Nonlinear mathematical model of the five-container vibration system

: 10-18
Received: June 20, 2022
Revised: July 28, 2022
Accepted: August 30, 2022
Computer-Aided Design System Department, Lviv Polytechnic National University
Design and Operation of Machines Department, Lviv Polytechnic National University

The construction of a non-linear mathematical model of movement and interaction of  the commanding and executive components of vibration systems is an important task. It implements vibration technologies of separation, grinding, mixing, compaction, transportation, surface  product  processing  and  technology for regulating the vibration effect on systems and mechanisms for their further research to increase the efficiency of vibrating machines, devices, and mechanisms and relevant technological processes. The article presents a generalized diagram of a five-container  vibration  system.  On  its  basis,  a  mathematical model was developed, which in the future will make it possible to research the effectiveness of vibration machines, devices, and mechanisms. The calculation scheme of the system and the methods of nonlinear mechanics were used to build the mathematical model. The obtained mathematical model makes it possible to determine the horizontal and vertical components of the amplitude of any point of the containers of the vibration system. This will make it possible to investigate the influence of different modes of operation of the system on the amplitude and nature of vibrations of the containers, in particular, established regimes, influence reversing of the drive, the influence of the processing environment of the containers of the vibration system, influence processed parts. 

[1] Subach  A. P. Dynamyka  protsessov y mashyn objemnoi  obrabotky,  Ryha:  Zynatne, 1991. 240 s.  [In Russian]  
[2] Opirskyi B. Ya., Denysov P.D. Novye vybratsyonnye stanky, konstruyrovanye y raschet, Lviv: Svit, 1991, 158 s. [In Russian] 
[3] Boholiubov N. H., Mytropolskyi Yu. A. Asymptotycheskye metody v teoryy nelyneinykh kolebanyi. Yzd. 4-e. M.: Fyzmatyz, 1974. 501 s. [In Russian] 
[4] Stotsko Z. A., Sokil B. I., Topilnytskiy V. H. Intensification of processes of strengtening machine parts by volumetric vibration treatment, III International Conference Transport Systems Telematics TST’03, 13–15 November 2003, Katowice – Ustron, Poland, s. 73, 493–504. 
[5] Stotsko Z. A., Rebot D. P. (2014) Vplyv dynamiky ryhy sypkogo seredovyshcha na prodyktyvnist’ vibraciynych separatoriv. Naykovyi ghyrnal Technologichni Kompleksy 1(9), 150–153. [In Ukrainian] 
[6] Stotsko  Z.  A.,  Diveiev  B.  M.,  Sokil  B.  I.,  Topilnytskyi  V.  H.  Matematychni  modeli  keruvannia vibroaktyvnistiu tekhnolohichnykh mashyn, Mashynoznavstvo Vol 2, 2005, st. 37–42. [In Ukrainian] 
[7] Junpeng Qiao and other (2018) Research on screening mechanism and parameters optimization of equal thickness screen with variable amplitude based on DEM simulation. Powder Technology. Vol. 331. 15. p. 296–309.