PSI - Issue 36

Roman Dzhala et al. / Procedia Structural Integrity 36 (2022) 17–23 Roman Dzhala et al. / StructuralIntegrity Procedia 00 (2021) 000 – 000

22 6

The distance h from the axis of the conductor is determined by the gradient or parallax method. Substituting the above expressions of the components of magnetic field of currents in the formulas of depth h and current J , we obtain the analytical description of the measurements of h and J when moving along UP with insulation damage. For the gradient method:

(

)

( )

( ) h z H x g 

(

) z

0,2, 0,1,

( ) h z b H x x g    = H

)    − 1 ,

z

(11)

.

2 = 

0,1,

J z g

(

z

Here we assume that base b of observation points is equal to depth h of the occurrence of UP; distance y and distance z are given in base units b . According to the above given formulas, the calculations of MF UP components with current leakage and numerical modelling of non-contact measurements of the depth of UP and the current distribution along UP are carried out (Dzhala et al. (2012)). The results of numerical modelling of measurements by gradient J g and parallax J p methods of depth h and current J UP with leakage J s = 1, 2, 5% of the current J flowing along UP are shown graphically in Fig. 5. As shown by the calculations, the methodological error Δh s of measuring the depth of the UP, caused by current leakage, approaching the site of insulation damage z s ( z < z s ) is negative, and after z s is positive. Over the damage itself is ( z = z s ) Δh s = 0. As h decreases, the error Δh s increases. The current measurements gradually decrease from J to J – J s ; and over the damage z = z s we obtain a “plateau” with average value of J – J s /2.

1.01

a

1.005

hg z Js2  zs0  ( ) hg z Js2  zs1  ( ) hg z Js2  zs2  ( ) hg z Js2  zs3  ( )

1

0.995

0.99

10

5

0

5

10

15

z

1

b

0.995

Jg z Js2  zs0  ( ) Jg z Js2  zs1  ( ) Jg z Js2  zs2  ( ) Jg z Js2  zs3  ( )

0.99

0.985

0.98

10

5

0

5

10

15

z

Fig. 5. Dependence along UP measurements by gradient method of ( a ) depth h g and ( b ) current J g for the distances between defects Δz s / h = 0; 1; 2; 5.