Received: February 29, 2024
Revised: March 02, 2024
Accepted: March 09, 2024
Design and Operation of Machines Department, Lviv Polytechnic National University
Lviv Polytechnic National University

The developed mathematical model of a vibratory separator with sequential screen placement and spring suspension is nonlinear, unified, and parametric. It was derived based on the utilization of the second-order Lagrange equation and asymptotic methods of nonlinear mechanics. The model is intended for investigating the dynamics of the separator during its design and subsequent operation, particularly for selecting its optimal design parameters and determining the conditions of steady-state and transient operating modes. It is presented as a set of analytical dependencies representing the motion laws of arbitrary points of the separator's working body in terms of its geometric, mass-inertial, and kinematic parameters with the ability to cover a wide range of variations. The model can be integrated into systems for automated design and calculation of various vibratory separators, differing in the number of screens, arrangement, and complexity of the drive, suspension, working body, etc.

[1] E. Johnson, “Low profile vibratory screen separators. Increasing capacity for tough materials”, Powder and bulk engineering, Vol. 18, issue 12, pp. 17 – 23, 2004.

[2] R. Singh Vibratory separators still make the grade for screening dry bulk powders /R. Singh // Oxford, Eng. Elsevier Advanced Technology: Filtration and separation,  vol. 41,  no. 1, pp. 20-24, 2004.

[3] V. Topilnytskyy, V. Vyshatytskyy “Construction of a mathematical model of an unbalanced vibrating separator on a spring suspension”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 9, no. 2, pp. 36–44, 2023.

[4]  V. Kovshar, N. Terletska, Patent of Ukraine for Utility Model No. 132767 “Drum Separator for Cleaning and Separating Bulk Mixture“ , Published 11.03.2019, Bulletin No. 5., 2019.

[5] K. Lawinska, “Analysis of screen holes blocking in a vibrating screen and a rotary and drum screen”, Journal «Fizykochemiczne Problemy Mineralurgii – Physicochemical Problems of Mineral Processing», vol. 53, pp. 812–828, 2017.

[6] V. Topilnytskyy, “Modeling the dynamics of vibratory separator of the drum type with concentric arrangement of screens”, Eastern-European Journal of Enterprise Technologies: Applied Mechanics, vol 2, no. 7(86), pp. 26–35, 2017.

[7] D. Rebot, V. Topilnytskyy, “Nonlinear mathematical model of the five-container vibration system”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 8, no. 3, pp. 10–18, 2022.

[8] Yu. Mytropolskyi, Methods of Nonlinear Mechanics, Kyiv: Naukova Dumka, , 2005, 527 [in Ukrainian].