A Steel Wire Stress Measuring Sensor Based on the Static Magnetization by Permanent Magnets.

sensors Article

A Steel Wire Stress Measuring Sensor Based on the Static Magnetization by Permanent Magnets Dongge Deng, Xinjun Wu * and Su Zuo School of Mechanical Science & Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; [email protected] (D.D.); [email protected] (S.Z.) * Correspondence: [email protected]; Tel.: +86-139-7101-7626 Academic Editor: Xue Wang Received: 25 July 2016; Accepted: 30 September 2016; Published: 6 October 2016

Abstract: A new stress measuring sensor is proposed to evaluate the axial stress in steel wires. Without using excitation and induction coils, the sensor mainly consists of a static magnetization unit made of permanent magnets and a magnetic field measurement unit containing Hall element arrays. Firstly, the principle is illustrated in detail. Under the excitation of the magnetization unit, a spatially varying magnetized region in the steel wire is utilized as the measurement region. Radial and axial magnetic flux densities at different lift-offs in this region are measured by the measurement unit to calculate the differential permeability curve and magnetization curve. Feature parameters extracted from the curves are used to evaluate the axial stress. Secondly, the special stress sensor for Φ5 and Φ7 steel wires is developed accordingly. At last, the performance of the sensor is tested experimentally. Experimental results show that the sensor can measure the magnetization curve accurately with the error in the range of ±6%. Furthermore, the obtained differential permeability at working points 1200 A/m and 10000 A/m change almost linearly with the stress in steel wires, the goodness of linear fits are all higher than 0.987. Thus, the proposed steel wire stress measuring sensor is feasible. Keywords: stress evaluation; steel wire; static magnetization; permanent magnet; Hall element arrays

1. Introduction Because of good mechanical performance, steel cables have been widely used in industrial production and infrastructure construction. As key load-bearing components, their stress state is closely related to the structural stability and safety. Thus, it is of great significance to evaluate the stress in steel cables. The stress in ferromagnetic specimen can be measured by electromagnetic methods, because magnetic properties of ferromagnetic materials change with the applied stress [1]. To obtain the magnetic feature parameter for evaluating the stress, the tested specimen should be magnetized by excitation fields at first. According to whether the excitation field is artificial or not, electromagnetic methods can be divided into the passive magnetic method and the active magnetic method [2,3]. In passive magnetic methods such as the metal magnetic memory (MMM) technique also known as the residual magnetic field (RMF) technique, without application of an excitation field, the tested specimen is in the presence of ambient magnetic fields such as the geomagnetic field. The measured residual magnetic flux density parallel and perpendicular to the surface of the specimen correlate closely with the applied stress [2]. Though artificial excitation field is not needed, the weak detection signal in this technique is easily influenced by the external environment [4,5], it is difficult to measure the stress in steel cables quantitatively by this technique. In active magnetic methods, the steel cable is magnetized by an excitation field at first. Static magnetization, harmonic magnetization and pulse magnetization have been used to evaluate the stress in steel cables. Under the static magnetization, the magnetic field strength parallel to the magnetization direction measured in proximity to the steel cable is used to evaluate the stress [6]. The measurement is conducted at the uniformly magnetized Sensors 2016, 16, 1650; doi:10.3390/s16101650

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and pulse magnetization have been used to evaluate the stress in steel cables. Under the static magnetization, the magnetic field strength parallel to the magnetization direction measured Sensors 2016, 16, 1650 2 of in 18 proximity to the steel cable is used to evaluate the stress [6]. The measurement is conducted at the uniformly magnetized region. Thus, the feature parameter is obtained at a constant working point. It region. Thus, the feature parameter is obtained at a constant working point. It is hard to find the is hard to find the proper working point in this case [7]. Adopting harmonic magnetization, the eddy proper working point in this case [7]. Adopting harmonic magnetization, the eddy current technique current technique has also been used to characterization of stress in steel cables [8]. The has also been used to characterization of stress in steel cables [8]. The impedance [9,10] or the induced impedance [9,10] or the induced voltage [11] of an electromagnetic coil is utilized as feature voltage [11] of an electromagnetic coil is utilized as feature parameters. The research results indicate parameters. The research results indicate the close relationship between the feature parameters and the stress close relationship between feature andsize theeffect stress[12] in acaused steel cable withcurrent a special the in a steel cable with a the special size.parameters However, the by eddy in size. However, the size may effectlead [12]tocaused by results eddy current dynamic magnetization may to dynamic magnetization different for steelincables of different size. The sizelead effect different results for steel cables of different size. The size effect can be reduced when the sample is can be reduced when the sample is magnetized to technically saturate. Pulse magnetization is magnetized to technically saturate. Pulse magnetization is usually adopted to magnetize the and sample to usually adopted to magnetize the sample to the saturation for its low power consumption small the saturation for its low power consumption and small heat production [13]. It is widely used in the heat production [13]. It is widely used in the Elasto-magnetic (EM) sensor technique [14,15] to Elasto-magnetic (EM) sensor technique [14,15] to evaluate the stress in steel cables. evaluate the stress in steel cables. The EM a primary excitation coil coil and and a secondary induction coil. Itcoil. can The EM sensor sensorusually usuallyconsists consistsofof a primary excitation a secondary induction directly obtain the incremental permeability to measure the actual stress in a noncontact way [16–18]. It can directly obtain the incremental permeability to measure the actual stress in a noncontact Thus,[16–18]. it has been used to monitor theto stress in steel ten years. way Thus, it has been used monitor thecables stresson in field steel more cablesthan on field more The thanapplication ten years. effect of the EM effect sensorofisthe good installation Because it [19]. is inevitable The application EMexcept sensorthe is good except is thecomplicated installation [19]. is complicated Because to it wind both coils on steel a Smart Elasto-Magneto-Electric (EME) Sensor (EME) [20,21]Sensor which [20,21] can be is inevitable to wind bothcables, coils on steel cables, a Smart Elasto-Magneto-Electric installed more is recently put upisbyrecently Duan etput al. for evaluating. Thestress Magneto-Electric which can be easily installed more easily upstress by Duan et al. for evaluating. (ME) The sensing unit made of a ME-laminated composite is used to take place of the secondary induction Magneto-Electric (ME) sensing unit made of a ME-laminated composite is used to take place of coil. the Thus, there is no need to wind the second coil on steel cables. However, the primary excitation coil still secondary induction coil. Thus, there is no need to wind the second coil on steel cables. However, the has to be excitation wound [22]. thisbepaper is intended to develop feasibleis stress measuring sensor primary coilTherefore, still has to wound [22]. Therefore, thisa paper intended to develop a which is easier to install. Specially, as a preliminary study, a new stress measuring sensor is proposed feasible stress measuring sensor which is easier to install. Specially, as a preliminary study, a new to test measuring Φ5 and Φ7 sensor steel wires frequently in steel Without using the excitation coil and the stress is proposed to used test Φ5 and cables. Φ7 steel wires frequently used in steel cables. induction coil, the proposed sensor obtain the feature parameter related to the stress under the static Without using the excitation coil and the induction coil, the proposed sensor obtain the feature magnetization by permanent parameter related to the stressmagnets. under the static magnetization by permanent magnets. This paper is organized as follows.Section Section 2 interprets principle of the proposed sensor. This paper is organized as follows. 2 interprets thethe principle of the proposed sensor. In In Section 3, the sensor, which applies to both Φ5 and Φ7 steel wires, is developed. Section 4 tests the Section 3, the sensor, which applies to both Φ5 and Φ7 steel wires, is developed. Section 4 tests the performance of 5 lists thethe conclusion andand an outline of the performance of this this sensor sensorby byexperiments. experiments.At Atlast, last,Section Section 5 lists conclusion an outline of further work. the further work. 2. The Principle 2. The Principle Figure 1 shows the principle of the proposed sensor. The sensor is mainly composed of a Figure 1 shows the principle of the proposed sensor. The sensor is mainly composed of a static static magnetizing device and magneto-sensitive elements. The principle is based on the method for magnetizing device and magneto-sensitive elements. The principle is based on the method for measuring the magnetization curve of cylindrical bar specimen under static magnetization [23,24] put measuring the magnetization curve of cylindrical bar specimen under static magnetization [23,24] up by the author. put up by the author. L

σ

Static magnetizing unit Bmax B=f(L) Bmin (Hmax) (Hmin)

dL Cylindrical interface σ (L) D

Ferromagnetic bar

r z

(L)

(L, Lo)

(L, Lo)

Lo

Magneto-sensitive elements Measurement (L, Lo) and

(L, Lo) Extrapolation

(L,0) and

(L,0) at the interface Calculation

Differential permeability curve μ’(H) Integration

Magnetization curve B(H) Extraction

Feature parameters evaluating σ

Figure 1. The principle of the proposed steel stress measuring sensor. Figure 1. The principle of the proposed steel stress measuring sensor.

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As described in Figure 1, under the excitation of the static magnetizing device, a spatial magnetic field B = f (L) varying along the axial position L is induced in the cylindrical ferromagnetic bar. r (L, L ) Magneto-sensitive elements are used to measure the radial and axial magnetic flux densities Bair o z and Bair (L, Lo ) at different lift-offs Lo in the region where the distribution of axial magnetic flux density r (L, 0) around the cylindrical Bzf er (L) within the cross section and radial magnetic flux density Bair r (L, 0) interface is uniform for a given position L. Then, radial and axial magnetic flux densities Bair z r z and Bair (L, 0) at the interface could be extrapolated from the measured Bair (L, Lo ) and Bair (L, Lo ). r (L, 0) In this case, differential permeability curve µ’(H) can be calculated from the extrapolated Bair z and Bair (L, 0) according to the continuity of the tangential magnetic field strength, the Gauss’ law for magnetism, Rayleigh relation in Rayleigh region and the law of approach to saturation. Furthermore, magnetization curve B(H) could be integrated from the calculated µ’(H). At last, feature parameters at different magnetic field strengths can be extracted to evaluate the stress σ in the ferromagnetic bar. In the above steps to obtain feature parameters evaluating the stress σ, it is crucial to obtain r (L, 0) and Bz (L, 0). The corresponding steps are magnetization curve B(H) from the extrapolated Bair air listed as follows: (1) The axial magnetic flux density variation d[Bzf er (L)] across the unit length dL is got from the r (L, 0) at the interface as Equation (1) according to the Gauss’ law radial magnetic flux density Bair for magnetism. h i r ( L, 0) dL 4Bair (1) d Bzf er ( L) = D (2) The axial magnetic field strength variation d[H zf er (L)] across the unit length dL is got from the z (L, 0) at the interface as Equation (2) according to the continuity of the axial magnetic flux density Bair tangential magnetic field strength. h i z z d H zf er ( L) = [ Bair ( L + dL, 0) − Bair ( L, 0)] /µ0

(2)

0 (L) can be got from Equation (3) which is obtained by dividing (3) The differential permeability µin Equation (2) with Equation (1). Then combining with the axial magnetic field strength H zf er (L) at 0 (H z ) z different axial position L, the differential permeability µin f er (Hmin ≤ H f er ≤ Hmax) at the measurement region can be got.

h i r ( L, 0) dL d Bzf er ( L) 4Bair 0 i = z µin ( L) = h D Hair ( L + dL, 0) − H zair ( L, 0) d H zf er ( L)

(3)

(4) According to Rayleigh relation in Rayleigh region [25] and the law of approach to 0 (H z ) saturation [26] described in Equations (4) and (5), respectively, the differential permeability µin f er z 0 z (0 ≤ H zf er ≤ Hsa) at the magnetic field strength H f er ∈ [0, Hsa ] can be extrapolated from the µin (H f er ) (Hmin ≤ H zf er ≤ Hmax). Where, Hsa denotes the magnetic field strength which can magnetize the specimen to technical saturation. 0 µin = dB/dH = µ0 µr + 2νH (4) dB a 2b 3c 0 µin = = µ 0 Ms ( 2 + 3 + 4 + · · · ) + 1 + χ p (5) dH H H H 0 In Equation (4), the parameter υ is called Rayleigh constant. 2υ is equal to dµin /dH. In Equation (5), µ0 is the permeability of free space, Ms is the saturation magnetization, and the parameter “a” is called magnetic hardness [27]. Parameter b, c and the other higher parameters without any particular definition are constants related to the magnetocrystalline anisotropy of the material. The parameter χp is the paramagnetic susceptibility. Equation (5) is a general formula to describe the relationship between the differential permeability 0 and the applied magnetic field H. This equation includes too many terms that it cannot be used µin

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conveniently in practice. Thus, this equation needs to be simplified in some cases. In the most important special case, the terms about b, c and the other higher terms are neglected. This leads to WEISS saturation law, which can be described in Equation (6) [27]. 0 µin =

h i dB a = µ 0 Ms ( 2 ) + 1 dH H

(6)

The Equation (6) has been verified to be able to model the magnetization of prestressing steel without applied stress near saturation accurately [27]. When taking the stress dependency into account, the Equation (6) should be modified to Equation (7) as follows. 0 µin

σ dB a = = µ0 Ms ( 2 )(1 + ) + 1 dH cσ H

(7)

where cσ is called as magnetoelastic stress parameter. Compared with Equation (6), the terms related to the stress σ have been added into Equation (7). As can be seen from Equation (7), the differential 0 in the region approach to saturation changes linearly with the applied stress σ when permeability µin the magnetic field strength is constant. (5) At last, the Magnetization curve B(H) can be found by the point-by-point integration of 0 (H z ) at the interval [0, H ] described in Equation (8). The B(H) in the differential permeability µin sa f er Equation (8) is a variable limit integral function. Where H is the function variable and H zf er is the integration variable. B (H) =

Z H dBz f er 0

dH zf er

dH zf er

=

Z H 0

0 µin H zf er dH zf er ,

H ∈ [0, Hsa ]

(8)

Therefore, with the help of an magnetizing unit providing appropriate static magnetization, the magnetization curve B(H) of a cylindrical bar specimen could be obtained to evaluate the stress. Based on this, a sensor for evaluating the stress in Φ5 and Φ7 steel wires is developed in this paper. 3. The Development of the Proposed Sensor According to the principle illustrated above, the sensor should consist of a proper static magnetization unit and an appropriate magnetic field measurement unit containing magneto-sensitive elements. 3.1. Static Magnetization Unit The static magnetization unit should satisfy the uniform distribution conditions for the magnetic flux density. Namely, under the excitation of the magnetization unit, the distribution of axial magnetic r (L, 0) around the flux density Bzf er (L) within the cross section and radial magnetic flux density Bair cylindrical interface are uniform for a given position L. In principle, DC coils [23] or circular permanent magnets, which can be placed coaxial with the steel wire, should be adopted as the static magnetization r (L, 0) around the unit. In such cases, the uniform distribution of radial magnetic flux density Bair cylindrical interface can be easily satisfied. However, DC coils is hard to be wound on the steel wire. The circular permanent magnets could be only installed from the end of the steel wire, which is impossible when the steel wire is anchored. Thus, a static magnetization unit shown in Figure 2 was adopted by the author to magnetize the 2 m length Φ7 steel wire [24].

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Spatially varying magnetized region Uniformly magnetized region N N

Steel wire Permanent magnet

S

Yoke iron

S 40

A-A

Permanent magnetizer

θ r

θ=90º θ=0º Lo=0

Figure Thedimensions dimensions of static magnetization unit for evaluating stress in (Unit: steel wires Figure 2.2.The of static magnetization unit for evaluating the stressthe in steel wires mm). (Unit: mm).

The static magnetization unit consists of two permanent magnetizers which are symmetrically The static magnetization unit consists of two permanent magnetizers which are symmetrically arranged on the center of the steel wire. The permanent magnetizer is composed of the yoke iron with a arranged on the center of the steel wire. The permanent magnetizer is composed of the yoke iron high level of permeability and NdFeB N35 magnets. Different form the present electromagnetic method with a high level of permeability and NdFeB N35 magnets. Different form the present adopting static magnetization [6] where the uniformly magnetized region is served as the testing electromagnetic method adopting static magnetization [6] where the uniformly magnetized region region. The spatially varying magnetized region under the excitation of the static magnetization unit is is served as the testing region. The spatially varying magnetized region under the excitation of the utilized as the testing region. The field varying along the axial position L in this region is adopted as the static magnetization unit is utilized as the testing region. The field varying along the axial position excitation field. This is because that only using this excitation field can magnetic parameters at different L in this region is adopted as the excitation field. This is because that only using this excitation field magnetic field strengths be obtained under a static magnetization. In addition, a similar field under a can magnetic parameters at different magnetic field strengths be obtained under a static static magnetization has been adopted by other researchers to obtain the magnetic hysteresis loss of magnetization. In addition, a similar field under a static magnetization has been adopted by other the inspected members [28]. In the region from L = 55 mm to L = 910 mm, the uniform distribution researchers to obtain the magnetic hysteresis loss of the inspected members [28]. In the region from conditions for the magnetic flux density is satisfied [24]. Furthermore, there is no size effect caused by L = 55 mm to L = 910 mm, the uniform distribution conditions for the magnetic flux density is eddy current. This static magnetization unit may also be suitable for Φ5 steel wire. Thus, a 3D finite satisfied [24]. Furthermore, there is no size effect caused by eddy current. This static magnetization element model for magnetizing Φ5 steel wire with this static magnetization unit is created by ANSYS unit may also be suitable for Φ5 steel wire. Thus, a 3D finite element model for magnetizing Φ5 steel software to analyze the distribution of the magnetic flux density. The geometrical size of the model is wire with this static magnetization unit is created by ANSYS software to analyze the distribution of shown in Figure 2. The lift-off of the magnets from the steel wire is 1 mm. The air surrounding the the magnetic flux density. The geometrical size of the model is shown in Figure 2. The lift-off of the static magnetization unit and the steel wire is a 3-m length cylinder with the radius of 200 mm. The 3-D magnets from the steel wire is 1 mm. The air surrounding the static magnetization unit and the steel magnetic scalar solid 96 element is used to mesh the established entity. The entities in the model are wire is a 3-m length cylinder with the radius of 200 mm. The 3-D magnetic scalar solid 96 element is associated with the corresponding material properties, where the coercivity, remanent induction and used to mesh the established entity. The entities in the model are associated with the corresponding relative permeability of the magnets are set to 876400 A/m, 1.184 T and 1.075, respectively according to material properties, where the coercivity, remanent induction and relative permeability of the the performance testing report provided by the supplier (Shenzhen Xunci Magnetism Co., Ltd., China). magnets are set to 876400 A/m, 1.184 T and 1.075, respectively according to the performance testing The B-H curves for the yoke iron and the steel wire are shown in Figure 3. The B-H curve for the report provided by the supplier (Shenzhen Xunci Magnetism Co., Ltd., China). The B-H curves for steel wire is measured by magnetizing coils and measuring coils in our laboratory, the corresponding the yoke iron and the steel wire are shown in Figure 3. The B-H curve for the steel wire is measured measurement system has been given in an earlier paper [29]. by magnetizing coils and measuring coils in our laboratory, the corresponding measurement system has been given in an earlier paper [29].

1 1 Table Data

BH BH

Table Data

Table For Material Table For Material

2 2

T1=0.00 Sensors 2016, 16, 1650 T1=0.00Sensors 2016, 16, 1650

1 1 Table Data Table Data T1=0.00 T1=0.00

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JUN 3 2016 JUN 12:23:39 3 2016 12:23:39

4

3.6 3.2

1.8 1.6

3.2 2.8

1.6 1.4

2.8

1.4 1.2

B B

2 2 1.6 1.6 1.2 1.2 .8

.6 .4

.8

.4 .2

.4 (x10**3)

0

200 100 100

20 steel bar 20 steel bar

200

400 300 300

400

600 500

H500 H/A· m-1 H m-1 H/A·

600

(x10**3) 1000

800 700 700

800

900

1 2016

(b) (b)

1 .8 .8 .6

0 0

JUL

1 2016 6JUL of15:07:29 18 6 of15:07:29 17 6 of 17

1.2 1

B/T B/T

B/T B/T

2.4

.4 0

5 5

2 1.8

2.4

B B

Table For Material Table For Material

2

(a) (a)

4 3.6

BH BH

1000

.2 0

(x10**1)

0 0 0

250 125 125

900

250

500 375 375

500

750 625

750

(x10**1) 1250

1000 875

H625 H/A·m-1875 H H/A· m-1

1000

1125 1250 1125

Figure 3. The B-H curves for the yoke iron (a) and the steel wire (b). Figure 3. The B-H curves for the yoke iron (a) and the steel wire (b).

After establishing the the model, the the difference scalar scalar potential (DSP) (DSP) method method is is adopted and and the After After establishing establishing the model, model, the difference difference scalar potential potential (DSP) method is adopted adopted and the the Jacobi Conjugate Gradient (JCG) iterative equation solver is used to solve the model Jacobi (JCG) iterative equation solver solver is used isto solve and Jacobi Conjugate ConjugateGradient Gradient (JCG) iterative equation used the to model solve quickly the model quickly and accurately. The calculated axial magnetic flux density and the radial magnetic flux accurately. calculated magnetic fluxmagnetic density and radialand magnetic flux density in flux this quickly andThe accurately. Theaxial calculated axial fluxthe density the radial magnetic density in this model are shown in Figure 4a,b, respectively. model are shown in Figure 4a,b, respectively. density in this model are shown in Figure 4a,b, respectively.

(a) (a)

(b) (b)

L L

L=910 L=910

L=0 L=0

Figure 4. The calculated axial magnetic flux density (a) and the radial magnetic flux density (b). (b). Figure 4. The calculated axial magnetic flux density (a) and the radial magnetic flux density (b).

The magnetic flux flux densities in the steel wire wire is the the vector addition addition of the the magnetic flux flux density The in the The magnetic magnetic flux densities densities in the steel steel wire is is the vector vector addition of of the magnetic magnetic flux density density created by the two permanent magnetizers according to the magnetic field superposition principle created created by by the the two two permanent permanent magnetizers magnetizers according according to to the the magnetic magnetic field field superposition superposition principle principle which is frequently frequently to be be used to to create aa special special magnetic field field such as as the homogeneous homogeneous magnetic which which is is frequently to to be used used to create create a special magnetic magnetic field such such as the the homogeneous magnetic magnetic field created by the Helmholtz coil [30]. As depicted in Figure 4a, the axial magnetic flux density is is field in Figure field created created by by the the Helmholtz Helmholtz coil coil [30]. [30]. As As depicted depicted in Figure 4a, 4a, the the axial axial magnetic magnetic flux flux density density is varying along the axial location L. While the distribution of the axial magnetic flux density in the varying flux density varying along along the the axial axial location location L. L. While While the the distribution distribution of of the the axial axial magnetic magnetic flux density in in the the cross section sectionofofthe thespatially spatially varying magnetized region seems uniform. Figure 4b describes the cross varying magnetized region seems uniform. Figure 4b describes the radial cross section of the spatially varying magnetized region seems uniform. Figure 4b describes the radial magnetic flux density in the steel wire on the right side of the magnetization unit. In the magnetic flux density in the steel wiresteel on the right the side magnetization unit. In the section radial magnetic flux density in the wire on side the of right of the magnetization unit. Innear the section near the axial location L = 0 namely the right end of the magnetization unit, the distribution the axialnear location L = 0location namelyLthe endthe of the magnetization unit, the distribution the radial section the axial = 0right namely right end of the magnetization unit, the of distribution of the radial magnetic flux density around the cylindrical interface is not homogeneous. The bad magnetic fluxmagnetic density around the cylindrical interface is notinterface homogeneous. The bad homogeneity of the radial flux density around the cylindrical is not homogeneous. The bad homogeneity in the region near the magnetizers is due to that the two permanent magnetizers are in the region near the magnetizers due to that the twotopermanent magnetizers not rotational homogeneity in the region near theismagnetizers is due that the two permanentare magnetizers are not rotational symmetry about the axial line of the steel wire. In such case, when the axial position L symmetry about the axial line of the steel wire. In such case, when the axial position L is near the right not rotational symmetry about the axial line of the steel wire. In such case, when the axial position L is near the right end of the magnetization unit, the distribution of the superimposed magnetic field end of the unit, the distribution of the the distribution superimposed field is complex through is near themagnetization right end of the magnetization unit, of magnetic the superimposed magnetic field is complex through the vector addition of the magnetic field. However, when the axial position L the vector addition thevector magnetic field. of However, when the axial positionwhen L has the some distance from is complex throughofthe addition the magnetic field. However, axial position L has some distance from the magnetization unit, a small length of the steel wire can be regarded as a the magnetization unit, a small length of the steel wire can be regarded as a particle approximately and has some distance from the magnetization unit, a small length of the steel wire can be regarded as a particle approximately and the homogeneity of the magnetic field becomes better, which can be the homogeneity of the magnetic field becomesofbetter, which canfield be indicated Figure 4. Thus, particle approximately and the homogeneity the magnetic becomes in better, which canthe be indicated in Figure 4. Thus, the magnetic flux density in the region from L = 55 mm to L = 910 mm is magnetic flux density in thethe region from flux L = density 55 mm to = region 910 mm is extracted to to further indicated in Figure 4. Thus, magnetic in L the from L = 55 mm L = 910analyze mm is extracted to further analyze the distribution uniformity. The distribution of the axial magnetic flux extracted to further analyze the distribution uniformity. The distribution of the axial magnetic flux

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Bzf er (L)

the distribution uniformity. The distribution of the axial magnetic zflux density in the plane z z z B the θ 0°, axial magnetic flux B in the θ 90° the ◦ and z (L) fer(L) fer(L) density Bfer (L) in inmagnetic the plane planeflux θ ==density 0°, the the B axial magnetic fluxθdensity density Bfer (L) in the plane plane θ == flux 90° and and the θdensity = 0◦ , the axial in the plane = 90 the radial magnetic density f er r r radial magnetic flux density B (L, 0) in the cylindrical interface r = 2.5 mm are shown in Figure 5a–c. r air(L, radial magnetic flux density B 0) in the cylindrical interface r = 2.5 mm are shown in Figure 5a–c. air B (L, 0) in the cylindrical interface r = 2.5 mm are shown in Figure 5a–c. air

(a) (a)

0 0 400 400

600

600 L/mm L/mm

800 800

1000 1000

2.5 2.5

2 2

1.5 1.5

1 1

0.5 0.5

r/mm r/mm

0 0

1.2 1.2 0.6 0.6

rr

0.6 0.6

0 0 200 200

400 400

L/mm L/mm

600 600

1 1

800 800

1000 1000

2.5 2.5

2 2

(c) (c)

0.015 0.015

BBairair(L,0)/T (L,0)/T

zz

1.2 1.2

200 200

(b) (b)

1.8 1.8

BBferfer(L)/T (L)/T

zz

BBferfer(L)/T (L)/T

1.8 1.8

1.5 r/mm 1.5 r/mm

0.5 0.5

0 0

0.01 0.01

0.005 0.005 0 0 200 200

400 400

600

600 L/mm L/mm

800 800

1000 1000

0 60 0 120 60 120 180 240 180θ/oo θ/ 300 240 360 300 360

zzz (L) in the plane θ = 0◦ (a), Bzz z (L) in the plane θ = 90◦ (b) and rrBr (L,0) Figure of B (L) (L) (L,0) air in er in Figure 5. 5. The The distribution distribution of of B Bffer (L) in in the the plane plane θ θ == 0°(a), 0°(a), B Bfer in the the plane plane θ θ == 90°(b) 90°(b) and and B Bair in ferer ferf(L) air(L,0) in the cylindrical interface r = 2.5 mm (c) from L = 55 mm to L = 910 mm. the cylindrical interface r = 2.5 mm (c) from L = 55 mm to L = 910 mm. the cylindrical interface r = 2.5 mm (c) from L = 55 mm to L = 910 mm. z

Figure 555 depicts depicts that thatin inthe theregion regionfrom fromLL L===55 55mm mmtoto to910 910mm, mm,atat ata aafixed fixedaxial axiallocation location “L”, Bzfer (L) Figure depicts that in the region from 55 mm 910 mm, fixed axial location “L”, (L) Figure “L”, BzfB erfer(L) r r ◦ ◦ r in the planes θ = 0° and θ = 90° are approximately identical, B (L, 0) around the cylindrical interface air 90° are are approximately approximately identical, identical, BBair in the planes θθ == 00° and θθ == 90 (L, 0) 0) around around the cylindrical interface air(L, = 2.5 2.5 mm mm are are also also approximately identical. Namely, distribution of the axial axial also approximately approximately identical. Namely, in this this region, region, the the distribution of the rr = Namely, in magnetic flux flux density densityin inthe thecross crosssection sectionofof ofthe the steel wire and the radial magnetic flux density in flux density in the cross section the steel wire and radial magnetic density in magnetic steel wire and thethe radial magnetic fluxflux density in the the cylindrical interface can be both considered uniform for a given position L. Thus, under the the cylindrical interface can be considered both considered uniform for aposition given position L. Thus, the cylindrical interface can be both uniform for a given L. Thus, under the under excitation excitation the shown in 2, uniform distribution for excitation ofmagnetization the static static magnetization magnetization unit shown in Figure Figure 2, the the uniform conditions distribution conditions for of the staticof unit shown unit in Figure 2, the uniform distribution forconditions the magnetic the magnetic flux density in Φ5 steel wire can be satisfied. That is to say, not only appropriate for the magnetic flux density in Φ5 steel wire can be satisfied. That is to say, not only appropriate for flux density in Φ5 steel wire can be satisfied. That is to say, not only appropriate for Φ7 steel wire, Φ7 this unit can be to Φ7 steel steel wire, this static static magnetization magnetization unit cantoalso also be used usedΦ5 to magnetize magnetize Φ5 steel steel wire. wire. this staticwire, magnetization unit can also be used magnetize steel wire. Φ5 Based on on the the analysis analysis above, above, the the static static magnetization magnetization unit is developed, as shown in Figure 6. Based magnetization unit unit is is developed, developed, as as shown shown in in Figure Figure 6. 6. An aluminum alloy box is used to contain the permanent magnetizer described in Figure 2. Then, contain the the permanent permanent magnetizer described in Figure 2. Then, An aluminum alloy box is used to contain Then, an aluminum aluminum alloy shell combining handle is used to box. At last, the aluminumalloy alloyshell shell combining the handle is to used to package package the box.the Attwo last,aluminum the two two an combining the the handle is used package the box.the At last, aluminum alloy shells are are by connected by Hinges Hinges and Hasps to tothe constitute the magnetization magnetization unit. aluminum shells connected by Hasps constitute the unit. alloy shellsalloy are connected Hinges and Hasps and to constitute magnetization unit. Unlocking Unlocking the hasp, unit is fold the Then locking the Unlocking themagnetization hasp, the the magnetization magnetization unit is open open to fold steel the tested tested steel wire. Then locking the hasp, the unit is open to fold the to tested wire. steel Thenwire. locking the hasp, the hasp, the magnetization unit is closed to magnetize the steel wire. hasp, the magnetization unitto is magnetize closed to magnetize the steel wire. magnetization unit is closed the steel wire. Handle Handle

Hinge Hinge Hasp Hasp

Box Box containing containing aa permanent permanent magnetizer magnetizer

Steel Steel wire wire

Aluminum Aluminum alloy alloy shell shell Figure 6. developed static magnetization unit. Figure 6. 6. The The unit. Figure The developed developed static static magnetization magnetization unit.

3.2. Field Measurement Unit 3.2. Magnetic Magnetic Unit 3.2. Magnetic Field Field Measurement Measurement Unit According According to to the the principle principle illustrated illustrated in in Section Section 2, 2, the the magnetic magnetic field field measurement measurement unit unit should should According to the principle illustrated in Section 2, the magnetic field measurement unit should contain the magneto-sensitive elements which can pick up the radial and axial magnetic contain the magneto-sensitive elements which can pick up the radial and axial magnetic flux flux r z contain theBmagneto-sensitive elements which can lift-offs pick up the radialthe andsteel axial magnetic fluxthe densities r z densities L oo) and B L oo) at different L oo from wire under static air (L, air (L, densities B (L, L ) and B (L, L ) at different lift-offs L from the steel wire under the static air r (L, L ) and z Bair BTo Lo ) this atairdifferent lift-offsthe Lo magneto-sensitive from the steel wireelements under the static apply magnetization. o air (L, magnetization. meet requirement, should to static static magnetization. To meet this requirement, the magneto-sensitive elements should apply to To meet this requirement, the magneto-sensitive elements should apply to static magnetic field magnetic field measurement, have high spatial resolution, large linear measuring range and magnetic field measurement, have high spatial resolution, large linear measuring range and high high measurement, have high spatial resolution, large linear measuring range and high sensitivity. sensitivity. sensitivity. In In addition, addition, the the elements elements should should be be easily easily configured configured in in array. array. In addition, the elements shouldHall be easily configured in array. Induction Induction coils, coils, GMR GMR and and Hall elements elements are are frequently-used frequently-used in in magnetic magnetic field field measurement. measurement. Induction coils coils are are not not sensitive sensitive to to the the static static magnetic magnetic field. field. GMR GMR has has high high sensitivity sensitivity but but aa low low Induction linear measuring range. While the Linear Hall elements have many advantages: ratiometric linear linear measuring range. While the Linear Hall elements have many advantages: ratiometric linear output output proportional proportional to to the the magnetic magnetic field, field, high high spatial spatial resolution resolution for for its its small small size, size, immune immune to to the the

Sensors 2016, 16, 1650

8 of 18

Induction coils, GMR and Hall elements are frequently-used in magnetic field measurement. Induction coils low Sensors 2016, 16, 1650are not sensitive to the static magnetic field. GMR has high sensitivity but a 8 of 17 linear measuring range. While the Linear Hall elements have many advantages: ratiometric linear packing stress and to thethe temperature variation for itsresolution on-chip temperature compensation output proportional magnetic field, high spatial for its small size, immune toand the magnetic characteristics robust against mechanical stress. Thus, linear HAL1823 and elements in packing stress and the temperature variation for its on-chip temperature compensation magnetic TO92UA Package produced by MICRONAS are adopted in this work. Its volume and sensitive area characteristics robust against mechanical stress. Thus, linear HAL1823 elements in TO92UA Package are 4 × 3 ×by 1.5MICRONAS mm3 and 0.2are × 0.1 mm2, in respectively. Its volume sensitivity linearity are3 produced adopted this work. Its andand sensitive areameasuring are 4 × 3 ×range 1.5 mm 2.5 respectively,Its which can satisfy request for magnetic field in andmv/G 0.2 ×and 0.1±1000 mm2 ,G, respectively. sensitivity and the linearity measuring range aremeasurement 2.5 mv/G and this work. ±1000 G, respectively, which can satisfy the request for magnetic field measurement in this work. To easilyconfigure configurehall hall elements in array, a printed circuit(PCB) boardis designed (PCB) is and designed and To easily elements in array, a printed circuit board developed, developed, shown in Figure 7. Then the Hall array “A” containing 4 Hall elements the for as shown inas Figure 7. Then the Hall element arrayelement “A” containing 4 Hall elements for measuring measuring the radial magnetic flux densities, the Hall element array “B” containing 4 Hall elements radial magnetic flux densities, the Hall element array “B” containing 4 Hall elements for measuring for measuring the axial magnetic flux densities and the connector are soldered to the PCB. the axial magnetic flux densities and the connector are soldered to the PCB. Printed circuit board

Connector

0.5 5 Hall element array A Hall element array B 2 14

Shell of the magnetic field measurement unit Figure 7. The magnetic field measurement unit for evaluating the stress in steel wires. Figure 7. The magnetic field measurement unit for evaluating the stress in steel wires.

Under the the configuration configuration depicted depicted in in Figure Figure 7, 7, the the sensitive sensitive area area of of Hall Hall element element array array “A” “A” and and Under “B” thethe position of “B” can can be be easily easilyensured ensuredperpendicular perpendiculartotothe theradial radialand andaxial axialdirection. direction.Furthermore, Furthermore, position Hall elements can be easily fixed. They are placed together and closely to the end of the PCB which is of Hall elements can be easily fixed. They are placed together and closely to the end of the PCB contacted to the surface of the steel wire. Thus, the minimal and maximal lift-offs of Hall elements of which is contacted to the surface of the steel wire. Thus, the minimal and maximal lift-offs of Hall array “A”of arearray 0.5 mm mm, respectively. The space between adjacent Hallthe elements of array elements “A”and are5 0.5 mm and 5 mm, respectively. Thethe space between adjacent Hall “A” is 1.5 mm. The minimal and maximal lift-off of Hall elements of array “B” are 2 mm and 14 elements of array “A” is 1.5 mm. The minimal and maximal lift-off of Hall elements of array “B”mm, are betweenThe the space adjacent Hall elements of array is 4 mm. They “B” can is measure 2respectively. mm and 14 The mm,space respectively. between the adjacent Hall“B” elements of array 4 mm. radialcan magnetic fluxradial densities at the lift-off Lo = 0.5, at 2, 3.5, mm and at They measure magnetic flux densities the 5lift-off Lo axial = 0.5,magnetic 2, 3.5, 5flux mmdensities and axial the lift-off L = 2, 6, 10, 14 mm. Then, to fix and protect the PCB, a shell is made, as shown in Figure 7. o densities at the lift-off Lo = 2, 6, 10, 14 mm. Then, to fix and protect the PCB, a shell is magnetic flux The shell made in from the resin which non-ferromagnetic by 3Dwhich printing. This material won’tby affect made, as is shown Figure 7. The shellis is made from the resin is non-ferromagnetic 3D the measurement result of the Hall elements. printing. This material won’t affect the measurement result of the Hall elements. 3.3. The The Assembly Assembly of of the the Proposed Proposed Sensor Sensor 3.3. Figure 88shows assembled sensor, which consists of the of static unit, the unit, magnetic Figure showsthe the assembled sensor, which consists themagnetization static magnetization the field measurement unit, the bracket supporting and the guideway. magnetic field measurement unit, the bracket supporting and the guideway. Static magnetization unit

Magnetic field measurement unit

Bracket supporting r z

Scale film Guideway Slider

Steel wire

Figure 8. The assembly of the proposed sensor.

The static magnetization unit and the bracket supporting are connected with the different ends of the guideway. The contact surfaces of the static magnetization unit and the bracket supporting

printing. This material won’t affect the measurement result of the Hall elements. 3.3. The Assembly of the Proposed Sensor Figure 8 shows the assembled sensor, which consists of the static magnetization unit, the 9 of 18 magnetic field measurement unit, the bracket supporting and the guideway. Sensors 2016, 16, 1650

Static magnetization unit

Magnetic field measurement unit

Bracket supporting r z

Scale film Guideway Slider

Steel wire

Figure 8. 8. The The assembly assembly of of the the proposed proposed sensor. sensor. Figure

The The static static magnetization magnetization unit unit and and the the bracket bracket supporting supporting are are connected connected with with the the different different ends ends of of the the guideway. guideway. The The contact contact surfaces surfaces of of the the static static magnetization magnetization unit unit and and the the bracket bracket supporting supporting with the steel wire are coplanar to make the guideway parallel to the steel wire. The magnetic field measurement unit is connected with the slider which can scan along the guideway. Thus, the magnetic field measurement unit can pick up the axial and radial magnetic flux density at different lift-offs in the spatially varying magnetized region of the steel wire. When measuring the stress in steel wires, the static magnetization unit is open to fold the steel wire. Then closing the static magnetization unit, the sensor can be installed on the steel wire. The installation is convenient for no need to wind coils. 4. Experimental Investigation of the Proposed Sensor To investigate the performance of the proposed sensor, steel wires specimen are prepared and the experimental setup is built. In the first place, the measurement accuracy of the sensor for magnetization curve is studied, which is the first step to obtain the steel wire stress. Secondly, the feasibility to evaluate stresses in the Φ5 steel wire by the sensor is analyzed. At last, the performance of the sensor for the Φ7 steel wire is tested. 4.1. Specimen Preparation Three 2 m length Φ5 steel wires and three 2 m length Φ7 steel wires are adopted as the specimens. The steel wires are provided by LIUZHOU OVM ENGINEERING CO., LTD. They are made from the SWRS82B steel whose chemical composition is shown in Table 1. Table 1. Chemical composition of the SWRS82B steel (wt%). C

Si

Mn

P

S

Ni

Cr

Cu

0.81

0.22

0.82

0.013

0.014

0.01

0.26

0.01

Through the continuous drawing, hot-dip galvanizing and stabilizing treatment, their tensile strength can reach 1670 MPa. Because of such good mechanical properties, they are usually used to produce parallel wire cables. The axial stress in them is about 600 MPa in the practical application. The tested steel wires are shown in Figure 9, the upsetting process is conducted on both ends of the steel wire. The left and right anchors are adopted to ease of anchoring the steel wire. Furthermore, the thread is machined on the right anchor to ease of applying stress in the steel wire.

Through the continuous drawing, hot-dip galvanizing and stabilizing treatment, their tensile strength can reach 1670 MPa. Because of such good mechanical properties, they are usually used to produce parallel wire cables. The axial stress in them is about 600 MPa in the practical application. The tested steel wires are shown in Figure 9, the upsetting process is conducted on both ends of the steel wire. The left and right anchors are adopted to ease of anchoring the steel wire. Sensors 2016, 16, 1650 10 of 18 Furthermore, the thread is machined on the right anchor to ease of applying stress in the steel wire.

Upsetting Left anchor

Right anchor Thread Upsetting

Steel wire

Figure 9. The tested steel wires specimen.

4.2. The Setup 4.2. The Experimental Experimental Setup Figure 10 10 shows shows the the experimental experimental system the performance performance of proposed sensor. m Figure system to to test test the of the the proposed sensor. A A 22 m length steel wire is anchored on the loading machine. The loading machine mainly consists of the length steel wire is anchored on the loading machine. The loading machine mainly consists of the loading frame, frame, fixing fixing nut, nut, support support frame, frame, scotch scotch yoke, yoke, baffle baffle and and the the sleeve sleeve nut. nut. Screwing Screwing the the sleeve sleeve loading nut on on the the right, right, the the steel steel wire wire can can be be loaded. loaded. During During the the loading, loading, the the scotch scotch yoke yoke prevents prevents the the steel steel nut wire from rotating. The scotch yoke, support frame and the baffle are all made of the wire from rotating. The scotch yoke, support frame and the baffle are all made of the non-ferromagnetic non-ferromagnetic aluminum alloy material. This material will not affect the magnetization of the aluminum alloy material. This material will not affect the magnetization of the steel wire. The sensor steel wire. on Thethe sensor is installed on the steel wire. The center unit of itsis static magnetization unit is is installed steel wire. The center of its static magnetization 1000 mm from the right end Sensors 2016,from 16, 1650 10 of 17 1000 mm the right end of the steel wire. of the steel wire.

Figure 10. The experimental system to test the performance performance of of the the sensor. sensor

When conducting conductingthe the experiments, applied load T is acquired by the sensor pressure sensor When experiments, the the applied load T is acquired by the pressure connected connected with an axial load meter (YJZ-500A, Jinan at Industry and trade co., LTD, Jinan, with an axial load meter (YJZ-500A, Jinan at Industry and trade co., LTD, Jinan, Shandong, China) Shandong, China) and transmitted to the personal computer. The steel wire is magnetized by the and transmitted to the personal computer. The steel wire is magnetized by the static magnetization static The magnetization fromisLadopted = 55 mm to 345 mm is adopted as region. the magnetic unit. region from unit. L = 55The mmregion to 345 mm as the magnetic measurement As the z measurement region. As the axial magnetic flux density B z fer at the location L = 345 mm is already axial magnetic flux density B f er at the location L = 345 mm is already close to zero, which can be seen close to zero, which can be seen in Figure 5. The distance between two adjacent measuring points is in Figure 5. The distance between two adjacent measuring points is 10 mm. The radial and axial 10 mm. The radial and axial magnetic fluxes at different lift-offs in this region are measured by the magnetic fluxes at different lift-offs in this region are measured by the magnetic field measurement magnetic field measurement unit connected with a FLUKE8808A multimeter. Specially, Hall unit connected with a FLUKE8808A multimeter. Specially, Hall element arrays in the measurement element arrays in the measurement unit converts the magnetic signals into the voltage signals. The unit converts the magnetic signals into the voltage signals. Ther FLUKE8808A multimeter picks up the z FLUKE8808A multimeter picks up the voltage signals VBair and VBair and uploads them to the r z voltage signals VBair and VBair and uploads them to the personal computer. Combining the load T r z personal computer. Combining the load T with voltage signals VBair and VBair, the differential r z with voltage signals VBair and VBair , the differential permeability curve and magnetization curve of permeability curve and magnetization curve of the steel wire are calculated by the software Matlab the steel Further, wire are the calculated the software Matlab axial R2013a. Further, feature parameter to evaluate R2013a. featureby parameter to evaluate stress in thethe steel wire is extracted. axial By stress in the steel wire is extracted. using the experimental system described in Figure 10, the performance of the proposed Byisusing the experimental described in Figure 10, the performance of the proposed sensor sensor tested through severalsystem experiments. is tested through several experiments. 4.3. Measurement Accuracy of the Sensor for Magnetization Curve Firstly, the measurement accuracy of the sensor for magnetization curve is investigated, which is the basis of the stress evaluation. The proposed sensor is put on a Φ5 steel wire whose axial stress is zero. Three repeated measurements of radial and axial magnetic flux densities at different lift-offs are conducted. The measured data are shown in Figure 11. 0.012

0.012

Lo=0.5 mm

(b)

Lo=2 mm

r

z

FLUKE8808A multimeter picks up the voltage signals VBair and VBair and uploads them to the r z personal computer. Combining the load T with voltage signals VBair and VBair, the differential permeability curve and magnetization curve of the steel wire are calculated by the software Matlab R2013a. Further, the feature parameter to evaluate axial stress in the steel wire is extracted. By using the experimental system described in Figure 10, the performance of the proposed Sensors 2016, 16, 1650 11 of 18 sensor is tested through several experiments. Curve 4.3. Measurement Accuracy of the Sensor for Magnetization Curve Firstly, the themeasurement measurementaccuracy accuracyofofthe thesensor sensorfor formagnetization magnetization curve investigated, which Firstly, curve is is investigated, which is is the basis stress evaluation. The proposed sensor is put a Φ5 steel wire whose axial stress the basis of of thethe stress evaluation. The proposed sensor is put onon a Φ5 steel wire whose axial stress is is zero. Three repeated measurements of radial axial magnetic densities at different lift-offs zero. Three repeated measurements of radial andand axial magnetic fluxflux densities at different lift-offs are are conducted. measured are shown in Figure conducted. TheThe measured datadata are shown in Figure 11. 11. 0.012

0.012

0.01

Lo=2 mm Lo=6 mm Lo=10 mm Lo=14 mm

(b)

Lo=0.5 mm Lo=2 mm Lo=3.5 mm Lo=5 mm

(a)

0.01

0.008

Bair(L,Lo)/T

Bair(L,Lo)/T

0.008

0.006

r

z

0.006

0.004

0.004

0.002

0.002

0 50

100

150

200

250

300

0 50

350

100

150

200

250

300

350

L/mm

L/mm

11. Three measurements of radial (a) and magnetic flux densities at different SensorsFigure 2016, 16, 1650 11 of 17 11. Threerepeated repeated measurements of radial (a) axial and (b) axial (b) magnetic flux densities at lift-offs the measurement region. region. differentinlift-offs in the measurement

Figure 11 demonstrates the average, minimum and maximum values of the measured radial and axial magnetic flux densities. It can beminimum seen that and the measurement repeatability is good. radial Then, Figure 11 demonstrates the average, maximum values of the measured r z according to the principle in Section 2, radial and axial magnetic flux densities B (L, 0) and B (L, 0) air air and axial magnetic flux densities. It can be seen that the measurement repeatability is good. Then, r z r z at the interface are extrapolated from the measured B (L, 0) and B (L, 0) to obtain air according to the principle in Section 2, radial and axial magnetic flux densitiesair Bair (L, 0) and Bair (L,the 0) r (L, 0) and z (L, 0) to magnetization curve. The extrapolation is referenced to Bprevious research [31–33]. Specially, at the interface are extrapolated from the method measured Bair obtain the magnetization air at a fixed point, a third-order polynomial is used to fit the relationship between the curve. Themeasuring extrapolation method is referenced to previous research [31–33]. Specially, at a fixed r radial magnetic density B the lift-off Lorelationship shown in Figure 11a. fitting air(L, Lo) and measuring point, flux a third-order polynomial is used to fit the between theThen radialthe magnetic r coefficients can be obtained. The polynomial value at L o = 0 is considered as the radial magnetic flux density Bair (L, Lo ) and the lift-off Lo shown in Figure 11a. Then the fitting coefficients canflux be r r (L, 0) at densities B 0) at the interface. the radial flux densities at other B measuring air(L, obtained. The polynomial value at LSimilarly, as magnetic the radial magnetic flux densities o = 0 is considered air z points can be Similarly, obtained. the Theradial extrapolation for the axial magnetic flux densities (L,obtained. 0) is the the interface. magneticmethod flux densities at other measuring points canBairbe r z r (L,are same with B (L, 0). The extrapolated radial and axial magnetic flux densities at the interface air The extrapolation method for the axial magnetic flux densities Bair (L, 0) is the same with Bair 0). shown in Figure 12. The extrapolated radial and axial magnetic flux densities at the interface are shown in Figure 12. 0.012

0.014

(a)

The extrapolated Brair(L,0)

The extrapolated Bzair(L,0)

(b)

Fitting line

Fitting line

0.01

0.012 0.008 z air

0.008

-0.0655L

B (L,0)=0.2772e

Bair(L,0)/T

Bair(L,0)/T

0.01

0.006

-0.01045L

-0.006711e

2

r

z

R =0.9988

0.006

0.004

0.004 0.002

0.002

r air 2

-0.01711L

B (L,0)=1.131e

-0.01832L

-1.19e

R =0.9928 100

0

150

200

250

300

100

150

200

250

300

L/mm

L/mm

Figure 12. 12. The extrapolated radial (a) and axial (b) magnetic flux densities at the interface and the corresponding fitting fitting lines. lines. r

z

In order to calculate the differential permeability curve, the extrapolated Bair(L, 0) and Bair(L, 0) should be fitted to obtain the corresponding distribution functions. The double exponential r z function is used to fit extrapolated B air (L, 0) and B air (L, 0) by Matlab R2013a. The obtained r z distribution functions for B air (L, 0) and B air (L, 0) are shown in Figure 12a,b, respectively. The r

z

100

150

200

250

100

300

150

200

250

300

L/mm

L/mm

Figure 12. The extrapolated radial (a) and axial (b) magnetic flux densities at the interface and the corresponding fitting lines. Sensors 2016, 16, 1650 12 of 18 r

z

In order to calculate the differential permeability curve, the extrapolated Bair(L, 0) and Bair(L, 0) r (L, 0) and Bz (L, 0) In order calculate differential permeability curve, the functions. extrapolatedThe Bair air should be fittedtoto obtainthethe corresponding distribution double exponential r z should be fitted to obtain the corresponding distribution functions. The double exponential function is function is used to fit extrapolated B (L, 0) and B air (L, 0) by Matlab R2013a. The obtained r (L, 0) and Bz air(L, 0) by Matlab R2013a. used to fit extrapolated Bair obtained distribution functions r air B z (L, 0) are shown The distribution functions for B (L, 0) and in Figure 12a,b, respectively. air air r (L, 0) and Bz (L, 0) are r (L, 0) The for Bair shown in Figure 12a,b, respectively. The goodness of the fits for Bair r z air goodness zof the fits for Bair(L, 0) and Bair(L, 0) are 0.9928 and 0.9988, respectively. The fitting results and Bair (L, 0) are 0.9928 and 0.9988, respectively. The fitting results are good. Then, taking dL = 0.01 mm, are good. Then, taking dL(1)–(3) = 0.01described mm, according (1)–(3) describedcurve in Section 2, the 0 at the according to Equations in Sectionto2, Equations the differential permeability µin ’ z z differential permeability curve μ at the magnetic field strength H ∈ [141.5, 8944.7] applied to in fer magnetic field strength H f er ∈ [141.5, 8944.7] applied to the measurement region is calculated from the the r z r region z (L, 0), which measurement is calculated fromisthe average 0) in and Bair(L, air(L, average Bair (L, 0) and Bair shown as the B blue line Figure 13.0), which is shown as the blue line in Figure 13. -4

9

x 10

Before the extrapolation After the extrapolation

8 7

μ’in/H·m

-1

6 5 4 3 2 1 0

0

2000

4000

6000

8000

10000

12000

-1

H/A·m

Figure 13. 13. TheThe differential beforeand andafter after extrapolation. Figure differentialpermeability permeability curve curve before thethe extrapolation. 0 (H z ) 0 z z The differential permeability µin f er (0 ≤ H f er ≤ Hsa) is further extrapolated from µin (H f er ) according to the Rayleigh relation in Rayleigh region described in Equation (4) and the law of approach 0 in the to saturation described in Equation (7) in Section 2. In such cases, the differential permeability µin Rayleigh region and the region approach to saturation can be both obtained by the linear extrapolation. The extrapolated points for both regions are listed in Table 2.

Table 2. The extrapolated points for Rayleigh region and the region approach to saturation. Working Region 10−4

(H1 , µ’in1 )/(A/m, × H/m)) (H2 , µ’in2 )/(A/m, × 10−4 H/m))

Rayleigh Region

Region Approach to Saturation

(141.5, 5.404) (143.0, 5.424)

(8906.9, 0.1088) (8944.7, 0.1073)

0 (H z ) z The obtained differential permeability µin f er (0 ≤ H f er ≤ Hsa) is shown as the green line in Figure 13. At last, the magnetization curve for the steel wire can be obtained by the integration shown in Equation (8). The magnetization curve measured by the proposed sensor is shown in Figure 14a. Comparing with the magnetization curve measured by coils shown in Figure 3b, the error of the magnetization curve measured by the proposed sensor can be obtained and shown in Figure 14b. As shown in Figure 14b, the error under different magnetic field strengths is different. All the errors are within the range of ±6%. Namely, the proposed sensor can obtain the magnetization curve for the steel wire accurately. Based on this, the proposed senor is used to evaluate the axial stress in steel wires.

’

z

z

The obtained differential permeability μin(Hfer) (0 ≤ H ≤ Hsa) is shown as the green line in Figure 13. At last, the magnetization curve for the steel wire can be obtained by the integration shown in Equation (8). The magnetization curve measured by the proposed sensor is shown in Figure 14a. Comparing with the magnetization curve measured by coils shown in Figure 3b, the error of the Sensors 2016, 16, 1650 13 of 18 magnetization curve measured by the proposed sensor can be obtained and shown in Figure 14b. fer

4

1.8

(b)

(a) 1.5

2

1.2

0.9

Error/%

B/T

0 5 mm steel wire Magnetization curve measured by coils

-2 0.6

-4

0.3

0

0

2000

4000

6000

8000

10000

-6

12000

235

1500

1790

-1

1970

3010

4070

6825 10640

H/A·m-1

H/A·m

Figure Figure14. 14.The Thecalculated calculatedmagnetization magnetizationcurve curve(a) (a)and andthe thecorresponding correspondingerror error(b). (b).

AsPerformance shown in Figure 14b, the underwith different magnetic 4.4. The of the Sensor for error Steel Wires 5 mm in Diameterfield strengths is different. All the errors are within the range of ±6%. Namely, the proposed sensor can obtain the magnetization All the three Φ5 steel wires are used in the stress evaluating experiment, the axial stress applied curve for the steel wire accurately. Based on this, the proposed senor is used to evaluate the axial to the Φ5 steel wire is changed from 400 MPa to 800 MPa with the step of 50 MPa. Under the applied stress in steel wires. r (L, L ) and Bz (L, L ) at different lift-offs axial stresses, the radial and axial magnetic flux densities Bair o o air Lo from the Φ5 steel wire are measured by the proposed sensor. Three repeated measurements are 4.4. The Performance of the Sensor for Steel Wires with 5 mm in Diameter also conducted for each Φ5 steel wire. The magnetic property of the steel wire are calculated form the r (L, z (L, All the three wires are used to in the themethod stress evaluating experiment, axial stress measured Bair Lo ) Φ5 andsteel Bair Lo ) according described in Section 4.3.the Specially, the applied to the Φ5 steel wire is changed from 400 MPa to 800 MPa with the step of 50 MPa. Under obtained average differential permeability curves before and after the extrapolation for the No.1 Φ5 r z the wire applied axial stresses, thestresses radial are andshown axial magnetic flux densities Bair(L, Lo) and Bair(L, Lo) at steel under different axial in Figure 15. Sensors 2016, 16, 1650 13 of 17 different lift-offs Lo from the Φ5 steel wire are measured by the proposed sensor. Three repeated measurements are also conducted for each Φ5 steel wire. The magnetic property of the steel wire x 10 x 10 8 r z8 x 10 (b) Lo) according are calculated Lo) and Bair(L, to the method described in （a） form the measured Bair(L, 400MPa 400MPa 7 450MPa 450MPa 7 Section7 4.3. Specially, the obtained average differential permeability curves before and after the 500MPa 500MPa 6.5 550MPa 550MPa extrapolation for the No.1 Φ5 steel wire under different axial stresses are shown in Figure 15. 6 6 -4

-4

-4

4

5

5.5

-1

μ'in/H·m

-1

5

600MPa 650MPa 700MPa 750MPa 800MPa

6

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Figure Figure 15. 15. The The differential differential permeability permeability curves curves before before (a) (a) and and after after (b) (b) the the extrapolation extrapolation for for No.1 No.1 Φ5 Φ5 steel steel wire wire under under different different axial axial stresses. stresses.

The differential stress areare different from each other. As The differential permeability permeabilitycurves curvesunder undervarious variousaxial axial stress different from each other. can be seen in Figure 15b, the differential permeability μ’(H = 1200) at the working point about 1200 A/m As can be seen in Figure 15b, the differential permeability µ’(H = 1200) at the working point about decreases with the stress. While the differential permeability μ’(H = 10000) at the working point about 1200 A/m the differential permeability µ’(H = 10000)with at the 10,000 A/mdecreases increaseswith withthe the stress. stress. While The variation of the differential permeability theworking stress is point about A/m increases with stress. The variation of the differential with similar with10,000 the research results in thethe reference [34]. The relationship of axial permeability stress in No.1 Φ5 the similar with thepermeability research results the reference The relationship of axial in steelstress wire iswith differential at Hin = 1200 A/m and[34]. H = 10,000 A/m are shown as stress the blue line in Figure 16a,b, respectively. -4

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1.7 No1_Φ5_steelwire Fitting line for No1_Φ5_steelwire No2_Φ5_steelwire Fitting line for No2_Φ5_steelwire No3_Φ5_steelwire

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steel wire under different axial stresses.

The differential permeability curves under various axial stress are different from each other. As can be seen in Figure 15b, the differential permeability μ’(H = 1200) at the working point about 1200 A/m decreases with the stress. While the differential permeability μ’(H = 10000) at the working point 14 about Sensors 2016, 16, 1650 of 18 10,000 A/m increases with the stress. The variation of the differential permeability with the stress is similar with the research results in the reference [34]. The relationship of axial stress in No.1 Φ5 steel wire withwire differential permeability at H = 1200 andA/m H = and 10,000 A/m are A/m shown the blue No.1 Φ5 steel with differential permeability at HA/m = 1200 H= 10,000 areasshown as line in Figure 16a,b, respectively. the blue line in Figure 16a,b, respectively. -4

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Figure 16. The relationship of axial stress in the three Φ5 Φ5 steel wires with differential permeability at working points H = 1200 A/m A/m(a) (a)and andHH==10,000 10,000A/m A/m(b). (b).

The blue blue lines lines in in Figure Figure 16 16 demonstrates demonstrates the the average, average, minimum minimum and and maximum maximum values values of of the the The calculated μ’ (H = 1200) and μ’ (H = 10000) for the No.1 steel wire under different axial stresses. In addition, calculated µ’(H = 1200) and µ’(H = 10000) for the No.1 steel wire under different axial stresses. In addition, the average, average, minimum minimumand andmaximum maximumvalues valuesofof μ’=(H1200) = 1200)and andµ’μ’(H(H== 10000) 10000) for No.3 the thethe µ’(H forthe theNo.2 No.2 and and No.3 steel wires are calculated and shown as the green and red lines in Figure 16. The average values of steel wires are calculated and shown as the green and red lines in Figure 16. The average values of both μ’ (H = 1200) and μ’(H = 10000) for the three Φ5 steel wires are approximately coincident. Furthermore, both µ’(H = 1200) and µ’(H = 10000) for the three Φ5 steel wires are approximately coincident. Furthermore, both of of them them change change almost almost linearly linearly with with the the applied applied stress. polynomial is both stress. The The first first order order polynomial is used used to to fit fit the relationship relationship of of the the average average μ’ (H = 1200) and μ’(H = 10000) with the applied axial stress for the three steel the µ’(H = 1200) and µ’(H = 10000) with the applied axial stress for the three wires. The obtained fitting function and goodness R-square of fitted curves μ’(H = 1200) (σ) and steel wires. The obtained fitting function and goodness R-square of fitted curves µ’(H = 1200) (σ) and μ’(H = 10000) (σ) for the three different Φ5 steel wires are list in Table 3. µ’(H = 10000) (σ) for the three different Φ5 steel wires are list in Table 3. Table 3. The fitting function and goodness R-square of fitted curves µ’(H = 1200) (σ) and µ’(H = 10000) (σ) for different Φ5 steel wires. Specimen Number

Feature Parameters

Fitting Equation

R2

No.1

µ’(H = 1200) µ’(H = 10000) µ’(H = 1200) µ’(H = 10000) µ’(H = 1200) µ’(H = 10000)

µ’(H = 1200) = −3.4345 × 10−7 σ + 8.3691 × 10−4 µ’(H = 10000) = 1.4798 × 10−8 σ + 4.3456 × 10−6 µ’(H = 1200) = −3.4298 × 10−7 σ + 8.3679 × 10−4 µ’(H = 10000) = 1.4626 × 10−8 σ + 4.2536 × 10−6 µ’(H = 1200) = −3.4626 × 10−7 σ + 8.4293 × 10−4 µ’(H = 10000) = 1.4773 × 10−8 σ + 4.2894 × 10−6

0.9890 0.9948 0.9891 0.9974 0.9892 0.9970

No.2 No.3

As can be seen in Table 3, the R-square of fitted curves µ’(H = 1200) (σ) and µ’(H = 10000) (σ) for the three different Φ5 steel wires are all higher than 0.989. This proposed sensor can be used to obtain the proper magnetic feature parameter to evaluate the axial stress in Φ5 steel wire. Comparatively speaking, the R-square of fitted curves µ’(H = 10000) (σ) is better than the R-square of fitted curves µ’(H = 1200) (σ) for each Φ5 steel wire. 4.5. The Performance of the Sensor for Steel Wires with 7 mm in Diameter At last, the applicability of the sensor for steel wires with 7mm in diameter is studied. Three Φ7 steel wires are used as the specimens. The axial stress applied to Φ7 steel wires is also changed from 400 MPa to 800 MPa with the step of 50 MPa. The measurement steps for the radial and axial magnetic

μ’(H = 1200) (σ) for each Φ5 steel wire. 4.5. The Performance of the Sensor for Steel Wires with 7 mm in Diameter At last, the applicability of the sensor for steel wires with 7mm in diameter is studied. Three 15 of 18 Φ7 steel wires are used as the specimens. The axial stress applied to Φ7 steel wires is also changed from 400 MPa to 800 MPa with the step of 50 MPa. The measurement steps for the radial and axial r z r magnetic flux B densities Bair(L, Lzo) and Bair(L, Lo) at different lift-offs Lo from the Φ7 steel wire are same flux densities air (L, Lo ) and Bair (L, Lo ) at different lift-offs Lo from the Φ7 steel wire are same with withΦ5 thesteel Φ5 wire. steel wire. In addition, repeated measurements are conducted for Φ7 each Φ7 wire. steel the In addition, three three repeated measurements are conducted for each steel wire. The calculation method for the magnetic parameters of the Φ7 steel wire is similar with the Φ5 The calculation method for the magnetic parameters of the Φ7 steel wire is similar with the Φ5 steel steel wire. The calculated differential permeability curves before and after the extrapolation for wire. The calculated differential permeability curves before and after the extrapolation for No.1 Φ7 No.1 wire Φ7 steel wire under different axialare stresses are steel under different axial stresses shown inshown Figure in 17.Figure 17. Sensors 2016, 16, 1650

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Figure Figure 17. 17. The The differential differential permeability permeability curves curves before before (a) (a) and and after after (b) (b) the the extrapolation extrapolation for for No.1 No.1 Φ7 Φ7 steel steel wire wire under under different different axial axial stresses. stresses.

withFigure Figure be that found that the ofexcitation of the static Comparing with 15a,15a, it canit becan found under theunder excitation the static magnetization magnetization unit from the proposed sensor, the maximum magnetic field strength applied to unit from the proposed sensor, the maximum magnetic field strength applied to No.1 Φ7 steel wire in No.1 Φ7 steel wire in the measurement region is smaller than the Φ5 steel wire. However, as seen in the measurement region is smaller than the Φ5 steel wire. However, as seen in the partial enlarged the partial enlarged views described in Figure 17b, the change of the µ’differential permeability views described in Figure 17b, the change of the differential permeability µ’(H = 10000) (H = 1200) and μ’(H = 1200) (H = 10000) thesteel axial stress insame the Φ7 steel is the same with more, the Φ5the steel wire. with the and axialμ’ stress in with the Φ7 wire is the with thewire Φ5 steel wire. Further average, Further more, the average, minimum values of the μ’(Hthree = 1200) and μ’(H =wires 10000) for the minimum and maximum values of the and µ’(H =maximum for the Φ7 steel under 1200) and µ’ (H = 10000) Sensors 2016, 16, 1650 15 of 17 three Φ7 steel wires under different axial stressesinare calculated different axial stresses are calculated and shown Figure 18. and shown in Figure 18. -5

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Figure 18. The relationship differential permeability at relationship with withthe theaxial axialstress stressininthe thethree threeΦ7 Φ7steel steelwire wireofof differential permeability working points H =H1200 A/m (a)(a) and HH = =10,000 at working points = 1200 A/m and 10,000A/m A/m(b). (b).

Comparing with withFigure Figure16, 16,it itcan can found that average values of µ’ the (H = 1200) and μ’(H = 10000) Comparing bebe found that thethe average values of the and µ’(H (H μ’ = 1200) = 10000) for Φ7 steel wires are slightly different from Φ5 steel wires. However, both the μ’ (H = 1200) and μ’ (H 10000) for Φ7 steel wires are slightly different from Φ5 steel wires. However, both the µ’(H = 1200) =and for Φ7 steel wires are basically in coincidence and change almost linearly with the applied stress. The fitting function and goodness R-square of first order polynomial fitted curves μ’(H = 1200) (σ) and μ’(H = 10000) (σ) for the three different Φ7 steel wires are list in Table 4. Table 4. The fitting function and R-square of fitted curves μ’ (H = 1200) (σ) and μ’ (H = 10000) (σ) for different

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µ’(H = 10000) for Φ7 steel wires are basically in coincidence and change almost linearly with the applied stress. The fitting function and goodness R-square of first order polynomial fitted curves µ’(H = 1200) (σ) and µ’(H = 10000) (σ) for the three different Φ7 steel wires are list in Table 4. Table 4. The fitting function and R-square of fitted curves µ’ different Φ7 steel wires.

(H = 1200)

(σ) and µ’

(H = 10000)

(σ) for

Specimen Number

Feature Parameters

Fitting Equation

R2

No.1

µ’(H = 1200) µ’(H = 10000) µ’(H = 1200) µ’(H = 10000) µ’(H = 1200) µ’(H = 10000)

µ’(H = 1200) = −3.4404 × 10−7 σ + 8.325 × 10−4 µ’(H = 10000) = 1.4179 × 10−8 σ + 4.232 × 10−6 µ’(H = 1200) = −3.446 × 10−7 σ + 8.2729 × 10−4 µ’(H = 10000) = 1.3432 × 10−8 σ + 4.4126 × 10−6 µ’(H = 1200) = −3.4241 × 10−7 σ + 8.2994 × 10−4 µ’(H = 10000) = 1.468 × 10−8 σ + 3.7638 × 10−6

0.9886 0.9902 0.9879 0.9896 0.9885 0.9904

No.2 No.3

Comparing with Table 3, it can be found that the R-square of fitted curves µ’(H = 1200) (σ) and µ’(H = 10000) (σ) for Φ7 steel wires are close to Φ5 steel wires. All the R-squares are higher than 0.987. Thus, this proposed sensor also applies to the stress evaluating in the Φ7 steel wire. Comparatively speaking, the R-square of fitted curves µ’(H = 10000) (σ) is also better than the R-square of fitted curves µ’(H = 1200) (σ) for each Φ7 steel wire. This indicates that µ’(H = 10000) may be a more suitable feature parameter for stress evaluating in steel wires by this proposed sensor. 5. Conclusions This paper proposes a stress measuring sensor for steel wires based on the static magnetization by permanent magnets. Comparing to the existing Elasto-magnetic sensor for measuring the stress, primary excitation coils and induction coils are replaced by a static magnetization unit and a magnetic field measurement unit containing Hall element arrays, respectively. Especially, the static magnetization unit is made of permanent magnets and yokes. It can be opened conveniently to fold the steel wire, which can ease the installation of the proposed sensor. Under the excitation of the static magnetization unit, a spatially varying magnetized region in the steel wire is adopted as the measurement region. In this region, the distribution of the axial magnetic flux density in the cross section and the radial magnetic flux density around the cylindrical surface of the steel wire are uniform for a given position L. Radial and axial magnetic flux densities at different lift-offs from the steel wire in this region are measured by the measurement unit. Then, the differential permeability curve and the magnetization curve are calculated from the measured magnetic flux density. At last, the differential permeability µ’(H = 1200) and µ’(H = 10000) are extracted to evaluate the stress in steel wires. An experimental system is set up to test the performance of the proposed sensor. Experimental results show that the sensor can measure the magnetization curve of the steel wire accurately with the error located in the range of ±6%. The obtained differential permeability µ’(H = 1200) decreases almost linearly with the stress in steel wires. While, the differential permeability µ’(H = 10000) increases almost linearly with the stress in steel wires. The goodness of the corresponding linear fits are higher than 0.987. Thus, the proposed sensor is feasible to evaluate the stress in steel wires. However, the proposed sensor only applies to evaluating the axial stress in Φ5 and Φ7 steel wires in the laboratory. The sensor still has to be developed to evaluate the stress in other steel components. For example, the influence of the leakage magnetic field between the steel wires needs to be analyzed, when evaluating the stress in steel strands by the sensor. In addition, the influence of plastic protective covers on the signals of the sensor need to be researched, when the sensor is used to evaluate the stress in steel cables on site. These will be the topic in our following research. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 51477059).

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Author Contributions: Dongge Deng contributed to the theory research, the design of experiments, writing and revising of the manuscript. Xinjun Wu proposed the idea of the new sensor and gave a help in revising of the manuscript. Su Zuo contributed to conducting the experiments. Conflicts of Interest: The authors declare no conflict of interest.

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