# Mathematical Model of Movement of Bulk Material in a Vibratory Separator

2022;
: pp. 67 - 74
Authors:
1
Computer-Aided Design System Department, Lviv Polytechnic National University
2
Design and Operation of Machines Department, Lviv Polytechnic National University

Aim. The aim is to construct the mathematical model of the movement of loose material in a vibrating separator. Method. The calculation scheme of the vibration separator with two eccentric vibrators with an independent drive was built. Based on the scheme, it is assumed that the vibration separator performs only vertical oscillations in the plane of rotation of the eccentric vibrators. A cylindrical vibrating separator was considered, due to the possibility of transmitting vibrations of greater force to the sieve and significantly more efficient use of the entire screening surface. A mathematical model of the motion of an arbitrary point of motion of the medium in the vibrating separator was also constructed. The methods of nonlinear mechanics and Lagrange equation of the second kind are used to build a mathematical model. The basis of the mathematical model of any movement of a point in the working capacity of the vibration separator is the law of movement of the centre of mass. Results. The obtained mathematical model makes it possible to investigate the influence of the parameters of the vibrating separator and the characteristics of the loose material on the efficiency and productivity of the separation process. The differential equations describing the movement of the geometric centre of the separator container and the equations describing the movement of an arbitrary point of the layer of loose material make it possible to construct the absolute trajectory of its movement and determine the effect of a change in the amplitude-frequency characteristics of the vibrating separator on the natural frequency of the loose material. Also, when substituting the necessary specified parameters of the separator into the mathematical model, we get equations for determining the amplitude and frequency of any point of the working container. Scientific novelty. Using the methods of nonlinear mechanics, a mathematical model of the movement of an arbitrary point in a vibrating separator was built, taking into account the parameters of the vibrating separator and the loose material. Practical significance. This mathematical model can be used in the future in the study of dynamic processes during vibration transportation and processing.

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