# Wireless Magnetoelastic Resonance Sensors: A Critical Review

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## Abstract

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## Introduction

_{40}Ni

_{38}Mo

_{4}B

_{18}(Metglas brand 2826MB) and Fe

_{81}B

_{13.5}Si

_{3.5}C

_{2}(Metglas 2605SC) ribbons [15] that have a high mechanical tensile strength (~1000-1700 MPa), and a low material cost allowing them to be used on a disposable basis. In addition, these Metglas ribbons have a high magnetoelastic coupling coefficient, as high as 0.98, and magnetostriction on the order of 10-5 [17,18,19]. The high magnetoelastic coupling allows efficient conversion between magnetic and elastic energies and vice versa. When excited by a time varying magnetic field, the large magnetostriction allows these materials to exhibit a pronounced magnetoelastic resonance the resonance frequency of which can be remotely detected either by magnetic, acoustic, or optical means. The environmental parameter of interest is measured by tracking the resonant frequency of the sensor.

**Figure 1.**The magnetoelastic sensor is interrogated with an excitation coil producing a magnetic field impulse, and can be detected magnetically with a pickup coil, acoustically with a microphone, or optically with a laser emitter and a phototransistor.

**Figure 2.**(a) A sensor free of external forces is modeled as a thin plate exhibiting vibration in the x-direction. (b) When immersing in a liquid, the sensor is modeled as a vibrating plate bounded by two infinite planes from a distance h and two infinite planes touching the sensor surface.

**Figure 3.**The frequency response of a 4 cm × 1.3 cm × 28 µm as-cast Metglas 2826MB ribbon. The resonant frequency is the maximal of the frequency spectrum.

## Theoretical Model

_{S}is the density of the sensor, σ is the Poison’s ratio, and E

_{s}is Young’s modulus. The resonant frequency of the sensor is determined by solving Eq. (1) as:

_{0}(n = 1) is considered because of the higher signal amplitude and lower frequency. The fundamental resonance for a 4 cm × 1.3 cm × 28 µm Metglas 2826MB sensor ribbon, measured in air at room temperature, is shown in Fig. 3, where the resonant frequency is at the peak of the curve at 58.18 kHz.

#### Effect of Mass Loading the Sensor

_{s}in Eq. (1) can be replaced by (m

_{S}+ Δm) Ad where m

_{s}is the mass of the sensor, A is the surface area, and d is the thickness of the sensor. Solving the equation of motion using the modified ρ

_{s}yields a new fundamental resonant frequency f

_{load}[23]:

#### Effect of Liquid Viscosity and Density

_{l}is shown in Fig. 2b, where the liquid is represented by an incompressible fluid bounded by two infinite planes on each side, one touching the sensor surface and one shifted h in the z-direction. The plane shifted h from the sensor is fixed, while the plane touching the sensor surface is vibrating in the x-direction and creating a damping force against the sensor vibration so the equation of motion in Eq. (1) becomes [8]:

_{l}f)

^{1/2}. Solving Eq. (5) the fundamental resonant frequency of the sensor immersed in a viscous liquid f

_{liquid}is:

#### Effect of Coating Elasticity

_{eff}and density ρ

_{eff}of a uniformly coated sensor are expressed as [24]:

_{c}and E

_{s}are the Young’s modulus of the coating and the sensor, respectively, and ρ

_{c}and ρ

_{s}are the density of the coating and sensor, respectively, and α

_{c}and α

_{s}are the fractional thicknesses of the coating and the sensor, respectively. Substituting Eqs. (9) and (10) into Eq. (2), and assuming the Poisson ratio σ is close to zero, the fundamental resonant frequency of the coated sensor f

_{coat}is:

_{c}to the total mass m

_{t}and the sensor mass m

_{s}as [24]:

#### Effect of Temperature and Applied Field

_{s}is the magnetostriction, H is the applied field, M

_{s}is the saturation magnetization, H

_{kσ}is the anisotropy field when the sensor is under a longitudinal stress σ, E

_{M}is the modulus of elasticity at constant magnetization, and E

_{s}is the modulus of elasticity at field H. Substituting Eq. (16) into Eq. (2) and including the temperature dependence of the different variables, the resonant frequency f

_{0}is expressed as [26]:

## Detection Systems

#### Time-Domain Measurement

**Figure 4.**(a) The excitation signal is a series of sinusoidal bursts. (b) The sensor response is an exponentially decaying sinewave, or the ring-down.

**Figure 5.**Time domain detection system. (a) In the two-coil configuration, the excitation coil is used to generate the excitation pulse and the pick-up coil receives the sensor response. (b) Only one coil is needed for excitation and reception if an electronic switch is used to isolate the excitation circuit and receiving circuit.

**Figure 6.**The electronics of a time-domain system using only one coil for excitation and receiving. The resonant frequency of the sensor is determined via frequency counting using a Dallas Semiconductor Corporation DS87C520 microcontroller.

#### Frequency-Domain Measurement

**Figure 7.**The frequency-domain detection system. A function generator is used to excite the sensor, and the response of the sensor is recorded via a lock-in amplifier.

#### Impedance De-tuning Method

**Figure 8.**The magnetoelastic sensor can be detected by placing inside a solenoid and measuring the impedance variation of the solenoid.

## Applications

#### Temperature Monitoring

#### Humidity Monitoring

_{2}) on a 4 × 1.3 cm Metglas 2826MB ribbon [4]. As the humidity increases, water vapor is absorbed into the TiO

_{2}layer, increasing the effective mass on the sensor. Fig. 10 shows the increase in humidity decreases the resonant frequency. In addition to TiO

_{2}, alumina (Al

_{2}O

_{3}) was also used as a coating for humidity monitoring [5], and the results are similar to that of TiO

_{2}.

**Figure 9.**The resonant frequency shifts of a magnetoelastic sensor verses temperature and bias field H. The highest positive temperature dependency happens at H = 9.9 Oe, highest negative temperature dependency at H =16.51 Oe, and zero-temperature dependency at H = 7.01 Oe.

**Figure 10.**The resonant frequency shift of a TiO

_{2}-coated humidity sensor as a function of humidity concentration; the TiO

_{2}coating changes mass in response to humidity level, in turn shifting the resonant frequency of the sensor.

#### Pressure Monitoring

_{B}is the Boltzmann’s constant, and m

_{g}is the mass of gas. Eq. (18) indicates the resonant frequency decreases with increasing pressure. This conclusion is consistent with the experimental results in Fig. 11, where the resonant frequency of a 4 × 1.3 cm 2826MB Metglas reduces linearly with pressure, and the pressure dependence increases with curvature of the sensor.

**Figure 11.**The resonant frequency decreases as the atmospheric pressure increases; r denotes the radius of curvature of the curved sensor.

#### Flow Rate Monitoring

**Figure 12.**The resonant frequency decreases quadratically at laminar liquid flow (<115 cm/s), and increases again when the liquid switches from laminar to turbulent flow.

#### Measurement of Liquid Viscosity and Density

_{l}. In the equation η and ρ

_{l}are inseparable, hence it is not possible to measure η and ρ

_{l}with a uniformly smooth sensor. However, due to surface roughness, liquid is trapped by the sensor surface and acts as a mass load. To compensate for the liquid density and surface roughness dependent mass loading, an additional term is added in Eq. (8) [7]:

_{s}is the mass of the sensor. From Eq. (19) the liquid density and viscosity can be separated by using two sensors with different surface roughnesses, indicated by subscript 1 and 2, with the difference in the resonant frequencies of the two sensors given by:

_{2}on both sides giving the two sensors different degrees of surface roughness.

#### Measurement of Thin-Film Elasticity

_{s}, ρ

_{s}, and ρ

_{c}are measured before the experiment. The Young’s modulus of the material of interest E

_{c}is determined by substituting the calculated β into Eq. (15). Fig. 13 plots the frequency shift of a silver-coated sensor as a function of coating mass. The data points were fitted with Eq. (21) and E

_{s}of silver is determined as 74.8 GN/m2, a difference of only 1.6% from the theoretical value. Experiments for calculating the Young’s moduli of aluminum, polyurethane paint, and acrylic paint have also been conducted with errors of less than 2% with theoretical values [24].

**Figure 13.**The relative resonant frequency of a magnetoelastic sensor decreases linearly with increasing mass of silver coating. A least square-fit (dashed line) is used to calculate the Young’s modulus of the silver.

#### Chemical and Gas Sensing

_{2}) [13], ammonia (NH

_{3}) [14], and pH [15]. Generally, the mass change for these chemically responsive layers is small, so the resonant frequency shift is linear as described in Eq. (5). For example, Fig. 14 shows that the resonant frequency of the CO

_{2}sensor, based on an acrylamide and isooctylacrylate coating, decreases linearly with the percentage CO

_{2}. Fig. 14 also shows the sensitivity of the sensor increases with the coating thickness until 20 µm, where the mass load is too large for the sensor to resonate. Table 1 lists various magnetoelastic chemical (liquid and gas) sensors that have been built and tested.

**Figure 14.**A magnetoelastic CO

_{2}sensor, where the slope of the resonant frequency shift increases with the coating thickness.

**Table 1.**Magnetoelastic sensors have been used to monitor CO

_{2}, NH

_{3}, pH, and glucose based upon the mass change of chemically responsive layers.

Sensor | Chemically Responsive Layer | Sensitivity | Range | Stability | Ref |
---|---|---|---|---|---|

CO_{2} | Acrylamide + isooctylacrylate | -5.6 Hz/vol% | 0 – 50 vol% | Stable | 13 |

NH_{3} | Poly(acrylic acid-co- isooctylacrylate) | -14 Hz/log(vol%) | 0 – 100 vol% | Stable | 11 |

PH | Acrylic acid (20 mol%) + iso-octyl acrylate(80 mod%) | -333 Hz/pH | 5.5 – 8.5 pH | Stable | 14 |

Glucose | PVA and a co-polymermade of DMAA, BMA, DMAPAA, and MAAPBA | -13 Hz / (mg/L) | 0 – 100 mg/L | Dissolves after 3 - 4 high/low cycles | 28 |

## Magnetoelastic Sensor Arrays

**Figure 15.**A magnetoelastic sensor array consisting of four sensor elements (the four horizontal strips at the center) mounted on a tube at its support tabs (the top and bottom strips). The major scale is in cm.

**Figure 16.**The frequency response of the four-element sensor array measured by inserting the sensor array into a solenoid. The impedance of the solenoid is eliminated with a background subtraction.

## Optimizing Sensor Performance

_{s}, the so-called ΔE effect, due to the changing bias field. Fig. 17 shows there is an optimal bias field where sensor amplitude is maximum, which corresponds to the anisotropy field of the sensor H

_{k}[25].

**Figure 17.**The resonant frequency and amplitude of a magnetoelastic sensor varies with applied field amplitude H due to changing elasticity (ΔE effect).

**Figure 18.**The applied bias field required for the sensor to exhibit maximum ΔE effect increases with decreasing sensor length to width ratio.

_{k}does not change with sensor length, the applied H field has to be increased when the length of the sensor is reduced to compensate for the demagnetizing field and to maintain the internal field, H

_{i}, at H

_{k}. The internal field H

_{i}is given as:

_{i}= H − MD

**Figure 20.**Transverse-field annealing of the magnetoelastic sensor increases the ΔE effect and decreases the anisotropy field H

_{k}.

_{k}is reduced by 30%.

## Conclusions

## Acknowledgments

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## Share and Cite

**MDPI and ACS Style**

Grimes, C.A.; Mungle, C.S.; Zeng, K.; Jain, M.K.; Dreschel, W.R.; Paulose, M.; Ong, K.G.
Wireless Magnetoelastic Resonance Sensors: A Critical Review. *Sensors* **2002**, *2*, 294-313.
https://doi.org/10.3390/s20700294

**AMA Style**

Grimes CA, Mungle CS, Zeng K, Jain MK, Dreschel WR, Paulose M, Ong KG.
Wireless Magnetoelastic Resonance Sensors: A Critical Review. *Sensors*. 2002; 2(7):294-313.
https://doi.org/10.3390/s20700294

**Chicago/Turabian Style**

Grimes, Craig A., Casey S. Mungle, Kefeng Zeng, Mahaveer K. Jain, William R. Dreschel, Maggie Paulose, and Keat G. Ong.
2002. "Wireless Magnetoelastic Resonance Sensors: A Critical Review" *Sensors* 2, no. 7: 294-313.
https://doi.org/10.3390/s20700294