Кінематика руху і визначення ударного імпульсу під час контакту гранул із стінкою вібраційного контейнера

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Abstract
Purpose. The study aims to investigate the influence of the motion kinematics of the cylindrical container of a vibrating machine on the magnitude of the impact impulse during contact between the granules of the processing medium and the container wall. Relevance. Vibration processing of parts is a complex system whose efficiency depends on many factors, such as the parameters of the drive and the elastic suspension of the container, the shape and dimensions of its working elements, the properties of the processing media themselves, and the factors of interaction between the processing medium and the container. In known analytical methods, the container motion of vibrating machines is described by the equations of rigid body mechanics, while the working medium receives impact impulses from the container walls. Analyzing the container’s motion kinematics and determining the magnitude of the impact impulse during granule–wall contact allows for a more accurate determination of processing parameters in vibrating machines. Methodology. The container–working medium system is considered under the assumption that the impact during collision between the wall and the working medium is instantaneous and elastic. The motion of the granules of the processing medium in the vibrating container is based on the laws of Newtonian mechanics and probability theory. Results. During the analysis of the contact between the container wall and the particles of the working medium, it is taken into account that the particle concentration in the layer near the container walls is not constant but periodically varies. The dependence of the change in the root mean square (RMS) velocity of the working medium particles during wall motion was determined. Scientific novelty. New mathematical relationships have been obtained for determining the RMS velocity of the working medium at any given moment in time. Practical significance. Based on the conducted research, dependencies of the RMS velocity of the working medium during vibration processing of products have been obtained.

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