MATHEMATICAL AND BOND GRAPH MODEL OF FORCED OSCILLATIONS

Abstract

Matter is exchanged through material channels, while energy channels form paths for the exchange of energy (mechanical, electrical, thermal, chemical, etc.). Information channels are mediums for the transmission of signals. Technological recognition and design of the technological process are carried out through modeling. Modeling is used when applying mathematics to the study of nature. That is the basic research method of modern science, which boils down to the compilation and constant improvement of models of studied phenomena and systems. Modeling is based on the fact that certain phenomena are easily recognized and monitored on another system that is analogous to it. An analysis of the second-order self-excited system originating from noise was performed using the bond graph. A mathematical model that describes the dynamics of self-excited oscillation and a bond graph model that graphically solves the modeling problem are presented. Studying self-excited oscillations is a difficult task due to the occurrence of vibrations. Self-excited oscillations, which include noise, are frequently present in everyday life, not only in engineering practice, what is danger to human health. That is why it is necessary to reduce the amplitude of these oscillations. Solving this problem boils down to the introduction of external harmonics or absorbers. A self-exciting system is undesirable, it is necessary to measure oscillations, which is most often read by the static force of friction and slippage, as well as the phase speed of friction. Quasi-harmonic oscillations are sinusoidal in the slip phase and it is necessary to limit their value. Bond graph models are used to simulate models of various physical systems (electrical, mechanical, hydraulic system, etc.) and their combinations (electromechanical, mechanical-hydraulic system, etc.). Bond graphs are based on the exchange of energy through ports 0 and 1. Effort, labeled e represents physical quantities: force, voltage, pressure, etc.. Flow, labeled f represents current, speed, volume. All these physical quantities are used to analyze the physical model and description for the bond graph model, which is a powerful tool for modeling engineering systems, especially when physical domains are involved. Each connection is with labeled and directed graphs. The Bond graph model can be decomposed into sub-models, the arrows represent the direction of energy or flow from ports 0 or 1. It is possible to automatically reduce the bad features of the model by analyzing the prediction. Model simulations can be obtained in several ways, using Matlab/Simulink models or Dymole with the Modelica library, which contains Bond graph elements for obtaining output, speed and other quantities.