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1

Solving nonlinear thermal problems of friction by using method of lines

Och E.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 1

33--37

EN

One-dimensional heat conduction problem of friction for two bodies (half spaces) made of thermosensitive materials was considered. Solution to the nonlinear boundary-value heat conduction problem was obtained in three stages. At the first stage a partial linearization of the problem was performed by using Kirchhoff transform. Next, the obtained boundary-values problem by using the method of lines was brought to a system of nonlinear ordinary differential equations, relatively to Kirchhoff’s function values in the nodes of the grid on the spatial variable, where time is an independent variable. At the third stage, by using the Adams's method from DIFSUB package, a numerical solution was found to the above-mentioned differential equations. A comparative analysis was conducted (Och, 2014) using the results obtained with the proposed method and the method of successive approximations.

2

Frictional heating during sliding of two semi-spaces with arbitrary thermal nonlinearity

Och E.

Acta Mechanica et Automatica

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2014

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Vol. 8, no. 4

204--208

EN

Analytical and numerical solution for transient thermal problems of friction were presented for semi limited bodies made from thermosensitive materials in which coefficient of thermal conductivity and specific heat arbitrarily depend on the temperature (materials with arbitrary non-linearity). With the constant power of friction assumption and imperfect thermal contact linearization of nonlinear problems formulated initial-boundary thermal conductivity, using Kirchhoff transformation is partial. In order to complete linearization, method of successive approximations was used. On the basis of obtained solutions a numerical analysis of two friction systems in which one element is constant (cermet FMC-845) and another is variable (grey iron ChNMKh or aluminum-based composite alloy AL MMC) was conducted.

3

Frictional heating of sliding semi-spaces with simple thermal nonlinearities

Och E.

Acta Mechanica et Automatica

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2013

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Vol. 7, no. 4

236--240

EN

In the article the nonstationary thermal problem of friction for two semi-spaces with taking into account their imperfect thermal contact and thermosensitivity of materials (simple nonlinearity), has been considered. The linearization of this problem has been carried out using Kirchhoff transformation, and next using the Laplace integral transform. The analytical solution to the problem in the case of con-stant speed sliding, has been obtained. On the basis of the obtained solutions and using Duhamel's formula, the analytical solution to the problem for sliding with constant deceleration, has been obtained, too. The results of numerical analysis are presented for two friction pairs.

4

Corrosion Resistance of Mechanically Alloyed 14% Cr ODS Ferritic Steel

Oksiuta Z., Och E.

Acta Mechanica et Automatica

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2013

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Vol. 7, no. 1

38-41

EN

New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.