Analytical Determination of Disturbing Load for Vibratory Compaction of Metal Powder
Keywords:
rheological model, metal powder, stress, deformation, amplitude of oscillationsAbstract
The serial technology of vibratory compaction of metal powders, which is currently in use, has proven that the technological equipment created on its basis does not take into account certain specific features and properties of the dispersed powder mixture, which is under the action of a vibrating punch. This, in turn, does not allow taking into consideration the impact of metal powder on the behavior of the working body, to determine the rational parameters of the vibration equipment and does not provide an opportunity to obtain high-quality and reliable products from metal powder. Based on the analysis of the behavior of bulk materials and existing rheological models of media subjected to vibration, it was determined that to describe the properties of a dispersed mixture of metal powder, which is subjected to vibration, a generalized rheological model is proposed, which simultaneously takes into account elastic properties and internal friction between metal particles, which connects tangential stresses (viscosity) and changes in the velocity of the powder medium. The analysis of literary sources proved that in existing analytical studies this rheological model was not used to describe the behavior of metal powders as a continuous medium, and their oscillations under the action of vibration loading were not described by the wave equation of oscillations. Therefore, for the proposed rheological model of the compacting powder medium, which takes into account its elastic, viscous and plastic properties, the wave equation of oscillations was compiled and the corresponding boundary conditions were recorded. For the theoretical analysis of the wave equation of oscillations, the method of solution in complex functions was applied. As a result of the theoretical studies, the phase velocity of the propagation of the disturbance in the powder medium was determined, the solution of the wave equation of oscillations was found and new analytical expressions were derived to determine the regularities of the motion of the metal powder, the amplitude stress that arises on the surface and in the base of the compacted layer of metal powder depending on the coordinate and the current time. Based on the condition describing the compactability of the medium, a new analytical expression has been obtained to determine the amplitude of the disturbance of the surface of the metal powder, which is necessary to achieve its complete compaction. The determined value of the disturbance amplitude determines the amplitude value of the disturbing force of the vibration exciters for equipping the drive of the vibrating working body with them.
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