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MODELING OF GRAIN MOTION TRAJECTORY BY WORKING ELEMENTS OF PNEUMOMECHANICAL PEELING MACHINE
... Подобные устройства применяются в различных отраслях промышленности, например, в горной -для получения заданного размера частиц горной породы [5], в химическойдля доизмельчения сырья [6,7], в пищевойдля разделения продуктов на фракции [7,8], сельском хозяйстве, включая сепарацию зерна [1], его измельчение [2] и смешивание [4]. При этом ось вращения подобных роторов может располагаться как горизонтально [8,9], наклонно [10], так и вертикально [6,11]. С учетом различий расположения оси вращения рабочих органов и показателя кинематического режима по-разному осуществляется силовой баланс приложенных к рабочему органу или материальным частицам действующих сил. ...
The purpose of the research is to substantiate the critical rotation speed of a rotor with bent blades based on force analysis and modeling the movement of mixture particles in a horizontal loader of a circulation mixer. The research method[1]ology included the substantiation of the highest rotation frequency of the loader blade rotor based on a force analysis of moving particles of forces when they were moved by the bent blades of the loader and compliance with the conditions for the entry of flying particles into the tray. The numerical analysis performed on the basis of the obtained expressions using the Mathcad mathematical package made it possible to establish the critical values of the rotation speed of the rotor-loader with bent blades based on the condition of the material coming off the blade and the condition of the flight of particles from the blade into the receiving tray. With radial blades, the limitation is the entry of particles into the receiving tray at a critical frequency of 43 min ⁻¹ , then for a blade bend of 30° – about 60 min ⁻¹ , for a blade bend of 45° – about 70 min ⁻¹ , for a blade bend of 60° – about 80 min ⁻¹ . The lowest critical values of the rotor-loader rotation frequency from the condition of particle movement along the blade correspond to the blade bend angle of 27–60° and are determined by the friction coefficient of the material, amounting to 83–78 min ⁻¹ . With an increase in material friction, the critical values of the rotor rotation speed from the condition of material coming off the blade decrease slightly, and the bend angle for the rotation speed extremum increases. The highest rotation speed of the rotor - loader with a radius of 0.12 m is limited to 78 min ⁻¹ at a blade bending angle of the order of 30–60°, determined by the friction of the material on the blade.
The research was carried out with the aim of mathematical modeling of the process of filtering finely dispersed non-Newtonian suspensions in intermittent pre-wash filters. The power-law fluid model is used to describe the rheological state of the medium. At the beginning of the filtration cycle, a layer of auxiliary material is washed, which is used as a filtering partition. A finely dispersed suspension during the filtration process forms a second layer, as it grows, the resistance to the flow of the liquid phase increases. The filtration cycle ends after reaching the critical values of pressure or productivity, depending on the operating mode of the device. Filtration equations are written in a cylindrical coordinate system separately for each layer. At the interface between the layers, pressure and velocity jumps arising due to the difference in porosity are taken into account. To calculate the thickness of the formed sediment layer, a differential equation was built. It is shown that the constructed mathematical model can be used to calculate the filtration of suspensions with a linear model of the rheological state, if the passage to the limit is performed. It is also shown that after passing to the limit, the results of the work allow modeling the process of filtering non-Newtonian media in plate-type filters. Numerical calculations are carried out for the filtration mode with a constant speed. The regularities of the effect of equivalent viscosity, the degree of medium nonlinearity, as well as the initial concentration of the dispersed phase on the filtration process were studied. It is shown that with an increase in these parameters, the pressure limit in the apparatus reaches earlier, which will lead to a reduction in the filter cycle time.
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