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Magnetic Leakage Field inside and outside a Slot on the Cylindrical Surface of a Disc caused by the Threading-Bar Technique

Wei-Chang Zhong
Nanjing Gas Turbine Research Institute, 47 Northern Central Road, Nanjing, 210037,
People's Republic of China
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Abstract:

1. Theoretical bases

2. Basic hypotheses

3. Analyses and derivation

4. Checking computation and plotting

Suppose there are two slots: D,n and hD,N, from expression (3') and (5), there will be
(6)
(7)
According to reference [1]: Ro = 72mm, d=6121824mm, if h =3, k =23/8, from expressions (6) and (7), the value of n can be calculated, and from expression (4), sml can be gained as in the Table.1.

D (mm) D = d/Ro(%) n smla(2 - n)n sml/sml(D = 1 %)
0.70 1.00 1/192.8 0.010346542 1.00
6.00 8.33 1/21.1 0.092540599 8.9441091
12.00 16.66 1/10.3 0.18474880 17.856092
18.00 25.00 1/7 0.26530612 25.642009
24.00 33.33 1/5.5 0.33057851 31.950628
Table 1: The watershed and linear magnetic charge density of different slot depth

The author already gave the analytic expression for the magnetic leakage field inside and outside a slot on the cylindrical surface of a disc at the symmetrical axis of the slot as [2]:

(8)

in which, 2b is the width of the slot (m), 2w is the length of the slot (m).

And the magnetic leakage field Hsum, measured by the classical experiment [1] is the sum of' and the applied magnetizing field Ha

(9)
or
(10)
here, Io is the magnetizing electric current through the threading - bar (A).
According to reference [1], w = 7.5mm, if b = 6mm and Ha = 0.2861084 A/m, from expressions (8) and (10) the result listed in the Table.2 and curves plotted in Fig.6 can be obtained.

No. d 6 12 18 24
1 1.4722377 3.2305838 4.8085795 6.0875369
2 Hsum 1.7583461 3.5166932 5.0946879 6.3736453
3 Hsum/Hsum(6) 1 2 2.8974318 3.6247957
4 Experimental result 1 2.0196078 2.9019608 3.3921569
5 Absolute error 0 -0.0196078 -4.52899×10-3 0.23263880
6 Relative error (%) 0 -0.9708716 -0.156066 +6.8581380
Table 2: The magnetic leakage field strength at the center of slots with different depth

5. Conclusion

Acknowledgment

References

  1. The Japanese Society for Non - Destructive Inspection edited: Magnetic Particle Inspection Testing A. 2nd Ed. Tokyo, Japan, 1973: 36 - 37
  2. W. C. Zhong: Analytic expression for the magnetic leakage field inside and outside of a slot on the cylindrical surface of a disc. <Proceedings of The 14th World Conference on NDT> New Delhe, India. December 8 - 13, 1996: 1581 - 1584
  3. K. H. Zao & X. M. Chen: Electromagnetism. People's Education Press, Beijing, China. 1978
  4. W. B. Tao: Eddy effect in magnetic particle inspection. <ChSNDT 7th Conference on NDT and International Research Symposium> Santou, China. October 26 - 30, 1999: 486 - 488
  5. L. A. Pipes; H. S. Cao & L. J. Zhang translated: Applied mathematics for engineers and physicists. Long - Men Integrated Press. Shanghai, China. 1952
  6. B. N. Domashevsky & A. I. Greiser: Polarization of crack magnetized by a longitudinal a. c. field. Defectoskopiya. 1976. (2): 89 - 95
  7. W. C. Zhong: Effect of slot depth in work piece surface on magnetic leakage field. (Chinese Journal of ) NDT. 1997. 19 (11): 304 - 307

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