Abstract
The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.
Highlights
The problem of Friction-Induced Vibration and noisE (FIVE) is crucial due to its huge impact for both the acoustic discomfort or the potential poor system performances [1,2,3,4,5]
The stability analysis of a mechanical system regulated by state feedback control with time delay and the determination of the critical time delay τc are discussed
Based on comparison with direct time responses of the controlled system, it is demonstrated that the real critical time delay τc for the mechanical system subjected to friction-induced vibration does not coincide with the critical time delay τlim predicted by the frequency sweeping approach; it corresponds to a specific point of the stability border predicted by the frequency sweeping approach
Summary
The problem of Friction-Induced Vibration and noisE (FIVE) is crucial due to its huge impact for both the acoustic discomfort or the potential poor system performances [1,2,3,4,5]. The performance of active vibration control suffers severe degradation for the case in which the time delay has to be taking into account This explains why time-delayed feedback control methods have received outstanding attention in the domain of mechanical systems subjected to friction-induced vibration in the past decades [15,17,20,21,26]. One of the main originality of the proposed study is to answer this question by developing a hybrid method which combines the efficiency of the frequency sweeping test [33] with an expansion based approach of the delayed term for approximating the eigenvalues problem It will be shown in this paper that this hybrid method makes it possible to efficiently calculate the critical time delay in the context of mechanical systems subjected to friction-induced vibration, as opposed to using the frequency sweeping approach alone. Numerical examples are undertaken to discuss the relevance of the two methodologies and a mixed strategy is developed to predict efficiency the critical time delay of the controlled system
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