Vibrations in engineering and technology

Solona Olena – Candidate of Technical Sciences (Ph. D in Engeneering), Associate Professor of the Department of General Technical Disciplines and Labor Protection, Vinnytsia National Agrarian University (3, Solnyschaya St., Vinnytsia, Ukraine,21008, e-mail: solona_o_v@ukr.net).

Zamrii Mykhailo – graduate, аssistant at the Department of General Technical Disciplines and Occupational Safety of the Faculty of Engineering and Technology of the Vinnytsia National Agrarian University. Office address: Vinnytsia, str. Sonyachna 3, VNAU 21008. ORCID iD 0000-0002-9433-6714)

Vibrating mills are one of the most advanced types of grinders, which have high productivity and combine a sufficiently high intensity of technological action with a relatively simple construction.

The main parameter of vibrating mills is the amount of maximum power transmitted to the load through the chamber by the vibrating exciter at a given value of the forcing power developed by it. It was found that the maximum power is transmitted to the load when the chamber moves along a circular trajectory. Thus, it was determined that an equivalent forcing power should be applied near the center of inertia of the oscillating part of the vibrating mill.

The aggregation of vibration exciters can significantly reduce the time and cost of engineering and manufacturing of vibrating mills, while simplifying their maintenance and repair. In other cases, the use of several low-power vibration exciters instead of one of equal power is due to the need to disperse the forcing power over the vibrating working body of a large-sized vibrating mill.

The article considers the dynamic scheme of a vibrating mill with aggregated vibration exciters, which will ensure their self-synchronization. A mathematical model of a three-axis vibrating installation with four uniformly rotating vibration exciters is proposed in the form of a system of ordinary linear differential equations, which allows studying the movement of its actuators. The solutions of the system of differential equations corresponding to the stable synchronous and out-of-phase motions of the unbalance shafts of a three-mass four-vibrator two-chamber vibrating mill with active additionally installed rotating unbalanced masses are also presented. Based on the received results, the graphs of functions describing the steady oscillatory motion (A = const) of the executive bodies of the vibrating mill were constructed.

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2. Spirin A.V., Solona O.V., Kilimnyuk V.I. (2005). Otsinka na konkurentozdatnistʹ vibratsiynoho mlyna [Evaluation of the competitiveness of the vibrating mill] Vibrations in technology and technologies. № 2 (40). 93-95. [in Ukrainian].

3. Solona O.V. (2020). Kerovanyy vibratsiynyy mlyn dlya pomolu sypkoho seredovyshcha. [Controlled vibrating mill for grinding a loose medium]. Vibrations in engineering and technology. № 4 (99). 11-20. [in Ukrainian].

4.   Solona O.V. (2009). Vibratsiyni mlyny z prostorovo-tsyrkulyatsiynym rukhom zavantazhennya dlya tonkoho pomelu sypkykh materialiv. [Vibrating mills with spatial circulation movement of loading for fine grinding of loose materials]. Vinnytsia. RVV VDAU. [in Ukrainian].

5. Yaroshevich M.P., Tymoshchuk V.M., Silivonyuk A.V. (2011). Self-synchronization of unbalanced exciters with multiple rotation frequencies in vibrating machines with flat movement of the working body. [in Ukrainian].

6. Yaroshevich N.P., Zabrodets I.P., Dutchak B.I., Yaroshevich T.S. (2018). Dynamika pusku vibratsiynykh mashyn z nevrivnovazhenym pryvodom z urakhuvannyam yoho pruzhnosti. [Start dynamics of vibrating machines with unbalanced drive considering its elasticity]. Scientific Bulletin. №3. P. 100-107. [in English].

7. Yaroshevich N.P., Zabrodets I.P., Dutchak B.I., Yaroshevich T.S. (2015). Dynamika pusku vibratsiynykh mashyn z nevrivnovazhenym pryvodom pid chas ploskykh kolyvanʹ korpusu pidshypnyka. [Dynamics start vibrating machines with unbalanced drive in case of flat vibrations of bearing body]. Scientific Bulletin. №3. P. 39-45. [in English].

8. Bulgakov V., Pascuzzi S., Ivanovs S., Kaletnik G., Yanovich V. (2018). Modelʹ kutovykh kolyvanʹ dlya prohnozuvannya produktyvnosti vibratsiynoho kulʹovoho mlyna dlya tonkoho pomelu zerna. [Angular oscillation model to predict the performance of a vibratory ball mill for the fine grinding of grain]. Biosystems engineering. № 171. P. 155-164. [in English].

9. Solona O., Kupchuk I. (2022). Rozrobka funktsionalʹnoyi modeli vibratsiynoho mlyna z adaptyvnoyu systemoyu keruvannya rezhymnymy parametramy. [Development of a functional model of a vibrating mill with adaptive control system of mode parameters]. Modernization of research area: national prospects and European practices. Riga, Latvia: Baltija Publishing. P. 302-328. [in English].