KINETIC ENERGY OF A SIMPLIFIED KINEMATIC MODEL OF A VIBRATING TABLE WITH A LEVER-MOUNTED UNBALANCED VIBRATION EXCITER

Modern construction production for forming concrete products is equipped with various vibrating machines. Much research and development devoted to identifying the features of these machines' operation, explaining, and applying in practice certain effects that vibration causes on the treated medium. The mentioned forming machines also include a uniquely designed vibrating table for producing small-sized concrete products, where a mechanical centrifugal unbalance vibration exciter is fixed on a lever of a certain length vertically in the center under the vibrating table plate, which is its working body. The mathematical model of such a vibrating table is quite cumbersome and difficult for its optimization analysis. This article discusses a simplified kinematic model of said vibrating table. In this case, according to the accepted legitimate assumptions, the mechanical system modeling a real vibrating table consists of three material bodies, has three degrees of freedom, and its motion is determined by three generalized coordinates. All characteristics of the disturbing force generated by the vibration exciter's imbalance during its rotation in the operating mode have been established. Since the study's planned goal is to obtain a mathematical model describing this mechanical system's motion using Lagrange equations of the second kind, the initial stage requires finding the system's kinetic energy, which is done in this work. The motion type of each mechanical system body is established, and according to Koenig's theorem, using the coordinate method for determining kinematic characteristics and elements of vector calculus, the kinetic energy of each body is found. The total kinetic energy of the mechanical system is defined as the sum of these bodies' kinetic energies, expressed as a functional dependence on the system's inertial and kinematic characteristics. In further research, it is planned to find the generalized forces of the mechanical system corresponding to the generalized coordinates using the Lagrange equations of the second kind, to make a mathematical model of the vibrating table and to conduct an appropriate analytical study of this model in order to establish the optimal value of the length lever and the effect of this length on other technological characteristics of the vibrating table.