The purpose of research. The main purpose of the work is to develop mathematical software for studying the dynamics of vibration machines of volumetric processing, and calculate the influence of various factors on the efficiency of the process based on applied systems of automated mathematical calculations, including MathCad and MatLab. Method. The research was carried out on the basis of a class of vibrating machines with unbalanced drive type and spring suspension. A mathematical model of loading vibrating processing machines with vertical perturbation is constructed, which is represented by a layering of flat beams that perform vertical oscillations. Methods of nonlinear mechanics were used to build a mathematical model. Results. The dynamic processes at vibration compaction of loading and separation of its fractions for the purpose of increase of intensity of the given technological processes are investigated. The dependences for determining the influence of physical and mechanical properties of loading components on the process dynamics are obtained. Scientific novelty. New approaches for construction of mathematical models of research of processes in machines of vibration processing, in particular vibration consolidation and separation are considered. In the course of research, differential equations were used to determine the change in the amplitude and frequency of loading from the influence of external and internal parameters of the vibration processing process. Practical significance. The obtained mathematical model makes it possible to investigate the dynamics of loading of the vibrating machine, to determine the amplitude and frequency of oscillations of loading of the vibrating machine depending on its properties and the properties of the vibrating machine. The obtained solutions of nonlinear differential equations to describe the motion of loading in vibrating machines allow to automatically determine the amplitudes, frequencies and trajectories of different components of loading depending on the parameters of the system "vibrating machine - loading", by algorithmizing them in applied systems of automated mathematical calculations.
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