Ji-hui ZHOU，Qing-song CAO，Jing TAO，Jian LI

(School of Mechanical and Electronical Engineering，East China Jiaotong University，Nanchang 330013，China)

1 In troduction

With the rapid development of industrial technology，the structure of a lot of machines or workpieces becomemore and more complicated and the working conditions and environments become worse．The work develops normal or not directly affects the industrial and agricultural production，and even endangers human life and property safety．Therefore，defects testing and condition monitoring on workpieces become necessary，at the same time，the influence on the parameters，complex working condition and the environment of workpiece itself also need to be considered．Although electromagnetic nondestructive testing and system integration technique have been widely used in areas such as aviation，nuclear power station，automobile，ships，manufacturing，petroleum and national defense，the traditional electromagnetic detecting techniques are unable to actively change the instrument parameters to adapt to the environment．Therefore，it could notbe effectively used to the defects testing in a complex environment．

In order to adapt to the detection of workpiece under complex environment，this paper presents an active electromagnetic detecting technique［1］，which is based on electromagnetic measurement technique and it could obtain the size ofworkpiece actively，and according to the size of the workpiece to take the initiative to adjust．It is the base of this active adjustment to obtain the thickness of the workpiece．In terms of thickness measurement of workpiece with electromagnetic eddy current testing，most of scholars conducted the research from both sides of the reflection type eddy current［2－4］and pulsed eddy current［5-7］．Although the above-mentioned studies could obtain high-er precision，these are the only simple solutions for the thicknessmeasurement for workpiece．In this paper，the device designed not only is capable tomeasure the thickness of workpiece，but also is capable to actively adjust subsequently．Therefore，the method presented in this paper could be used in the subject of themeasurement ofworkpiece’s thickness．

Consequently，in order to realize the active adjustment，the research of measuring technique of transmission-type workpiece’s thickness was conducted and themeasuringmodel ofworkpiece’s thicknesswas established based on the basic principle of eddy current testing by transmission-type．The experimental results and simulation data were obtained and compared in this paper．It was confirmed that the presented model has important theoretical and application significance to realize the active adjustment of electromagnetic detection device．Moreover，it could play an important role to realize the automatic eddy current detection device．

2 Active electrom agnetic detection device and the p rincip le of thicknessmeasurement

According to the theory of electromagnetic detection，the active control and low frequency transmission-type eddy current testing method could be introduced to design an active electromagnetic detection device，as shown in Fig．1．The low frequency transmission-type double probes are symmetrically fixed by two bracket of semicircle insulation，and the probes are at any both ends of circle diameter．As can be seen from this figure，no matter how the position of the workpiece between the probes changes，the distance of these two probes is always the same，which could effectively reduce the influence of lift-off effect，at the same time，it also could avoid the skin effect and edge effect that caused by the uneven movement speed ofworkpiece．The detection device is capable to effectively reduce the impact of three effects［8］．

As shown in Fig．1，if the adjustable inner diameter of device isΔR，the thickness ofmeasured workpiece(or the diameter of the cross section)is rx．Based on the active detection，the device could build a structural characteristics of mathematical model between the detection device and the thickness ofmeasured workpiece，i．e．，themathematicalmodel between the size parameters of theworkpiece and the structure parameter of the support．Themathematicalmodel for the size parameters ofworkpiece and the electric parameters of sensor probe could be established according to the periphery system of the detector device．Based on the mathematicalmodel and the theory of electromagnetic detection，the thicknessmeasurementmodel of workpiece could be obtained，and the voltage amplitude of the detection signal could be chosen as the feedback quantity of the control system．At the beginning，the feedback quantity was input to the industrial PC with corresponding control algorithm，and then the thickness of workpiece could be obtained after the calculation，and the outputmotor will use the signals to control the stepmotor to adjust themechanical device．In order to pick up the detection signal，the calculation of industrial PC with the corresponding control algorithm will be sent to the incentive signal circuit to realize the active adjustment of incentive probe through the incentive voltage and frequency，and then the best detection signal could be obtained．Finally，the electric parameters of sensor probe and structure parameters of the detection device could be automatically adjusted and the active electromagnetic detection of the measured workpiece could be realized aswell．

Fig．1 Active electrom agnetic detection device

Therefore，in order to realize the active adjustment device，itmust obtain the thickness information of the workpiece first．According to the theory of electromagnetic detection，once the incentive coil is connected to a sine incentive signal，the surface of workpiece will be formed by eddy current field．The eddy current is not always evenly distributed on the surface of the workpiece．The higher eddy current density will present an exponential decay with the increase of infiltration distance，the distance of eddy current infiltration in workpiece is named as the‘penetration’．The actual numerical values of standard penetration depth means the depth of the density of eddy current attenuate to the same value as 1/e(37%)of the eddy current density on the surface of workpiece，which is called skin depth［9］．When the thickness of workpiece is less than the skin depth，the eddy current field could penetrate the workpiece，and on the other side of workpiece，there exist the magnetic induction lines，and thesemagnetic induction lines can produce electrical signals in the detecting coil．The thicker the workpiece，the less the eddy current signal，and the detecting coil in the formation of the electrical signal will be weak and strong conversely．Therefore，the thickness information of theworkpiece can be obtained through the induction electrical signals．

3 M easurem ent modeling for the thickness of workpiece

3．1 Equivalent circuits

As shown in Fig．1，the thicknessmeasurement device of workpiece is presented，and the equivalent drive coil，detecting coil and the eddy current in workpiece to three interacting coils are shown in Fig．2．

In this Figure，R1and L1are Dc resistance and the inductance of the incentive coil，R2and L2，represent equivalent resistance and inductance of eddy current equivalent coil;R3and L3are Dc resistance and inductance of the detecting coil，M1is mutual inductance between the incentive coil and eddy current equivalent coil，M2is mutual inductance between the detecting coil and eddy current equivalent coil．

Fig．2 Princip le d iag ram o f equivalen t circuit

The distance of incentive coil to the upper surface of the workpiece and the detecting coil to the lower surface of the workpiece are x0，the distance between these two coils isΔR．Assume the thickness ofmeasured workpiece is rx，then it could be obtained as follows:

ρ1is the resistivity of incentive coil，l is the wire length of incentive coil，s0is the cross section area of wire，μ1is themagnetic permeability of incentive coil，D is the average diameter of eddy current ring，c is the axial thickness of eddy current ring，d=b/D，e=c/d，and N is turn number of the incentive coil．Among these variables，the parameters b，c，d，e，D could be calculated by combining the specific parameters of probe and the suitable calculation formula［9］．

3．2 Measuring model about the thickness ofworkpiece

According to Fig．2，the following equations could be obtained:

Ignore the eddy current distribution on the surface of the workpiece and the influence of eddy current，the equivalent impedance of incentive coil could be obtained as follows:

By using the Biot-Savart Law［10］，the relationship of themagnetic induction intensity on the axis of incentive coil and the distance of incentive coil lower end face to the surface of the measured workpiece could be expressed as follows:

Where，r0，ras，L are the inside radius of the coil，the outer radius and the axial thickness，respectively．

The result of the formula(8)is themagnetic field strength of the workpiece’s upper surface．During the detecting process，the magnetic field strength of the workpiece’s lower surface could be determined by the detecting coil．Therefore，it is necessary to analyze the spreading situation of electromagnetic wave in the workpiece and obtain themagnetic field strength of the workpiece’s lower surface．

According to the theory of plane electromagnetic wave propagation in the semi infinite conductor［11］，assume theworkpiece’s upper surface is z=0，the instantaneous value of the magnetic field strength produced by eddy current field in the depth z of workpiece could be obtained as follows:

In the above formula，Hemis the magnetic field strength produced by eddy current field on the surface of workpiece(z=0)，，σ is the electrical conductivity ofworkpiece，μ ismagnetic permeability ofworkpiece．The relationship between Hemand themagnetic field strength on the eddy current surface is:

Based on the formula(8)，(9)，(10)，the following equation could be obtained:

Assume themagnetic flux ofworkpiece’s lower surface by eddy current penetration is B1，by using the formula(11)，there is:

Where，N1is the detecting coil’s number of turns;S is the equivalentarea of eddy current ring，and S=π(r2a-r2i)。In the formula(12)，if the environment and condition is not changed，then U·ias the incentive signal of damper is constant;x0is the distance between incentive coil and workpiece’s surface;the parameters such as r0，ras，L and˙z could be evaluated by the corresponding formula．Therefore，the formula(12)could be simply as follows:

Plug the formula(14)into the formula(13)，it yields:

Therefore，the induction electromotive force output by detecting coil is:

According the formula(15)，the relationship of workpiece’s thickness rxand the electromotive forceoutput by detecting coil could be expressed as:rx－．

From the formula(15)，the induction electromotive force output by detecting coilmainly depend on the incentive signal and workpiece’s thickness rxin the incentive coil，other parametersmight have known or could be obtained through the calculation，but in specious situationis constant，when the thickness of the workpiece gets changed，the induction electrical signal output by detecting coil willmainly influenced by the thickness of workpiece．Therefore，the thickness of workpiece could be obtained by the output voltage of detecting coil．

4 The sim u lation of workpiece thickness m easurem entm odel

In order to check the accuracy of the measurement model，the MATLAB software is adopted to conduct the simulation．According to the parameters of the probemade by laboratory，the setting correlative parameters of probe are as follows:number of turns on the incentive coil and detecting coil are N=N1=500，wire radius rt=0．05 mm，resistivity ρ1=1．724 1 ×106Ω·m，inside radius of the incentive coil r0=5．1 mm，outside radius ras=8．1 mm，axial thickness L=30 mm，vacuum magnetic permeability μ0=4π ×10－7H/m，relative magnetic permeabilityμr=1．Assume the distance between incentive coil and detecting coil isΔR=10 mm。

Since the signal from the incentive coil is in the range of 5 V and frequency of200 Hz，the skin depth of workpiece could be evaluated h=11．1 mm based on the calculation formula．Therefore，during the simulation process，the thickness of workpiece rxshould be less than the skin depth h，assume rxis integer within the range between 0 and 10．Take the advantage of above known values，all the related parameters are known．Therefore，the respond curve of the magnetic field strength caused by incentive coil and the induction electromotive force output by detecting coil to thickness of the workpiece could be show as Fig．3 and Fig．4．

As shown in Fig．3，with the increase of thickness of measured workpiece，themagnetic field strength of the incentive coil will get increased distinctly．It means that the closer themeasured workpiece apart from the incentive coil，the higher the magnetic field strength of the incentive coil．Meanwhile，it is also presented that in the electromagnetism detection，and the lift off height has a remarkable influence on the incentive signal．

Fig．3 Relationship betw een m agnetic induction o f incen tive coil and w o rkpiece thickness

As shown in Fig．4，with the increase of thickness of measured workpiece，the inverse electromotive force output by detecting coil will get increased distinctly;however，when the thickness is approaching to a certain level，the inverse electromotive force output by detecting coil will get decreased gradually．Within a certain range，the thickness increasementofworkpiece might reduce the lift off height，and enhance the detecting signal;however，when the thickness of workpiece continues to increase，the penetration of eddy current signalwill become veryweak，which leads to a weak signal．

Fig．4 Relationship betw een electrom otive force o f detecting coil and w orkpiece thickness

In short，based on the measurementmodel of the thickness established in the previous section，the thickness variation of the measured workpiece would affect the original incentive magnetic induction strength，and the detecting coil could detect the change of electrical signal caused by the thickness variation of the workpiece．Therefore，as the results of the simulation，this paper established the measurementmodel for the thickness ofworkpiece and it could reveal the corresponding relationship between detecting signal and the thickness of the workpiece．

5 Experim ent and analysis

In order to verify the correctness and accuracy of the workpiece’s thickness measurement model，the experimental results are compared with the simulation data．At the start of the experiment，adjust the distance between two probesΔR=0 mm，using function generator to access sine exciting signal，amplitude U0=5 V，frequency f=200 Hz．

Two pieces of homemade disk in the laboratory with thickness 1 mm and 2 mm were chosen as the workpiece to bemeasured．Acquisition detection signal，as shown in the Fig．5 and Fig．6．In addition，according to themodel which is established in the third section，the MATLAB program was used to calculate the theoretical amplitude of detecting signal corresponding to the different thickness．

Fig．5 Detection signal(rx=1 mm)

Fig．6 Detection signal(rx=2 mm)

Experimental results are shown in Table 1．As shown in this table，there exist some errors between the theoretical value and the actual measured data，the reasons are as follows．

1)Modeling is based on the assumption that the uniform distribution of workpiece and the nonuniform distribution of eddy current on the surface of workpiece is ignored;2)probes used in the experiments are laboratory homemade eddy current probe，detecting results has certain error;3)exciting signal produced by the function generator in the laboratory also introduce some error．However，the error iswithin acceptable range．Therefore，in this paper，the established the thickness of themeasurementmodel is feasible．

Table 1 Theo retical resu lts com pared w ith the experim ental results o f thickness m easurem entm odel

6 Conclusions

The accurate thickness information of workpiece is the basis to realize the active adjustment by using active electromagnetic detection technology．In this paper，the active electromagnetic detection technology was used to study the problem of active measurement for the thickness of workpiece，based on the relevant theory of detection technology for transmission-type eddy current and the measurement model for workpiece’s thickness．By using Matlab software，the simulation model was numerically solved and analyzed．Based on the experimental data，the correctness and accuracy of the workpiece’s thickness measurement model have been verified．It has been confirmed that the established model has important theoretical and practical significance in the process of subsequent workpiece defect detection to realize the active adjustment of device，and plays a promoting role in the realization of the eddy current detector automation．

Acknow ledgem ents

This paper is supported by Natural Science Foundation of Jiangxi(No．20132BAB216029)and the Key Laboratory of Ministry of Education for Conveyance and Equipment(No．14JD05)．

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