A new isolator for vibration control

A New Isolator for Vibration Control

Majid Behrooza, Joko Sutrisno

b, Xiaojie Wang

b, Robert Fyda

b,

Alan Fuchsb and Faramarz Gordaninejad

a†

a Department of Mechanical Engineering

b Department of Chemical and Materials Engineering

University of Nevada, Reno

Reno, Nevada 89557, USA

ABSTRACT

This study presents the feasibility of a new variable stiffness and damping isolator (VSDI) in an integrated vibratory

system. The integrated system comprised of two VSDIs, a connecting plate and a mass. The proposed VSDI consists of

a traditional steel-rubber vibration absorber, as the passive element, and a magneto-rheological elastomer (MRE), with a

controllable (or variable) stiffness and damping, as the semi-active element. MREs’ stiffness and damping properties

can be altered by a magnetic field. Dynamic testing on this integrated system has been performed to investigate the

effectiveness of the VSDIs for vibration control. Experimental results show significant shift in natural frequency, when

activating the VSDIs. Transmissibility and natural frequency of the integrated system are obtained from properties of

single device. The experimental and predicted results show good agreement between the values of the natural frequency

of the system at both off and on states. However, system damping predictions are different from experimental results.

This might be due to unforeseen effects of pre-stressed MREs and nonlinear material properties.

Keywords: Semi-active, isolator, magneto-rheological elastomers

1. INTRODUCTION

Magneto-rheological elastomers (MREs) have the potential to be used as semi-active controllable elements in base

isolators1 and tuned vibration controllers,

2-6 because their stiffness can be controlled by an applied magnetic field.

MREs are analogous to magneto-rheological fluids, with micron sized magnetic particles dispersed in an elastomeric

medium. MREs are solid, flexible, can operate at a wide range of frequencies, and tolerate large deformations in

tension, compression and shear. MREs also have a very fast response time (about one millisecond) under an applied

magnetic field. Using MREs in vibration devices has the advantage of no-leakage and no-sedimentation of ferrous

particles in comparison with MRFs. Furthermore, MREs can be used in variable stiffness devices for tuned vibration

control, since their stiffness changes when subjected to a magnetic field.

Variable stiffness isolators are intended to avoid resonant response during severe excitation motions by changing the

stiffness of the structure; thus, suppressing the system response. Most of the conventional VSIs are mechanical or

hydraulic systems and have inherent disadvantages, such as, complex structures, slow responses and leakage7-8

. A

variable stiffness and damping isolator (VSDI) employing MRE materials, which may provide a solution to overcome

these issues, has been proposed and investigated by the authors9. Figure 1 shows the schematic design of the proposed

† [email protected], Phone: 1-775-784-6990; Fax: 1-775-784-1701

VSDI device. The VSDI is composed of two low-carbon steel caps each embedding two coils to generate a closed-loop

magnetic field. The steel shims, rubbers and MREs are placed between the two thick steel plates. The MREs can be

activated by the magnetic field which is induced by four embedded coils inside the thick plates; thus, the shear modulus

of MREs can be adjusted by input electric current to the coil, resulting in variable stiffness and damping characteristics.

Previous study has shown that the VSDI is capable of simultaneously increasing its stiffness for over 30% and damping

properties for over 40%, when it is fully activated9.

In this study, an integrated system which consists of two VSDIs as vibration absorbers and a rigid plate with a mass as a

representative of a structure is designed, built and tested. The performance of the VSDI for vibration reduction of the

integrated system has been experimentally investigated using a shaking table test. By measuring the frequency response

of the integrated system, the capability of VSDIs in shifting the natural frequency of the system is observed. Unlike the

results of previous work, which assumed that the damping of MREs would not play a role in reducing vibration when a

magnetic field was applied 4-6

, the proposed MRE device provided damping change along with stiffness change.

2. MATERIAL PREPARATION

The elastomers used for MREs matrix should be durable with excellent mechanical properties. Two types of material

systems are developed and employed in the proposed VSDI device: (1) Plasticized silicone–RTV MRE (70wt.% iron)

was synthesized using GE Silicones RTV615 A which is vinylmethylpolysiloxane and RTV615 B which is

methylhydrogenpolysiloxane (GE). Iron particles were added, mixed completely, and poured into the mold. Then, the

pre-cured polymer was degassed at 25in-Hg vacuum for 30 minutes to remove the bubbles, and cured under 1.0 Tesla of

magnetic flux density at 70oC. (2) Silicone MRE (80wt.% iron) was synthesized using QM107A and QM107A

(hardness 7 durometer). Iron particles were added at 80wt%, mixed completely, and poured into the mold. Then, the

pre-cured polymer was degassed at 25in-Hg vacuum for 30 minutes to remove the bubbles, and cured under 1 Tesla of

magnetic flux density at 70oC. Rubber support was fabricated from a mixture of QM 113A and QM 113B. The

fabricated rubber support and mold are shown in Figure 2.

The formation of chainlike structures of magnetic particles within MREs is important for better performance. The

chains are formed by exposing the pre-cured silicone–RTV MREs mixture to a magnetic field during the curing process.

The chains formed in a MRE are locked in place during chemical cross linking of the elastomer. The distribution of iron

particles within MREs can be confirmed using optical or electron microscopy. The strength of the chainlike structure

depends on the strength of the electromagnetic field. The cross-section of silicone–RTV MRE images from an optical

microscope are shown in Figure 3.

Figure 1. Schematic structure of the proposed VSDI employing MRE9.

MREs Coils Rubber

supports

A B

Direction of the

magnetic field

Figure 2. The fabricated rubber support and mold.

Figure 3. The optical images of aligned iron particles in silicone–RTV MREs:

(a) 2x, and (b) 20x in magnification.

3. VSDI CHARACTERIZATIONS

To use VSDI in systems for vibration control, their mechanical properties should be identified. Constant acceleration

vibration tests with swiping frequency technique are used to characterize each VSDI device, as well as, the integrated

system. By measuring the frequency response of the prototype, the transmissibility function versus sweeping frequency,

and different control input electric currents are obtained. The transmissibility function which is the ratio of magnitude of

output acceleration to the input acceleration and the phase angle difference of input and output accelerations as a

function of frequency are obtained.

New MREs and rubber materials along with new coil windings make the new VSDI’s properties different from the

previous testing results9. In this study all tests have been started from room temperature to ensure less temperature effect

on material property changes resulting in more repeatable results. In each test, the input electric current is kept at a

constant level of 0.0, 1.0, 2.0 and 3.0Amps, respectively. The same method in previous work9 has been used here to

obtain the stiffness and damping of the VSDI employing new MRE and rubber materials. The obtained stiffness (K) and

damping coefficient (C) of the VSDI with 80% wt. MREs under different input currents are listed in Table 1. These

results will be used in the theoretical analysis of an integrated system with two VSDIs in the next section.

Table 1. Characteristics of VSDI for Different Input Electric Currents and Acceleration Excitations.

4. PERFORMANCE OF THE INTEGRATED SYSTEM

In order to demonstrate the feasibility of utilizing the proposed VSDI for vibration control, two VSDIs are connected in

parallel to form a mass-spring-damper system. Its performance is studied under various vibration conditions using the

LDS shaking table, as shown in Figure 4. The VSDIs are installed on a horizontal LDS-Dactron air cooled shaking table

which runs on an oil film to reduce friction. VSDIs are secured to the shaking table and a connecting plate is glued on

top of them. A mass is introduced to the system, as the controlled mass. Two accelerometers are calibrated and installed

on the shaking plate and upper mass to measure the input and output accelerations, respectively. The total weight of the

mass component in the integrated system is 12.42Kg which consists of two VSDI top caps, a connecting plate and

supported mass.

The experiments are carried out using constant acceleration excitation inputs of 0.05, 0.10 and 0.20g with a frequency

range of 5 to 60Hz. An electric current ranging from 0 to 3Amps is applied to the VSDIs to change their damping and

stiffness during each set of tests. Each test has been started from room temperature. The proposed integrated system

with two VSDIs is considered a single-degree-of-freedom (SDOF) vibration system which consists of a mass, adjustable

stiffness spring and variable damping dashpot, as shown in Figure 4 (b). Data acquisition system is used to collect both

input and output accelerations and further to obtain transmissibility function for each applied current.

(a) (b)

Figure 4. a) Photo of the experimental setup for integrated system of VSDIs b) equivalent

mechanical model with mass, a variable spring and a variable dashpot system.

0.05g 0.10g 0.20g

Input Current

(Amp) K (KN/m) C (N.s/m) K (KN/m) C (N.s/m) K (KN/m) C (N.s/m)

0 75.36 52.89 148.49 81.94 141.06 74.29

1 86.26 57.76 164.77 80.99 152.98 95.12

2 96.20 63.39 185.89 88.61 172.92 89.02

3 100.98 60.77 209.26 86.58 177.08 91.41

Power input

(connection to

power supply)

m

K(I) C(I)

Accelerometer

Controlled

mass

Shaking

chamber

Accelerometer

Shaking

direction

Variable Stiffness and

Damping Isolator

(VSDI)

5. RESULTS AND DISCUSSION

The stiffness and damping properties of the single VSDI has been obtained are listed in Table 1. These properties are

functions of applied electric currents and input acceleration amplitudes. To model the behavior of the integrated system

based on the SDOF system with variable stiffness and damping characterizations, the following formula is used to find

the transmissibility function of the tested system as a function of frequency and applied currents10

:

2

2

2

2

2

)(2

)(4)1(

)(2

)(41

)(

rImK

ICr

rImK

IC

rT

+−

+

=

(1)

where K(I) and C(I) are the variable stiffness and damping coefficient, and r is the frequency ratio and is equal to f/fpeak.

Here, f is the input frequency of the transmissibility function, and fpeak is the peak frequency (or natural frequency)

obtained from the following equation:

m

ImK

ICIK

f peak

−

=

2

)(2

)(21)(

2

1

π

(2)

A comparison of experimental and theoretical results using Equation (1) with parameters K and C from Table 1, are

shown in Figure 5 for both off state (zero applied input current) and on state (3Amp applied input current). This is a

typical transmissibility function of the integrated system in response to the base motion with peak 0.10g acceleration

sinusoidal excitations. For an ideal SDOF system, the transmissibility function shows that increased stiffness results in

shift in natural frequency to the right while damping increase results in peak amplitude of the transmissibility decrease.

As can be seen, the predicted peak values of the transmissibility function at both off and on states are not close to the

experimental results for the integrated system with two VSDIs installed. The possible reasons may be due to use of the

adopted damping coefficient into the SDOF model. The system damping properties play a significant role in reducing

vibration amplitude at resonance. Additional damping forces are not considered in the SDOF model including the

friction force within connection parts and enhanced damping force due to the compression of MREs with large mass

weight on them. Another possible explanation may be the excess height of the integrated system compared to a single

VSDI which results in rotational motion of the mass rather than single transitional motion. However, experimental and

predicted results show good agreement between the values of the natural frequency of the system at both off and on

states. This demonstrates that the obtained stiffness values of the single VSDI are more accurate than the values of

damping coefficients. Present experimental study also verifies that the shaking table testing method11

is appropriate to

characterize the VSDI stiffness properties, but not the damping.

The predicted natural frequency of the system is compared to that of the experiments. The results of experimental

natural frequency and the predicted ones for different activation currents are shown in Figure 5. The predicted natural

frequencies are slightly higher than that of the experimental ones for the entire range of applied electric currents. But,

the differences are within acceptable error range.

Additional results of acceleration transmissibility and phase angle of the integrated system, changed with activation

electrical currents, are presented in Figures 7a, 7b, 8a and 8b for 0.05g and 0.20g sinusoidal acceleration inputs,

respectively. Different trends in alteration of transmissibility and phase angle results in these Figures, demonstrate the

fact that system response is dependent of the input acceleration. From insert to Figure 7a and insert to Figure 8a, it can

be found that as a result of the temperature control test procedure, natural frequency increased almost linearly with input

current. This means that the MREs inside of the VSDI devices are not saturated by the applied current of 3Amp, which

means VSDI devices have the potential to induce more changes in the stiffness and the damping of the system, if more

electric current is applied.

0

2

4

6

8

10

12

14

5 10 15 20 25 30 35 40 45 50 55 60

Acce

lerati

on

tra

nsm

isib

ilit

y (

g o

ut/

g i

n)

Frequency (Hz)

Experimental 0 Amp

Experimental 3 Amp

Theoretical 0 Amp

Theoretical 3 Amp

Figure 5. Theoretical and experimental results of transmissibility function of the integrated system.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 1.0 2.0 3.0

Pea

k freq

uen

cy

(H

z)

Applied current (Amps)

Experimental

Theoretical

Figure 6. Theoretical results of natural frequencies of the integrated system

compared to experimental results for different applied currents.

0

1

2

3

4

5

6

7

5 15 25 35 45 55

Acce

lerati

on

tra

nsm

isib

ilit

y (

g o

ut/

g i

n)

Frequency (Hz)

19.0

21.0

23.0

25.0

27.0

29.0

0.0 1.0 2.0 3.0

Pea

k f

req

uen

cy (

Hz)

Applied current (Amps)

Increasing

magnetic

field

1 Amp 3 Amp

2 Amp

0 Amp

Figure 7a. Transmissibility of 0.05g sinusoidal constant amplitude acceleration input

for different input electric currents ranging from 0 to 3Amp.

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

5 15 25 35 45 55

Ph

ase

an

gle

dif

feren

ce, d

egree

Frequency (Hz)

Increasing

magnetic

field

1 Amp 3 Amp

2 Amp0 Amp

Figure 7b. Phase angle of 0.05g sinusoidal constant amplitude acceleration input

for different input electric currents ranging from 0 to 3Amp.

0

1

2

3

4

5

6

7

5 15 25 35 45 55

Acc

ele

rati

on

tran

smis

ibil

ity

(g

ou

t/g

in

)

Frequency (Hz)

19.0

21.0

23.0

25.0

0.0 1.0 2.0 3.0Pea

k f

req

uen

cy (

Hz)

Applied current (Amps)

Increasing

magnetic

field

1 Amp

3 Amp

2 Amp

0 Amp

Figure 8a. Transmissibility of 0.20g sinusoidal constant amplitude acceleration input

for different input electric currents ranging from 0 to 3Amp.

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

5 15 25 35 45 55

Ph

ase

an

gle

dif

feren

ce, d

egree

Frequency (Hz)

Increasing

magnetic

field

1 Amp 3 Amp

2 Amp0 Amp

Figure 8b. Phase angle of 0.20g sinusoidal constant amplitude acceleration input

for different input electric currents ranging from 0 to 3Amp.

6. CONCLUSIONS

Performance of an integrated system consisting of two VSDIs, a connecting plate and a controlled mass is investigated

using shaking table tests. Results illustrate that both stiffness and damping of the system can be changed by applying an

electric current to the VSDIs. The change in natural frequency of the integrated system shows that the proposed VSDIs

are capable of isolating structures from the ground vibration.

Predictions of the integrated system response based on characterization properties of a single VSDI device has been

carried out and the results are compared with experimental test data. A good agreement between the values of the

natural frequency of the system at both off and on states is achieved. However, system damping predictions are far from

experimental results; the predicted peak vibration reduction is about half of experimental results. This could be due to

several reasons. The additional mass in the integrated system which cause pre-stress in the MRE/rubber layer, may

increase friction and hence damping properties in the MRE. The nonlinear behavior of the system as a result of

rotational motion induced by increased height of the system versus a single VSDI, and also the non-linear nature of

MREs which are not considered in the simple SDOF model, could be other reasons for the difference between the

damping predictions with the experimental results.

ACKNOWLEDGEMENTS

This work was supported by the U.S. National Science Foundation. The authors are thankful for the encouragement of

Dr. M. P. Singh, the Program Director at NSF.

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