INVESTIGATION OF THE DYNAMICS OF NONLINEAR MECHANICAL SYSTEMS WITH LONG POWER LINES THROUGH DIGITAL MODELING

Abstract

Many of the mechanisms used in industry contain input and output links connected by long lines of force. Increasing the efficiency and service life of mechanical systems with long lines is of great importance for the country's economy. For a more rational use of these devices, it is important to maintain these operating modes with maximum accuracy, usually including the required speed of the actuator and the voltage in the lines. Such parameters can spontaneously change depending on the operating conditions of the system. In the presence of various influences, similar tasks to determine the marked regimes and parameters indicating the need for their change can be solved only with the help of the corresponding theory and research methods. The article presents the problems and the method of studying two-tier mechanical systems with an infinite number of degrees of freedom on the basis of the equations of momentum and moment of momentum in differential form. Transformations with the use of well-known wave equations are proposed, which made it possible to explicitly take into account the oscillations of the speeds of motion and stresses in the force lines of mechanical systems when describing dynamic processes. The solution of systems of partial differential equations is given using the Laplace transform, which made it possible to obtain general equations of motion and, after some simplifications, proceed to ordinary differential equations that take into account the dynamic features of systems with distributed parameters. The modernized Runge-Kutta method obtained solutions and carried out numerical simulation of transient processes in the hydraulic drive, the results of which have good convergence with full-scale experiments.