setup for the evaluation of properties of the MRE isolator at various temperatures. The sine sweeping-frequency waveform produced by a signal generator (Model 33120A, Agilent, USA) is amplified by a power amplifier (Model YE5874, Sinocera Piezotronics, China) to drive an electromagnetic exciter (Model JZK-50, Sinocera Piezotronics, China). A horizontal sliding table constructed by ourselves is connected with the exciter to form a complete excitation system. The MRE isolator is installed on the sliding table and moves along with it. Two accelerators (Model 333B52, Piezotronics, USA) are arranged on the surface of the sliding table and the top cover to measure the excitation and response signals. Two kinds of signals are collected by a data acquisition instrument (Model MDR-05, Beijing Aerostandard New Technology Company, China) and transferred to a computer. Meanwhile, the DC power is used to supply DC current and change the internal temperature recorded by the thermocouple thermometer whose probes are arranged at measuring point 3 in real time for the MRE isolator.

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For all tests, a sine sweeping-frequency excitation within a range from 5 Hz to 40 Hz was chosen to test the transmissibility of the MRE isolator, while DC current was independently altered from 0 A to 3 A in 1 A increments. A set of tests were carried out at intervals of 10 °C as recorded by the thermometer; the initial and final temperatures were 30 °C and 80 °C respectively.

3.2.2. Analysis and discussion of results

The magnitude-frequency curves of transmissibility with different currents under the conditions of high temperature (80 °C) and low temperature (30 °C) are displayed in figure 8. As is shown in the figure, the resonant frequency of the MRE isolator at high temperature is smaller than that at low temperature with the same current, while the peak of transmissibility is higher. The parameters of the MRE isolator, such as stiffness and damping, with the mass of 0.5 kg under different currents can be identified based on the test results and the formulas in [16, 31].

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Figure 9 presents the relationship of the resonant frequency and temperatures with several applied currents. It can be seen that the frequency decreases linearly with the increase of the internal temperature and the decreasing trend of different currents is basically consistent. Figure 10 gives the curves of different frequencies versus currents at several temperatures, which shows the nonlinear increase with consistent trend. Besides, the higher the temperatures are, the lower the resonant frequencies, which is consistent with the result shown in figure 9.

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All of the testing data are listed in the table 1. The maximum attenuation of the resonant frequency reaches 13.85% with the current of 3 A, while the temperature increases from 30 °C to 80 °C. Furthermore, as the temperature rises, the maximum increase of the frequency caused by currents will be attenuation and this phenomenon shows that high temperature can reduce the working width of the MRE isolator's frequency.

Table 1.  Resonant frequency (Hz) of the isolator with various currents and temperatures.

	Currents (A)
Temperature (°C)	0	1	2	3	Increase (0–3 A)
30	16.38	18.48	21.78	24.41	49.02%
40	16.17	18.08	21.23	24.00	48.42%
50	15.84	17.73	20.64	23.13	46.02%
60	15.50	17.03	19.66	22.56	45.55%
70	15.31	16.63	19.28	22.00	43.69%
80	14.88	16.16	18.88	21.03	41.33%
Attenuation(30–80 °C)	9.16%	12.55%	13.31%	13.85%

The resonant frequency of the MRE isolator is mainly influenced by its internal temperature and the excitation current, which has been demonstrated by the test results. The relationship between the resonant frequency, the temperature and the excitation current can be described by the following equation:

$$\begin{eqnarray}&&f=(\alpha {I}^{2}+\beta I+\gamma )T+bI+c\end{eqnarray} \tag{ 3 }$$

where $f$ is the resonant frequency, $I$ is the excitation current, $T$ is the internal temperature, and $\alpha ,$ $\beta ,$ $\gamma$, $b$ and $c$ are corresponding parameters. Based on the equation, it is found that when the excitation current is certain, there is a linear function between the internal temperature and the resonant frequency. $\alpha {I}^{2}+\beta I+\gamma$ is the slope of the function and $bI+c$represents the initial resonant frequency. On the other hand, if the internal temperature is certain, the relationship between the excitation current and the resonant frequency will be expressed by a quadratic function, of which $\alpha T,$ $\beta T+b$ and $\gamma T+c$ are the three coefficients. To evaluate the equation's effectiveness for predicting the performance of the MRE isolator at various currents and temperatures, a set of parameters are identified for the equation to fit the experimental data shown in figure 8 and table 1. In the identification process, a least-square method in MATLAB (2010a) is employed to determine the appropriate values listed in table 2 and root mean square error (RMSE) is used to evaluate the results. Figure 11 presents the comparisons between the predicted and experimental responses with the maximum RMSE of 0.73 Hz, which illustrates the validity of the formula (3).

Table 2.  Parameter values of the temperature-frequency equation.

Parameters	$\alpha$(Hz A−2 °C−1)	$\beta$(Hz A−1 °C−1)	$\gamma$(Hz °C−1)	$b$(Hz A−1)	$c$(Hz)
Values	0.0029	−0.0212	−0.0297	3.1306	17.1605

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Figures 12 and 13 present the curves of the stiffness and the damping, respectively, versus diverse temperatures with different currents. It is obvious that both stiffness and damping have a linear decreasing trend with the increase of temperature. All of the data are given in tables 3 and 4, where the maximum attenuation of the stiffness can reach 26.42% while the maximum attenuation of the damping is 34.55% with the temperature from 30 °C to 80 °C. Therefore, the internal temperature of the MRE isolator rising sharply during the long hours of work will seriously affect its stiffness and damping. High temperature causes the polymer matrix of the MRE to become soft, which leads to the decrease of the overall stiffness. In addition, the higher the temperature is, the shorter the relaxation time of polymer molecule chains [42]. The content of the tangled molecular chains of the RTV silicon rubber reduces with increasing temperature, and the friction between molecular chains of the MRE is reduced, which leads to the decrease of the damping with the increase of temperature [42].

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Table 3.  Stiffness (N m⁻¹) of the MRE isolator with various currents and temperatures.

	Currents (A)
Temperature (°C)	0	1	2	3	Increase (%)
30	5363.57	6857.74	9596.74	12109.75	125.78
40	5219.91	6551.66	9096.14	11655.45	123.29
50	4999.74	6294.97	8575.84	10802.72	116.07
60	4781.89	5807.72	7763.81	10268.03	114.73
70	4644.11	5528.19	7455.54	9762.53	110.21
80	4399.43	5210.80	7136.11	8910.60	102.54
Attenuation(30–80 °C)	17.98%	24.02%	25.64%	26.42%

Table 4.  Damping (N s m⁻¹) of the MRE isolator with various currents and temperatures.

	Currents (A)
Temperature (°C)	0	1	2	3	Increase (%)
30	8.213	10.798	15.270	18.660	127.20
40	7.663	9.959	14.120	16.902	120.57
50	6.860	9.481	12.913	15.566	126.91
60	6.288	9.107	11.589	14.889	136.78
70	5.879	8.317	10.868	14.448	145.76
80	5.375	7.483	9.999	13.443	150.10
Attenuation(30–80 °C)	34.55%	30.70%	34.52%	27.96%

The increase of temperature changes the properties of the MRE's matrix, so that the stiffness and the damping are reduced.  Whether the initial characteristics of the MRE isolator are changed over a long time at high temperature will directly affect its stability and controllability. With this in mind, a temperature repeated experiment at room temperature (26 °C) after working at high temperature is undertaken. The experimental system is shown in figure 7 and the MRE isolator is supplied 3 A current for 145 min until the internal temperature rises to 85 °C before each sweeping-frequency test. When the temperature is reduced to room temperature, the sine sweeping-frequency vibration experiment is carried out, whose measuring conditions are described in section 3.2. Five groups of tests are accomplished under the same test method and the interval between each test is 24 h. The results are presented from figures 14–17.

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The results show that the magnitude-frequency curves and the phase-frequency curves of transmissibility are basically the same at the same current. All test data listed in table 5 show that under the same current, the five groups of results are slightly in disagreement, with the maximum RMSE of 0.198 Hz, and there is no regular pattern between the data. Consequently, the transmissibility curves of the MRE isolator are basically consistent at room temperature after the repeated test. This means that high temperature only makes the matrix of the MRE become softer, and does not cause damage to the MRE. When the temperature is reduced to room temperature, the MRE restores to its original performance. As a result, good temperature repeatability of the MRE isolator has been attested, which is crucial for the stability and controllability of the isolator.