Mathematical simulation of kinematics of vibrating boiling granular medium at treatment in the oscillating reservoir

The mathematical simulation results of the circulating flow of a granulated working medium within the oscillating reservoir of a finishing-grinding vibration machine are presented. The model is based on the physical phenomenon where the granulated medium enters a vibro-boiling state through the vibration action. Solutions to Navier-Stokes equations provide expressions for Bessel function and associated integral transformations. The model solutions capture the complex cycloid-trochoid nature of working medium kinematics in vibration treatment operations, and allow the determination of the velocities and displacements of medium flows at any point within the reservoir. It is necessary to determine the technological parameters and equipment required, and their complex influence, on vibration treatment effectiveness. The zones within the reservoir where increased impulse loading coupled with energetic action schemes in the working medium and processed products, were observed.