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Magnetostrictive Transducers, Sensors, and Actuators

A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Electronic Sensors".

Deadline for manuscript submissions: 30 December 2024 | Viewed by 6140

Special Issue Editors


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Guest Editor
School of Energy and Electronic Engineering, University of Portsmouth, Portsmouth PO1 3DJ, UK
Interests: kinetic energy harvesters; linear generators and motors; smart materials and structures
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
School of Engineering and the Built Environment, Birmingham City University, Birmingham, UK
Interests: artificial intelligence for engineering; control; piezoelectric actuators
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Sensors and actuators are key elements of any control system. In the last two decades, smart materials have played a significant role when it comes to enhancing the performance of mechatronic systems in industries. The high magneto-mechanical coupling coefficient, high Young’s modulus, and low cost combined with the ductility of some alloys (e.g., Galfenol and Permendur) and operating in the harsh environment make the magnetostrictive material a suitable candidate for manufacturing sensors and actuators. Joule, Wiedemann, and Delta-E are useful effects to develop linear and torsional actuators for operating in resonant and non-resonant conditions. Matteucci and Villari are another two effects employed to develop various types of sensors to measure some quantities such as the position, force or stress, magnetic field, torque, and residual stress. Recent developments in both the performance and affordability of magnetostrictive sensors and actuators make them suitable as the first choice in most industrial applications.         

This Special Issue aims to highlight advances in the development, testing, modeling, and controlling of magnetostrictive transducers, on the component level as well as within control systems. Topics include, but are not limited to:

  • Material characterization of magnetostrictive
  • Dynamic and static force/torque sensor
  • Noncontact torque sensor
  • Position or displacement sensor
  • Ultrasonic magnetostrictive sensor
  • Magnetostrictive fiber optic sensor
  • Amorphous ribbon sensor
  • Magnetic field sensors
  • Error modelling, calibration, and advanced transducer characterization techniques
  • Resonant and non-resonant magnetostrictive actuators
  • Active vibration control
  • Shunt damping vibration control
  • Noise cancelation and antivibration systems

This special issue is focused more on sensors. Papers focus on actuators may choose our joint Special Issue in Actuators (ISSN 2076-0825).

Dr. Mojtaba Ghodsi
Dr. Morteza Mohammadzaheri
Guest Editors

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Keywords

  • Magnetostrictive
  • Transducers
  • Sensors
  • Actuators
  • Joule effect
  • Wiedemann effect
  • Villari effect
  • Matteucci effect
  • Delta-E effect
  • Resonant
  • Non-resonant
  • Control systems
  • Self-sensing

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Published Papers (3 papers)

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Research

20 pages, 20556 KiB  
Article
A Contactless Low-Carbon Steel Magnetostrictive Torquemeter: Numerical Analysis and Experimental Validation
by Carmine Stefano Clemente, Claudia Simonelli, Nicolò Gori, Antonino Musolino, Rocco Rizzo, Marco Raugi, Alessandra Torri and Luca Sani
Sensors 2024, 24(21), 6949; https://doi.org/10.3390/s24216949 - 29 Oct 2024
Viewed by 496
Abstract
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based [...] Read more.
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based on the inverse magnetostrictive effect represent an effective alternative to conventional ones. Most known ferromagnetic materials have an inverse magnetostrictive behavior: applied stresses induce variations in their magnetic properties. This paper investigates the possibility of measuring torsional loads applied to a shaft made of ferromagnetic steel S235 through an inverse magnetostrictive torquemeter. It consists of an excitation coil that produces a time-varying electromagnetic field inside the shaft and an array of sensing coils suitably arranged around it, in which voltages are induced. First, the system is analyzed both in unloaded and loaded conditions by a Finite Element Method, investigating the influence of relative positions between the sensor and the shaft. Then, the numerical results are compared with the experimental measurements, confirming a linear characteristic of the sensor (sensitivity about 0.013 mV/Nm for the adopted experimental setup) and revealing the consistency of the model used. Since the system exploits the physical behavior of a large class of structural steel and does not require the introduction of special materials, this torquemeter may represent a reliable, economical, and easy-to-install device. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
Show Figures

Figure 1

Figure 1
<p>Schematic view of the torque measurement system.</p>
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<p>Ampere-turn equivalent model of a sensor with an excitation coil and a single couple of sense coils.</p>
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<p>Meshed domain for the FE analysis: shaft portion and air box (<b>a</b>), and flux density distribution on the shaft surface (<b>b</b>).</p>
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<p>Complete sensor over a ferromagnetic shaft in air. The excitation and sensing coils layout over the under-testing shaft is visible. The pickup coils 1 and 4, 2 and 5, and 3 and 6 are electrically connected in series.</p>
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<p>Amplitudes of the induced voltages as functions of the gap.</p>
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<p>Amplitudes of the induced voltages with respect to the pitch angle.</p>
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<p>Amplitudes of the induced voltages with respect to the displacement along the x-axis.</p>
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<p>Amplitudes of the induced voltages with respect to the yaw angle.</p>
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<p>FE model of the analyzed geometry.</p>
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<p>Amplitude of the magnetic flux density in the 3D FE model at 0 Nm (<b>a</b>), 600 Nm (<b>b</b>), and 1200 Nm (<b>c</b>). Values are expressed in milliTesla.</p>
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<p>FE computed sensing coils peak voltages versus applied pure torque.</p>
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<p>FE computed sensing coils peak voltage difference (with respect to torque = 0 Nm) versus applied pure torque.</p>
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<p>Sample shaft used to test the proposed system coupled to a 2 m long bar and a test rig.</p>
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<p>Experimental setup used to produce the static mechanical excitation.</p>
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<p>Sample shaft under test with mounted probehead (<b>a</b>) and 3D printed probehead support (<b>b</b>).</p>
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<p>Peak voltages on the sensing coils as a function of applied pure torque. Experimental results.</p>
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<p>Sensing coils peak voltage difference (with respect to null torque) versus applied pure torque. Experimental results.</p>
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<p>Sensing coils peak voltage difference (with respect to null load) versus applied torque in case of non-pure torque test. Experimental results.</p>
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<p>Sensing coils peak voltage versus applied torque: loading and unloading cycle. Experimental results.</p>
Full article ">Figure 20
<p>Sensing coils peak voltages versus yaw angles, in unloaded shaft conditions. Experimental results.</p>
Full article ">
20 pages, 5793 KiB  
Article
Static, Dynamic, and Signal-to-Noise Analysis of a Solid-State Magnetoelectric (Me) Sensor with a Spice-Based Circuit Simulator
by Yuri Sindler and Simon Lineykin
Sensors 2022, 22(15), 5514; https://doi.org/10.3390/s22155514 - 24 Jul 2022
Cited by 2 | Viewed by 2153
Abstract
Modeling the non-electrical processes by equivalent electrical circuits is a widely known and successfully used technique in research and development. Although finite element methods software development has supplanted electrical analogy techniques due to greater accuracy and intuitiveness in recent decades, the modeling of [...] Read more.
Modeling the non-electrical processes by equivalent electrical circuits is a widely known and successfully used technique in research and development. Although finite element methods software development has supplanted electrical analogy techniques due to greater accuracy and intuitiveness in recent decades, the modeling of physical processes based on analogies has several advantages in some cases. Representation of physical processes in the form of lumped circuits and graphs allows researchers to estimate the system with an alternative view, use standardized methods for solving electrical circuits for non-electrical systems, and, most importantly, allows us to use electrical circuit simulators with their unique capabilities. Of particular interest for using the analogy technique are systems that include electronic components along with components belonging to other physical domains, such as mechanical, thermal, magnetic, and others. A solid-state magnetoelectric (ME) sensor equipped with a charge amplifier is proposed in this study as an example of analysis using the equivalent electrical circuit and simulating these circuits using SPICE-based circuit simulators. Sensor analysis is conducted with an emphasis on noise budgeting and optimizing the sensor’s signal-to-noise ratio and resolution. In addition, the steady state, the phasor, and transient types of analyses were employed to study the static and dynamic behavior of the system. Validation of the model using analytical calculations and comparison with experimental data demonstrated superior results. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
Show Figures

Figure 1

Figure 1
<p>A magnetostrictive material exhibits a response to a magnetic field by variation in its dimensions in the direction of the field. (<b>a</b>) The solenoid carries the DC, and the AC electric current induces the field. (<b>b</b>) Relative elongation of the material due to the field. The large (quiescent) signal is shown with a thick solid line, and the small field/deformation signals are shown by thick solid lines enveloped by dashed lines.</p>
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<p>An example of a magnetoelectric sensor was proposed in [<a href="#B29-sensors-22-05514" class="html-bibr">29</a>]. (<b>a</b>) Mechanical topology and dimensions. All the layers are bonded mechanically with epoxy resin. (<b>b</b>) Block diagram of multi-domain signal conversion starting from the magnetic domain to the mechanical domain and then to the electrical domain.</p>
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<p>The equivalent diagram of the ME sensor is shown in (<b>a</b>). The charge <math display="inline"><semantics> <mi>q</mi> </semantics></math> is proportional to the field <math display="inline"><semantics> <mi>H</mi> </semantics></math> with the coefficient <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>Q</mi> </msub> </mrow> </semantics></math>. The <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>Q</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>b</mi> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> is shown in (<b>b</b>). The data for the plot adapted with permission from ref. [<a href="#B29-sensors-22-05514" class="html-bibr">29</a>]. 2011, John Wiley and Sons. An input signal is a magnetic flux <math display="inline"><semantics> <mi>B</mi> </semantics></math> [T] corresponding to a magnetic field <math display="inline"><semantics> <mi>H</mi> </semantics></math>[Oe] in the air with a factor of 10 k.</p>
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<p>The block diagram of the system with feedback. (<b>a</b>) General form, where <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> is an open loop gain of the amplifier, <math display="inline"><semantics> <mi>G</mi> </semantics></math> is a constant gain, <math display="inline"><semantics> <mi>β</mi> </semantics></math> is a feedback gain, and <math display="inline"><semantics> <mi mathvariant="sans-serif">Σ</mi> </semantics></math> is a summing unit. The signals are: <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>s</mi> </msub> </mrow> </semantics></math> is a source signal, <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>o</mi> </msub> </mrow> </semantics></math> is an output signal, and <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>ε</mi> </msub> </mrow> </semantics></math> is an error signal. (<b>b</b>) The circuit with the disabled error signal <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>ε</mi> </msub> </mrow> </semantics></math> and nonzero source signal <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>s</mi> </msub> </mrow> </semantics></math>. (<b>c</b>) The circuit with the disabled source signal <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>s</mi> </msub> </mrow> </semantics></math> and nonzero output signal <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>o</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>ME-sensor equivalent scheme (<a href="#sensors-22-05514-f003" class="html-fig">Figure 3</a>) with charge amplifier circuitry. The charge amplifier consists of an opamp with open-loop gain <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math>, input impedance <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math>, and the feedback elements <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>f</mi> </msub> </mrow> </semantics></math> that form the gain and bandwidth. An output impedance of the opamp is negligible compared to a feedback resistor at low frequencies.</p>
Full article ">Figure 6
<p>Simplified schemes for defining the components of a block diagram of a feedback system: (<b>a</b>) the error signal <math display="inline"><semantics> <mrow> <msubsup> <mi>v</mi> <mi>ϵ</mi> <mo>'</mo> </msubsup> </mrow> </semantics></math> is suppressed while the input signal <math display="inline"><semantics> <mi>B</mi> </semantics></math> is nonzero and (<b>b</b>) the input signal <math display="inline"><semantics> <mi>B</mi> </semantics></math> is suppressed while the output signal <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> is nonzero.</p>
Full article ">Figure 7
<p>Illustration of Expressions (9) and (10): (<b>a</b>) the current <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>c</mi> </msub> </mrow> </semantics></math> is the time derivative of the voltage <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) the voltage <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> </mrow> </semantics></math> is the time integral of the current <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>c</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Generation of voltage noise with a desired spectral density <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mi>n</mi> </msub> </mrow> </semantics></math> of the white component and a knee frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> of the flicker noise component. (<b>a</b>) The way the circuit looks in the LTSpice.LTSPICE, and (<b>b</b>) The LTSPICE graphical output for noise spectral density at the “out” node.</p>
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<p>A hierarchical block of the capacitance and the <math display="inline"><semantics> <mrow> <mi>E</mi> <mi>S</mi> <mi>R</mi> </mrow> </semantics></math> thermal noise of the piezoelectric material as it looks in LTSpice, where <math display="inline"><semantics> <mrow> <mi>v</mi> <mi>c</mi> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>v</mi> <mi>c</mi> <mn>2</mn> </mrow> </semantics></math> are capacitor terminals, <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>p</mi> <mi>z</mi> </mrow> </semantics></math> is a parameter of the capacitance of the piezoceramic element, <math display="inline"><semantics> <mrow> <mi>b</mi> <mi>o</mi> <mi>l</mi> <mi>t</mi> <mi>z</mi> </mrow> </semantics></math> is a PSPICE built in Boltzmann’s constant, <math display="inline"><semantics> <mrow> <mi>T</mi> <mi>k</mi> </mrow> </semantics></math> is a temperature in kelvin, <math display="inline"><semantics> <mrow> <mi>f</mi> <mi>c</mi> <mi>e</mi> <mn>1</mn> </mrow> </semantics></math> is the <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <msub> <mi>C</mi> <mrow> <mi>E</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>e</mi> <mn>1</mn> <mi>k</mi> </mrow> </semantics></math> is the <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <msub> <mi>n</mi> <mrow> <mi>E</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>A hierarchical block that has the magnetic signal <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>i</mi> <mi>n</mi> </mrow> </semantics></math>, in tesla, at its input and electrical charge <math display="inline"><semantics> <mrow> <mi>Q</mi> <mi>p</mi> </mrow> </semantics></math> in coulombs at its output is depicted in (<b>a</b>). This is the way the circuit looks in the LTSpice. The DC-magnetic field input <math display="inline"><semantics> <mrow> <mi>H</mi> <mi>b</mi> <mi>i</mi> <mi>a</mi> <mi>s</mi> </mrow> </semantics></math> in oersteds sets the bias for magnetostrictive material. The voltage-dependent voltage source <math display="inline"><semantics> <mrow> <mi>E</mi> <mn>1</mn> </mrow> </semantics></math> has the gain of <math display="inline"><semantics> <mrow> <mi>T</mi> <mn>2</mn> <mi>O</mi> <mi>e</mi> <mo>=</mo> <mn>10</mn> <mi>k</mi> </mrow> </semantics></math> (tesla to oersted factor for free space). The <math display="inline"><semantics> <mrow> <mi>E</mi> <mn>2</mn> </mrow> </semantics></math> voltage source has a unity gain, and a behavioral voltage source <math display="inline"><semantics> <mrow> <mi>B</mi> <mn>1</mn> </mrow> </semantics></math> includes a look-up table shown graphically in (<b>b</b>) multiplied by the sum of the fields <math display="inline"><semantics> <mrow> <mi>H</mi> <mi>i</mi> <mi>n</mi> <mi>O</mi> <mi>e</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>H</mi> <mi>b</mi> <mi>i</mi> <mi>a</mi> <mi>s</mi> <mi>O</mi> <mi>e</mi> </mrow> </semantics></math>.</p>
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<p>A map of noise sources. The <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> is the current noise corresponding to the thermal noise of the leakage resistance <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> and the <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>E</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </mrow> </semantics></math> is the ESR voltage noise source. The <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mi>n</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>n</mi> </msub> </mrow> </semantics></math> are correspondingly the voltage and the current equivalent input noise sources of the opamp, and <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> </mrow> </semantics></math> is the current noise source of the feedback resistor <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>f</mi> </msub> </mrow> </semantics></math>. All the resistors and opamp are noiseless.</p>
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<p>Scheme for simulating an ME sensor with a two-stage charge amplifier implemented in the LTSPICE environment. The hierarchical blocks circuitry X1 and X2 are shown in <a href="#sensors-22-05514-f009" class="html-fig">Figure 9</a> and <a href="#sensors-22-05514-f010" class="html-fig">Figure 10</a>. Opamps U1 and U2 use a modified built-in “universalopamp” model. All values of each element are provided in the schematic as global parameters under directive <b>param</b>. Each circuit element references a specific parameter in curly brackets. All the parameters are described in <a href="#sensors-22-05514-t004" class="html-table">Table 4</a>.</p>
Full article ">Figure 13
<p>The frequency sweep of the model signals. (<b>a</b>) The solid line is a small signal gain (left axis), and the dashed line is the phase (right axis) of the transfer function of the charge amplifier in the frequency range of interest. (<b>b</b>) Output voltage at an input signal of <math display="inline"><semantics> <mrow> <mn>10</mn> <mo> </mo> <mi>nT</mi> </mrow> </semantics></math> vs. the bias magnetic field.</p>
Full article ">Figure 14
<p>The results of the time-domain (transient analysis) of the system are presented here. The system has a sine wave magnetic field with amplitude <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo> </mo> <mn>10</mn> <mo> </mo> <mi>nT</mi> </mrow> </semantics></math> and frequency <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi>Hz</mi> </mrow> </semantics></math> at the input. The simulation time is <math display="inline"><semantics> <mrow> <mn>200</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The last two cycles of the output waveform are displayed. (<b>a</b>) The output voltage waveform vs. time is shown. The maximum and the minimum values are indicated with arrows. (<b>b</b>) The output voltage amplitude is dependent on the bias field. The <b>step</b> directive serves for scanning the bias field value (hbiasOe) in the range from <math display="inline"><semantics> <mrow> <mn>1</mn> <mo> </mo> <mi>mOe</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mn>12.25</mn> <mo> </mo> <mi>Oe</mi> </mrow> </semantics></math> with an increment of <math display="inline"><semantics> <mrow> <mn>500</mn> <mo> </mo> <mi>mOe</mi> </mrow> </semantics></math>. The <b>measure</b> directive calculates the amplitude for each value of the scanned parameter.</p>
Full article ">Figure 15
<p>The equivalent input noise and the equivalent input noise components due to each noise source. The dominant noise source <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>n</mi> </msub> </mrow> </semantics></math> is the equivalent current noise source of amplifier <math display="inline"><semantics> <mrow> <mi>U</mi> <mn>1</mn> </mrow> </semantics></math>. The equivalent voltage noise units <math display="inline"><semantics> <mrow> <mi mathvariant="normal">V</mi> <mo>/</mo> <msup> <mi>Hz</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> correspond to magnetic field noise units <math display="inline"><semantics> <mrow> <mi mathvariant="normal">T</mi> <mo>/</mo> <msup> <mi>Hz</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 16
<p>Simulated equivalent input magnetic noise spectral density (<b>a</b>) total equivalent input noise spectral density and contribution of dielectric noise, DC resistance noise, and feedback resistor. (<b>b</b>) Simulated equivalent input noise spectrum compared with equivalent input noise spectrum measured in [<a href="#B29-sensors-22-05514" class="html-bibr">29</a>]. The data is adapted with permission form ref. [<a href="#B29-sensors-22-05514" class="html-bibr">29</a>], 2011, John Wiley and Sons.</p>
Full article ">
14 pages, 4497 KiB  
Communication
Bendductor—Transformer Steel Magnetomechanical Force Sensor
by Przemysław Grenda, Monika Kutyła, Michał Nowicki and Tomasz Charubin
Sensors 2021, 21(24), 8250; https://doi.org/10.3390/s21248250 - 10 Dec 2021
Cited by 5 | Viewed by 2180
Abstract
In this paper, the design and investigation of an innovative force sensor, based on the Villari effect, is presented. The sensor was built from electrical steel, in a pressductor pattern, but working in bending load mode. The results of the experimental research allowed [...] Read more.
In this paper, the design and investigation of an innovative force sensor, based on the Villari effect, is presented. The sensor was built from electrical steel, in a pressductor pattern, but working in bending load mode. The results of the experimental research allowed for the evaluation of transducer’s performance, mitigation of measurement hysteresis, and optimization of its functional parameters. Several issues have been examined, among them the selection of supply and measured signals, the measured values’ impact on measurement hysteresis, harmonic analysis, and the selection of proper current waveforms and frequencies. The proposed sensor is robust, made from inexpensive materials, and has high sensitivity, as compared to other magnetoelastic sensors. It has much higher stress sensitivity than other magnetoelastic sensors due to deformation mode. Based on the tests, its measuring range can be defined as 0.5–5 N with a near-linear characteristic, SNR of 46 dB, and 0.11 N uncertainty. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
Show Figures

Figure 1

Figure 1
<p>Distribution of magnetic field lines in the pressducer under the action of a non-zero compressive force [<a href="#B3-sensors-21-08250" class="html-bibr">3</a>,<a href="#B30-sensors-21-08250" class="html-bibr">30</a>].</p>
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<p>Force sensitive element—electrical steel sheet drilled and wound with orthogonal magnetizing and sensing windings in pressductor pattern.</p>
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<p>Plate loading scheme.</p>
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<p>Diagram of the stand for measuring physical quantities other than voltage.</p>
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<p>Photo of the test stand with equipment numbered accordingly with the schematic diagram in <a href="#sensors-21-08250-f004" class="html-fig">Figure 4</a>.</p>
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<p>Measurement results of THD of output signal.</p>
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<p>The results of measuring the phase shift between the set and the measured signal for a variable load on the plate.</p>
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<p>The results of measurements of voltage and magnetic flux for successive masses loading the tested plate.</p>
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<p>The results of the measurement of the signal amplification measured at the given loads for successive harmonics.</p>
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<p>Measurement results of the voltage induced on the measuring coils and the phase shift of the measured signal against the set one in the second harmonic for different masses loading the plate.</p>
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<p>Hysteresis curves for: (<b>a</b>) voltage, (<b>b</b>) noise, (<b>c</b>) phase shift, and (<b>d</b>) magnetic flux measurements depending on the weight loading the plate.</p>
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<p>Hysteresis curves for: (<b>a</b>) voltage, (<b>b</b>) noise, (<b>c</b>) phase shift, and (<b>d</b>) magnetic flux measurements depending on the weight loading the plate.</p>
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<p>Dependence of the induced voltage on measuring coil on the load for different frequencies of the supply current.</p>
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<p>The dependence of the magnetic flux changes on the load for different frequencies of the supply current.</p>
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<p>Comparison of maximum hysteresis errors depending on the frequency of the plate magnetizing current.</p>
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<p>Measurement hysteresis curves for measuring: (<b>a</b>) voltage, (<b>b</b>) magnetic flux when magnetizing the plate with a triangular signal with a frequency of 300 Hz.</p>
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<p>Measurement hysteresis errors for voltage and magnetic flux measurements with an AM modulated magnetizing current supply.</p>
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