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Magnetism and Magnetostriction
Coupled linear equations
The magnetostrictive process relating the magnetic and mechanical states can be described with two
coupled linear equations (Clark, 1980). These equations of state for an element are expressed in terms
of mechanical parameters (strain ε", stress σ and Young’s modulus at constant applied magnetic field
EHy), magnetic parameters (applied magnetic field H, magnetic induction B, and permeability at constant
stress μ^σ), and two magneto-mechanical coefficients d=∂ε/├ ∂H┤|_σ and ├ d^*=∂B/├ ∂σ┤|_H )
■(ε& =σ/(E_y^H )+dH @&) (1)
B=d^* σ+μ^σ H (2)
In these equations ε and B are dependent on σ and H, which are externally applied. The application of a
stress will cause a change in the magnetic induction as seen in Equation (2).
This can also be expressed as a change in permeability by writing Equation (2) in a more general form,
B=μH (3)
Ampere’s law of magnetism
In the early nineteenth century, Oersted discovered that a moving charge generated a magnetic field in a
plane perpendicular to the direction of charge motion. Thus, a current in a conductor could be used to
produce a magnetic field around the conductor.
Ampere’s law describes this electromagnetic relationship. For a long, thin solenoid of number of turns,
Nc, and length, Lc, a simple expression is derived,
H=(N_c I)/L_c (4)
Faraday–Lenz law of magnetism
Placing a magnetostrictive element inside such an excitation coil (solenoid) with an impressed current I
provides an efficient means of magnetizing the element. The law of electromagnetic induction (Faraday–
Lenz law) describes how a magnetic flux, ’¼BAc in area Ac, induces a potential in an electrical conductor
to which it is flux-linked. In its simplest differential form, the Faraday–Lenz law is given by
V=-N_c dφ/dt=-N_c A_c dB/dt (5)
where V is the induced voltage in the solenoid of constant area Ac. The negative sign indicates that the
voltage measured is 180˚ out of phase with flux φ. According to this law, a potential will be induced in
any electrically conducting material that makes up the magnetic circuit.
Gauss’s law of magnetism
The excitation coil described by Equation (4) can be used to generate a magnetic field in a sample
spatially separated from the coil. According to Gauss’s law of magnetism,
∇.B=0 (6)
the divergence of B is zero. This means that the magnetic flux is always conserved. Thus, magnetic flux
lines close, defining a magnetic circuit, and elements of the magnetic circuit through which magnetic flux
flows are said to be flux-linked.
This makes it possible to magnetize one component of the magnetic circuit by generating a magnetic
field in another component.
Based on the principle expressed by Equations (5) and (6), it is possible to measure the magnetic flux
density in a magnetic circuit by the voltage induced in a flux-linked coil. These coils are often referred to
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as detection, receiving, or sensing coils.
aspects of a material’s magnetic-mechanical coupling
Various aspects of a material’s magnetic-mechanical coupling can be employed to sense parameters of
interest.
The Joule effect
The first of the magnetomechanical effects to be thoroughly documented (in 1842), is a longitudinal
change in length due to an applied magnetic field. A transverse change in length and associated
volumetric change are also observed. Although the Joule effect is usually associated with the actuation
capability, numerous sensor configurations rely on the excitation of the magnetostrictor to facilitate
sensing.
The Joule effect has an important reciprocal effect known as the Villari effect; a stress induced in the
material causes a change in the magnetization. This change in magnetization can be sensed, and once
calibrated, used to measure the applied stress or force. The Villari effect has been the subject of much
research (Lee, 1955; du Tremolet de Lacheisserie, 1993; Jiles, 1995) and has been employed in load
cells, force cells, and accelerometers (du Tremolet de Lacheisserie, 1993).
The Wiedemann effect
Another effect of interest is the Wiedemann effect, a twisting which results from a helical magnetic field,
often generated by passing a current through the magnetostrictive sample. Twisting a magnetostrictive
element or magnetized wire causes a change in the magnetization that can be measured and related to
the external torque.
Magnetostrictives Applications
Earlier works with magnetostrictives, such as nickel, iron, and permalloy identified many sensing
applications. Some of the earliest uses of magnetostrictive materials from the eighteenth century and the
first half of this century include the telephone receiver, hydrophone, and scanning sonar (Hunt, 1982),
which were developed with nickel and other magnetostrictive materials that exhibit bulk saturation
strains of up to 100×10^(-6). In fact, one of the first telephonic receivers, tested by Philipp Reis in the
1860s, was based on magnetostriction (Hunt, 1982).
Currently work continues to develop giant magnetostrictive material such as Terfenol-D, which has
applications as an actuator and as a sensor. In addition, magnetostrictive amorphous wire and thin films
find a variety of sensing applications. Examples of successful sensor designs include hearing aids, load
cells, accelerometers, proximity sensors, torque sensors, magnetometers and many more (Ewing, 1900;
du Tremolet de Lacheisserie, 1993; Calkins and Flatau, 1997).
Overview of Magnetostrictive Sensor Technology*
WebEquation (2). This can also be expressed as a change in permeability by writing Equation (2) in a more
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general form, B ¼ H: ð3Þ In Equation (3), the effects of stress are included in …
Dielectric Properties of Highly Oriented Lead Zirconium ...
Thus, a current in a conductor could be used to produce a magnetic field around the conductor. Amperes law
describes this electromagnetic relationship for a ...
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https://www.academia.edu/67692465/Dielectric_Properties_of_Highly_Oriented_Lead_Zirconium_Titanat
e_Thin_Films_Prepared_by_Reactive_RF_Sputtering
cpb-us-w2.wpmucdn.com › u › distOverview of Magnetostrictive Sensor
Technology*
Placing a magnetostrictive element inside such an excitation coil (solenoid) with an impressed current I
provides an efficient means of magnetizing the element. The law of electromagnetic induction (Faraday–Lenz
law) describes how a magnetic flux, ’¼BA c in area A c, induces a potential in an electrical conductor to
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which it is flux-linked.
https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/18-Journal-of-IntelligentMaterial-Systems-and-Structures_2007.pdf
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BACKGROUND
where V is the induced voltage in the solenoid of constant area Ac. According to this law, a potential will be
induced in any electrically conducting ...
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https://bpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/1flatau_dapino_calkins_magnetostrictive-apps.pdf
Considerations in the Development of a Piezoelectric ...
... of constant area Ac. According to this law, a potential will be induced in any electrically conducting
material that makes up the magnetic circuit.
91%
https://www.academia.edu/27246387/Considerations_in_the_Development_of_a_Piezoelectric_Transduce
r_Cochlear_Implant
Considerations in the Development of a Piezoelectric ...
The excitation coil described by equation 4 can be used to generate a magnetic field in a sample spatially
separated from the coil. According to Gauss's law ...
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https://www.academia.edu/27246387/Considerations_in_the_Development_of_a_Piezoelectric_Transduce
r_Cochlear_Implant
cpb-us-w2.wpmucdn.com › u › distOverview of Magnetostrictive Sensor
Technology*
flux is always conserved. Thus magnetic flux lines close, defining a magnetic circuit, and elements of the
magnetic circuit through which magnetic flux flows are said to be flux-linked. This makes it possible to
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magnetize one component of the magnetic circuit by generating a magnetic field in another component.
https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/18-Journal-of-IntelligentMaterial-Systems-and-Structures_2007.pdf
Materials for Smart Systems III
by M Wun-Fogle · 1999 — This means that the magnetic flux is always conserved. Thus magnetic flux hnes
close, defining a magnetic circuit, and elements of the magnetic circuit ...
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https://apps.dtic.mil/sti/pdfs/ADA381141.pdf
cpb-us-w2.wpmucdn.com › u › distOverview of Magnetostrictive Sensor
Technology*
Based on the principle expressed by Equations (5) and (6), it is possible to measure the magnetic flux
density in a magnetic circuit by the voltage induced in a flux-linked coil. These coils are often referred to as
73%
detection, receiving, or sensing coils. Various aspects of a material’s magnetic-mechanical
https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/18-Journal-of-IntelligentMaterial-Systems-and-Structures_2007.pdf
cpb-us-w2.wpmucdn.com › u › distOverview of Magnetostrictive Sensor
Technology*
A transverse change in length and associated volumetric change are also observed. Although the Joule
effect is usually associated with the actuation
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https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/18-Journal-of-IntelligentMaterial-Systems-and-Structures_2007.pdf
Analysis of Stress Strain State of X-60 Pipe Weld Joints ...
by HSH Elhag · 2016 · Cited by 3 — ... the first of the magnetomechanical effects to be thoroughly
documented (in 1842), is a longitudinal change in length due to an applied magnetic field.
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Page 3 of 4
https://file.scirp.org/Html/10-8102600_69335.htm
Overview of Magnetostrictive Sensor Technology*
Webvolumetric change are also observed. Although the Joule effect is usually associated with the actuation
capability, numerous sensor configurations rely on the excitation of the magnetostrictor to facilitate sensing.
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TheJouleeffecthasanimportantreciprocaleffectknown …
Analysis of Stress Strain State of X-60 Pipe Weld Joints ...
by HSH Elhag · 2016 · Cited by 3 — The Joule effect has an important reciprocal effect known as the Villari
effect; a stress induced in the material causes a change in the magnetization.
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https://file.scirp.org/Html/10-8102600_69335.htm
(PDF) Overview of Magnetostrictive Sensor Technology(PDF) Terfenol-D Sensor
Design And Optimization
The Villari effect has been the. subject of much research (Lee, 1955; du Tremolet de. Lacheisserie, 1993;
Jiles, 1995) and has been employed in. load cells ...The Villari effect has been the. subject of much research
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[6,7,8] and has been employed in load cells, force cells, and. accelerometers [4,8].
https://www.researchgate.net/publication/240600701_Overview_of_Magnetostrictive_Sensor_Technolog
y
(PDF) Terfenol-D Sensor Design And Optimization
Another effect of interest is the Wiedemann effect, a twisting which results from a helical magnetic field,
often generated by passing a current through the ...
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https://www.academia.edu/18883519/Terfenol_D_Sensor_Design_And_Optimization
Re- view of Characteristic Applications and Patents
by D G Dimogianopoulos · 2012 · Cited by 4 — Twisting a magnetostrictive element or magnetized wire
causes changes in the magnetization, which may be mathematically related to the external torque. The.
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https://www.ingentaconnect.com/content/ben/eeng/2012/00000005/00000002/art00003?crawler=true
Overview of Magnetostrictive Sensor Technology*
WebIn addition, magnetostrictive amorphous wire and thin films find a variety of sensing applications.
Examples of successful sensor designs include hearing aids, load cells, …
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https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/6/105859/files/2021/06/18-Journal-of-IntelligentMaterial-Systems-and-Structures_2007.pdf
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