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DINAME2019
DINAME2019
Two coupling mechanisms compared by their Lagrangians
Submission Author:
Roberta Lima , RJ , Brazil
Co-Authors:
William Manhães, Rubens Sampaio, Roberta Lima, Peter Hagedorn
Presenter: William Manhães
doi://10.26678/ABCM.DINAME2019.DIN2019-0065
Abstract
Electromechanical systems are very common. The importance of constructing the dynamical equations of motors coupled with mechanical systems suggests a new strategy. In the literature, often, the derivation of the dynamical equations is wrong. One thinks that the standard derivations of the dynamical equations of purely mechanical systems can be mimicked to electromechanical systems. Unfortunately, it cannot. The main reason is that in electromechanical systems one deals with the presence of electromagnetic fields, continuous entities. This fields store electrical and mechanical energies. In purely mechanical systems the conservative mechanical energy is stored as elastic or gravitational energy , and the nonconservative terms enter the equation as nonconservative forces. This cannot be done in electromagnetic systems. This paper shows the right way to derive the dynamical equations applying the results for two systems. Both systems are formed by a motor, the electromagnetic subsystem; a coupling mechanism; and a mechanical subsystem. In one case the coupling is the scotch-yoke mechanism and the mechanical part is a cart, modeled as a particle. In the other the coupling mechanism is a slider-crank mechanism and the mechanical system is a sliding mass, again a particle. To explain clearly the ideas, the dynamical equations are derived in a different way, putting in evidence the common errors. The examples were taken from the recent literature, but the mistakes are older.
Keywords
Electromechanical systems, Lagrangians, Coupled systems, nonlinear dynamics, Coupling mechanisms
