Yu Miao， Xianglong Liu， Ze Liu,N， Yuanli Yue， Jianli Wu，Jiwei Huo and Yong Li

（1. School of Electronic Information Engineering, Beijing Jiaotong University, Beijing 100044,China；2. School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China）

Abstract: A novel electromagnetic tomography(EMT) system for defect detection of high?speed rail wheel is proposed, which differs from traditional electromagnetic tomography systems in its spa?tial arrangements of coils. A U?shaped sensor array was designed, and then a simulation model was built with the low frequency electromagnetic simulation software. Three different algorithms were applied to perform image reconstruction, therefore the defects can be detected from the reconstruc?ted images. Based on the simulation results, an experimental system was built and image recon?struction were performed with the measured data. The reconstructed images obtained both from numerical simulation and experimental system indicated the locations of the defects of the wheel,which verified the feasibility of the EMT system and revealed its good application prospect in the future.

Key words: electromagnetic tomography(EMT)；high?speed rail wheel；defect detection；image reconstruction

In recent years, the mileage of high?speed railways in China has increased a lot and so does the speed of trains. When the train is running at high speed, the residues in wheel, which prob?ably left in casting and processing, are likely to cause deep cracks in the rim and spoke parts. At the same time, in the process of long?term use of the wheel, defects such as cracks and peeling may occur because of material fatigue, wear, and scratches[1]. Once these defects of wheel caused the axle fracture or radial crack of wheel, train collapse and other accidents include catastrophic consequences would not be avoided, since the wheels of the train run under high?speed operat?ing conditions[2].

At present, domestic and foreign high?speed electric multiple units(EMUs) regularly carry out safety inspections on wheels according to the run?ning mileage. Commonly used nondestructive testing methods include magnetic powder tes?ting[3?4], piezoelectric ultrasonic testing[5?6], electro?magnetic ultrasonic testing[7?8], and machine vis?ion testing[9], etc. The advantage of magnetic powder inspection is more intuitive and the dis?advantage is that only defects on the surface and near surface of the wheel can be detected, and the wheel needs to be unloaded during the detec?tion, which brings inconvenience to the opera?tion; piezoelectric ultrasonic detection equipment can detect defects in wheel rims and spokes, and it is not necessary to withdraw the wheels.However, due to the limitations of the equip?ment and the coupling state, the defects are diffi?cult to measure accurately, and when the piezo?electric ultrasonic longitudinal wave is used to detect the defects on wheel tread, the detection results of the peeling of the near surface are not satisfied because the near surface is the blind area of the detection. Electromagnetic ultrasonic defect detection does not require coupling materi?al, which is more convenient to use, and it has a better detection effect on the shallow surface of the tread, but it is more difficult to detect the defect at the rim and spoke, and its detection sensitivity varies with the distance between the transducer and the wheel surface, and will de?crease rapidly with the distance increasing. Ma?chine vision inspection can only detect surface defects, and the detection accuracy is greatly af?fected by illumination and collection noise.

Electromagnetic tomography(EMT) is a new type of non?destructive testing technology that does not require coupling material and has the characteristics of non?contact, non?intervention,non?radiation, etc. It can quickly detect defects in various parts, and able to image and display the location and size of defects[10?11], and has a good application prospect in different areas.

In this paper, the electromagnetic tomo?graphy technology is applied to the defect detec?tion of rail wheel. A U?shaped sensor array was designed and a simulation model was set up with the low frequency electromagnetic simulation software. Defects with different sizes were set in different positions of wheel. Three different al?gorithms were used to perform image reconstruc?tion, and the results were used to evaluate the detection effect. An experimental system was built based on the simulation model, and the im?ages reconstructed by experimental data were used to verify the feasibility and the effect of electromagnetic tomography technology in the application of detection of rail wheel defect is evaluated. Simulation and experimental results show that electromagnetic tomography techno?logy applying in the detection of rail wheel de?fect can not only reveal the defect on different parts of the wheel, but also display the location of the defect and have a good application pro?spect in the future.

1 Introduction to EMT

Electromagnetic tomography is a non?de?structive testing technology based on the prin?ciple of electromagnetic induction, and its basic composition structure is shown in Fig. 1[10]. The principles of electromagnetic tomography are de?scribed as follows: a excitation current with a certain frequency and amplitude, generated and controlled by the signal generation and excita?tion module, is applied to the excitation coil to generate the main magnetic field in the object field surrounded by the coils; according to the principle of electromagnetic induction, the con?ductive substance in the object field generates in?duced current under the action of alternating magnetic field, thereby a secondary magnetic field is generated; under the action of the com?posite magnetic field of main magnetic field and secondary magnetic field, a boundary induced voltage in detection coil is detected and if se?quentially collecting the induced voltage of the detection coils, signals in multiple projection dir?ections are obtained. By sequentially applying ex?citation current to different excitation coils and obtaining the voltages of the detection coils, mul?tiple sets of detection data can be obtained, and the distribution of objects in the object field can be reconstructed from the detection data accord?ing to a certain image reconstruction algori?thm[10?12].

Fig. 1 Basic composition of electromagnetic tomography system

2 Principle of EMT

Electromagnetic tomography usually deals with two types of problems: forward problem and inverse problem[13]. The forward problem is that,given the spatial distribution of conductive or magnetically permeable substances in the meas?ured object field, the boundary measurement val?ues in each projection direction are obtained[14].

The forward problem of EMT can be descri?bed qualitatively shown as

The forward problem of EMT usually has the following three ways to solve: analytical method, numerical solution and experimental method. The analytical method is to obtain the boundary measurement value of the detection coil around the object field by expressing the characteristics of the electromagnetic sensitivity field of the measured object field space with an analytical formula. However, if there are conduct?ive objects or magnetically permeable objects or both in the object field, the conditions for de?termined solution are complicated and the ana?lytical solution is very difficult to obtain. There?fore, the analytical method is difficult to be widely used to solve the forward problem of EMT, and the numerical solution provides a good solution. The finite element method is one of the numerical solution, which is based on the vari?ation principle and the subdivision, interpolation methods and proved to be an effective method in solving the boundary value problem. In this pa?per, the finite element method is used to solve the EMT forward problem.

The inverse problem is to reconstruct the distribution image of objects with electrical con?ductivity or magnetic permeability in the object field according to a certain imaging algorithm when the sensitivity maps and measured values are known[15].

The qualitative description of the EMT in?verse problem is shown as[15]

where gμ, gσand gεrepresent the spatial sensitiv?ity of magnetic permeability, electrical conductiv?ity and dielectric constant in the EMT sensitiv?ity field, respectively. U is the measured voltage values. The relationship between the EMT for?ward problem and the inverse problem can be de?scribed as shown in Fig. 2.

Fig. 2 Relationship of the forward and the inverse problem

3 EMT Simulation System for Defects Detection of High-Speed Rail Wheel

3.1 Design of sensor array in simulation system

According to the structure of high?speed rail wheels and defect detection requirements, the sensor array was arranged in an “inverted U ”shape, with a total of 16 coils, including 2 coils on the flange, 2 coils on the tread, 6 coils on in?side rim and 6 coils on outer side rim. The red circles are the coils as shown in Fig. 3, and dis?tributed at equal distances along the wheel. The coils had the same size and shape, with an inner diameter of 5 mm, an outer diameter of 10 mm,and a height of 5 mm. It can be seen from Fig. 3 that the distribution of the sensor basically covered the tread, and the rims on both sides,which can meet the requirements of the detected area. The front view, top view and 3D view of the sensor distribution are shown in Fig. 3.

Fig. 3 Front view, top view and 3D view of high?speed rail wheel simulation model

Due to the skin effect, the eddy current is mainly concentrated on the surface of the con?ductive material, and the skin depth is described as[16]

where δ is the skin depth; ω is the excitation fre?quency; μ is the magnetic permeability; σ is the conductivity. When the measured substance is determined, the magnetic permeability and con?ductivity of the material are determined too, and the skin depth is only related to the excitation frequency. For the defect detection of high?speed rail wheel, excessive frequency selection will make the skin depth too small to detect defects below the shallow surface; on the other hand, too small frequency selection will weaken the magnetic field and obtain a small signal. Therefore, considering the effects of skin depth and magnetic field,100 kHz was selected as the excitation frequency in simulation and 10 A as the excitation current.

3.2 Design of defects in simulation system

The defects in high?speed rail wheels are tread damage and fatigue defects[17]. Tread dam?age mainly includes peeling, abrasion and ther?mal cracking. Fatigue defects are mainly categor?ized into two classes: rim crack and spoke crack.In order to simulate the defects of wheel, eight defects were set in different locations with 3 dif?ferent widths and depths, 1 mm × 1 mm, 2 mm ×2 mm and 3 mm × 3 mm, that means totally 24 defects had been designed in the simulation sys?tem. The defects of 3 mm × 3 mm in different locations are shown in Fig. 4. The notches in simulation model in Fig. 4 are defects in differ?ent locations.

Fig. 4 Eight 3 mm×3 mm simulated samples of wheel defects on different locations

3.3 Solution of sensitivity map

The sensitivity map is priori condition for solving the inverse problem of electromagnetic tomography. If the area of the measured object field is divided into many pixels, assuming that each pixel can be represented by an object of the same area, then in some given field projection, a distribution plot of the induction sensitivities with regard to each pixel for a detector is called a sensitivity map[14]. It reflects the changes of the electromagnetic sensitivity field detected by all detectors when the conductive substance in the every pixel of the measured object field is changed. It can be defined as follows

where f (σ, μ) is the variation of electromagnetic properties and v is the change of induced voltages.

Generally, there are three methods for solv?ing the sensitivity map, namely the model per?turbation method, the measurement perturba?tion method and the field value extraction meth?od[18?21]. In this paper, the sensitivity map was ob?tained by the model perturbation method.

In order to obtain sensitivity map, the meas?ured area must be divided into many pixels. Con?sidering the influence of the eddy current skin ef?fect, the detection of EMT is mainly aimed at the defects of the surface and shallow surface,and only the area 10 mm below the surface of the wheel in the coverage area of the sensor are di?vided into triangular elements in the simulation system, which means the tread, the flange, both sides of the rim are divided into triangular ele?ments at different levels of precision. The mesh tool of the electromagnetic field finite element analysis software is used and a total of 424 trian?gular elements are obtained. The finite element mesh division is shown in Fig. 5.

Fig. 5 Finite elements mesh division

What is different from the usual method in calculating the sensitivity maps in this paper is that in general the sensitivity map is obtained by placing a small copper rod in each of the split cells in the measured object field as a disturb?ance; while in this simulation system, the sensit?ivity map was obtained by simulating defects by sequentially hollowing out each split unit in the measured object field

In the simulation system, the sensitivity map is composed of the mutual inductance value between different coils and the self?inductance value between the same coils. Since there are 16 sensor coils in the system, according to the prin?ciple of one coil exciting and other coils detect?ing, there are 256 values for one split cell and size of the sensitivity map is 424 × 256.

4 Image Reconstruction

Image reconstruction is an important part of the inverse problem of electromagnetic tomo?graphy. The quality of reconstructed images can reflect the accuracy of the measurement results.

4.1 Principle of image reconstruction

According to Eq. (1) in Section 2, the for?ward problem of EMT can be described qualitat?ively as follows

When the field is densely divided, σ (x,y) is approximately a constant value, and when the disturbance is small, it can be assumed that the sensitivity map has nothing to do with the con?ductivity distribution of the substance in the measured object field, then Eq. (5) can be sim?plified as

where U is the normalized measured voltage value vector with m×1 dimensional; S is the nor?malized sensitivity map with m×k dimensional; g is the normalized conductivity distribution vec?tor with k×1 dimensional, which represents the image gray value, where m is the number of measured values and k is the number of divided units. Among them, the normalized measured voltage U can be obtained by

The essence of image reconstruction of EMT is to solve for g in the case of U and S known in Eq. (10).

4.2 Results of image reconstruction in simulation system

There are different algorithms used in image reconstruction, which are classified into two types, non?iterative and iterative algorithms.Non?iterative algorithms mainly include linear back projection LBP algorithm and Tikhonov regularization algorithm[22?23]; iterative algori?thms mainly include Landweber algorithm,etc[24?26]. In order to analyze the reconstruction quality of different algorithms for image recon?struction, three different algorithms were selec?ted for imaging, which are LBP back projection algorithm, Tikhonov regularization algorithm,and Landweber algorithm. The imaging results for eight defect samples are shown in Tab. 1.

Tab. 1 Reconstructed images when defects size is 3 mm×3 mm

Tab. 1 Reconstructed images when defects size is 3 mm×3 mm (Continued)

In Tab. 1, the red area in reconstructed im?ages represents the position and shape of the de?fects. It can be seen from Tab. 1 that the images reconstructed by the linear back projection al?gorithm are less effective; the Tikhonov regulariz?ation algorithm and the Landweber iterative method are better, and can reproduce images for defects at different positions. Therefore, it is feas?ible to apply EMT to detect the defects of high?speed rail wheels.

5 Experimental System of Defects Detection of High-Speed Rail Wheel and the Image Reconstruction Results

In order to further verify the feasibility and evaluate the performance of electromagnetic tomography technology in the defects detection of high?speed rail wheel, an EMT experimental system was designed and built.

The system consists of two parts: electronic and mechanical parts. The electronic part in?cludes a sensor array, a signal generator and channel switching modules, and a host computer.The mechanical part includes the inspection plat?form. The block diagram of the electronic part of the electromagnetic tomography in the detection system of defects in high?speed rail wheels is shown in Fig. 6[27].

The actual EMT experimental system is shown in Fig. 7, the experimental system used a proportionally reduced high?speed rail wheel model to simulate the real high?speed rail wheels,which is shown in Fig. 8a, and the sensor array uses the same U?shaped sensor structure as that in the simulation system and the coils are placed in the holes of the sensor bracket, which is shown in Fig. 8b.

Fig. 6 Block diagram of the electronic part of the high?speed rail wheel defect detection system with EMT

Fig. 7 Photo of the experimental system

Different defects were fabricated in different positions of the wheel model, the locations of the defects are shown as the labels in Fig. 9. For ex?ample, three defects are located in the outer side rim, inner side rim and tread respectively as shown in Fig. 9e, but only the defects in the out?er side rim and tread can be observed and the in?ner side rim is in the opposite position of the out?er side, thus it cannot be seen from Fig. 9e.

Fig. 8 Photos of the defect detection bench and the sensor bracket

Fig. 9 Photos of practical machining defects samples

In order to verify the imaging quality of the system on different defects, LBP algorithm, Tik?honov regularization, Landweber iterative were used for image reconstruction on the defects of Fig. 9a, Fig. 9b, Fig. 9c, Fig. 9d and Fig. 9e re?spectively. The results are shown in Tab. 2. In Tab. 2, the red area in reconstructed images rep?resents the position and shape of the defects.

Tab. 2 Reconstructed images by different algorithms for different kinds of detects

Tab. 2 Reconstructed images by different algorithms for different kinds of detects (Continued)

It can be seen from Tab. 2 that the results of image reconstruction of the experimental sys?tem and the simulation system are similar. The image reconstruction results of the LBP back projection algorithm cannot accurately show the location of the defects. The Tikhonov regulariza?tion method and the Landweber iterative meth?od can approximatively determine the approxim?ate location of the defects. Compared with the reconstructed image of the defects in the outer side rim, the reconstructed images of the defects in inner side rim cannot be seen clearly partly be?cause the liftoff of the coils on the flange is lar?ger than that of the coil on the tread, and to im?prove is the future research plan

6 Conclusion

The feasibility of applying electromagnetic tomography technology to defect detection of high?speed rail wheels is studied and verified in this paper. The basic principle of electromagnet?ic tomography is firstly introduced and the EMT defects detection simulation of high?speed rail wheel is performed through the electromagnetic field simulation software. Different algorithms are used for image reconstruction and the results are analyzed. Based on the simulation results, an ex?periment system of electromagnetic tomography for defects detection of high?speed rail wheels is designed. By imaging different defects in the high?speed rail wheels’ different positions, the ef?fects of different algorithms for image reconstruc?tion are compared. Both the simulation and ex?perimental results demonstrate that the defects of high?speed rail wheels can be detected by elec?tromagnetic tomography technology and the loc?ation of the defects can be revealed by the recon?structed images, which indicates that electromag?netic tomography technology has a good applica?tion prospect in the defect detection of high?speed rail wheels.