Problem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.
Goal. It consists in substantiating the inertial-rigid and force parameters of a high-efficient discrete three- mass inter-resonance oscillation system of a vibratory machine with an electromagnetic drive and in forming its mathematical model taking into account the drive. Significance. Despite the widespread use of one- and two-mass vibratory machines in the industry, their three-mass analogs in the inter-resonance oscillation zone have significant dynamic potential. New approaches to the calculation and design of three-mass inter-resonance vibratory machines would facilitate their mass introduction in enterprises of various industries as technological equipment. Method. A mathematical model of a three-mass inter-resonance oscillatory system of a vibrating machine with an electromagnetic drive in the form of a system of linear differential equations is considered. Based on it, dependencies are formed to determine the required inertial-rigid and force parameters of a highly efficient vibratory machine. Based on the already known power parameters of the system is a technique for establishing the necessary parameters for the design of the vibratory machine electromagnetic drive. The above parameters are embedded in the mathematical model of the vibratory machine. The time dependences of the motion of oscillating masses are investigated taking into account the processes occurring in the electromagnetic vibrator. Results. Inertial-rigid, force parameters of the oscillatory system are substantiated. A mathematical model of a three-mass inter-resonance oscillatory system is formed, which takes into account electromagnetic processes in the drive. Scientific novelty. A mathematical model of a three-mass inter-resonance oscillatory system of a vibratory machine is formed, taking into account the processes occurring in the electromagnetic drive, where the force action of the electromagnet is formed through the current in the coil of the vibrating exciter. Practical significance. The proposed method of calculations of three-mass inter- resonance vibratory machines with electromagnetic drive can be used in the design of high-efficiency vibratory process equipment.
Goal. The problem can be solved in research by studying the effect of the ratio of the volume of gas passing through the dust unloading holes to the amount of gas passing through the tangential inlet to the hydraulic resistance and cleaning efficiency in the cyclone with intermediate removal of precipitated dust. Actualіty of the work is that the establishment of the optimal ratio between the flow of air sucked through the dust holes and the total air flow in the cyclone with intermediate removal of deposited dust will obtain the highest efficiency of this type of device while reducing hydraulic resistance. The method is that to determine the hydraulic resistance and cleaning efficiency using CFD - programs in the CAD - program was built a cyclone model with intermediate removal of deposited dust, the design of which is presented in [5] by the method according to [6]. Results. The optimal ratio between the flow of air sucked through the dust unloading holes and the total air flow in the cyclone with the intermediate removal of deposited dust for different connection schemes of the device. Scientific novelty. For the first time with the help of theoretical researches the optimum ratio between the expenses of the air sucked out through dust unloading openings and the general expenses of air in a cyclone with intermediate removal of the deposited dust is established. Practical significance. The use in a cyclone with intermediate removal of deposited dust, the optimal ratio between the flow of air sucked through the dust discharge holes and the total air flow allows to obtain higher efficiency of air purification from dust at lower energy costs.
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