Research on magnetic excitation model of magnetic flux leakage for coal mine hoisting wire rope

Abstract

This study presents the optimal design of a magnetic excitation model for developing a nondestructive sensor for coal mine hoist wire ropes. The model was established using axial-symmetry finite-element analysis and calculations. The influence of the excitation device parameters on the local magnetization effect of the wire rope was investigated in detail using the axial-symmetry finite-element model. The excitation model parameters of the sensor were optimally designed using a combination of finite-element analysis and an optimization method. The experiments were performed to measure the leakage flux and evaluate the performance of the optimally designed sensor. The results show that the sensor based on the newly designed excitation model can not only improve the signal-to-noise ratio for defect detection in a coal mine hoist wire rope by 11% compared to an existing sensor but also reliably detect small defects with a high detection speed (5 m/s) along the length of the coal mine wire rope.

Introduction

A wire rope is a type of cable that consists of several strands of metal wire formed (or twisted) into a helix. Wire ropes are universally used in coal mine hoisting and transmission because of their advantages of high flexibility, high strength, and low weight. The wire rope is the key component of the main and auxiliary shafts of coal mines. In the application process, metal fatigue and abrasion, corrosion, deformation, broken wires, and other flaws are unavoidable; these lead to the decrease in the strength of the wire rope or even its sudden destruction. Destructive accidents occur during the application of the wire rope. Therefore, the safety of wire ropes in active service is of utmost importance. In view of the application problems of wire ropes, many methods have been used to test wire ropes in recent years, among which the electromagnetic inspection method is recognized as the most reliable and practical on-line detection method.^1–3 However, the existing electromagnetic inspection technology cannot meet the requirements of coal mine worksite popularization application. Coal mine hoist accidents caused by wire rope destruction occur occasionally. Only a few coal mine operations departments use the existing electromagnetic inspection devices as auxiliary testing tools during the management and maintenance of wire ropes. Many application departments still adopt the methods of manual examination and regular change for wire ropes, one of the important reasons why the existing sensor technology based on the electromagnetic inspection principle falls short.

The on-line flaw detection in wire ropes remains a difficult problem worldwide. In order to obtain accurate quantitative data for all flaws in wire ropes, some sensor principles and technologies have been proposed and studied. Singh et al. ⁴ designed and developed a sensor array to detect both local fault (LF) and loss of metallic cross-sectional area (LMA)-type defects in track rope. Jomdecha and Prateepasen ⁵ designed a modified electromagnetic main-flux sensor to inspect the damage in wire ropes. Xu et al. ⁶ implemented two permanent magnets and a Hall sensor to detect the magnetic flux density from steel stay cables of large diameters. Feng and Tan ⁷ proposed the use of the magnetic bridge principle to inspect the flaws in the metallic cross-sectional area of wire ropes. Zhong and Zhang ⁸ proposed and designed two excitation magnetic circuits and double-detecting Hall element arrays to detect the flaws of coal mine hoist wire rope. Yang and Kang ⁹ applied the magnetic concentrating principle for measuring the magnetic flux leakage (MFL) caused by broken wires in wire ropes. Kalwa and Piekarski ¹⁰ designed a Hall-effect sensor for the magnetic testing of steel wire ropes. These studies mainly discussed the design of the detection elements and the acquisition mode of the detection signal. They greatly improved the reliability of the signal measurement component of the MFL detection of wire ropes, which constitutes the foundation of this study. However, according to the MFL detection principle, ¹¹ the magnetic head sensor is composed of a magnetization component and signal measurement component; the former is the key problem in the design of the magnetic head sensor for steel wire ropes. The problem is characterized by the following questions. In the design of a wire rope magnetization device, what impact do the magnetization structure parameters have on the local magnetization effect of the steel wire rope? How should the main parameters of the magnetic circuit structure be designed in order to obtain the optimal magnetization effect? Owing to present restrictions in technology, many irrelevant and unreported studies have been performed to answer the above questions.

In this study, the finite-element numerical method was used for investigating these issues. Additionally, for the first time, the finite-element analysis method combined with an optimization method was applied for the optimal design of a coal mine hoist wire rope magnetization device. Furthermore, the principle for the selection of a Hall-effect sensor is proposed. This article has technological and theoretical significance for further improving the performance of wire rope sensors. The remainder of this article is organized as follows: in section “Finite-element analysis modeling and calculations,” the finite-element analysis modeling and calculations are developed and analyzed; in section “Effect of permanent magnet thickness on local magnetization of wire rope,” the effect of the permanent magnet thickness on the local magnetization is studied; in section “Effect of magnetic pole width on local magnetization of wire rope,” the effect of the magnetic pole width on the local magnetization is examined; in section “Effect of magnet clearance on local magnetization of wire rope,” the effect of magnet clearance on the local magnetization is studied; in section “Optimization design of magnetizing device for wire rope,” the optimized design of the magnetizing device for wire ropes is investigated; and in section “Analysis and discussion of experimental results,” the experimental results are discussed.

Finite-element analysis modeling and calculations

Based on the characteristics of the axial-symmetry structure of a wire rope, an axial-symmetry finite-element analysis model (Figure 1) was designed using the Multiphysics software package to study the relation between the magnetization structure parameters and the magnetization effect. The magnetic circuit was mainly composed of the permanent magnet, armature, wire rope, and air. In Figure 1, the orange part represents the wire rope. F or simplicity, the coal mine wire rope (length 160.0 mm, outer diameter 24.5 mm) was assumed as a solid rod in the model. The permanent magnets are indicated as purple and red areas. The different colors of the permanent magnets represent different magnetic polarities. Neodymium–iron–boron (NdFeB) N48 was selected as the permanent magnet material. The relative magnetic permeability of the permanent magnet was assumed constant as 1.2. The armature is represented by the pink parts and has the structure of a half-ring body. Industrial pure iron DT3 was selected for the armature. The outer green part and the small pink part on the right of the wire rope represent air. The Hall-effect sensors are placed in the small pink region. The Hall-effect sensor and the velocity effects were not modeled. Considering the distribution of the external magnetic field, the Dirichlet boundary condition was applied at the outer boundaries of the model. The characteristic magnetization curve of the wire rope is shown in Figure 2.

Figure 1.

Model used for the axial-symmetry finite-element analysis.

Figure 2.

Characteristic magnetization curve of the wire rope.

The intensity of the magnetic field can be calculated using Maxwell’s equations and a constitutive equation ¹²

$$\nabla \times \{H\}=\{J_s\}$$

(1)

$$\nabla \times \{B\}=0$$

(2)

$$\{B\}=\mu \{H\}$$

(3)

where $\{H\}$ is the magnetic field intensity vector, $\{B\}$ is the magnetic flux density vector, $\{J_s\}$ is the applied source current density vector, and $\mu$ is the magnetic permeability.

The magnetic flux density $\{B\}$ in equation (2) is non-divergent. On introducing a magnetic vector potential $\{A\}$ , we have

$$\{B\}=\nabla \times \{A\}\nabla •\{A\}=0$$

(4)

By combining equations (1), (3), and (4), we obtain

$$\nabla \times \frac{1}{\mu }\nabla \times \{A\}=\{J_s\}$$

(5)

Equation (5) can be solved in two dimensions using the finite-element method. Figure 3(a) shows the mesh generated to simulate the geometry, which consists of the coal mine rope, permanent magnet, armature, and air. The magnetic vector potential was computed in the solution region. Figure 3(b) displays the cloud image of the calculation results for the wire rope magnetization loop field. Figure 3(c) shows the corresponding magnetic induction intensity vector. As can be seen from Figure 3(b) and (c), the magnetic flux density in the wire rope is greater than 1.24 T. The interior of the wire rope is magnetized to the saturation magnetic flux density.

Figure 3.

(a) Mesh generated to simulate the geometry, (b) the cloud image of the calculation results, and (c) the corresponding magnetic induction intensity vectors.

Effect of permanent magnet thickness on local magnetization of wire rope

With the above method, the corresponding two-dimensional axial-symmetry finite-element models for permanent magnets of different thickness were established, and the analysis and calculation for the magnetic circuit were performed. In these models, the outer diameter of the wire rope was 24.5 mm, and its length was 160 mm. The length of the armature was 140 mm, and its thickness was 20 mm. The magnetic clearance was 25 mm. The width of the permanent magnet was 30 mm, and the examined thicknesses were 5, 10, 15, 20, 25, 30, and 35 mm. The peripheral air layer was sufficiently large. Previous related studies showed that the magnetic leakage field signal is mainly distributed in the axial direction and that magnetic leakage in the radial direction (Bx) is rare. ¹³ Most information concerning coal mine wire rope damage is concentrated in the axial component of the magnetic flux density. Figure 4(a) shows the distribution of the axial component of the magnetic flux density ( $\left|\mathrm{By}\right|$ ) in the wire rope for different permanent magnet thicknesses. Figure 4(b) illustrates the relationship between the magnet thickness and the average value of the axial component of the magnetic flux density in the effective magnetization region of the wire rope.

Figure 4.

(a) Magnetic field distribution for different magnet thicknesses and (b) relationship between average magnetic flux density and magnet thickness.

As can be seen from Figure 4(a) and (b), when the permanent magnet thickness increases, the magnetization ability of the wire rope magnetization device is enhanced. However, when the permanent magnet thickness increases from 5 to 15 mm, the highest magnetic flux density in the wire rope increases by less than 8%. When the thickness increases from 15 to 35 mm, the average value of the magnetic flux intensity increases only by 11%, indicating that the changes in the permanent magnet thickness do not have a significant impact on the wire rope magnetization effect. Figure 4(a) also shows that the local magnetic flux intensity in the steel wire rope decreases with the enhancement in magnetization, which implies that the magnetization ability is too high and that a greater part of the magnetic flux field has dissipated into the air.

Effect of magnetic pole width on local magnetization of wire rope

To study the effect of the magnetic pole width on the magnetization of the wire rope, a series of axial-symmetry finite-element models were established and solved. In these models, the outer diameter of the wire rope was 24.5 mm and its length was 160 mm. The length of the armature was 140 mm, and the thickness was 20 mm. The magnetic clearance was 25 mm. The thickness of the annular permanent magnet was 25 mm, and its examined widths were 5, 10, 20, 30, and 40 mm. Figure 5(a) shows the distribution of the axial component of the magnetic flux density ( $\left|\mathrm{By}\right|$ ) in the wire rope for different magnetic pole widths of the permanent magnet. Figure 5(b) displays the relationship between the magnet width and the average value of the axial component of the magnetic flux density in the effective magnetization region of the wire rope.

Figure 5.

(a) Magnetic field distribution for different magnetic pole widths and (b) the relationship between average magnetic flux density and magnetic pole width.

As can be seen from Figure 5(a) and (b), the permanent magnetic pole width is the main factor affecting the magnetization state of the wire rope. On increasing the pole width, the magnetic flux density in the local effective magnetization region of the wire rope gradually changes from the unsaturated state to the saturated state. The influence of the pole width on the magnetization effect in the wire rope is obvious. The results also show that when the local part of the wire rope is super-saturated, the magnetic flux density in the wire rope decreases with the increase in the magnetic pole width; this indicates higher MFL into the air.

Effect of magnet clearance on local magnetization of wire rope

A series of axial-symmetry finite-element models were developed to study the effect of magnet clearance on the local magnetization in the wire rope. In these models, the outer diameter of the wire rope was 24.5 mm, and its length was 160 mm. The thickness of the annular permanent magnet was 25 mm, and the width was 30 mm. The length of the armature was 140 mm, and its thickness was 20 mm. The examined magnetization clearance values were 15, 20, 25, 30, and 35 mm. The calculation results are shown in Figure 6.

Figure 6.

(a) Influence of different magnetization clearance values on the magnetic field and (b) the relationship between average magnetic flux density and magnetization clearance.

As can be seen from Figure 6, a larger magnetic clearance of the magnetizing device results in lower average magnetic flux density in the effective magnetization region of the wire rope. This can be verified by the calculation and analysis of the air gap resistance. The air gap magnetic resistance between the interior of the annular magnet and the outer surface of the steel wire rope is

$$R_{\delta }=\underset{R_w}{\overset{R_w+\delta }{\int }}\frac{\mathrm{dr}}{2\pi {\mu }_0{l}_{m}r}=\frac{\ln ((R_w+\delta )/R_w)}{2\pi {\mu }_0{l}_m}$$

(6)

where R_w is the radius of the wire rope, $\delta$ is the magnetic clearance, and l_m is the width of the permanent magnet. It can be seen from equation (6) that when R_w and l_m are constant, greater magnetic clearance implies greater reluctance of the air gap; furthermore, a greater magnetic flux in air indicates that a lower magnetic flux in the effective magnetization region of the wire rope is provided by the permanent magnet and that lower average magnetic flux density is produced in the effective magnetization region of the wire rope. Nevertheless, as can be seen from Figure 6(b), when the magnetic clearance increases from 15 to 35 mm, the average magnetic flux density only decreases by 2.2%; this is because, in the structure of the multi-loop circumferential magnetization, when the magnetization clearance increases, the area of the permanent magnet pole simultaneously increases, which offsets the flux reduction by a large amount. Therefore, in a multi-loop circumferential magnetization device, when the wire rope is magnetized to saturation, the change in the magnetization clearance within a certain range has little effect on the magnetization state of the wire rope. This conclusion has practical significance because shake is generated during the on-line flaw detection of a wire rope. If the magnetization clearance decreases, the detection instrument can be easily damaged because of the collision friction of the steel wire rope and the detection equipment. Therefore, with the purpose of ensuring the saturation magnetization of the wire rope, the magnetization clearance should be increased accordingly.

Optimization design of magnetizing device for wire rope

The optimization of the MFL testing device for wire ropes was considered as a problem of constrained nonlinear programming. The optimization objective was to decrease the requisite expenditures (the volume and weight of the magnetizing device) to the minimum within the magnetic flux intensity limits of the wire rope.

The first-order optimization method was used for the optimization of the wire rope magnetization device. The procedure was as follows: first, the initial design analysis was performed, and the analysis results were evaluated according to the design requirements; subsequently, the design was revised and modified. This process was repeated until all the design requirements were satisfied.

The first-order optimization method calculates and uses derivative information for optimization. The constrained optimization problem is converted into an unconstrained optimization problem by using a penalty function. Then, the derivative of the penalty function for the objective function and the state variable is calculated, and the search direction in design space is formed. During each design iteration, the steepest-descent and dual-direction searches are implemented until convergence is reached.

The unconstrained objective function can be expressed as follows ¹⁴

$$\begin{array}{l}Q(x,q)=\frac{f}{f_0}+{\displaystyle \sum _{j=1}^m{P}_x}(X_j)\\ +q\left({\displaystyle \sum _{j=1}^{n_1}{P}_g}(g_i)+{\displaystyle \sum _{j=1}^{n_2}{P}_h}(h_i)+{\displaystyle \sum _{j=1}^{n_3}{P}_w}(w_i)\right)\end{array}$$

(7)

where Q is the unconstrained objective function; P_x, P_g, P_h, and P_w are the penalty functions for each constraint design and state variable; and f₀ is the reference function value.

When the search direction is determined, the equation can be expressed as follows

$$Q(x,q)=Q_f(x)+Q_p(x,q)$$

(8)

where Q_f and Q_p represent the objective function and penalty constraint, respectively, and Q_f = f/f₀.

For each optimization iteration, the optimized search direction d^(j) is designed, and then the next design variable is as follows

$$x^{(j+1)}=x^{(j)}+s_j{d}^{\left(j\right)}$$

(9)

where s_j is the line search parameter, which corresponds to the minimum Q along the search direction d^(j).

The basic structure of the wire rope magnetization device is shown in Figure 7. The research object is the steel wire rope. In the structure model, the coal mine wire rope (length 160.0 mm, outer diameter 24.5 mm) was assumed to be a solid rod. The armature material was electrical iron. The permanent magnet (width l_m, thickness h_m) was NdFeB; the armature parameters were length L (L = L_m + 2 × l_m), thickness T, and magnetic gap $\delta$ .

Figure 7.

Multi-loop excitation structure.

According to the experimental results and the size of the existing wire rope flaw detection sensor,^9,15 the initial size of the magnetizing device was set as follows:

• Permanent magnet: l_m = 0.01 m, h_m = 0.022 m; armature: L = 0.14 m, T = 0.02 m; magnetization clearance: 0.025 m.

To reduce the calculation time of the nonlinear programming, on the basis of the above analysis of the influence of the magnetization device parameters on the local magnetizing state of the wire rope, several key parameters were first considered in this study. Assuming that

1. The thickness of the permanent magnet is invariant at h_m = 0.022 m

2. The magnetization clearance is invariant at δ = 0.025 m, the optimization design variables were the width of the permanent magnet l_m, the length of the armature L, and its thickness T.

The constraint conditions of the optimization process were as follows:

1. The magnetic flux intensity of the strongest point at the center of the effective magnetization region of the wire rope B1x ≥ 1.4 T (this condition ensures the saturation magnetization of the wire rope).

2. The maximum of the magnetic flux intensity in the path where the center of the magnetization device is 10–30 mm away from the wire rope surface, that is, B2x < 190 mT (this condition ensures that the magnetic sensors work in the linear range).

3. The strongest magnetic flux intensity at the center of the armature B3x < 2.0 T (this condition ensures that the armature has high permeability).

The objective function is the numerical value to be minimized, and it should be a function of the design variables. The weight of the magnetization device f(x) was selected as the objective function in this study.

As mentioned above, the optimal mathematical model for the examined problem is as follows:

• Design variables: l_m (0.005 < l_m < 0.06), T (0.005 < T < 0.08), L (0.01 < L < 0.2); state variables: B1x (1.4 < B1x < 2.0), B2x(0 < B2x < 0.19), B3x (0 < B3x < 2); objective function: $f(x)\to minf(x)(x=[x_1,x_2,x_3]=[l_m,L,T])$ .

According to the equation used to calculate the weight of the magnetization component of the magnet senor head, the weight f(x) is as follows

$$f(x)=\rho *V$$

(10)

where ρ is the density of the objects, which is constant, and V is the volume of the objects. Thus, f(x) is a function of l_m, L, and T when h_m is invariant.

The next step is to optimize the analysis design. The optimization design procedure is as follows:

1. Generate the analysis documents. The generation of the analysis file is a key task of the optimization process. The optimization program uses the analysis file to structure the circular file. Then, the circular analysis is performed.

2. Establish the parameters of the optimization process, specify the analysis file, and determine the optimization variables, that is, specify which parameters are design variables, which are state variables, and what the objective function is.

3. Select the optimization tools or optimization methods. Specify the mode of the optimization cycle control.

4. Perform the optimization analysis.

5. Verify the design sequence results.

Figure 8(a)–(c) shows the optimization curves of the design variables, state variables, and objective function. According to Figure 8, the optimization model tends to converge after 11 iterations. Therefore, the number of iterations was set as 11. According to Figure 8(a), during the optimization process, the magnet width tends to be constant after two iterations. The armature thickness and length tend to be constant after three iterations. According to Figure 8(b), the magnetic flux intensities B1x and B2x tend to be constant after two iterations. Additionally, B3x tends to be constant after three iterations. According to Figure 8(c), during the optimization process, the magnetic head sensor weight first increased and then decreased; it tends to be constant after 11 iterations. The results show that the magnetization component of the magnetic head sensor is optimally designed to ensure the saturation magnetization of the wire rope.

Figure 8.

(a) Optimization curve of the design variables, (b) optimization curve of the state variables, and (c) optimization curve of the objective function.

The best results of the optimization design are as follows:

• Design variables: l_m = 0.02916 m, L = 0.131 m, T = 0.0209 m.

• State variables: B1x = 1.38 T, B2x = 0.181 T, B3x = 0.309 T.

• Objective function: f(x) = 12.3 kg.

According to the above optimization analysis results and the actual size of the components, such as sintered NdFeB and electrical pure iron, the excitation device parameters were selected as follows: width of permanent magnet: 30 mm, thickness of the armature: 20 mm;, and length of the armature: 131 mm.

Analysis and discussion of experimental results

To validate the effectiveness of the above finite-element analysis method, an experimental platform of the MFL detection for the wire rope was built, as shown in Figure 9. The platform was made by strictly following the conditions of coal mine hoist production, which mainly includes a wire rope, magnetic sensor head, sensor bracket, hoisting sheave, direct current (DC) power supply, and oscilloscope.

Figure 9.

Experimental platform of the magnetic flux leakage detection for wire ropes.

The magnetic inspection sensor head for the wire rope was developed and designed according to the above results (Figure 9). In order to decrease the influence of the operation speed on the reliability of the detection results, the linearly integrated Hall element UGN3501 was used. The distance between the Hall-effect sensor and the surface of the wire rope was 10 mm. The operation speed of the wire rope on-line inspection sensor was 5 m/s. The testing results show that the operation speed of the wire rope has little effect on the detection signal. The operation speed of 5 m/s can meet the inspection requirements of a coal mine.

Many experiments have been conducted using the laboratory platform shown in Figure 9. A new coal mine wire rope specimen 24.5 mm in diameter was fabricated for the experiment by filling six steel cable strands. Each cable strand was constructed from 19 wire elements 1.6 mm in diameter.

Four levels of LMA or LF damage were formed at the coal mine wire rope specimen. First, at damage level I, a 4.5% cross-sectional loss was induced to form LMA damage. Second, four cables located at the surface of the wire rope were cut. At level III, eight cables located at the surface of the wire rope were cut. Finally, at level IV, two cables located at the center of the cross section were cut.

As shown in Figure 9, by using the sensor head, the wire rope detection signals from the damaged specimen were measured for each damage level. The sampling displacement resolution was 0.5 mm.

A comparative signal detection technique was implemented in this study. Figure 10(a) shows the damage signal collected by the sensor head developed in this study. Figure 10(b) shows the damage signal collected by an existing and widely used sensor head. ¹⁶ The signal-to-noise ratios of the signals collected by the sensor heads developed in this study and the existing method were computed. The signal-to-noise ratio of the signals collected by the sensor head developed in this study was greater than 25 dB (27.2 dB). The signal-to-noise ratio of signals collected by the existing sensor head was less than 25 dB (24.6 dB). This constitutes an improvement of 11% on using the sensor head developed in this study.

Figure 10.

(a) Detection signal from the sensor developed in this study and (b) detection signal from the existing sensor.

Figure 10 shows the damage signal collected by the sensor head when the operation speed of the wire rope on-line inspection sensor was 5 m/s. According to Figure 10(a), the four levels of damage signal can be easily distinguished using the inspection sensor head developed in this study, and these measurements are consistent with the actual damage locations. However, only three levels of damage signal can be distinguished using the existing sensor head. A small damage located at a distance of 8000–10,000 mm was missed during the inspection because of its small amplitude, which can be a safety hazard for coal mine wire ropes. The experimental results show that testing with the sensor head developed in this study method is more effective than testing with the existing method.

Conclusion

1. The excitation model of a nondestructive detection sensor for coal mine hoist wire rope has been optimally designed for fast MFL testing.

2. The influence of the excitation device parameters on the local magnetization effect of the wire rope has been investigated in detail.

3. The excitation model parameters of the sensor have been optimally designed using a combination of the finite-element analysis and optimization methods.

4. Experiments of leakage flux measurements have been conducted to evaluate the performance of the optimally designed excitation model of the sensor.

5. A sensor based on the newly designed excitation model not only showed a higher signal-to-noise ratio for detecting defects in a coal mine hoist wire rope but also obtained information on small defects reliably.

6. With the development of new materials and magnetization aggregation technology, the application of a new poly demagnetizer to the excitation model will be studied, and the performance of the sensor will be further improved.