Exploring the vibration control potential of magneto-sensitive rubber

Exploring the vibration control

potential of magneto-sensitive rubber

Peter Blom

Stockholm 2005

Licentiate Thesis Royal Institute of Technology School of Engineering Science

Department of Aeronautical and Vehicle Engineering

Akademisk avhandling som med tillst˚and av Kungliga Tekniska H¨ogskolan i Stock-holm framl¨aggs till offentlig granskning f¨or avl¨aggande av teknologie licentiatexa-men torsdagen den 26:e maj 2005, kl 14.00 i sal MWL 74, Teknikringen 8, KTH, Stockholm.

TRITA-AVE -2005:18 ISSN -1651-7660

c

Abstract

Two new aspects of the dynamic behaviour in the audible fre-quency range of magneto-sensitive (MS) rubber are highlighted: the exis-tence of an amplitude dependence of the shear modulus—referred to as the Fletcher–Gent effect—for even small displacements, and the appearance of large MS effects. These results have been obtained experimentally and are subsequently used to model two examples of magneto-sensitive rubber isola-tors to show how by means of MS rubber they can be improved. The first model calculates the transfer stiffness of a torsionally excited isolator and the second one the energy flow into the foundation for a bushing inserted between a vibrating mass and an infinite plate. In both examples notable improvements in isolation can be obtained.

Licentiate Thesis

This licentiate thesis consists of this summary and three appended papers listed below and referred to as Paper A to Paper C.

Paper A

P.Blom, L. Kari 2005: “Amplitude and frequency dependence of magneto-sensitive rubber in a wide frequency range”. Accepted by Polymer Testing.

Paper B

L. Kari, P. Blom 2005: “Magneto-sensitive rubber in a noise reduction context—exploring the potential”. Submitted to Plastics, Rubber and Com-posites: Macromolecular Engineering.

Paper C

P. Blom, L. Kari 2005: “Smart audio frequency energy flow control by magneto-sensitive rubber isolators”. Submitted to Smart Materials and Struc-tures.

Contents

1 Introduction

1

2 Summary

2

2.1

Dynamic shear modulus measurements . . . .

2

2.2

Torsionally excited vibration isolator . . . .

3

2.3

Vibration isolation rubber bushing

. . . .

4

3 Future works

13

Acknowledgments

13

Paper A

Paper B

Paper C

1

Introduction

Materials have historically been categorized into two groups following their functions: structural materials utilized for their mechanical properties and so-called functional materials, of interest because of their physical/chemical properties. From that early partition the situation has evolved notably; the term intelligent or smart materials was coined some twenty years ago—before that, in the beginning of the last century the concept of multifunctional mate-rials denoting matemate-rials used for both their structural and physical/chemical properties was established—and research has since gained enormous clout and become a common denominator in fields previously considered disparate, such as medicine and mechanics. Smart materials can very roughly be said to be materials whose properties can be changed to meet changing conditions. Narrowing that wide concept down to that of magneto-sensitive materials the research into the field of magneto-sensitive materials was started in the end of the forties by Rabinow (1) who was working on magneto-sensitive fluids. Concurrently, Winslow (2) was working on electro-sensitive (ES) fluids. In tandem with their discoveries, research on MS and ES materials gained mo-mentum, but focus has until recently remained on ES materials. On the other hand MS materials have proven more commercially successful enhancing the notion of their large potential; this has lately prompted a large number of publications of research reports on MS fluids and solids alike (3; 4; 5; 6; 7). Magneto-sensitive rubber has become the subject of much research because of the wide presence of rubber in applications such as bushings and engine mounts for instance; the interest lies in the capability to dynamically change the apparent rubber stiffness and damping, achieved by applying a magnetic field over a rubber containing iron particles. The application of a magnetic field gives rise to a magnetic dipole-dipole interaction between the iron par-ticles causing the apparent changes in stiffness and damping.

Whereas the quasi-static behaviour of MS rubber has lately been studied extensively (8; 9; 10; 11; 12; 13), the dynamic properties, ranging into the audible frequency range, have been given less attention. Nonetheless, consid-ering the above mentioned examples of engine mounts and bushings—these are frequently subjected to vibrations ranging far into the audio frequency range—merely the quasi-static properties are not sufficient in describing the rubber behaviour. Because of the viscous nature of rubber the viscoelas-tic behaviour needs also be incorporated in order to properly describe the complex characteristics of rubber. Some research performed in this dynamic

range has yielded promising results in displaying among other things large responses to externally applied magnetic fields. Kari (14) has studied the MS effects over the same frequency range as in this work; however, since the displacement amplitude was not constant, the influence of the Fletcher– Gent effect (15) alone could not be observed. Lokander and Stenberg (16) have studied amplitude phenomena in the low frequency range (< 50 Hz) thus considering the Fletcher–Gent effect, but only for strains of 1.1 % and more. Bellan and Bossis (17), and Bossis, Coquelle and Kuzhir (18), have studied the amplitude dependence and magnetic sensitivity of the E modu-lus for strains of varying order, but only for low frequencies (5 Hz and 1 Hz respectively). In the first article include in this licentiate thesis the shear modulus and its magnetic sensitivity in the audible frequency range have been studied from 100 to 1000 Hz. Due to this wide frequency span, visco-elastic effects are covered in addition to magnetic ones, while simultaneously at all strains allowing for observation of the Fletcher–Gent effect—the rubber is subjected to constant shear strains as small as 0.0084 %. In this manner a more complete understanding of the separate effects of magneto-sensitive materials in the audible frequency range and their relative importance are ob-tained. Furthermore, the magneto-sensitivity is revealed to be surprisingly large, especially for small amplitudes. In the following two articles which are theoretical applications based on the experimental results obtained from the first one it is shown how vibration isolators in two cases can be greatly improved by adopting magneto-sensitive rubber.

2

Summary

2.1

Dynamic shear modulus measurements

Three pair of samples, with an iron particle volume concentration 0, 26 and 33 %, of natural and silicone rubber were tested. The particles are ran-domly dispersed within the rubber and irregularly shaped. Their size is less than 60µm. A test rig (Fig.1) was designed for dynamic shear modulus mea-surements. Two test samples of dimensions L×W×T=20 mm×15 mm×2 mm (length, width and thickness), are sandwiched between two brass plates used as fixtures. The excitation gives rise to a vertical motion that is transmitted by the brass plates to the test segments that in turn set the blocking mass in motion. The magnetic field is generated by an electro-magnet made by a

power-supplied coil wired round an iron C-frame directing a magnetic field perpendicularly to the shear direction. The excitation signal was a stepped sine signal, starting at 100 Hz and increasing with a constant frequency step of 10 Hz to the maximum frequency—1000 Hz for the three smallest ampli-tudes. The amplitude of the signal was constant at all frequencies and set to seven different values, ranging from 0.11 mm to 0.00017 mm. The results for the smallest amplitude for the silicone and natural rubber are displayed in Figs. 2 and 3. The strong magneto-sensitivity can be viewed in both figures for the magnitude of the shear modulus. Noteworthy is also the very small dependence of the loss factor on magnetic field, a fact that will greatly facilitate future modelling. The dynamic shear modulus for each of the two materials displays an amplitude dependence that is relatively large for even the smallest amplitudes. This can be deduced by comparing the curves in Figs. 4 and 5 representing shear modulus versus strain. Analysis of those graphs leads to the following: a decreasing vibration amplitude gives rise to an increasing magnitude and decreasing loss factor of the shear modulus. This behaviour derives from a phenomenon referred to as the Fletcher–Gent effect (15), whose influence on rubber subjected to small deformations is normally negligible. However, our observations reveal that in the entire fre-quency range the Fletcher–Gent effect is a highly important feature of MS rubber, therefore not to be disregarded even for very small amplitudes—these are of special interest in a structure-borne sound context where strains are often of small order, comparable to the ones presented in these experiments.

2.2

Torsionally excited vibration isolator

In this study a magneto-sensitive isolator’s audible dynamic stiffness is of interest. Consider the magnetic field exposed, cylindrical vibration in Fig.6, of height H=100 mm and diameter D=150 mm isolator, bonded to two cir-cular steel plates and torsionally excited by a rotation of Ω_e radians at the upper lateral surface, while being blocked at the lower surface by an applied torsional moment of T Newton meters per radian. The magneto-sensitive rubber consists of natural rubber with an iron particle volume concentration of 33%. For simplicity, assume a vibration displacement sufficiently small to permit a linearization with respect to amplitude while using the correspond-ing shear modulus at the smallest amplitude (correspondcorrespond-ing to the smallest strain in Fig.3). This results in a transfer stiffness according to Fig.7. The magnitude graphs reveal an almost 15 dB drop at around 150 Hz obtained by

applying a magnetic field of 0.8 T. Once the 0 T dynamic stiffness peak has been passed the magnetic field can be switched off according to the optimal path graph. This is of course a reversible process, meaning that frequencies can be shifted up and down and back and forth. Furthermore it can be done rapidly, due to iron’s magnetic properties.

2.3

Vibration isolation rubber bushing

A rubber vibration isolator bushing is studied. The isolator standing on a concrete floor of infinite extent can be viewed in Fig.8. It consists of a magneto-sensitive rubber bushing firmly bonded to an exterior circular iron shell. On the inside it is bonded to an iron rod connecting to the floor. The cylindrical shell supports a force excited rigid mass acting as a simplified source model. Between the mass and the iron shell is depicted a rigid non-magnetic ring whose mere function is to isolate the magnetic field from the mass. The magneto-sensitive rubber consists of natural rubber with an iron particle volume concentration of 33 %. For this rubber, the required shear modulus data at zero magnetic induction and at magnetic saturation is available from Fig.3 and is utilized in the model. Transmissibility with and and without applied magnetic field is displayed in Fig.9. Optimal isolation corresponds to as low an energy flow transmissibility as possible, and it can be seen that in a wide frequency range around 200 Hz a large reduction in transmitted energy is obtained when magnetically saturating the rubber. It is the first internal anti-resonance—the first dynamic peak stiffness frequency— that can thus be shifted upwards in frequency by applying a magnetic field. In this manner a maximum reduction of approximately 7 dB is obtained.

Vibration exciter Personal computer Control ch: in1 Control level: 0.04v Amplifier Power supply Charge amplifiers Frequency analyser Blocking mass Test samples Magnetic field Wire coil Accelerometers Auxiliary isolators Accelerometer

Figure 1: Measurement set-up

0 0.5 1 1.5 2 x 107 SR 33% Fe, 0.00017mm Magnitude (N/m 2 ) 100 200 300 400 500 600 700 800 900 10000 0.2 Loss factor Frequency (Hz) 0.8T 0.55T 0.3T 0T

Figure 2: Shear modulus magnitude |G| and loss factor Imag G/Real G versus frequency at induced magnetic field of 0, 0.3, 0.55 and 0.8 T, and constant dis-placement amplitude of 0.00017 mm. 0 5 10x 10 6 _{NR 33% Fe, 0.00017mm} Frequency (Hz) Magnitude (N/m 2 ) 100 200 300 400 500 600 700 800 900 10000 0.2 0.4 Loss factor Frequency (Hz) 0.8T 0.55T 0.3T 0T

Figure 3: Shear modulus magnitude |G| and loss factor Imag G/Real G versus frequency at induced magnetic field of 0, 0.3, 0.55 and 0.8 T, and constant dis-placement amplitude of 0.00017 mm.

0 0.5 1 1.5 2x 10 7 _{SR 33% Fe, 150 Hz} Magnitude [N/m 2 ] 10−4 10−3 10−2 0 0.05 0.1 0.15 0.2 Loss factor Strain 0.8T 0.55T 0.3T 0T

Figure 4: Shear modulus magnitude |G| and loss factor Imag G/Real G versus strain at induced magnetic field of 0, 0.3, 0.55 and 0.8 T at a frequency of 150 Hz.

0 2 4 6 8x 10 6 _{NR 33% Fe, 150 Hz} Magnitude [N/m 2 ] 10−4 10−3 10−2 0 0.05 0.1 0.15 0.2 Loss factor Strain 0.8T 0.55T 0.3T 0T

Figure 5: Shear modulus magnitude |G| and loss factor Imag G/Real G versus strain at induced magnetic field of 0, 0.3, 0.55 and 0.8 T at a frequency of 150 Hz.

Magnetic field Rubber matrix Iron particles ΩΕ T ∅D H Magnetic field z r

Figure 6: Magnetic field applied to a torsionally excited cylindrical vibration isolator of natural rubber with an iron particle volume concentration of 33%.

70 80 90 100

Rubber cylinder stiffness, NR 33% Fe

Magnitude [dB rel. 1 Nm/rad

] 100 200 300 400 500 1000 −800 −600 −400 −200 0 Phase [degrees] Frequency [Hz] 0.8T 0.55T 0.3T 0T Optimal

Figure 7: Torsional stiffness magnitude and loss factor versus frequency for a cylindrical vibration isolator of natural rubber with an iron particle volume con-centration of 33%.

Force on foundation ff

Concrete floor of infinite extent Excitation force fe The magneto-sensitive rubber bushing Cylindrical outer shell axially shearing the rubber Iron rod A non-magnetic, mechanically stiff ring Mass Iron ring directing the magnetic flow back through the rod

Bearing

uf Foundation displacement

z r

Figure 8: Picture of the axially symmetric designed model.

100 200 300 400 500 600 700 800 900 1000 −40 −35 −30 −25 −20 −15

Energy flow transmissibility

Frequency [Hz] 10log 10 |T e | dB Saturated state 0T Optimal transmissibility

Figure 9: Energy flow transmissibility with and without magnetic field. The path for optimal isolation is marked by circles.

3

Future works

Future works consists in creating a non-linear model—including the ampli-tude dependence—for the constitutive behaviour of the magneto-sensitive rubber based on the experimental results from the first article. A fractional derivative representation will be employed to describe the viscoelastic be-haviour and a frictional model for the amplitude dependence. In addition to this the magneto-sensitivity will be included in the model.

Acknowledgments

The financial support from the Swedish Research Council (Contract no: 621-2002-5643) is gratefully acknowledged. I would like to express my special thanks to my supervisor Leif Kari for excellent guidance through the course of this project. My thanks also to Kent Lindgren and Danilo Prelevic for pro-fessional and encouraging assistance in my experiments and to my colleagues at MWL. Finally I thank my family and friends for their cordial support.

References

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