Vibration Suppression on a Rotating Machine by the Use of Electromagnetic Actuators and a Pid Controller

Pereira, I.; Carvalho, Felipe Carmo; Leão, Leandro de Souza; Cavalini, Aldemir Ap; Steffen, Valder

doi:10.26678/abcm.creem2019.cre2019-0073

Cited by 1 publication

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“…The role of a high frequency AC of an EA and the dynamics of an excited cantilever beam is explored by Bichri et al [16] by means of analytical and numerical procedures near the primary resonance. Pereira et al [17] applied EA to a rotating machine on the learning position, and a proportional derivative controller is used for deriving the desired control laws. The Timoshenko beam theory and finite elements method are considered.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

et al. 2023

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In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined.

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Section: Introductionmentioning

confidence: 99%