Browsing by Author "Maistruk, Volodymyr"

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Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table
(Видавництво Львівської політехніки, 2022-02-22) Lanets, Oleksii; Maistruk, Pavlo; Maistruk, Volodymyr; Derevenko, Iryna; Lviv Polytechnic National University
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.
Optimization of cyclone operating modes with intermediate dust removal using gas flow structure analysis
(Видавництво Львівської політехніки, 2022-02-22) Maistruk, Volodymyr; Lviv Polytechnic National University
The analysis of works in which designs of the dust collecting devices which are often used in the industry are investigated is carried out. It is established that forecasting the work of dust collecting devices in certain conditions is most effective to perform methods of numerical modeling and simulation of the separation process, which are widely used for research of devices of this type. Using numerical simulation methods, it is defined the structure of the gas flow in the cyclone with intermediate dust removal for different modes of operation, which was obtained by suction of gas through the dust unloading holes at constant total costs. For this cyclone, the change in the radius of the tangential, radial, and axial velocity component for different operating modes is investigated. In the course of the research, it is established that in the separation space the tangential component of velocity with increasing radius changes according to the parabolic law. The maximum values are 16–17 m/s. The suction of part of the gas in the amount of up to 20 % through the dust unloading holes slightly reduces the tangential component of the speed (up to 5 %) in the separation zone. It is determined that in the conical part the maximum values of the tangential component of the velocity decrease to 6–7 m/s. The reduction occurs both due to the flow of gas flow from the descending to the ascending, and the suction of gas through the dust unloading holes. It is established that the radial component of the velocity varies from 1 m/s in the separation zone to 5.5 m/s in the conical part. It has been found that the suction of gas through dust unloading holes in the amount of more than 15 % of the total volume leads to a change in the direction of the radial velocity component in the conical part. It is determined that the axial component of the velocity of the separation zone receives maximum values of 9–11 m/s. In the conical part of the device, it decreases to 2–4 m/s. The suction of part of the air through the dust unloading holes leads to a shift of the axis of the internal vortex relative to the geometric axis of the apparatus below the lower end of the exhaust pipe.It is established that the creation of a directed flow of gas through the dust unloading holes in the additional dust collector in the amount of up to 15 % of the total gas volume contributes to a more efficient operation of the dust collector. A further increase in the amount of exhaust air leads to greater turbulence of the flow and less efficient operation of the apparatus.