Electronic Theses and Dissertations (Masters)

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Browsing Electronic Theses and Dissertations (Masters) by Keyword "Lagragian mechanics"

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    Developing of a parametrically resonw1t vibrating screen, modelling, simulation and dynamic testing
    (University of the Witwatersrand, Johannesburg, 2023-07) Mohanlal, Mishal; Li, Kuinian
    A novel coupled spring pendulum vibrating screen is proposed with the goal of developing efficient screening using parametric resonance. A simple spring pendulum is initially studied to provide the basis of the dissertation. The theoretical model of the proposed vibrating screen is developed using Lagrangian mechanics which includes damping and generalized forces. Two derivations of the vibrating screen are proposed, the first being a 4DOF (degree of freedom) system and the second being a 3DOF system. The 3DOF system is found to present better numerical stability and is thus utilized for the study. It is shown that the 3DOF system is comparable to the simple spring pendulum for the case where initial conditions are applied to similar coordinates. The proposed vibrating screen presents motion which is not indicative of traditional vibrating screens. It is found that a system where attributes are sized for parametric resonance requires far smaller excitation forces to achieve higher accelerations and displacements compared to traditional vibrating screens. The proposed vibrating screen is an unfeasible design due to the large displacements; high foundation loads and limitations on mechanical components. Discrete element method (DEM) simulations of the proposed vibrating screen are performed to study the efficiency with varying inclinations of the mesh deck. The results are compared to a linear motion vibrating screen. The proposed screen requires far less energy compared to traditional vibrating screens and achieves higher efficiencies with larger deck inclinations. The derived differential equations are verified by experimental testing using free vibrations. The numerical simulations and experimental tests present a good correlation. Signal processing is implemented to compare the natural frequencies from the experimental testing and numerical simulations, the results present a good correlation.