Theoretical Foundations of Vibration Processing Modeling

The results of the mathematical model development describing the motion of a load mass in a U-shaped container of a vibrating machine are presented, allowing one to take into account the influence of the field inhomogeneity of the oscillation trajectories of the container walls on the process productivity. The dependence of the determination of the circulating velocity of the working medium and the power expended on the processing of the product depending on the operation modes and the structural arrangement of the vibrating machine units is obtained, which determines the conditions for ensuring the stability of this movement, taking into account the mutual arrangement of the main units of the vibrating machine—vibration exciter and container. The possibility of increasing the operational properties of products as a result of vibrating treatment on finishing-peeling and strengthening operations on machines with a U-shaped container without a rigid kinematic connection between the elements of the technological system with increasing process productivity due to an external field-induced vibration excitement, which is a superposition of two planes-parallel fields: solenoidal-potential and vortex are theoretically proved.