Eddy current pulsed thermography for fatigue evaluation of gearGui Yun Tian, Aijun Yin, Bin Gao, Jishan Zhang, and Brian Shaw Citation: AIP Conference Proceedings 1581, 1652 (2014); doi: 10.1063/1.4865022 View online: http://dx.doi.org/10.1063/1.4865022 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1581?ver=pdfcov Published by the AIP Publishing

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Eddy Current Pulsed Thermography for Fatigue Evaluation of Gear

Gui Yun Tiana, c, Aijun Yinb, c*, Bin Gaoa, c, Jishan Zhangd, and Brian Shawd

aSchool of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731 P. R. China

bState Key Laboratory of Mechanical Transmission College of Mechanical Engineering, Chongqing University, P. R. China

cSchool of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

dDesign unit, School of Mechanical Engineering and System, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

Abstract. The pulsed eddy current (PEC) technique generates responses over a wide range of frequencies, containing more spectral coverage than traditional eddy current inspection. Eddy current pulsed thermography (ECPT), a newly developed non-destructive testing (NDT) technique, has advantages such as rapid inspection of a large area within a short time, high spatial resolution, high sensitivity and stand-off measurement distance. This paper investigates ECPT for the evaluation of gear fatigue tests. The paper proposes a statistical method based on single channel blind source separation to extract details of gear fatigue. The discussion of transient thermal distribution and patterns of fatigue contact surfaces as well as the non-contact surfaces have been reported. In addition, the measurement for gears with different cycles of fatigue tests by ECPTand the comparison results between ECPT with magnetic Barkhausen noise (MBN) have been evaluated. The comparison shows the competitive capability of ECPT in fatigue evaluation.

Keywords: Eddy Current Pulsed Thermography; Gear Fatigue; Evaluation; Non-Destructive TestingPACS: 41.20.-q

INTRODUCTION

Metals are the most widely used materials in engineering structures. The safety and durability of structures has become more important due to the sudden failure of complex systems such as nuclear power plants, automobiles, aircraft and pressure vessels may cause many injuries, much financial loss and even environmental damage. Since many of these parts, e.g. gear, are subjected to repeated multiaxial loadings, fatigue failure is one of the most common failure modes in metal structures. Therefore, fatigue evaluation becomes one of the major considerations in the design, state measurement and life prediction of structures [1, 2].

Generally, for fatigue measurement, the SEM, X-ray, et al. require special sample preparation, and are destructive evaluation methods. The development of advanced diagnostic systems that are able to identify and detect material degradation is a new challenge for non-destructive evaluation. Moorthy et al. carried out evaluation of contact fatigue damage and bending fatigue on gears using the magnetic barkhausen noise technique [3, 4]. John et al. showed that substantial acoustic harmonic generation could be obtained from dislocation dipoles generated during plastic deformation and fatigue [5]. Mouritz et al. investigated non-destructive detection of fatigue damage in thick composites by pulse-echo ultrasonics [6]. Grimberg,et al. used eddy current sensors array for detection and measurement of fatigue in ferromagnetic and austenitic steels [7]. Oka et al. showed NDE of fatigue in austenitic stainless steel by measuring remnant magnetization method [8, 9]. In addition, acoustic emission (AE) method is investigated for fatigue measurement [10]. In current years, the lock-in infrared thermography, as a non-destructive, real-time and non-contact method, was used to visibly identify the superficial temperature distribution of a material or a component subjected to fatigue loading [11].

In above works, the methods, including ultrasonics, acoustic emission, and eddy current rely on sensors that are put on several points of the tested materials. Therefore, only limited information can be obtained from these points and they are not able toefficiently measure the fatigue. Infrared thermography based energy dissipation process is easily affected by noise. Moreover, infrared thermography based outside heat source, such as lamp with pulse heat, it mainly reflects thermal conductivity for different fatigue state of material, which is not enough for material

40th Annual Review of Progress in Quantitative Nondestructive EvaluationAIP Conf. Proc. 1581, 1652-1662 (2014); doi: 10.1063/1.4865022

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property evaluation. To solve the above problems, the paper proposes eddy current pulsed thermography (ECPT) method to evaluate fatigue of metal and application for gear. As a rapidly developing technique, pulsed eddy current (PEC) testing has found applications in metal thickness measurement [12], defect detection in multi-layered structures [13, 14], stress measurement [15] and corrosion detection [16, 17] amongst others. PEC based characterization theory and feature extraction techniques have also been developed and studied [18]. As PEC responses can sense multiple system and material parameters such as lift-off, electrical conductivity and magnetic permeability, it is important to understand their influence and responses in both the time and frequency domains.However, the method has also limitations for high spatial resolution, high sensitivity and stand-off measurement distance [19-21]. Eddy current and thermography techniques have been integrated to form eddy current pulsed thermography [22-24]. The major advantage of thermography over other techniques is the potential for rapid inspection of a large area within a short time, though currently it is mostly applied to samples in the lab instead of in-situ structures [24]. This technique has been applied for composite defect inspection and classification [25] and crack detection of rolling contact fatigue of rail tracks [26]. Yin et al. decomposed the two physical phenomena given the different stages of eddy current and thermal propagation [27]. This paper introduces eddy current pulsed thermography for gear fatigue tests.

The paper is organized as follows: Section 2 discusses the principle of pulsed eddy current and eddy current pulsed thermography; Section 3 introduces the experimental arrangement; Section 4 present the experimental results and compression of other electromagnetic methods. The conclusions are given in Section 5.

METHOD

Eddy Current Pulsed Thermography

Eddy current (EC) can be represented as a function of the system with the detected sample using Equation (1):� �aflFP ,,,,, ���� (1)

where � denotes the sensor geometry factor; f , a denotes the frequency and of the excitation, respectively;� denotes the electrical conductivity of material; � denotes the magnetic permeability of the material and ldenotes the lift-off (distance between the sensor and sample). EC density is mainly focused on surface-near zones ofthe material because of skin effect. In previous work, analysis has predominantly focused on the time response signal [13,15]. The influence of conductivity � is prominent in the rising edge, it is inversely proportional to electrical intensity which explains the inverse relation between conductivity and magnetic induction B. The influence of permeability � is prominent in the stable phase of the transient response [15]. The lift-off l and the sensor geometry factor � also influence the distribution and density of the EC [27-30].

When an EM field is applied to a conductive material, the temperature increases owing to resistive heating from the induced electric current. This is known as Joule heating. In general, by taking account of heat diffusion and Joule heating, the heat conduction equation of a specimen can be expressed as:

� �tzyxqCz

TyT

xT

CtT

pp

,,,12

2

2

2

2

2

��

���

���

���

��

��

���

(2)

where � �tzyxTT ,,,� is the temperature distribution, is the thermal conductivity of the material (W/m K),

which is dependant on temperature. � is the density (kg/m3), pC is specific heat (J/kg K). � �tzyxq ,,, is the internal heat generation function per unit volume, which is the result of the eddy current excitation [22,27].According to Eq. (1) and Eq. (2), it is influenced by � �tzyxT ,,, , � , � , � , � , and l. which have been demonstrated as mentioned before.

The resultant surface heat distribution from Joule heating and the heat diffusion procedure is recorded using a thermographic sensor, e.g. an infrared camera. Thus, the recorded video shows the variation of temporal temperatureresulting in material properties variation during fatigue process, such as conductivity � , permeability � and thermal conductivity .

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Feature Extraction from ECPT Using Single Channel Blind Source Separation

During ECPT testing, when eddy current encounters a discontinuity e.g. fatigue, they are forced to divert, leading to areas of increased and decreased eddy current density and resultant hot and cool areas due to Joule heating. The reflected temperatures characterized by these different areas are assumed uncorrelated and the thermography image captured by the infrared camera is considered as a mixing observation )(tY .

Assuming the mixing procedure follows the linear instantaneous mixing model [31-33]., the mathematical model can be described as:

� ���

�iN

iii tmt

1)( XY (3)

� �si Nim ,,1, �� is the mixing vector which describes the contribution of the thi position area to the recorded thermography image. sN denotes the number of independent signal images.

To solve the above ill-posed problem, we adopt a decomposition-based approach where was employed formerlyin analyzing non-stationary sources by expressing a fixed-length segment drawn from transient response, such that continuous transient slices of length N can be chopped out of a set of image sequences from t to 1t N � , and the subsequent segment is denoted as equivalent as image sequences captured by N independent infrared cameras

� �( ) vec( ( )), vec( ( 1)), , vec( ( 1))t t t t N� � � TY Y Y Y� where ‘ T ’ denotes the transpose operator and ‘ vec ’denotes the vectorize operator. The constructed image sequences are then expressed as a linear combination of the signals generated by the independent areas such that

( ) ( )t t� ��Y MX (4)

where 1 2( ) vec( ( )), vec( ( )), , vec( ( ))sNt t t t� �� � � �

TX X X X� . Hence, ( )t�Y can be transformed into uncorrelated

sources by means of a whitening matrix using the eigenvalue decomposition (EVD) of the covariance matrix

� �( ) ( )E t t� � �T TY Y EDE , where E is the orthogonal matrix of eigenvectors and � �1diag , , N �D � which

reflects the quantity of information, being 1 N � �� the eigenvalues. It is found that the variation in the rate of information corresponding to higher order PCs (larger than 2) are highly correlated with detail information. In the experiment, we have applied the proposed method to separate the ECPT mixing sequences and extract the relevantinformation rate of PCs. Thus, the correlation between the separated sources with fatigue in gear given different fatigue cycles are generated. More details will be presented in Section 4.

EXPERIMENTAL ARRANGEMENT

Sample Description

Gear manufacture and fatigue testing were carried out at Design Unit – Gear Technology Centre, Newcastle University. The 6 mm module helical test gears had a 44 mm face width. The gears were manufactured from a 18CrNiMo7 steel bar, shown as Fig.1. The gears were tested on a 160 mm centre distance back-to-back contact fatigue test rig at 3000 rpm (pinion) with BAG oil at 9��� [34]. A stepwise micropitting test involves running gears at incrementally increasing contact stress levels with each stage running for up to 8 million cycles as illustrated in Fig.2. MBN and ECPT deviation are measured after each stage of running.

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FIGURE 1. Fatigue test gear with inductor (coil).

FIGURE 2. Procedure of the stepwise micropitting test.

ECPT System

The eddy current pulsed thermography (ECPT) is shown in Fig. 3. An Easyheat 224 from Cheltenham Induction Heating is used for coil excitation. The Easyheat has a maximum excitation power of 2.4 kW, a maximum current of 400 Arms, and an excitation frequency range of 150-400 kHz (200 Arms and 256 kHz are used during this study). This measurement system has a quoted rise time (the heating period to full power) of 5ms, which was verified experimentally. Water cooling of the coil is implemented to counteract direct heating of the coil [22-24].

1000MPa / 8×106cycles

1200MPa / 8×106cycles

1350MPa / 8×106cycles

1500MPa / 8×106cycles

1600MPa / 8×106cycles

1700MPa / 8×106cycles

1800MPa / 8×106cycles

End of test:

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FIGURE 3. ECPT experimental system.

An SC7500 IR camera is a Stirling cooled camera with a 320 × 256 array of 1.5-���� ��� ���������� �����camera has a sensitivity of 20 mK and a maximum full frame rate of 383 Hz, with the option to increase frame rate with windowing of the image. A rectangular coil is constructed to apply directional excitation. This coil is madeof 6.35 mm high conductivity hollow copper tubing. During the experiment, only one edge of the rectangular coil is used to stimulate eddy current to the underneath sample. In this study, the frame rate is 383Hz with a 320 × 256 array, and 2s videos are recorded in the experiments.

RESULTS AND DISCUSSION

MBN Results

In a ferromagnetic material, Barkhausen noise is generated by the discontinuous movement of irreversible domain walls. This noise can be detected in the form of voltage pulses which are induced in a coil placed near the surface of the material, called magnetic Barkhausen noise (MBN). Therefore, MBN is expected as a useful way of NDE and many researchers have studied MBN for iron-based materials. Moorthy et al. investigated evaluation of contact fatigue damage and bending fatigue on gears using MBN [34-35].

The high-frequency MBE measurements have been made using the commercially available u-Scan/Rollscan 500-2 system supplied by Stresstech, Finland. A standard flat-surface probe with a ferrite-cored electromagnet with a pole gap distance of 3mm and a ferrite-cored MBE pick-up fixed at the centre of the pole gap has been used. The variations in MBN levels measured on three different teeth are shown in Fig.4 with progressive number of cycles.

Govindaraju et al. used the MBE for identifying the fatigue softening, saturation, crack propagation stages during low-cycle fatigue in medium strength steel [36]. Moorthy et al have shown that both MBE peak and profile can be used to assess the various stages of deformation and fracture during the fatigue propagation [34-35]. According tothese works, Figure 5 indicates that RMS variation of MBN is faint at initial stage (less 25 million cycles ) because of small variation in gear material stage. After a certain number of cycles, the RMS value increases as the cyclesincrease, which could be due to the combined effects of deformation induced transformation of retained austenite into martensite and fatigue softening. However, when number of cycles reaches 45 million, this results (1) plastic deformation induced formation of more compressive residual stresses and cyclic hardening of the microstructure;(2)the transformation of retained austenite to martensite would be completed. (3) additional dislocations would begenerated which cause decrease in the displacement length of magnetic domain walls. This could contribute to the decrease in the MBN level from maximum [34-35].

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0 10 20 30 40 50 6015

20

25

30

35

40

Number of million cycles

MB

N D

ispl

ay M

val

ue, A

.U

Tooth 1Tooth 2Tooth 3

FIGURE 4. The variations in MBN level with progressive number of cycles.

ECPT Results

A 400ms heating time followed by 1600ms cooling time is applied at the maximum frame data acquisition rate of 383 fps. Because the emissivity of the sample is unknown, digital level (dl) is used to describe the temperature rather ������� The heat patterns of gear with 40×106cycles at 0.2s are shown in Fig. 5. Macro-pitting, micro-pitting andwear will be occurred on contact surface during fatigue running, which could cause a similar change in temperature at the surface of rolling contact fatigue [26].

50 100 150 200 250 300

50

100

150

200

250 0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

Time (s)

T (d

l)

FIGURE 5. ECPT of No.2 tooth with 40×106cycles: (a) Thermal image at 0.2s after heating; (b) transient temperature response at impact point against time.

In general, during transformation of retained austenite into martensite and fatigue softening,the permeability �and the thermal conductivity increase as the number of cycles increase. After a certain number of cycles,dislocations accumulation contribute to the decrease in the permeability � and the thermal conductivity from maximum. However, the conductivity � decreases as the number of cycles increase during the fatigue process. Chen et al. apply normalization of the transient temperature response at the impact point against time for evaluation of cracks. However, the transient temperature response at point is affected by many factors, such as geometry, lift-off, reflection and around other points [25], and these method do not evaluate whole surface state. Moreover,

Impact point

Coil

Contact surface

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variation in material properties is very weak for fatigue, which is difficult to obtain temperature variationinformation for different fatigue cycles. At the same time, fatigue is reflected by not one or many points, but an area.

This paper proposes a statistical method based on single channel blind source separation to extract details of gears with different fatigue cycles. The top six principal components of ECPT of No.2 tooth with 40×106cycles are shown as Fig.6, and the information ratio of the top six principal components of ECPT with different cycles for No.2 tooth are shown as Fig.7.

When using PCA on the whole ECPT image sequences, the order of PCs can be ranked with N ���1 by using eigenvalues which provide a subspace of data that is maximally informative. Thus, we define the order with which the sum of the nonzero singular values divide the sum of all PC nonzero singular values i.e.

��

��N

iiiP

1%100 (5)

where i corresponds to nonzero eigenvalues in D which reflect the quantity of information for each PC. In our experiments the first two PC are already account for above 99% of the whole singular values. The rest components reflect the detail areas of ECPT which only account for less than 1%. It can be seen in Fig.7, the first two components emphasize the area that reflects the overall process of Joule heating and hearing diffusion, where they are inferred by several impacts such as liftoff, geometric shape and environment. The rest components emphasize the areas that reflect the variation of material property because of the fatigue. In addition, the information of these components will increase when the more severe of fatigue exists. This has been shown in Fig.8.

No.1

100 200 300

50

100

150

200

250No.2

100 200 300

50

100

150

200

250No.3

100 200 300

50

100

150

200

250

No.4

100 200 300

50

100

150

200

250No.5

100 200 300

50

100

150

200

250No.6

100 200 300

50

100

150

200

250

FIGURE 6. The top six principal components of ECPT of No.2 tooth with 40×106cycles.

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1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of PCA component

Info

rmat

ion

ratio

0 million cycles16 million cycles24 million cycles32 million cycles40 million cycles48 million cycles56 million cycles

FIGURE 7. Information ratio of the top six principal components of ECPT with different cycles for No.2 tooth.

Figure 9 shows the information ratio of the top six principal components of ECPT with different cycles for three teeth. Fig. 9, No.1 and No.2 express the first two PCs showing that the sum is maximally informative. It is difficult to find the fatigue information from these first two PCs as it reflects the overall process of Joule heating and hearing diffusion. However for the third PC (Fig. 9 No.3), the information starts to reflect the detail. This implies that the material property (e.g conductivity � , permeability � and thermal conductivity ) vary more obviously with the increasing number of fatigue circles and illustrate the correlation results. However, the correlation does not always retain consistency when choosing higher order PCs. The reason is that the higher order PCs are less informative and are easily to be inferred by noise.

CONCLUSIONS AND FUTURE WORK

A new application of ECPT for gear fatigue testing has been investigated. The feasibility studies have illustrated promising results. MBN can measure the fatigue status via the RMS of the Barkhausen noise amplitude. The RMS value increases as the increase cycles. After a certain number of cycles, the MBN level decreases from maximum. The top two principal components are general forms of ECPT with more than 99% information, which indicate heat diffusion and Joule heating effect. These are affected by lift-off, surface state, and so on. Details are shown by other components with less than 1% information, which indicates temperature information variation. The variation results in material property variation (such as conductivity � , permeability � and thermal conductivity ) during fatigue process of gear. The information ratio of components increases as the increase cycles. The results show the competitive capability of ECPT in gear fatigue evaluation. during the fatigue process.

In future work, a flexible coil design will be developed to adapt complex geometry of the inspected objects. An integrated system will be designed for multiple-parameter measurement, such as electric and thermal conductivities, strain and stress, etc. In addition, an advanced detail extraction and de-noising algorithm will be investigated forquantitative NDE and low calculation cost. The quantitative NDE and the robust features for fatigue evaluation and their relationships to ECPT response and gear material evaluation for lifecycle management of gears such as wind power gears will be further investigated [37-38].

ACKNOWLEDGMENTS

This work is funded by Newcastle University and Chongqing University of China. This project is also funded by EPSRC (EP/E005071/1) and the National Natural Science Foundation of China (Grant No. 51105396). Aijun Yin would like to thank the Chinese Scholar Council (CSC) for funding him to undertake one year visiting study at Newcastle University. And the author would like to thank Hong Zhang of Newcastle University for his help during gear fatigue measurement.

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0 10 20 30 40 50 600.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.1 component0 10 20 30 40 50 60

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.2 component

0 10 20 30 40 50 602

4

6

8

10

12

14x 10

-3

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.3 component

0 10 20 30 40 50 600.5

1

1.5

2

2.5

3x 10

-3

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.4 component

0 10 20 30 40 50 600.5

1

1.5

2

2.5

3

3.5x 10

-4

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.5 component

0 10 20 30 40 50 601

2

3

4

5

6

7

8x 10

-5

Number of million cycles

Info

rmat

ion

ratio

Tooth 1Tooth 2Tooth 3

No.6 component

FIGURE 8. Information ratio of the top six principal components of ECPT with different cycles for three teeth.

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