The results of mathematical simulation have been carried out for the pattern of working medium motion providing the technological process of finishing-grinding treatment in an oscillating reservoir. With use of physics laws, it is ascertained and grounded that the flow of granules at the plane wall of reservoir is travelling oppositely to the source of vibrations, whereas the granules are drifting on the cycloidtrochoid trajectories from the wall of reservoir, where the looped displacement is maximal, to the center of reservoir in which the shift of granules is reduced to minimum because of damping and dissipation effect. The received theoretical regulations have a fundamental nature and can be used at the account of technological parameters of designed vibration machines.

The results of mathematic simulation of directed motion of the circulating flow of granulated working medium in the oscillating reservoir of finishing-grinding vibration machine are given. The model is based on the physical phenomenon, at which the granulated medium changes into vibro-boiling state clue to the action of vibrations. The solutions of Navier-Stokes implicated equations give the expressions of Bessel functions and their integral transformations. The model solutions ground the complex cycloid-trochoid nature of working medium kinematics on the vibration treatment operations and allow to determine the velocities of displacements of medium flows in any point of the reservoir. It is necessary for determination of the technological parameters and required equipment as well as their complex influence on the vibration treatment effectiveness. The zones of reservoir with increased impulse loading at combining the schemes of energetic action into the working medium and processed products are observed.

Vibration treatment in finishing processes is becoming a more complex technology, sometimes leading to weak shock waves occurring in the abrasive working medium. Here, the preconditions are discussed for the appearance of the effect of a shock wave of the vibrating working medium in a vibrating machine reservoir during multi-energy vibration processing. The peculiarities of the propagation of the force pulse of abrasive granules in the working medium, as in a pseudogas, are considered based on the kinetic theory of gases and the equations of gas dynamics. The paper also describes the motions of the parts in the working medium and the mechanism of the appearance of a weak shock wave, such as the compressive shock wave of abrasive granules. The interaction of the surface of the oscillating processed part with the granules of the working medium is studied. The characteristic of the Hugoniot adiabat for working medium granules is given. The influence of compression shock wave on the process of vibration processing is revealed. A comparison is made with experimental data.

The multi-energy vibration processing, namely the combination of different energies or forces acting on a free abrasive medium for grinding of metal parts, is becoming more used in finishing processes, in recent years. However, the complexity that is involved in the aforementioned process requires a careful look in the particularities of the process itself in general and the movement of the abrasive media, in particular. In this paper, the nature of the collective movement of abrasive granules between the independently oscillating surfaces of the reservoir and the processed parts is described. This study presents the dissipation of the kinetic energy of the granules in a pseudo-gas from the working medium granules. The motion of the medium granules near the part surface, which is caused by pseudo-waves initiated by vibrations of the working surfaces of the vibration machine reservoir, is demonstrated. Furthermore, the nature of the motion of the granules near the oscillating part surface is described. The analysis that is presented here permits the determination of metal removal quantity from the surface of the workpiece as a result of multi-agent group action of the vibrating reservoir surface and the processed part. The optimal conditions for the finishing process can be determined based on the analysis presented.

In this paper, the dependences of the tangential component of the velocity of movement of the medium granules, inside the oscillating reservoir, on its radius and oscillation period are obtained. For the analysis, the circulatory motion of working medium granules under the influence of a rotating impeller and the dynamics of a pseudo-gas from abrasive granules exposed to rotating processed parts and an impeller, are considered. From the results, the comparison of the energy impact on the working medium of the rotating processed parts and the impeller is carried out and the distribution of the pseudo-gas velocity from the abrasive granules and its pressure on the surface of the processed parts are obtained. Furthermore, the mechanism of pseudo-gas flow around a rotating part from granules of the working medium is presented. Finally, the schemes of the arrangement of the part in a cylindrical reservoir and its flow around the lateral surface of the rotating part are shown.