Passive, Wireless Strain Sensors Using Microfabricated Magnetoelastic Beam Elements

Passive, Wireless Strain Sensors Using Microfabricated Magnetoelastic Beam Elements
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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
1
Passive Wireless Strain Sensors Using
Microfabricated Magnetoelastic Beam Elements
Venkatram Pepakayala, Scott R. Green, and Yogesh B. Gianchandani
Abstract— This paper describes resonant wireless strain sensors fabricated from magnetoelastic alloys. The transduction
mechanism is the E effect—the change in stiffness of magnetoelastic materials with applied strain or magnetic field.
This is measured as a shift in the resonant frequency and is
detected wirelessly using pick-up coils utilizing the magnetoelastic
coupling of these materials. The sensors are fabricated from
a 28-μm-thick foil of Metglas 2826 MB (Fe40 Ni38 Mo4 B18 ),
a ferromagnetic magnetoelastic alloy, using microelectrodischarge machining. Two sensor types are described—single
and differential. The single sensor has an active area of
7 × 2 mm2 , excluding the anchors. At 23°C, it operates at
a resonant frequency of 230.8 kHz and has a sensitivity of
13 × 103 ppm/mstrain; the dynamic range is 0.05–1.05 mstrain.
The differential sensor includes a strain independent reference
resonator of area 2 × 0.5 mm2 in addition to a sensing element
of area 2.5 × 0.5 mm2 that is divided into two segments. The
sensor resonance is at 266.4 kHz and reference resonance is at
492.75 kHz. The differential sensor provides a dynamic range for
0–1.85 mstrain with a sensitivity of 12.5 × 103 ppm/mstrain at
23°C. The reference resonator of the differential sensor is used
to compensate for the temperature dependence of the Young’s
modulus of Metglas 2826 MB, which is experimentally estimated
to be −524 ppm/°C. For an increment of 35°C, uncompensated
sensors exhibit a resonant frequency shift of up to 42% of the
dynamic range for the single sensor and 30% of the dynamic
range of the differential sensor, underscoring the necessity of
temperature compensation. The geometry of both types of sensors
can be modified to accommodate a variety of sensitivity and
dynamic range requirements.
[2013-0330]
Index
Terms— Strain
measurement,
resonant sensing, Metglas, E effect.
magnetoelasticity,
I. I NTRODUCTION
S
TRAIN GAGES have long been used for applications
ranging from structural health monitoring to material
testing and evaluation across a wide range of sectors from civil,
aerospace, and infrastructure, to medical prostheses. Most
strain gages are made from metal foils that must be wired
to interface electronics and a power source. Wireless strain
sensors that can be remotely accessed are attractive for some
applications. An example is the in vivo monitoring of implants,
Manuscript received October 25, 2013; revised February 25, 2014; accepted
March 18, 2014. This WIMS2 Project was supported in part by the Food and
Drug Administration, Department of Health and Human Services, under Grant
2P50FD00378703. Subject Editor A. Seshia.
The authors are with the Center for Wireless Integrated MicroSensing and
Systems, Department of Electrical Engineering and Computer Science,
University of Michigan, Ann Arbor, MI 48109 USA (e-mail:
[email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2014.2313809
where wireless signaling is possibly the only practical way to
obtain a long-term strain measurement [1].
Wireless strain sensors can be either powered or passive.
Powered sensors require a battery or an energy harvesting
system or a combination of the two [2]. Passive sensors do not
require an inbuilt power source. The most widely investigated
techniques for passive strain sensing utilize inductive coupling,
RF electromagnetic backscattering, and surface acoustic waves
[3]–[8]. An optical method has also been reported [9]. Passive
sensors are usually simpler and more robust than powered
kinds. This work presents an RF wireless, passive sensor that
utilizes the resonance of magnetoelastic structures.
Magnetoelastic materials have proven to be very versatile
for a range of wireless sensing applications and magnetoelastic
devices have been used for sensing mass loading [10], viscosity [11], fluid flow [12], pressure [13], position [14], and other
physical parameters. The most common transduction methods
involve change in resonant frequencies of magnetoelastic
elements caused by changes in mass loading, viscosity or
magnetic field conditions [10]–[12], [16], [17]. A magnetic
field applied to a magnetoelastic material produces a strain
in an effect termed Joule magnetostriction. An inverse effect,
called the Villari effect, results in the magnetization of material
by applied strain. At the heart of both effects lies the rotation
of magnetic moments within domains that leads to the magnetization of the material. Joule magnetostriction is moment
rotation under an applied magnetic field, whereas Villari effect
is the moment rotation under strain. When an alternating
magnetic field is applied to a magnetoelastic material, the
induced mechanical vibration, through the Joule effect, results
in a strain-induced material magnetization, that is the Villari
effect. The resonance can be detected by an appropriately
positioned coil. A review of magnetoelastic resonant sensors
for a wide variety of applications is presented in [18].
Some physical phenomena can be exploited to induce a
change in the magnetization state of a material, effectively
modifying its permeability. The permeability change can be
measured as a change in inductance of a coil or the mutual
inductance between two coils wrapped around the magnetoelastic material [12], [13], [19].
Both the aforementioned techniques – change in resonant
frequency or change in magnetization – can be used for strain
sensing purposes. Strain applied to a magnetoelastic material
results in magnetization and change in permeability through
the Villari effect, which can then be detected using a read-out
coil [20]–[25]. A potential drawback of this technique is that
the signal is susceptible to the geometry of the coil and its
position relative to the magnetoelastic material.
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2
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 1. (a) Assembly of the single sensor showing the silicon supports and
bias magnet. (b) Differential sensor suspended on bias magnets with strainindependent cantilevered reference resonator. The sensors are fixed on a test
beam.
Another phenomenon observed in magnetoelastic materials – magnetization-induced change in Young’s modulus, i.e.,
the E effect – can be exploited to provide a strain dependence
to the resonant frequency. In [26], two magnetoelastic strips
held in close proximity were utilized together – one to provide
a strain-dependent biasing field for the other, which served as
the resonator. The dynamic range was limited by saturation
magnetization of the biasing strip and was reported to be
±50 μstrain.
This paper presents a passive, resonant, strain sensing
approach based on the E effect of magnetoelastic materials, where the strain is transferred to a doubly-anchored
suspended resonating structure.1 The resonant response of the
structure is detected wirelessly through interrogation coils and
is observed as a peak in the frequency spectrum of the coil
voltage. A strain-attenuating spring structure is provided to
increase the sensor dynamic range by preventing magnetic
saturation at low levels of applied strain. Two sensor types
are described – single and differential (Fig. 1). Both sensors
include doubly-anchored resonant strips; the differential sensor
has an additional cantilever exhibiting a strain-independent
resonant response. The theory and modeling of the devices are
outlined, followed by the design and fabrication. Finally, the
experimental methods and results are described.
II. T HEORY AND M ODELING
A. General Considerations
The interrogation of resonant magnetoelastic sensors generally involves a small amplitude vibration induced by a
1 Portions of this paper have appeared in conference abstract form in [27].
Fig. 2.
(a) Magnetostriction as a function of applied field for as-cast
Metglas 2826MB, an amorphous magnetostrictive alloy. Due to the presence
of demagnetizing fields, the magnetostriction characteristic is highly dependent on material geometry. (b) Small-signal stiffness (slope of the stressstrain curve, shown in the inset) for a typical demagnetized specimen of a
magnetoelastic material. Points A, B, C, and D are operating points under
increasing magnitude of applied magnetic field.
sinusoidal stimulation around a bias field. Although magnetostriction is a non-linear phenomenon, the small signal
response can be linearized at the bias as expressed by the
following pair of equations for a one-dimensional system
considering stress and field intensity as the independent variables [28]:
∂ε ∂ε σ
+
H
(1)
ε=
∂σ H
∂ H σ
∂ B ∂ B σ
+
H
(2)
B =
∂σ H
∂ H σ
where σ is stress, ε is strain, B is magnetic flux density and
H is magnetic field intensity (all small signal). The partial
derivatives
are as follows:
∂ε is
the
compliance at constant H, s H ;
∂σ H
∂B at constant stress, μσ ;
∂ H σ is the permeability
∂ε ∂B and ∂ H σ and ∂σ H are both represented by d, the magnetostrictive coefficient.
The magnetostrictive coefficient (also called small-signal
magnetostrictivity), d, is the slope of the magnetostriction
curve as a function of an applied DC magnetic field. The
magnetostriction curve for Metglas 2826MB, an amorphous
magnetoelastic material, is shown in Fig. 2(a) [29]. A bias
field that is too high or too low results in a low value of d
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PEPAKAYALA et al.: PASSIVE WIRELESS STRAIN SENSORS USING MICROFABRICATED MAGNETOELASTIC BEAM ELEMENTS
3
and lower response from the sensor. This bias field is usually
provided using a permanent magnet placed in proximity to the
magnetostrictive material.
For this work, equations (1) and (2) were used to implement
a coupled magnetomechanical simulation model in COMSOL
Multiphysics 4.3 following the approach described in [10].
This model was used to obtain the resonant frequencies and
mode shapes of the sensor designs.
B. The E Effect
In a magnetoelastic material under stress, strain is produced
by two processes: the first is elastic strain (as produced in
all materials); the second is from the Villari effect which
represents magnetic moment rotation. In materials with strong
spin-orbit coupling, rotation of magnetic moment results in
rotation of electron clouds. If the electron charge cloud
is anisotropically shaped, its rotation effectively results in
strain [30]. The Young’s modulus at a fixed DC magnetic bias
field, B0 can then be written as:
σ
(3)
E| B0 =
εel + εmag
where εel is the elastic strain and εmag is the strain due to
material magnetization.
The εmag component of strain reduces as the material is
exposed to higher stress levels and consequently, the Young’s
modulus increases. Additionally, if the magnetic field or
applied stress is such that the material is magnetically saturated, the only incremental contribution to strain is elastic,
and the E effect saturates. Fig. 2(b) shows a typical stressstrain relationship and the slope of the stress-strain curve, i.e.
Young’s modulus, as a function of stress [31]. Points A, B, C
and D indicate different bias levels of the magnetic field, that
result in different responses. Tuning the biasing magnetic field
or mechanically pre-stressing the sensor during attachment
shifts the baseline operating point of the sensor. This property
can be employed to allow measurement of both tensile and
compressive strains.
C. Material Considerations
A range of magnetoelastic materials – both crystalline
and amorphous – have been used in transducer applications
[32]–[35]. Crystalline rare-earth magnetoelastic alloys like
Terfenol-D, while showing excellent magnetostriction, have
low tensile strength and are brittle [36]. These materials can
also require a high bias field for resonant devices. For instance,
Terfenol-D can require bias fields of the order of hundreds of
oersteds while Metglas 2826MB, an amorphous alloy, requires
a bias field of a few oersteds [37], [38]. The lower bias field
allows the use of smaller magnets and reduces the overall
sensor size. Amorphous materials can also be tailored to have
a high magnetomechanical coupling coefficient (i.e. higher
efficiency for conversion of magnetic energy to mechanical
energy and vice-versa) through the process of annealing in
a magnetic field – a feature which can be advantageous in
transducer applications [39]–[41]. The E effect in amorphous
magnetoelastic materials can also be modified by annealing
Fig. 3.
Sensor designs: (a) Single sensor; (b) differential sensor. All
dimensions in mm.
under varying temperature and magnetic field conditions [42].
The availability of amorphous magnetoelastic metallic glasses
in the form of thin sheets that can be machined to small form
factors has contributed to their development for a range of
resonant sensing applications. All these considerations favor
the use of amorphous materials for resonant strain sensing.
In this work the sensors are made from Metglas 2826MB
(Fe40 Ni38 Mo4 B18 ), an amorphous magnetoelastic alloy manufactured by Metglas, Inc, Conway, SC. Available in foils
measuring 28 μm thick, it can be micromachined using
micro-electrodischarge machining (μEDM) or photochemical
machining (PCM). It has a saturation magnetostriction of
12 ppm and a DC permeability greater than 50000 [43]. The
high permeability can serve to attract and direct the magnetic
biasing field along the sensor, so the bias field need not be
perfectly aligned with the sensor.
The biasing magnetic field required for resonant operation
of the sensor is provided by a permanent magnet made
using 50 μm thick sheets of Arnokrome 5 (Arnold Magnetic
Technologies Corp., Rochester, NY) – an iron-manganese
alloy [44]. It shows a remanence of 12–16 kG and a coercivity
of 20–50 Oe.
III. D ESIGN AND FABRICATION
A. Resonating Elements
Two types of strain sensors are investigated in this effort –
single and differential (Fig. 3). The sensing element for both
types consists of a doubly-anchored suspended strip of Metglas
2826MB. It can be divided into two parts – a resonant strip
and a spring. The spring serves to attenuate the strain in
the resonant strip. This is necessary for sensor to provide
a wide dynamic range, as the E effect of magnetoelastic
materials typically saturates at low levels of strains [26].
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4
Higher strains do not result in any appreciable change in
stiffness and consequently no change in resonant frequency.
While the geometry and boundary conditions of the sensors
are such that both transverse (i.e. bending) and longitudinal
modes exist, the first longitudinal mode of each sensor type
is typically dominant in the wireless response of the sensor
because it provides the largest unidirectional strain (i.e. mainly
compressive or tensile at a given instant in time), which results
in the strongest response magnetic field.
In the single strain sensor, the resonating element is
5 × 2 mm2 in area. This area determines the strength of the
transmitted RF signal. The spring is 2 × 2 mm2 in area, and
is made with 200 μm wide elements. The entire structure is
28 μm thick. In the differential sensor, the sensing element is
divided into two parallel sections. The sensing element in each
section is 2.5 × 0.25 mm2 whereas the shared spring element
is 2 × 1 mm2 . The differential sensor also contains a reference
resonator. This is a cantilever and is unaffected by any strain
applied to the sensor. All elements are 28 μm thick. The
reference resonator is helpful because the Young’s modulus
of the sensor material varies with temperature [45], [46].
This (common mode) variation in the absence of strain can
be compensated by the response of the reference element.
For small shifts in resonant frequency, f , to which a linear
approximation can be applied:
f (4)
(ε, T ) ≈ ST (ε) ε + Sε (T )T
f 0 B0
where B0 is the biasing magnetic flux density through the
resonating element, assumed to be invariant;
f 0 is the base∂
line resonant frequency; ST (ε) is ∂ε f 0f , the sensitivity
T
f
∂
to strain at constant temperature; and Sε (T ) is ∂T
f0 ε ,
the sensitivity to temperature at constant strain. The term
Sε (T ) at zero strain is obtained from the response of the cantilever reference resonator in the differential device, whereas
the sensing element of the differential sensor and the single
sensor each provide the total sum. The ε, therefore, must be
calculated from the sum. Of course, ε itself has a temperature
dependence based on the expansion mismatch between the
sensor and the substrate to which it is attached. However, the
calculated strain does not differentiate between thermal and
mechanical sources of strain.
Initial experiments indicated that the E effect of Metglas
2826MB saturates at about 50 μstrain. In this work, the springs
were designed to limit the strain in the resonant strip to this
value at the target strain of 2 mstrain on the entire sensor.
Further, the sensors were sized to ensure that their resonant
frequencies were within the excitation and detection range of
the test setup. The compromise between sensor size and signal
strength were also considered in selecting the final dimensions
which are described in Fig. 3.
The coupled magnetomechanical model previously
described was used to simulate the resonant frequencies
and mode shapes for the devices. For the single sensor
the simulated resonant frequency was 230 kHz. For the
differential sensor, the resonant frequency of the sensing
element was 276 kHz, whereas the resonant frequency for the
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 4. Simulated mode shapes for single and differential sensor. (a) Single
sensor, (b) differential sensor, sensing element, and (c) differential sensor,
reference element. The Young’s modulus was assumed to be 120 GPa in this
simulation.
reference was 496 kHz. The simulated mode shapes for both
the single and differential sensors are shown in Fig. 4.
The sensor shows a shift in resonant frequency shift not
only due to E effect but also because of a change in its
equation of motion in presence of axial loads (i.e. strain
stiffening). This is seen in all materials regardless of the
magnetoelastic nature of the material. To analyze this effect
of axial loading, a pre-stressed eigenfrequency simulation was
performed for the sensors. In these simulations, the single
sensor showed an estimated sensitivity of 2700 ppm/mstrain,
while the differential sensor showed 1100 ppm/mstrain. These
simulated sensitivities are due only to the strain stiffening
effect.
Micro-electrodischarge machining (µEDM) is an attractive
technique that can be used for serial or batch-mode micromachining any conductive material [47], [48]. This approach
has been previously demonstrated for use in machining of
Metglas 2826MB [11]. In this effort, μEDM was used not
only to fabricate the sensors, but also the biasing magnets
that are described below. The fabricated sensors, single and
differential, are shown in Fig. 5.
B. Biasing Magnetic Field and Interrogation Coils
To read out the sensor response, a system consisting of
transmit and receive coils was employed (Fig. 6). The transmit
coils were used to sweep a range of frequencies within which
resonance was expected. The resonant frequency of the sensor
was detected by an elevated response in the receive coil.
In order to excite a longitudinal mode of vibration, the field
lines generated by the transmit coil should loop through the
sensor longitudinally. In order to minimize signal feedthrough,
the receive coils must be positioned at a null point in the
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PEPAKAYALA et al.: PASSIVE WIRELESS STRAIN SENSORS USING MICROFABRICATED MAGNETOELASTIC BEAM ELEMENTS
5
C. Sensor Attachment
The single sensor was suspended across two supporting
elements (300-μm thick silicon) that offset it from the beam.
The longitudinally magnetized Arnokrome 5 bias magnet
measuring 6 × 3 mm2 was located underneath the suspended
sensor. Cyanoacrylate adhesive was used for all attachments.
In the case of the differential sensor, to augment the strength
of biasing magnetic field, a stack of three longitudinally
magnetized Arnokrome 5 magnets was used as the support
at each end of the sensor. The magnets each measured
4 × 2.5 mm2 . As the magnets were in direct contact with the
sensor, a larger bias field was provided for sensor operation.
Based on magnetometer readings (Model 5180, F. W. Bell,
Milwaukie, OR), the magnets provided an estimated 5–10 Oe
field required for single sensor and 15–20 Oe field required
for the differential sensor. The sensor assemblies for the single
and differential sensors are shown in Fig. 1.
Fig. 5. (a) Microfabricated devices; (b) Single sensor; (c) Differential sensor.
IV. E XPERIMENTAL M ETHODS AND R ESULTS
For testing, the sensors and the biasing magnets were
attached to the upper surface of brass cantilevers. The free
ends of the cantilevers were pushed down using a force gage
(Fig. 6). To calibrate the force used with the strain generated
on the beam surface, a commercial strain gage (SGD-5/
350-LY13, one-axis general purpose strain gage, Omega Engineering, Inc., Stamford, CT) was first used on the cantilever
setup. The reported data is the strain on the beam surface.
The temperature dependence tests were conducted by heating the sensor assembly on a hot plate. Temperature measurements were taken using a thermocouple (Type K, model
5SRTC, Omega Engineering, Inc., Stamford, CT) affixed to
the brass beams near the sensors.
A. Single Sensor
Fig. 6. Coil configuration and test setup used for sensor readout. Blue lines
indicate field due to the transmit coils and red lines indicate the field as
generated by the sensor and picked up by the receive coils.
transmitted field. The transmit coils were 7 mm in diameter,
20 mm long, and had 10 turns each. The receive coils were
45 mm in diameter, 10 mm long and had 5 turns each. For this
work, the sensor was held at a distance of less than 5 mm from
the transmit coils. An Agilent model 4395A network analyzer
(Agilent Technologies, Santa Clara, CA) was used to read the
voltage induced on the receive coil by the sensor response.
To determine the strength of biasing field necessary for
device operation, the resonant frequency of the sensors was
first experimentally determined using Helmholtz coils to
provide the magnetic field. It was found that a biasing field of
5–10 Oe is sufficient for single sensor operation.
The differential sensor, being smaller than the single
sensor, required a stronger biasing field for operation [49].
For the differential sensor, a bias field of 15–20 Oe was
necessary.
The typical single sensor showed an unstrained resonance at
230.8 kHz at 23°C [Fig. 7(a)]. Under applied tensile strain of
1.05 mstrain, the resonant frequency increased to 233.8 kHz.
The typical resonance amplitude for the unstrained single
sensor was 150 μV; under maximum strain the amplitude
reduced to about 50 μV. The decrease in signal amplitude
was consistent with expectations because the small signal
magnetostrictivity, d, reduces at higher strain levels.
The typical change of resonant frequency as a function of
strain is shown in Fig. 7(b). The average sensitivity over this
range was typically about 13 × 103 ppm/mstrain. The slope
at higher strain levels decreases from a maximum value of
5.2 kHz/mstrain to 1.5 kHz/mstrain. This indicates saturation
of E effect as shown in Fig. 2(b). The initial decrease in
resonant frequency at small strains can be attributed to the
E effect: the localized slope of the stress-strain curve (i.e.
the incremental stiffness) does not monotonically increase with
applied strain at low levels of strain [30]. This is corroborated
by experiments done on similar amorphous alloys [42], [50].
Taking into account the decrease in resonant frequency at
lower strains, the single sensors typically showed a dynamic
range of 0.05–1.05 mstrain.
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6
Fig. 7. (a) Resonance of the single sensor at 23°C under no strain and
1.05 mstrain. (b) Resonant frequency and fractional change in resonant
frequency as a function of beam strain for a single sensor at 23°C.
B. Differential Sensor
For the differential sensor, a typical unstrained resonance
for the sensing element was at about 266.4 kHz at 23°C
[Fig. 8(a)]. Under applied tensile strain of 1.85 mstrain, the
resonant frequency increased to 272.5 kHz resulting in a sensitivity of 12.5 × 103 ppm/mstrain. As expected, the amplitude
of resonance for the sensing element reduced with increasing
strain: the baseline resonance amplitude was 150 μV, while at
maximum applied strain the amplitude was less than 10 μV.
The reference resonance was at 492.75 kHz. It was experimentally verified that this frequency did not change with applied
strains.
The dependence of resonant frequency on applied strain for
the sensing element is shown in Fig. 8(b). Unlike the single
sensor, the differential sensor did not show a reduction in
resonant frequency at strains below 0.05 mstrain. This was
because the sensor was biased by a stronger magnetic field at
an operating point above the initial dip in stiffness. As was
the case with the single sensor, the differential sensor showed
a reduced sensitivity at higher strain levels: it fell from a
maximum slope of 4.5 kHz/mstrain to 2.7 kHz/mstrain. These
measurements were taken at 23°C.
Over the range of temperatures approximately from 20°C
to 60°C, the resonant frequency of the reference cantilever
varied by −262 ppm/°C [Fig. 9(a)], and that of the sensing
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
Fig. 8. (a) Resonance of the sensing element of the differential sensor under
no strain and 1.85 mstrain at 23°C. (b) Resonant frequency and fractional
change in resonant frequency as a function of beam strain for the sensing
element of the differential sensor at 23°C.
element varied by −222 ppm/°C uncorrected by the output of
the reference element [Fig. 9(b)]. Based on this and equation
(4), the true strain observed in the sensor is plotted in the right
axis of Fig. 9(b). If the temperature compensation provided by
the cantilever is applied to the simple sensor, its temperature
coefficient of resonant frequency changes from −160 ppm/°C
uncorrected to 102 ppm/°C corrected [Fig. 9(c)].
V. D ISCUSSION
In case of the single sensor, there is an initial reduction in
resonant frequency at strain values below 0.05 mstrain. The
dynamic range can be extended to lower values by increasing
the biasing magnetic field, shifting the baseline resonant
frequency to a point in the response plot that is above this dip.
It can be seen in Fig. 7(b) shows how initial magnetization or
strain can affect the E behavior of magnetoelastic materials
and be applied to the strain sensor. A magnetic bias or applied
pre-strain can move the baseline operating point to A, where
the sensor will show continuous increase with applied strain.
Using an even stronger field or higher pre-strain can move the
baseline operating point to point B, where the sensor can detect
both tensile and compressive strains. It can be seen in Fig. 8
how the experiments for the differential sensor demonstrate
this – the magnetic field bias provides an operating point where
there is no decrease in resonant frequency with increasing
strains.
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PEPAKAYALA et al.: PASSIVE WIRELESS STRAIN SENSORS USING MICROFABRICATED MAGNETOELASTIC BEAM ELEMENTS
7
it can be concluded that it is indeed the E effect which
primarily determines the sensitivity of these devices.
In general, a change in temperature affects the resonant
frequency of a cantilever through change in Young’s modulus
or dimension change due to thermal expansion. For a cantilever
resonating in the longitudinal mode, the resonant frequency is
given by:
E
1
(5)
f0 =
4L ρ(1 − ν 2 )
where, E is the Young’s modulus, ρ is the density, ν is the
Poisson’s ratio, L is the length of the cantilever. The fractional
change in resonant frequency resulting from a temperature
change can be expressed as:
Sε (T ) T
=
1
4L(1+αT E T )
E (1+αγ T )(1+αT E T )3
ρ(1−ν 2 )
1
4L
E
ρ(1−ν 2 )
−
1
4L
E
ρ(1−ν 2 )
(6)
T is the temperature change, αT E is the thermal expansion
coefficient of Metglas 2826MB and αγ is the fractional
change, with temperature, in the Young’s modulus of Metglas
2826MB. However, αT E is 12 ppm/°C – negligible compared
to measured f / f 0 – and can thus be ignored for the temperature range under consideration. Equation (6) then simplifies to:
αγ
1
.
(7)
1 + αγ T − 1 ≈
Sε (T ) ≈
T
2
Fig. 9. Temperature compensation as used in differential and single sensor.
(a) Fractional change in resonant frequency of the reference resonator as
a function of the temperature of the brass beam. (b) Fractional change in
resonant frequency of sensing element of the differential sensor and corrected
beam strain as a function of temperature. (c) Fractional change in resonant
frequency of the single sensor and corrected beam strain as a function of
temperature.
As described in section III A, a shift in resonant frequency of the device can occur due to strain stiffening. Finite
element analysis shows that for the single and differential
sensors described in this work, the non-magnetic contributions
are 2700 ppm/mstrain and 1100 ppm/mstrain respectively.
These are minor compared to the overall measured sensitivity of 13 × 103 ppm/mstrain for the single sensor and
12.5 × 103 ppm/mstrain for the differential sensor. Hence,
From experimental results, Sε (T ) for the reference element in
the differential sensor is −262 ppm/°C which implies that αγ
is −524 ppm/°C.
The Young’s modulus of 2826MB reduces with increasing
temperature, lowering the resonant frequency. In contrast,
the expansion mismatch of brass and 2826MB, which have
thermal expansion coefficients of 19 ppm/°C and 12 ppm/°C,
respectively, results in tensile strain, assuming that the strain
sensor and the brass beam are at similar temperatures. Hence,
these factors influence the resonant frequency of the sensors
in opposing manner. For the single sensor, there is a decrease
of 1.27 kHz in the resonant frequency for a 35°C increase in
temperature. The substantial decrease in resonant frequency
with increasing temperature indicates that the decrease in
Young’s modulus of 2826MB is the dominant parameter
influencing the resonant frequency. Considering that the full
range of frequencies for the single sensor, observed over the
range of applied strain, is about 3 kHz, it is necessary for
the temperature variation to be factored into the measurement.
For the differential sensor, the sensor resonant frequency falls
by 1.85 kHz for a 35°C increase in temperature. Temperature
compensation using the response of the reference resonator
enables the calculation of the tensile strain caused by the temperature change. In these experiments, the differential sensor
and single sensor showed a strain dependence on temperature
of 7.45 μstrain/°C (ppm/°C) and 4.52 μstrain/°C (ppm/°C),
respectively. This corresponds well with the theoretical expansion mismatch between brass and 2826MB of 7 ppm/°C.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
8
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS
The device operation relies on the magnetic circuit formed
by the transmit and receive coils with the sensor. If the sensor
rests on a ferromagnetic substrate, it can potentially influence
this magnetic circuit. However, the permeability of Metglas
2826MB is much higher than most ferromagnetic materials
and the effect of the substrate on sensor read-out will be
accommodated by an appropriate calibration on a similar
substrate. Another possible concern, especially in relation to
possible application in structural health monitoring, is drift and
long-term stability. Although the mechanical integrity of the
sensor is not a concern, Metglas 2826MB is prone to corrosion
in high humidity environments. A thin layer of Parylene-C can
be deposited to prevent corrosion if necessary – a method that
has been employed in our previous work [38].
The signal quality of the sensor output may be improved in
the long term by employing strategies to exploit higher harmonics of the resonant response, thereby reducing feedthrough
of the interrogating signal. Pulsed interrogation methods may
also reduce signal feedthrough. In addition, the interrogation
range can be increased by using larger coils and higher input
power for the transmit coils.
VI. C ONCLUSION
This work presents the design, fabrication and experimental results of passive, wireless magnetoelastic strain sensors.
Using the E effect of magnetoelastic materials, the devices
detect strain as a change in its resonant frequency. The
single sensor incorporates only a sensing element, whereas
the differential sensor incorporates both a sensing element and
a reference resonator. Both sensors use spring structures to
attenuate the strain in the sensing element. This architecture
allows the sensitivity and dynamic range to be customized.
The sensors can be used to measure both tensile and compressive strains by mechanical pre-stressing or by selecting an
appropriate magnetic bias field. In the differential sensor, the
output of the reference resonator can be used to compensate for
resonant frequency change due to the temperature dependence
of the Young’s modulus of Metglas 2826MB. These sensors
are expected to find utility in biomedical and infrastructure
monitoring applications.
ACKNOWLEDGMENT
The authors acknowledge Metglas Inc. and ArnoldMagnetic
Technologies Corp. for the samples provided for this project.
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9
Venkatram Pepakayala received a B.Tech. degree
in electronics and telecommunication engineering
from Nagpur University, Nagpur, India, in 2010,
and an M.S. degree in electrical engineering from
the University of Michigan, Ann Arbor, USA, in
2012, where he is working toward a Ph.D. degree
in electrical engineering.
He is currently a Graduate Student Research Assistant with the Department of Electrical Engineering
and Computer Science, University of Michigan. His
research interests include magnetoelastic wireless
sensors and actuators with focus on applications as implantable microdevices.
Scott R. Green received a B.S. in mechanical
engineering from Rose-Hulman Institute of Technology in 2003, and an M.S. (2008) and Ph.D (2009)
in mechanical engineering from the University of
Michigan, Ann Arbor, with a focus in Microsystems.
He worked as a senior design engineer at Stryker
Corporation in the Instruments division from 20032005. He currently is an Assistant Research Scientist
at the University of Michigan, Ann Arbor. Research
interests include wireless magnetoelastic sensors and
actuators, miniature implantable medical systems,
and miniature and microfabricated high-vacuum sputter ion pumps.
Yogesh B. Gianchandani (S’83–M’85–SM’05–
F’10) is a Professor at the University of Michigan, Ann Arbor, with a primary appointment
in the Electrical Engineering and Computer Science Department and a courtesy appointment
in the Mechanical Engineering Department. He
also serves as the Director for the Center for
Wireless Integrated MicroSensing and Systems
(WIMS2 ).
Dr. Gianchandani’s research interests include all
aspects of design, fabrication, and packaging of
micromachined sensors and actuators (http://www.eecs.umich.edu/~yogesh/).
He has published about 300 papers in journals and conferences, and has
about 35 U.S. patents issued or pending. He was a Chief Co-Editor of
Comprehensive Microsystems: Fundamentals, Technology, and Applications,
published in 2008. Dr. Gianchandani has served on the editorial boards and
program committees of a number of conferences and journals. From 2007
to 2009, he also served at the National Science Foundation as the program
director for Micro and Nano Systems within the Electrical, Communication,
and Cyber Systems Division (ECCS).
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