Vibrations in engineering and technology

Kobylska Olena – Doctor of Technical Sciences, Professor, Professor of the Department of Educational, Mathematical Sciences and Informatics, Kremenchuk Mykhailo Ostrohradskyi National University (20, Universytetska St., Kremenchuk, 39600, Ukraine, e-mail: kobilskaya1983@gmail.com  +380988248130, ORCID:0000-0002-4210-1534)

Savelov Dmytro – Candidate of Technical Sciences, Associate professor, Associate Professor of the Department of Mechanical Engineering, Kremenchuk Mykhailo Ostrohradskyi National University (20, Universytetska St., Kremenchuk, 39600, Ukraine, e-mail: dvsavelov@gmail.com ; +380965512814, ORCID: 0000-0002-5170-9621)

Vakulenko Roman – Candidate of Technical Sciences, Docent, Associate Professor of the Department of industrial Engineering Mikhailo Ostrohradskyi Кremenchuk National University (St. University, 20, Кremenchuk, Ukraine, 39600, e-mail: rom.vak311@gmail.com ; +380984935240, ORCID: 0000-0002-8845-962X).

Improving the compaction efficiency of powder materials directly depends on the intensity of the vibrational effect. The use of linear oscillatory modes often fails to provide the required density. The purpose of this work is the mathematical modeling of the operating mode of a shaking table with rigid-elastic limiters to determine the regularities of changes in the stress-strain state of metal powder under vibro-impact loading and to establish its optimal design and dynamic parameters.

The presented research is based on fundamental methods of analytical dynamics of piecewise linear mechanical systems with asymmetric restoring force. For analytical description of complex periodic laws of motion of the moving frame of the vibrating table and accurate calculation of non-stationary impulse responses, the Fourier series method was used. To ensure the accuracy of the calculations, the series expansion was limited to the first four terms, which allowed to fully take into account the effect of higher harmonics during impact interaction.

Analytical solutions of differential equations of motion of the vibrating table for conditions of steady stationary oscillations in the presence of a structural gap were obtained. Based on the developed algorithm, the amplitudes of deformation of the frame and the exact values of dynamic stresses that arise in the base of the layer of finely dispersed tungsten metal powder were calculated. The dependences of the amplitude-frequency characteristics of the system on the variation of the stiffness coefficient of the limiters were constructed.

The scientific novelty of the work lies in the development of a generalized mathematical model of a hybrid dynamic system of a vibrating table, which takes into account the asymmetry of periodic impulse motion, the magnitude of structural gaps, and the effect of the vertical displacement of the dynamic center of oscillations of the system during the cyclic impact interaction of the platform with the limiter.

Engineering recommendations for the design of vibration equipment have been determined. It has been proven that to intensify pressing, the stiffness of the limiters should be three times higher than the stiffness of the elastic supports of the system. It has been established that the extreme compressive stress of the powder and the minimum time for its complete compaction are achieved with an optimal structural gap δ = 0.5 mm. The implementation of these parameters allows to increase the density of finished products by 12–15% and at the same time reduce the dynamic load on the foundation by 20%.

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