Dynamics of a balanced screen-loader with
DOI:
https://doi.org/10.33271/crpnmu/80.177Keywords:
vibration, screen reloader, eccentric drive, grates, out-of-phase motion, equation, amplitude-frequency, response, vibration trajectoriesAbstract
Purpose. To build a mathematical model of a balanced vibrating screen reloader with an eccentric drive and analyze the obtained dependencies in order to recommend rational design and technological parameters of the screen. The methods. The analysis of scientific research in this area was carried out. A design scheme of a dynamically balanced vibrating screen-overloader of the grate type was developed. A methodology for solving the problem based on the Lagrange equation of the second kind is proposed and its mathematical model in the form of a system of linear differential equations is compiled. On their basis, the solution for determining the amplitudes of linear and angular vibrations is formed by the method of uncertain coefficients. The final expressions take into account the dissipative properties of the system. A numerical example of calculating the dynamics of a screen reloader with an antiphase motion of the grates is given using the Mathcad software. The amplitude-frequency response of the screen and the oscillation trajectories of the characteristic points of its surface are plotted. Findings. A design scheme of a vibrating screen reloader with an antiphase movement of the grates was constructed. The mathematical model of the screen is described by seven linear differential equations of the second order. A program has been created to solve them and obtain the final expressions for studying the system. The dynamic calculation of the screen, taking into account the dissipative resistances of elastic elements, allowed us to study the amplitude-frequency response and showed the stabilization of the amplitude of oscillations at high frequencies. The surface of the grate bars performs elliptical oscillations that vary along their length, which, in combination with their out-of-phase motion, contributes to the loosening of the technological load layer. The originality. New analytical dependencies for the calculation of a three-mass oscillatory system with an eccentric drive and out-of-phase motion of the masses are proposed, which allow to study its dynamics taking into account structural and technological parameters. Practical implementation. The application of the research results will make it possible to create a rational design scheme of a dynamically balanced screen reloader, as well as to clarify the kinematic modes of movement of the technological load.References
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