The Delta-E effect in Terfenol-D and its application in a tunable mechanical resonator by Rick Allen

101 Pages·2003·1.13 MB·English

by  Alison Flatau

The Delta-E effect in Terfenol-D and its application in a tunable mechanical resonator

by

Rick Allen Kellogg

A thesis submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE

Major: Engineering Mechanics
Major Professor: Alison Flatau

Iowa State University
Ames, Iowa
2000

iii
TABLE OF CONTENTS

1. INTRODUCTION AND RESEARCH MOTIVATIONS 1

2. WATER-COOLED TRANSDUCER DESIGN 27

3. BLOCKED-FORCE TESTING AND RESULTS 33

4. CYCLIC STRESS TESTING AND RESULTS 44

5. AIR COOLED TRANSDUCER DESIGN 64

6. MECHANICAL RESONANCE TESTING AND RESULTS 72

7. CONCLUSIONS 81

APPENDIX A. WATER-COOLED TRANSDUCER DRAWINGS 83

REFERENCES 95
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ACKNOWLEDGMENTS

A number of people deserve recognition for their contributions, which made it possible for me to
complete the work presented in this thesis. I would like to acknowledge my POS committee: Alison B.
Flatau, David C. Jiles, Alan M. Russell and Jerald M. Vogel. I would like to give special thanks to my
major professor Alison B. Flatau, for her guidance, encouragement and support.
I would also like to thank Marcelo J. Dapino for his advice and collaboration. His healthy
skepticism helped keep me on track throughout my Terfenol-D research efforts. Additionally, Kenneth G.
McConnell’s guidance with vibration testing was invaluable. For their efforts in data collection, modeling
and building experimental equipment, I would like to acknowledge Nicholas Burgart and Nicholas
Lapointe.
I am grateful to the AEEM Department staff, whose help was definitely appreciated. These
individuals are: Jeff Eichorn, Thomas Elliot, Gayle Fay, Lauri Hoifeldt, Colleen Johnson and Delora
Pfeiffer. Furthermore, none of this experimental work would have come to fruition without the capable
efforts of the university’s machinists Kevin Brownfield, Richard Egger and Terry Soseman
I am indebted to my wife, Rebecca, for introducing me to the world of Engineering Mechanics and
her unwavering support.
The NSF Division of Civil and Mechanical Systems provided financial support for this research.
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ABSTRACT

The variability of Young’s modulus in giant magnetostrictive Terfenol-D has a significant impact
on the performance of Terfenol-D transducers. While elastic modulus variability introduces nonlinearities
in the transducer input/output relationship that are often deemed undesirable, it also affords opportunities
for achieving novel device performance attributes. Terfenol-D’s modulus of elasticity can be changed by
four-fold or more during operation through the variation of a d.c. applied magnetic field. This thesis
describes research conducted to better understand and demonstrate the potential use for modulus variability
to control transducer stiffness in real time and thereby achieve desired changes in the device performance.
The first part of this thesis focuses on a study of the blocked force characteristics of a Terfenol-D
transducer and provides data typical of output-force strain relationships under controlled thermal, magnetic,
and mechanical loading conditions. The design and construction of the transducers used in these
investigations are described. Results of compression tests for a range of applied magnetic fields and two
initial mechanical stress states are used to generate load lines and the blocked force characteristics for the
transducer. This test data is examined to quantify the variability in Young’s modulus with applied magnetic
field, strain and stress. In the second part of the thesis, the effect of Terfenol-D’s modulus of elasticity
variability is examined under quasi-static cyclic stress and d.c. applied magnetic field conditions. This
guides the development and testing of a transducer employed as a wide-band variable frequency
mechanical resonator. The design and construction of such a wide-band mechanical resonator for testing
under controlled thermal, magnetic and dynamic mechanical load conditions are described. Controllable
elastic modulus changes, the D E -effect, approaching 266% are demonstrated in the mechanical
H2H1
resonator utilizing a range of d.c. applied magnetic field levels of less than 61.0 kA/m. Additionally, an
increase in the transducer stiffness with a decrease in the externally imposed cyclic stress amplitudes is
observed.
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1. INTRODUCTION AND RESEARCH MOTIVATIONS

1.1 Motivation for research on the blocked force output and the delta-E effect in Terfenol-D
Effective use of a transducer requires knowledge of its displacement and force output under a
given input as well as its response to variable applied loads. As transducers utilizing the magnetostrictive
alloy Terfenol-D find increased use, a better understanding of their characteristics is needed to improve
modeling and control. Many effects are associated with the magnetostrictive phenomenon utilized in these
transducers one of which is an operational variability in the modulus of elasticity. The large
magnetomechanical coupling of Terfenol-D facilitates these large modulus changes. While modulus
variability complicates conventional transducer uses for generating outputs or sensing, it also opens the
door to new possibilities. The utility of a material with a Young’s modulus of elasticity that can be changed
through the variation of one DC electrical input parameter is extensive. Suggested applications include
variable frequency resonators, variable acoustic delay lines and parametric amplifiers.
This thesis explores the magnetostrictive material Terfenol-D using quasi-static and dynamic
experimental stress techniques. Quasi-static changes in transducer displacement and force output for
different applied magnetic field inputs will be examined. Furthermore, quasi-static methods are used to
examine the conditions under which continuous modulus changes exceeding 400% may be achieved.
Modulus changes approaching 266% are also demonstrated dynamically in a wide band variable frequency
resonator utilizing applied magnetic fields of less than 61.0 kA/m (760 Oersted). Additionally, observations
of an unusually high apparent modulus for low cyclic stress conditions are discussed. The design, modeling
and operation of the thermally controlled transducers used throughout this investigation are detailed.

1.2 Terfenol-D basics
Magnetostriction is the phenomenon of a ferromagnetic material undergoing a dimensional change
or strain induced by changes in its magnetization. Essential to understanding a Terfenol-D transducer’s
force and displacement output relationship as well as Terfenol-D’s variation in Young’s modulus, one must
have a basic understanding of the magnetostrictive process.

1.2.1 History of magnetostriction
Magnetostrictive strain, denoted by l , is defined as the change in length due to magnetization
divided by the original length. The magnetostrictive phenomena was first reported 1842 by James Joule
upon observing that when an iron (Fe) bar was subjected to a magnetic field it underwent a length change
as its magnetization changed [Lee 1955]. A reciprocal effect known as the Villari effect also occurs where
the stress induced dimensional change of a ferromagnetic material generates changes in its magnetization.
Further investigation of magnetostrictive materials into the 1900’s led to the utilization of nickel and
Permalloy in telephones and oscillators, sonar and torque meters [Hunt 1953]. Early examples of
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magnetostrictive materials include iron, nickel and cobalt with nominal saturation magnetostrictions of –9,
-40 and –60 ppm, respectively [Restorff 1994]. Later, in 1963 and 1964, it was discovered that rare earth
metals such as dysprosium (Dy) and terbium (Tb) exhibit giant magnetostriction (strains greater than 1500
ppm) at cryogenic temperatures [Meeks and Timme]. In 1971, through an effort at the Naval Surface
Warfare Center to improve sonar technology, a major advance was made in giant magnetostrictive
materials. It was found that when the rare earth metals Dy and Tb are alloyed with iron the resulting
material, coined Terfenol-D, exhibits giant magnetostrictive behavior at ambient temperatures [Clark
1980]. Terfenol-D’s strain of up to 2000 ppm is between ten to one hundred times greater than what was
observed in the early metals and alloys. Terfenol-D, with the stoichiometry of Tb Dy Fe where y @ 2.0
.x 1-x y
and x @ 0.3, became commercially available in the 1980’s through ETREMA Products Inc. of Ames, Iowa,
USA.

1.2.2 Magnetostriction processes
The phenomenon of magnetostriction is rooted in the interaction of electron spin and orbital
angular momenta with the crystal lattice spacing. Heavy rare earth elements of the lanthanide series such as
Samarium, Terbium, and Dysprosium exhibit large magnetic moments due to a coupling between their
electron spin and orbital angular momenta [Clark 1980]. As a result, in these materials the lattice spacing
and overall dimensions are strongly influenced by the state of magnetization. Described by [Jiles 1998]
among others, fundamental to the magnetization of ferromagnetic materials, regions of 1012 to 1018 atoms
achieve common alignment of their magnetic moments to form magnetic domains through the long-range
interaction, termed the Weiss mean field. The size and number of magnetic domains as well as their
orientation is governed by a balance between the crystalline anisotropy, elastic interaction and applied
magnetic field energies.
There are two regimes of magnetostriction. The first one, spontaneous magnetostriction denoted
by l , is the strain that occurs upon cooling of a ferromagnetic material through its Curie temperature. At
o
the Curie temperature, magnetic moments transition from an unordered paramagnetic state into ordered
domains. Above the Curie temperature, thermal energy overcomes the Weiss mean field thus disrupting the
alignment of magnetic moments and preventing the formation of magnetic domains.
The second regime of magnetostriction, which is pertinent to this investigation, occurs due to
magnetization changes of the material due to applied magnetic fields below the Curie temperature. The
process of magnetostriction may be understood in a classical sense with a material’s crystal lattice being
coupled to the magnetic domains. The crystal lattice is spatially elongated in the direction of the
magnetization vector for materials exhibiting positive magnetostriction. The end result is asymmetrical
lattice spacing with the strain of the material being determined by orientation of the magnetic domains.
There is, however, a limit on the amount of magnetostriction possible. Once all the magnetic moments
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become aligned with the applied field, a single domain is formed and little further strain is possible. This
strain limit is termed technical saturation magnetostriction and is denoted by l .
s

1.2.3 Magnetostriction in Terfenol-D
The Terfenol-D material used in this investigation has stoichiometry of Tb Dy Fe and was
0.27 0.73 1.95
manufactured as a monolithic crystal using the free-stand-zone melt process. The resulting crystal structure
is cubic. Terfenol-D has a positive magnetostrictive strain coefficient and features a large magnetostrictive
anisotropy in accordance with its crystallographic structure. Magnetostrictive anisotropy dictates the
material's preferred magnetic domain orientation through energy minimization and is determined in part by
the material’s stoichiometry. Figure 1.1 depicts a schematic of the crystallographic structure of Terfenol-D
within the confines of a cylindrical shaped sample as used in this study. The collective group of <1 1 1>
axes constitutes the easy axes. That is, the magnetocrystalline anisotropy favors alignment of the magnetic
domains along these axes. Considering magnetization vectors in the [1 0 0] plane, the [1 1 -1] vector is
within 19.5(cid:176) of the rod axis. Since Terfenol-D exhibits positive magnetostriction, domain rotation into the
direction of the [1 1 –1] vector causes the rod to lengthen. The [1 1 1] vector, which points in a direction
nearly perpendicular to the rod’s axis, is also an easy axis. Application of compressive stress along the
rod’s longitudinal axis favors the alignment of magnetic domains in the [1 1 1] direction. Note that
magnetostriction in Terfenol-D is the product of 90(cid:176) domain rotation processes. As a result, magnetization
due to an applied field in either the [1 1 -2] or [1 1 2] direction result in positive magnetostriction.

Figure 1.1 Crystallographic structure of Terfenol-D [Cedell 1995].
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Taking a closer look at the magnetization processes in the [1 0 0] plane, Figure 1.2 shows the
progression from the demagnetized state to technical saturation as a magnetic field is applied in the [1 1 –2]
direction. Stage 0 depicts the initial condition where Terfenol-D is in a demagnetized state. The magnetic
domain vectors are not collectively oriented and sum to zero magnetization. Upon the application of the
magnetic field, H, in stage I, domains more closely aligned with the applied field grow at the expense of
less favorably oriented domains. This process, termed domain wall motion, reflects the changes in domain
boundaries as magnetic moments reorient. As the applied field is increased further, stage II is reached,
where the material becomes one domain rotating into alignment with the [1 1 –1] axis. Completing the
magnetization process, stage III develops with an additional increase in applied field. The domain
orientation rotates from the easy [1 1 –1] axis into the [1 1 –2] direction of the applied field. At this point
technical saturation has been reached.

0 I II III
Figure 1.2 Magnetization process with applied field (Dapino 1999).

The magnetization and magnetostriction response of Terfenol-D are summarized graphically in
Figure 1.3 for an axially applied magnetic field increasing from zero. In stage I, as magnetization slowly
increases from zero with domain wall motion, strain also increases slowly. Stage II follows with a rapid
increase in magnetization as domain rotation into the [1 1 –1] easy axis occurs. Accompanying the rapid
magnetization, magnetostriction progresses rapidly forming the “burst region” of the magnetostrictive
process. With stage III, magnetization and magnetostriction increase at a diminishing rate finally reaching
technical saturation. Beyond technical saturation and technical magnetostriction, slight increases in
magnetization and magnetostriction occur as magnetic moments are forced out of precession into complete
alignment with the applied field [Jiles 1998].
5

(a) (b)
Figure 1.3 Simulated initial magnetization (a) and magnetostriction (b) with applied field (Dapino 1999).

Most ferromagnetic materials are anisotropic and the saturation magnetostriction varies along the
different crystal axes aligned with the applied magnetic field. Terfenol-D undergoes positive strain through
magnetic saturation regardless of the direction of the applied field. However, perpendicular to the applied
field, transverse magnetostriction occurs with a strain of opposite sign and one half the magnitude of that in
the axial direction. The net effect of axial and transverse strains results in a nearly constant volume process
thereby giving Terfenol-D a Poisson’s ratio of approximately 0.5 [Jiles 1998].
It is evident in the simplified simulation of Figure 1.3, that magnetostriction is a nonlinear process.
Furthermore, magnetostriction is also a nonsingular process. Figure 1.4 shows a typical strain response for
Terfenol-D in the [1 1 –2] direction with axially applied magnetic field.

ln,
o
stricti
o
et
n
g
a
M

0 0
Applied field, H
Figure 1.4 Magnetostriction versus applied field.