# Title

MATHEMATICAL MODEL OF ELECTROMAGNETIC FIELD
WITH SKIN-EFFECT IN CLOSED ELECTRICAL CONTACTS

# Authors

Stanislav N. Kharin, Merey M. Sarsengeldin,
H. Nouri, Samat A. Kassabek, Targyn A. Nauryz
Institute of Mathematics and Mathematical Modeling
Almaty, KAZAKHSTAN
Kazakh-British Technical University
Almaty, KAZAKHSTAN
University of the West of England
Bristol, UK

# Abstract

The mathematical model describing electromagnetic field in closed electrical contacts is elaborated. It takes into account a non-uniformity of the current density on the contact spot which can be explained by three factors: 1) physical phenomena of the constriction, 2) influence of the contact cross-section radius, 3) skin effect in the case of the alternative current. The effect of each above factors in dependence of given parameters is discussed. The model is based on the Maxwell equations which are reduced then to the solution of dual integral equations and series. It is shown that the skin-effect should be taken into consideration at the current frequencies which are greater than and for the contact forces which are greater than .

# History

Revised: January 30, 2017
Published: March 30, 2017

# AMS Classification, Key Words

AMS Subject Classification: 74Nxx
Key Words and Phrases: electrical contacts, Maxwell equations, skin-effect, dual integral equations and series

## Bibliography

1
K.K. Namitokov, Phenomena of electrical erosion, Energiya Edition, Moscow (1978), (in Russian).

2
S.N. Kharin, H. Nouri, D. Amft, Dynamics of Arc Phenomena atClosure of Electrical Contacts in Vacuum Circuit Breakers,IEEE Transactions on Plasma Science, 19, No. 1(2005), 491-497.

3
S.N. Kharin, H. Nouri, T. Davies, The Mathematical Models ofWelding Dynamicsin Closed and Switching Electrical Contacts, . 49th IEEE Holm Conf. On Electrical Contacts, Washington,USA, (2003), 107-123.

4
S.N. Kharin, Mathematical Models of Heat and Mass Transfer inElectrical Contacts, Proc. of 61th IEEE Holm Conference onElectrical Contacts, San Diego, CA, USA,(2014), 1-21.

5
C.M. Linton, and P. McIver,Handbook of Mathematical Techniques forWave/Structure Interactions, Boca Raton, FL: CRC Press, (2001).

6
R. Holm Electrical contacts, Springer-Verlag,(1981).

7
J. Cooks, C. Tranter, Dual Fourier-Bessel series, Quarterly Journal of Mechanics and Applied Mathematics, 25, No. 2 (1972), 247-263.

8
S.N. Kharin, M.M. Sarsengeldin, H. Nouri, S.A. Kassabek, T.A.Nauryz, Mathematical model of electromagnetic field withskin-effect in closed electrical contacts, KazakhMathematical Journal, 17, No. 1 (2017), 39-40.

# How to Cite?

DOI: 10.12732/ijpam.v113i4.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 103 - 115