The analysis of energy absorption in a blanket for contact electric resistance

A. V. Dmitriev   ; A. A. Ershov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 14-24

Résumé

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 two-dimensional 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 cross-section 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 non-conductive binder. It characterizes the contact electrical resistance at the pressing point contacts.

Détail

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.

Bibliographie

[1] Dmitriev A. V., Ershov A. A., Khimiya tverdogo topliva, 2011, no. 6, 47–54 (in Russ.) | MR

[2] Lavrent'ev M. A., Shabat B. V., Methods of the theory of functions of a complex variable, Nauka Publ., M., 1973, 212 pp. (in Russ.)

[3] Ershov A. A., Zhurnal vychislitel'noy matematiki i uravneniy matematicheskoy fiziki, 51:6 (2011), 1064–1080 (in Russ.) | MR | Zbl

[4] Khol'm R., Electrical contacts, Inostrannaya literatura Publ., M., 1961, 464 pp. (in Russ.)

[5] Dmitriev A. V., The scientific basis for the development of ways to reduce electrical resistivity of graphite electrodes, ChGPU Publ., Chelyabinsk, 2005, 197 pp. (in Russ.)

[6] Il'in A. M., Danilin A. R., Asymptotic methods in the analysis, Fizmatlit Publ., M., 2008, 248 pp. (in Russ.)

[7] Beytman G., Erdeyn A., Higher transcendental functions, Nauka Publ., M., 1974, 295 pp. (in Russ.)