Justification of vibrating hopper hole parameters during fine grained bulk material unloading

Надіслано: Червень 12, 2021
Переглянуто: Серпень 08, 2021
Прийнято: Грудень 26, 2021
Національний університет "Львівська політехніка"
Національний університет «Львівська політехніка»

Purpose. The leakage process of the fine grained bulk material (BM) from the unloading hopper is considered. As known the BM behaviour during the unloading process is directly related to the material stress state (active or passive) inside the hopper, which depends on  the  physical and mechanical bulk material  properties, as well as hopper geometric parameters. At the boundary of the transition from the cylindrical part to the conical part of the unloading hopper hole, the horizontal stresses that precede the leakage of the material increase sharply. The use of vibration reduces horizontal stresses in the hopper and thus improves the bulk product fluidity.  Also, the use of vibration reduces the probability of the free-fall arch formation over the outlet. Therefore, the present paper is aimed at developing the mathematical model of the fine grained bulk material flow under the vibration action from the conical hopper hole. Methodology. It is used one of the methods of studying the BM behavior, namely the analysis of the stress state of the conditionally stationary (pseudo-stationary) layer of the product and the force balance equation in the free-fall arch is made for further study of the geometric parameters of the unloading hole. Findings. In this paper, the mathematical model of the  BM  behavior in the conical hopper hole is developed. Since the most determining factor influencing the hopper productivity is the outlet diameter, so based on the developed model, it is established relationships that allow determining all parameters that affect the diameter. Graphical dependences  are  obtained,  which allow  to estimate the influence of  the angle inclination of the hopper hole walls on the value of the hopper outlet size at active and passive stress states. The dependence of the diameter of the unloading hopper hole on the BM properties is also established. The BM properties directly affect the initial shear resistance of the material. The influence of vibration on the unloading hole geometry is presented. Originality. The pseudo-immobile layer of bulk product is considered in the developed mathematical model, and it is investigated how  vibration affects  the  BM  behavior in this layer. Practical value. The practical value of  this paper  lies in  the  possibility  of  further  mathematical modeling  of  the influence  of  the  BM properties,  hopper  geometric  dimensions  and vibration on the product behavior in the material leakage process from the hopper. The results of the studies, presented in the form of graphs, can be used during the vibrating hopper design and the selection of rational modes of hopper operation. 

[1] P. Lin S. Zhang J. Qi et al., “ Numerical study of free-fall arches in hopper flows ”, Physica A: Statistical Mechanics and its Applications, vol. 417, pp. 29-40, 2015, https://doi.org/10.1016/j.physa.2014.09.032 
[2] A. Cyganiuk and P. Kurylo, “Modelling of the flow of streams of cohesionless and cohesive bulk materials in a conveyor discharge point with a flat conveyor belt”, IJAME, vol.  23,  No. 1,  pp.  24-35, 2018, https://doi.org/10.1515/ijame-2018-0002 
[3] G. Kache and J. Tomas, “Ausfliessen eines kohäsiven, hochdispersen pulvers” [“Outflow of the cohesive fine grained powder”], Süttgut [Loses Material], Vol. 6, pp. 246-252, 2010. 
[4] T. Kollmann, “Schwingungsinduziertes Fließen feinstkörniger, kohäsiver Pulver” [“Vibration induced flow of fine grained, cohesive powders”], Sc.D. dissertation, Otto Von Guericke University Magdeburg, Magdeburg, 2002. [in German]. 
[5]  N. I.  Maherus,  “Vplyv  parametriv  vibratsii  ta  heometrii  lunky  na  rukh  dribnodyspersnoho  sypkoho materialu u konichnii luntsi dozatora” [“Influence of vibration parameters and hopper geometry on the movement of fine bulk material in the conical hopper hole”], Vibratsii v tekhnitsi ta tekhnolohiiakh [Vibrations in technique and technologies], Vol. 2, pp. 71-78, 2014. [in Ukrainian]. 
[6] K. Hashemnia and S. Pourandi, “Study the effect of vibration frequency and amplitude on the quality of fluidization of a vibrated granular flow using discrete element method”, Powder Technology, Vol. 327, pp. 335-345, March 2018, https://doi.org/10.1016/j.powtec.2017.12.097 
[7]  S. V.  Vladimirov,  “Protsesy  fasuvannia  krupiv  kharchovykh  produktiv  i  rozrobka  konstruktsii obladnannia” [“Packing processes of  food groats and development of the equipment designs”], Ph.D. dissertation, Mykhailo  Tuhan-Baranovsky  Donetsk National University  of  Economics and Trade, Donetsk, Ukraine, 2008.  [in Ukrainian]. 
[8]  J.  Du,  C.  Liu  et  al.,  “Discharge of granular materials in a hemispherical bottom silo under vertical vibration”, Powder Technology, Vol. 372, pp. 128-135, July 2020, https://doi.org/10.1016/j.powtec.2020.06.006 
[9]  Y.  Sholoviy,  N.  Maherus,  et  al.,  “Modeling  of  the finely-dispersed  no  coherent  material  flow  from  the loading hopper under vibration”, in Proc. 18th Conf. on Optical Fibers and Their Applications, Naleczow, 2019, pp. 1104508. 
[10] A. V. Katalymov and V. A. Liubartovych, Dozuvannia viazkykh ta sypkykh materialiv [Dosage of viscous and bulk materials]. Lviv, Ukraine: Khimiia Publ., 1990. [in Ukrainian]. 
[11]  G.  Kache, “Verbesserung des Schwerkraftflusses kohäsiver Pulver durch  Schwingungseintrag” [“Improving the gravity flow of cohesive powders through vibration input”], Sc.D. dissertation, Otto Von Guericke University Magdeburg, Magdeburg, Germany, 2009. [in German].