СКЛАДАННЯ МАТЕМАТИЧНОЇ МОДЕЛІ ВІБРАЦІЙНОГО СТОЛУ

Abstract

In this article, a mathematical model is obtained, which combines the design and technological parameters of the technological set of equipment for the concrete goods production (vibrating table), in which the vibrating exciter is fixed on the lever vertically in the center under the plate compactor. This equipment is used for the manufacture of small-sized concrete products. The mathematical model is composedwith the help of Lagrange equations of the second kind, which are the most common method for solving problems about the motion of a mechanical system. Methods of mathematical physics and physical and mathematical modeling by methods of applied mechanics were used in the compilation.To determine the position and describe the free motions of the material bodies that make up the mechanical system under consideration, an orthogonal vi-brational reference system of three coordinate systems was used. Analyzing the kinematic diagram of the vibration table, it is determined that the position in space of all material bodies of the mechanical system, which simulates the specified vibrating table, can be uniquely set by the following independent parameters: Cartesian coordinates, vibration angles and the angle of rotation of debalance.Thus, the mechanical system in question has seven degrees of freedom with seven generalized coordi-nates.As a result, a mathematical model of a vibrating table for concrete products manufacturing in the form of seven second order differential equations system, which describes the vibrating table spatial motion surface, is obtained.The theoretical values of the vibrating table vibrations amplitude at variable lever length were also determined and compared with experi-mental data at the same initial parameters. The difference was 15%, which confirms the adequacy of the created mathematical model to the real technological process on the vibrating table, which is being studied.Analyzing the change in the vibration oscillations amplitude on the vibrating table working surface from the change in the lever length on which the vibrating exciter is fixed, it was found that the lever fixation allows an almost linear increase in the amplitude of vibration oscillations due to an increase in the lever length. This, in turn, makes it possible to reduce energy consumption when compacting the concrete mixture.