USE OF NONLINEAR MECHANICS METHODS IN THE RESEARCH OF THE MATHEMATICAL MODEL OF BENDING OSCILLATIONS OF THE ELECTROMECHANICAL SCREW

Abstract

A mathematical model of bending mechanical vibrations of the screw was obtained, taking into account the angular velocity of its rotation around a fixed axis and the relative movement along it of a homogeneous medium. The research methodology of the specified model has been developed, in particular, in the case of a short electromechanical auger. Equations in the standard form were obtained, which determine the main parameters of the dynamics of nonlinear oscillations. The influence of kinetic and physical-mechanical parameters on the characteristics of dynamic processes in a one-dimensional mathematical model of nonlinear oscillations of moving electromechanical screw equipment is analyzed. Convenient, from the point of view of engineering practice, calculation formulas are derived that describe the patterns of changes in the amplitude-frequency characteristics of the screw both for the non-resonant and for the resonant case. The important issue of studying the influence of the movement speed of mechanism elements on the oscillations of one-dimensional nonlinear elastic systems has not been considered in detail in the scientific literature. The main reason for this in the analytical study of dynamic processes was the shortcomings of the mathematical apparatus for solving the relevant nonlinear differential equations describing the laws of motion of these systems. The work uses methods of nonlinear mechanics to partially solve the specified problem. Numerical simulations are carried out for parameters close to those used in various industrial technological systems. The conditions of resonant and non-resonant modes of operation of the specified technological system were obtained. It was established that during longitudinal oscillations, the amplitude of oscillations also increases with an increase in the longitudinal velocity of the medium. It was also established that with increasing amplitude, the frequency of longitudinal oscillations sharply decreases, and if the system moves at a higher speed, then the frequency of oscillations decreases significantly.

Research using the methods of nonlinear mechanics allows the prediction of resonant phenomena and obtaining engineering solutions to improve the efficiency of technological equipment.

Keywords: nonlinear oscillations, mathematical model, resonance, amplitude, frequency, screw.