The problems of the dynamic interaction of the terminal pair of elements are covered. Physical properties of the material, behavior of their characteristics and the features of mechanical interaction are taken into account. Mathematical model of dynamics of contact layer conductivity fractal destruction for sliding shank of sections contact pairs is created.

Retaining structure of homogeneous fluid and granular stream is one of the main criteria for technological process assuring the high quality outcome in many industries, including mechanical engineering and oil & gas industry. For example, in oil and gas industry during the pipeline transportation of oils there is a strong trend for cluster aggregation, and particle coarsening and entanglement. Dehomogenization of particle stream results in reverse dynamics of the stream. The importance of prevention and minimization of small particles coalescence by separating the oil stream leads to the need of improving the properties of the dispersers to boost their efficiency. Our paper investigates the operating principle of the disperser for separating particles (separator), which is designed by the authors. We have considered a particle stream of dispersed structure. We have obtained the conformity with the stability of the disperser operation. To yield the results we use the extremum problems for differential equations. This approach provides strong evidence that there are optimum parameters of the dispersers, which result in better stability of the particle stream.

The sliding contact when the air together with wear particles flow in contact area between commutator and brush is considered. The dynamical interaction between two surfaces is probabilistic. The behaviour of space-time-varying process is described by the differential equations, which are generally very difficult to solve. The simple numerical solution applying the method of Galerkin approximation to estimate the change in the pressure field in thin contact layer is obtained. It was found that under the leading edge of the brush the pressure change doesn't exceed 0.07 of the maximum value. The numerical simulations of the absolute error are presented for the 0.1, 0.2, 0.5, and 1 of the relative length. The relative error of pressure changes for small contact area is smaller (1 -0.8e 0.1τ). It is concluded that the approximate solution tends to the exact one. Moreover, it is shown that as the sliding velocity decreases, the relative error of the pressure change tends to the zero.

Abstract. The article considers the separation of particles in channels with different relative length. It is shown that the intensity of turbulence at the inlet section of the channel varies considerably in its length. The dependence of the turbulence damping along the channel expressing by fraction of the distance is shown. The ratio of the particle separation efficiency out the gas flow in the rotor channel is defined. The values of particle separation efficiency in the channel for the angle Į=ʌ/4 in turbulent aerosol flow is shows, including without mixing the particles.

-T h e p roblem s o f the d y n a m ic in te rac tio n o f the collector elem ents a re covered. It tak e s in to acco u n t the physical p ro p e rties of the m ate ria l and b e h av io r o f th e ir p a ra m e te rs and the features of m echanical coupling. A m ath e m a tic al m odel of dynam ics of fractions o f ra n d o m d e stru ctio n in the c o n ta ct lay e r conductivity is created. It c rea te s for sliding con tact elem ents of collector in steady-state.