Vibrational Mechanics
Continious process of material treatment occurs in closed channel between two walls oscillating in anti-phase regime and moving along elliptical trajectories. The process is being implemented by periodical compression and loosening of granular material, which is being vibrotransporting along the channel.
The control of abrasive and compressive impact on material carrying out by сhoose of longitudinal and transverse stiffnesses of elastic elements, changing of vibration parameters and density of filling the working camera by material (patent RU 2675554).
Perspective applications of proposed method of attrition and mechanical activation of grained materials surface can be found in construction, mining, chemical, foundry and other industries.
References
1. Sizikov V.S. Vibration enrichment of fine concrete aggregates by the attrition and mechanical activation techniques // Bulletin of civil engineers. 2015. No. 6 (53). pp. 205–210.
2. Sizikov V.S., Sizikov S.A., Evtyukov S.A. Definition of parameters of experimental apparatus for mechanical activation // Bulletin of civil engineers. 2018. No. 1 (66). pp. 134–140.
3. Sizikov V.S., Evtyukov S.A. Rational regimes of fine concrete aggregate enrichment using the method of volumetric vibrational impact // Bulletin of civil engineers. 2018. No. 6 (71). pp. 156–162.
4. Sizikov V.S. The calculation technique of granular material layer transportation by two vibrotransportational walls of attrition-cleaning apparatus. PhD Dissertation abstract … // Saint-Petersburg State University of Architecture and Civil Engineering, 2020.
Exposure of the separator feed to intense vibration at the separator inlet eliminates the negative effects of adhesive interaction forces between finely divided particles on the process. The results include higher concentrate grades and improved recoveries.
These technologies may significantly reduce or completely eliminate the consumption of water currently used as a dispersion separation medium.
The studies were carried out at Mekhanobr-Tekhnika REC with the participation of employees of the Institute of Problems of Mechanical Engineering of RAS [1–5].
References
1. Golovanevskyi V. A., Arsentyev V. A., Blekhman I. I., Vasilkov V. B., Azbel Yu. I., Yakimova K. S. Vibration-induced phenomena in bulk granular materials // Intern. Journ. of Mineral Processing. 2011. Vol. 100. pp. 79–85.
2. Arsentyev V. A., Azbel Yu. I., Dmitriev S. V., Mezenin A. O., Andreev E. E. Effects of vibrational fluidization on the performance of dry magnetic separation of finely disseminated hematite ore // Obogashchenie Rud (Mineral Processing Journal). 2011. No. 6, pp. 13– 17.
3. Vaisberg L. A., Demidov I. V., Ivanov K. S. Mechanics of granular media under vibration action: the methods of description and mathematical modeling // Obogashchenie Rud (Mineral Processing Journal). 2015. No. 4. pp. 21– 31
4. Vaisberg L. A., Ivanov K. S, Demidov I. V. Disperse powder material layer vibrational fluidization state modeling with a view to describe dry concentration processes // Obogashchenie Rud (Mineral Processing Journal). 2016. No. 6, pp. 21–24.
5. Demidov I. V., Vaisberg L. A., Blekhman I. I. Vibrational dynamics of paramagnetic particles and processes of separation of granular materials // Intern. Journ. of Engineering Science. 2019. Vol. 141. pp. 141–156.
At a certain point when increasing the oscillation frequency of a vessel filled with liquid, a heavy rigid ball gets suspended and “freezes” at a distance from the bottom; at a higher frequency, the ball rises to the surface. When the frequency is reduced, the ball continues to float almost until the vibration stand stops completely. The low frequency of oscillations at the end of the experiment is indicated by the transparency of the liquid, free from any air bubbles captured from the surface. Similar effects are observed in wide vessels.
The suspension, rise to the surface, and retention of the body on the surface are associated with certain hydrodynamic and acoustic effects [2–4]. The latter are due to the compressibility of a liquid holding air bubbles and to the paradoxically low speed of sound in such a medium.
The work of many researchers in this area was largely inspired by the classic paper by V. N. Chelomey [1].
References
1. Chelomey V. N. Paradoxes in mechanics caused by vibrations // Reports of the USSR Academy of Sciences. 1983. Vol. 270, No. 1. pp. 62–67.
2. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B., Yakimova K. S. “Abnormal” phenomena in liquids under vibration // Reports of the Academy of Sciences. 2008. Vol. 422. No. 4. pp. 470–474.
3. Blekhman L. I. On vibratory buoyancy force and vibratory buoyancy // Obogashchenie Rud (Mineral Processing Journal). 2013. No. 4. pp. 21–29.
4. Blekhman I. I., Vasilkov V. B., Yakimova K. S., Shishkina E. V. Generation of slow fluid flows by a disk vibrating near the wall (on the theory of vibration pumps) // Obogashchenie Rud (Mineral Processing Journal). 2001. No. 1. pp. 36–38.
The video shows operation of an experimental prototype separator designed for particle sizing. The separator is based on the use of the phenomenon of vibrational gradient segregation of granular materials.
It is observed when, under sufficiently intense vibration applied to a granular mix, the particles of each specific size (fraction) slowly (as compared with the vibration rate) move in the direction of their lowest concentration, that is, in the direction opposite to the direction of the concentration gradient for this fraction [1–3]. The motion of relatively fine particles in a vibrating granular medium is similar to the processes of matter propagation during diffusion.
It is believed that deterministic factors play a major role in the segregation processes, while vibration only “dilutes” the mix, facilitating the manifestation of such processes. The vibration intensity of (3-5) g is deemed sufficient for these purposes. Higher vibration intensities usually render the opposite effect, leading to vibrational fluidization with intensified mixing and chaotization of the particle motion. This phenomenon enables separation using the chaotic particle motion in the mix, occurring under more intense vibration. The chaotic motion ensures an ordered and directional (gradient) flow of particles.
As a result, arbitrarily located, in particular, vertical (as in the video) screening surfaces prove to be more efficient in terms of fine fraction separation as compared to conventional bottom surfaces. The advantages of such separators include high separation efficiency and performance per unit of footprint and the ability to handle wet material (Patent Nos. RU 2550607; 2608142; 139262 PM, etc.).
References
1. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B., Yakimova K. S. On the phenomenon of vibrational diffusion segregation in granular materials // Reports of the Academy of Sciences. 2016. Vol. 466 No. 1. pp. 30–32.
2. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B. Gradient vibrational segregation in granular material sizing processes // Obogashchenie Rud (Mineral Processing Journal). 2015. No. 5. pp. 20–24.
3. Blekhman I. I., Blekhman L. I., Vasilkov V. B., Yakimova K. S. On the theory of gradient vibrational segregationin screening processes // Obogashchenie Rud (Mineral Processing Journal). 2015. No. 6. pp. 19–22.
If a vibrating vessel holding liquid has holes in its bottom or side wall, gas is sucked in, forming a series of bubbles. In this case, the liquid outflow is in the form of drops. Vibrational injection of liquid into liquid is also possible. The phenomenon may be used to intensify industrial processes and improve vibration devices, for example, for liquid dispensing and aeration (patents No. RU 2263883 and 2278738).
The vibrating-jet effect, another nonlinear phenomenon previously known and currently applied in technical devices (not shown in the video), implies that, when plates with conical holes vibrate in a liquid, tapering slow flows are generated in the direction of the holes.
Vibrational injection and the vibrating-jet effect may be regarded jointly [1], with the theory behind both phenomena viewed as special cases.In addition to their beneficial use [2, 3], these effects have been seen to cause accidents.
References
1. Blekhman I.I., Blekhman L.I., Vaisberg L.A., VasilkovV. B., YakimovaK.S. Nonlinear phenomena in liquid outflows from vibrating vessels // Reports of the Academy of Sciences. 2003. Vol. 391. No. 2. P. 185–188.
2. Blekhman I. I., Vaisberg L. A., Vasilkov V. B., Yakimova K. S. On the possibility of using vibratory injection in processing technologies // Obogashchenie Rud (Mineral Processing Journal), Vol. 4. 2004. P. 43–46.
3. Mikhailova N., Demidov I., Yasinskaya A., Samukov A. Development of the theory of vibratory injection of gas into liquid // Vibroengineering Procedia. 2020. Vol. 32. P. 216–222.
Two tubes are immersed in a vessel holding sand and are similar except that the end of one of the tubes is bent. The top and bottom ends of the tubes are open.
1. The tubes are empty. When the vessel vibrates, the bent tube is filled with sand, i.e., the granular material behaves like a liquid, while the straight tube remains empty and the material in it behaves differently.
2. The tubes are filled with sand. Under vibrations, the material flows from the straight tube into the vessel until it is almost completely empty, i.e., the straight tube acts as a vibration pump. At the same time, no changes are registered in the bent tube, as it remains filled.
The effects are observed both when the tubes are rigidly connected to the vessel and when they are generally fixed. The physical explanation and mathematical description for the phenomena are given in [1] and book [2]. Other effects demonstrating the peculiar behavior of a granular medium in communicating vibrating vessels are covered in [3, 4].
References
1. Blekhman I. I., Vaisberg L. A., Blekhman L. I., Vasilkov V. B., Yakimova K. S. On certain “anomalous” effects in the behavior of a granular medium in communicating vibrating vessels // Obogashchenie Rud (Mineral Processing Journal). 2007. No. 5. pp. 36–40.
2. Blekhman I. I. Vibrational Mechanics and Vibrational Rheology (Theory and Applications). Moscow. Fizmatlit. 2018.
3. Lipovsky M. I. On a type of vibrational displacement of a granular medium // Proceedings of the USSR Academy of Sciences, Solid Body Mechanics. 1969. No. 3. pp. 6–9.
4. Kremer E. B., Palilov V. F., Shifrina E. B. Behavior of a granular material in vibrating communicating vessels // New Areas in Raw Material Processing and Industrial Waste Recycling: Collection of Research Papers / Mekhanobr. Leningrad. 1986. pp. 31–44.
In this case, the difference from the classical pendulum with a vibrating suspension axis of (the Stephenson–Kapitza pendulum) is that the pendulum bob may move along the rod.
The resulting domain of attraction of the stable upper position of the pendulum reaches 70° (by the angular deviation from the vertical), as compared to the few degrees for a fixed bob.
References
1. Blekhman I. I., Sperling L. Zum Einfluss eines inneren Freiheitsgrades auf das Verhalten eines Pendels mit vibrierender Aufhängung // Technische Mechanik. 2004. Band 24. Heft 3-4. S. 277–288.
2. Vasilkov V., Chubinsky A., Yakimova K. The Stephenson-Kapitsa pendulum: Area of the Attraction of the Upper Positions of the Balance // Technische Mechanik. 2007. Band 27. Heft 1. S. 61–66.
The Indian rope trick effect is when a vibrating soft rope, with its one end fixed, takes a stable vertical position and maintains it at any deviation. The name of the effect is associated with the legend of Indian fakirs who managed to maintain vertical stability of a long rope with a monkey climbing to its top.
The works [1–8] study this phenomenon. The vibrational mechanics approach provides the following simple physical explanation for the effect [6–8]: as a result of vibration, the rope acquires additional bending rigidity EJv, which increases at higher products of amplitude A to vibration frequency ω. The same effect occurs for a string under rapid periodical tension changes. As a result, the string acquires additional vibrational rigidity, acting as an elastic rod (similarly to the Indian rope). Changes in vibration parameters may therefore be used to control the effective elastic properties of bodies, transforming them, in a way, into new (dynamic) materials.
In experiments [8] performed using a vibration stand, the length of the rope was 100 mm, the vibration amplitude was A = 7.5 mm, and the frequency was smoothly increased to reach ω = 200 s-1 (32 Hz). The bending vibrations observed are associated with the resonant phenomena that occur at higher frequencies. A sufficiently long rope may be straightened out on a vibrating flat support [8].
References
1. Otterbein S. Stabilisierung des n-Pendels und der Indische Seiltrick // Arch. for Rational Mech. and Analysis. 1982. Vol. 78. pp. 381–393.
2. Champneys A. R., Fraser W. B. The “Indian rope trick” for a parametrically excited flexible rod: linearized analysis // Proc. Roy. Soc. London. 2000. Vol. A456. pp. 553–570.
3. Fraser W. B., Champneys A. R. The “Indian rope trick” for a parametrically excited flexible rod: nonlinear and subharmonic analysis // Proc. Roy. Soc. London. 2002. Vol. A458. p. 1353–1373.
4. Weibel S., Kaper T. J., Baillieul J. Global dynamics of a rapidly forced cart and pendulum // Nonlinear Dynamics.1997. Vol. 13. pp. 131–170.
5. Blekhman I. I., Dresig H., Shishkina E. V. On the Theory of the Indian Magic Rope. Chapter 8. pp. 139–149. In: Selected Topics in Vibrational Mechanics (Ed. by I.I. Blekhman). Singapore, World Scientific, 2004.
6. Blekhman I. I. Vibrational Mechanics and Vibrational Rheology (Theory and Applications). Moscow. Fizmatlit. 2018. pp. 38–39; 147–172; 183–189.
7. Shishkina E. V., Blekhman I. I., Cartmell M. P., Gavrilov S. N. Application of the method of direct separation of motions to the parametric stabilization of an elastic wire // Nonlinear Dynamics. 2008. Vol. 54. pp. 313–331.
8. Vasilkov V. B. Influence of vibration on nonlinear effects in mechanical systems. Doctor of Engineering Dissertation, St. Petersburg / Institute of Problems of Mechanical Engineering of RAS, 2009
1.Universal Vibration Stand
The stand has unique capabilities for the implementation of various types of test table oscillations. It is indispensable when studying and optimizing vibration-based industrial processes, as well as when researching the effects of vibration on complex media, materials, and structures. A number of new nonlinear effects have already been discovered and investigated with the use of the stand, including the phenomenon of vibratory injection of gas into liquid. The wide applicability of the stand is due to the phenomenon of self-synchronization. (See [Universal vibration stand: Practical application in research, certain results. Scientific and Technical Bulletin of Saint-Petersburg State Institute of Technology. 2003. No. 3 pp. 224–227).
2.SV-2M Mechatronic Setup
(Control of Complex Systems Laboratory, IPME RAS, supervised by Professor A. L. Fradkov)
The design and wide research capabilities of this vibration stand are described in [Educational and research mechatronic setup for the study of vibration devices and processes. Problemy Mashinostroyeniya i Nadezhnosti Mashin (Problems of Mechanical Engineering and Reliability of Machines Journal). 2016. No. 4. pp. 91–97].
Employees
Blekhman L.I.
