
Vestn. YuzhnoUral. Gos. Unta. Ser. Matem. Mekh. Fiz., 2015, Volume 7, Issue 2, Pages 14–24
(Mi vyurm250)




Mathematics
The analysis of energy absorption in a blanket for contact electric resistance
A. V. Dmitriev^{}, A. A. Ershov^{} ^{} Chelyabinsk State University
Abstract:
The authors investigate piculiarities of the dissipation of electric energy at the point contacts
between the graphite flakes in a composition based on it. The analysis reveals the surface layer on the
surface of the graphite flake and carries out the calculation of the proportion of the output electrical
energy. The calculations are performed in the twodimensional approximation at the location of contacts
with the current flowing across and along one of the flat faces of the plate. The sizes of plate conductors
and electrical crosssection of the electrical spots of contacts between them have been used as
parameters. The authors have discovered the analytical dependences of the layer thickness of $x_p$ with a
predetermined proportion of the energy dissipation of $p$ of the crosssection contacts of $2\varepsilon$ tending to
zero. The authors have used boundary value problems as an elliptic function for the normal derivative.
The general solution is obtained using the Fourier expansion of the Bessel functions, special cases are
performed at the location of contact on the opposite side of the base and in the end sections. The method
of asymptotic expansions is used as the solution. For all three cases, the thickness of $x_p$ is expressed
through the multiplication of the power function of the proportion of crosssection of contact in the face
area and exponentially dependentant on the $p$ factor. The value of $p$ linearly enters the index gradedependence. The asynptotical analysis of the thickness of the layer with the release of 50, 90 and 95%of the electrical energy for the particular case is carried out. The compensation for the calculation of the
conditions under which the grid method is not applicable is given. The value of $x_{0,5}$ and the thickness of
the surface layer in which 50% of the energy is dissipated by the order of magnitude thinner than the
thickness of the natural graphite flakes are shown. When the defect layer is formed it determines the
properties of the electrical contacts in the composition of natural flake graphite with nonconductive
binder. It characterizes the contact electrical resistance at the pressing point contacts.
Keywords:
boundary value problem; lamellar crystal of graphite; asymptotic decomposition; small parameter; thickness of a defective layer; composite material; network of resistance; chain model; prevalence of contact electric resistance.
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UDC:
517.955.8 Received: 11.12.2014
Citation:
A. V. Dmitriev, A. A. Ershov, “The analysis of energy absorption in a blanket for contact electric resistance”, Vestn. YuzhnoUral. Gos. Unta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 14–24
Citation in format AMSBIB
\Bibitem{DmiErs15}
\by A.~V.~Dmitriev, A.~A.~Ershov
\paper The analysis of energy absorption in a blanket for contact electric resistance
\jour Vestn. YuzhnoUral. Gos. Unta. Ser. Matem. Mekh. Fiz.
\yr 2015
\vol 7
\issue 2
\pages 1424
\mathnet{http://mi.mathnet.ru/vyurm250}
\elib{https://elibrary.ru/item.asp?id=23142243}
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http://mi.mathnet.ru/eng/vyurm250 http://mi.mathnet.ru/eng/vyurm/v7/i2/p14
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