PSI - Issue 65

A.V. Byzov et al. / Procedia Structural Integrity 65 (2024) 48–55 A.V. Byzov, A.E. Konygin, D.G. Ksenofontov, O.N. Vasilenko / Structural Integrity Procedia 00 (2024) 000–000

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2.3. Description of methodology

2.3.1. Calculation of excitation current frequencies across the primary coil For the purpose of this study, it was required to calculate the frequencies of excitation current across the primary coil to control the penetration depth of eddy currents in the hardened layer in the range from 0.5 to 5 mm. The penetration depth of eddy currents is calculated by the formula

1

z



.

(1)

f        

0

The frequencies for eddy current testing used in the study are defined as follows:

1

f

.

(2)



2

z        

0

When the product is remagnetized, the amplitude of the magnetic field strength is such that the remagnetization processes in the product are reversible; therefore, the formula has the following form:

1

.

f

(3)



2

z in        

0

The calculated frequencies are summarized in Table 3.

Table 3 – The depth of the layer and the corresponding frequency of the excitation current

f , Hz

8888.0

2222.0

987.6

555.5

355.5

246.9

181.4

138.9

109.8

88.9

d , mm

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2.3.2. Calculation of ε rel The next step in this study is to carry out measurements of the eddy current system parameters. According to p. 2.2 of this paper, the measured parameters were the voltage across the measuring coil and the phase difference between the current across the excitation coil and the voltage across the measuring coil. These parameters were necessary to calculate the modulus of the relative reflected ε of the transformer eddy current transducer ε rel . The impedance of the excitation coil was not considered in this study since this value remains unchanged under the considered conditions and ε across the secondary coil because of its lower sensitivity to a change in the hardened

layer depth in relation to the relative reflected voltage. The following relations are used in the calculation:

2

2

   

   

   

   

U 

U 

refl

refl

Re

Im

e





;

(4)

rel

U

U

0

0

   

   

U refl 

U k

Re

cos

cos 0 

 

   

;

(5)

k

U U

0

0