Abstract
The results of mathematical simulation have been carried out for the pattern of working medium motion providing the technological process of finishing–grinding treatment in an oscillating reservoir. With use of physics laws, it is ascertained and grounded that the flow of granules at the plane wall of reservoir is travelling oppositely to the source of vibrations, whereas the granules are drifting on the cycloid–trochoid trajectories from the wall of reservoir, where the looped displacement is maximal, to the center of reservoir in which the shift of granules is reduced to minimum because of damping and dissipation effect. The received theoretical regulations have a fundamental nature and can be used at the account of technological parameters of designed vibration machines.
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Mitsyk A, Fedorovich V (2012) Classification of the methods of finishing-grinding treatment. The 3rd international scientific-technical conference «Theory and practice of rational designing, producing and exploitation of engineering structures». November 7–9. Lvov. pp. 163–164
Mitsyk AV, Fedorovich VA (2012) Development of new technologies of vibration finishing-grinding and hardening treatment of the products of common-engineering application // Visnyk NTU «KhPI». Series New solutions in modern technologies. – Kharkov NTU «KhPI». – – No 47 (953). pp. 226–233
Kamyar H, Amirhossein M, Spelt JK (2013) Development of a laser displacement probe to measure particle impact velocities in vibrationally fluidized granular flows. Powder Technol 235:940–952
Mitsyk AV, Fedorovich VA, Fadeev VA (2012) The effectiveness of new kinds of vibration treatment method of products. Modern engineering technologies: printed scientific works. Kharkov NTU «KhPI» 7:74–81
Naeini SE, Spelt JK (2011) Development of single-cell bulk circulation in granular media in a vibrating bed. Powder Technol 211(1):176–186
Sokołowska R, Majewski T (2007) Analysis of viscous-elastic model in vibratory processing. Recent Advances in Mechatronics. pp. 490–494
Hashimoto F, DeBra DB (1996) Modelling and optimization of vibratory finishing process. CIRP Ann Manuf Technol 45(1):303–306
Ciampini D, Papini M, Spelt JK (2008) Characterization of vibratory finishing using the Almen system. Wear 264(7–8):671–678
Ciampini D, Papini M, Spelt JK (2007) Impact velocity measurement of media in a vibratory finisher. J Mater Proc Technol 183(2–3):347–357
Babichev AP, Babichev IA (2008) The principles of vibration technology. Publishing centre of DSTU, Rostov-on-Don, p 694
Kartashov IN, Shainsky MYE, Vlasov VA (1975) The treatment of parts by free abrasives in vibrating reservoirs. Vyscha shkola, Kiev, p 188
Batchelor GK (2000) An introduction to fluid dynamics. Cambridge University Press, Cambridge, England, p 615
Patterson GN (1956) Molecular flow of gases. Wiley, New York, p 217
Hirschfelder JO, Charles F, Curtiss R, Bird B (1954) Molecular theory of gases and liquids. Wiley, New York, p 1219
Dudley RM (1999) Uniform central limit theorems. Cambridge University Press, Cambridge, England, p 436
Mitsyk AV Increase of the effectiveness of treatment of large-sized planed products by an activation of motion of the working medium in vibrating «U» – shaped containers. Thesis of candidate of technical sciences, 05.03.01. The dissertation is protected 10.04.2008, Kharkov NTU «KhPI», p 331
Yavorsky BM, Detlaf AA, Lebedev AK (2006) Reference book on physics, the 8th edn ONIKS. World and education, Moscow, p 1054
Peyret R, Taylor TD (1983) Computational methods for fluid flow. Springer, New York, p 358
Wesseling P (2001) Principles of computational fluid dynamics. Springer, Berlin, p 644
Tritton DJ (1989) Physical fluid dynamics, 2nd edn. Oxford University Press, Oxford, England, p 544
Kaplan W (1991) Advanced calculus, 4th edn. Addison-Wesley, Reading, MA, p 746
Goncharevich IF, Frolov KV (1981) The theory of vibration technics and technology. Science, Moscow, p 320
Riley KF, Hobson MP, Bence SJ (2010) Mathematical methods for physics and engineering. Cambridge University Press, Cambridge, England, p 1362
Kreith F, Black WZ (1980) Basic heat. Transfer Harper & Row, New York, p 512
Li Voti R, Liakhou GL, Paoloni S, Sibilia C, Bertolotti M (2001) Thermal waves physics. J Optoelectron Adv Mater 3(4):779–816
Mitsyk AV, Fedorovich VA, Fadeev VA (2012) Development of the problems of cinematics and dynamics of finishing-grinding treatment in vibrating reservoir. Cutting & tool in technological system: International Scientific-Technical Collection. Kharkov NTU «KhPI» 82:171–182
Korner TW (1989) Fourier analysis. Cambridge University Press, Cambridge, England, p 591
Jordan DW, Smith P (1994) Mathematical techniques. Oxford University Press, Oxford, England, p 806
Babichev AP, Motrenko PD, Gillespie LK (2010) Employing vibrational technology for processing burr work on machined parts. Publishing centre of DSTU, Rostov-on-Don, p 289
Babichev AP, Motrenko PD, Lebedev VA (2006) The application of vibration technologies to increase the quality of surface and service properties of products. Publishing centre of DSTU, Rostov-on-Don, p 213
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Mamalis, A.G., Grabchenko, A.I., Mitsyk, A.V. et al. Mathematical simulation of motion of working medium at finishing–grinding treatment in the oscillating reservoir. Int J Adv Manuf Technol 70, 263–276 (2014). https://doi.org/10.1007/s00170-013-5257-6
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DOI: https://doi.org/10.1007/s00170-013-5257-6