On the reduction of nonlinear electromechanical systems

Americo Cunha Jr (1) , Marcelo Pereira (1) , Rafael Avanço (2) , Angelo Tusset (3) , José Balthazar (4)

1 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]
2 UFMA - Universidade Federal do Maranhão = Federal University of Maranhão
3 UTFPR - Universidade Tecnológica Federal do Paraná [Curitiba, Brasil] = Federal Technological University of Paraná [Curitiba, Brazil] = Université technologique fédérale du Paraná [Curitiba, Brésil]
4 UNESP - Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found in the literature. Expressions for the characteristic time scales of dynamics are deduced from a physical analysis that establishes an analogy between electromechanical dynamics and the kinetics of a chemical reaction. It provides a physical justification, supplemented by non-dimensionalization and scaling of the equations, to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical system, a boundary layer phenomenon near the initial dynamic state, and the validity limits of the electromechanical quasi-steady-state assumption discussed here.

Mots clés: nonlinear dynamics; electromechanical dynamics; DC motor-cart system; model-order reduction; quasi-steady-state assumption

Domaines: Vibrations [physics.class-ph]; Science non linéaire [physics]; Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]; Génie mécanique [physics.class-ph]

Americo Cunha Jr, Marcelo Pereira, Rafael Avanço, Angelo Tusset, José Balthazar. On the reduction of nonlinear electromechanical systems. Meccanica, 2022, 57, pp.2679-2697. ⟨hal-03680269⟩