REC «Mekhanobr-Tekhnika» (Russia):

Kazakov S. V., Ph. D. in Engineering Sciences, Leading Design Engineer, atom2@inbox.ru

National Mineral Resources University (Mining University) (Russia):

Shishkin E. V., Ph. D. in Engineering Sciences, Associate Professor, Vice-Head of Chair, wiwki@rembler.ru

Taking into consideration severization of requirements to vibratory machines with respect to throughput rate, reliability and compact design, their improvement becomes increasingly important and difficult task. One of the promising ways to improve vibratory machines is changeover from one-mass and two-mass machines to machines based on three-mass system. A vibratory cone crusher based on two-mass system is distinguished by a number of advantages in comparison with one-mass machines. With that, it suffers from one significant deficiency: during operation impact loads are bound to recur, producing an extremely detrimental effect upon machine’s elements that are non-functioning directly in impact, in particular, on vibration exciters and their bearings. Creation of vibro-impact crusher based on three-mass system will permit to considerably decrease dynamic loads on bearings of vibration exciters’ rotors owing to so-termed vibration damping effect, that may almost completely isolate crusher’s foundation from unbalanced dynamic forces. In order to improve mechanical and performance parameters of vibratory cone crusher, a design model of machine based on three-mass system is proposed. Crusher’s body and cone vertical-plane oscillations are generated by a pair of inertial vibration exciters, installed on vibrating platform, which, in turn is supported on immovable foundation through vibration isolators of low stiffness. Differential equations of crusher’s motion, describing vertical-axis free-oscillation modes of crusher’s body and cone, as well as vibrating platform, are derived. Solution of these equations permitted to establish the expressions for machine’s natural frequencies and free-oscillation modes, analysis of which provides for assessment of its forced oscillation mode, specifically: to determine resonance frequencies and ratios of body and cone oscillation amplitudes to that of vibrating platform.
The work was performed with the financial aid from the Ministry of Education and Science of the Russian Federation for the Project No. 14.579.21.0048 UIPNI RFMEF157914X0048. R&D registration number 114093070077.

1. Vaisberg L. A. Proektirovaniye i raschet vibratsionnykh grokhotov (Design and calculation of vibrating screens). Moscow, Nedra, 1986, 144 pp.
2. Vaisberg L. A. Design and calculation of vibrating machines. Vibratsii v tekhnike. Spravochnik v 6 tomakh (Vibrations in technique: a handbook in 6 volumes). Vol. 4. Vibratsionnyye protsessy i mashiny (Vibrating processes and machines). Under ed. of E. E. Lavendela. Moscow, Mashinostroyeniye, 1981, pp. 135–145.

3. Rudin A. D. Dynamic properties and prospects of the three-mass system machines. Materialy nauchno-tekhnicheskoy konferentsii «Vibratsionnaya tekhnika» (Materials of Scientific and Technical Conference «Vibration Engineering»). Мoscow, 1966, pp. 330–335.
4. Blekhman I. I. Teoriya vibratsionnykh protsessov i ustroystv. Vibratsionnaya mekhanika i vibratsionnaya tekhnika (Theory of vibrational processes and devices. Vibrational mechanics and vibration technics). St. Petersburg, Publishing House «Ore and Metals», 2013, 640 pp.
5. Vaisberg L. A., Kazakov S. V., Lavrov B. P. Analysis of one of promising designs of vibroimpact crusher. Obogashchenie Rud = Mineral Processing, 2006, No. 3, pp. 41–43.
6. Safronov A. N., Kazakov S. V., Shishkin E. V. New trends in inertia cone crusher studies. Obogashchenie Rud = Mineral Processing, 2012, No. 5, pp. 40–41.
7. Vaisberg L. A., Zarogatskiy L. P., Turkin V. Ya. Vibratsionnyye drobilki. Osnovy rascheta, proyektirovaniya i tekhnologicheskogo primeneniya (Vibrational crushers. Bases for design, engineering and technological applications). St. Petersburg, VSEGEI, 2004, 306 pp.
8. Zniber A., Quinn D. D. Resonance capture in a damped three-degree-of-freedom system: Experimental and analytical comparison. Intern. Journ. of Nonlinear Mechanics, 2006, Vol. 41, Iss. 10, pp. 1128–1142.
9. Fidlin A., Drozdetskaya O. On the averaging in strongly damped systems: The general approach and its application to asymptotic analysis of the Sommerfeld’s effect. Book of Abstracts of IUTAM Symposium on Analytical Methods in Nonlinear Dynamics (Frankfurt, Germany, July 6–9, 2015). Germany, Technische Universität Darmstadt, 2015, pp. 19–21.
10. Sperling L., Merten F., Duckstein H. Rotation und Vibration in Beispielen zur Methode der Direkten Bewegungsteilung. Technische Mechanic, 1997, B. 17, H. 3, S. 231–243.
11. Rand R. H., Kinsey R. J., Mingori P. L. Dynamics of spin-up through resonance. Intern. Journ. of Nonlinear Mechanics, 1992, Vol. 27, Iss. 3, pp. 489–502.
12. Blekhman I. I., Indeitsev D. A., Fradkov A. L. Slow motions in systems with inertial excitation of vibrations. Journal of Machinery Manufacture and Reliability, 2008, No. 1, pp. 25–32.
13. Blekhman I. I., Vasilkov V. B., Yaroshevich N. P. Upon some possibilities of vibratory machines with self-synchronizing inertial exciters improving. Problemy mashinostroyeniya i nadezhnosti mashin = Journal of Machinery Manufacture and Reliability, 2013, No. 3, pp. 18–22.