On the Use of Linear and Nonlinear Controls for Mechanical Systems Subjected to Friction-Induced Vibration

Baptiste Chomette,Jean-Jacques Sinou

doi:10.3390/app10062085

Abstract

Friction-Induced Vibration and noisE (FIVE) is still a complex and nonlinear physical phenomenon which is characterized by the appearance of instabilities and self-sustained vibrations. This undesirable vibrational phenomenon is encountered in numerous industrial applications and can cause major failures for mechanical systems. One possibility to limit this vibration phenomenon due to the appearance of instabilities is to add a controller on the system. This study proposes to discuss the efficiency but also limitations of an active control design based on full linearization feedback. In order to achieve this goal, a complete study is performed on a phenomenological mechanical system subjected to mono or multi-instabilities in the presence of friction. Transient and self-excited vibrations of the uncontrolled and controlled systems are compared. More specifically, contributions of linear and nonlinear parts in the control vector for different values of friction coefficient are investigated and the influence of the control gain and sensitivity of the controller to the signal-to-noise ratio are undertaken.

Highlights

IntroductionFriction between two structures in contact can generate instabilities and self-sustained vibrations
Friction between two structures in contact can generate instabilities and self-sustained vibrations.This results in unwanted noise conventionally called under the name of brake squeal in the automotive industry
The possibility of using passive or active control for reducing self-excited vibrations of a mechanical system subjected to friction-induced vibration is nowadays a crucial point

Summary

Introduction

Friction between two structures in contact can generate instabilities and self-sustained vibrations. If the state vector cannot be measured, or in the case of partial poles placement, linearization feedback can be completed using nonlinear state observer introduced by Hu [14] and applied in the case of friction-induced vibration by Nechak [15] This approach is based on a model of the nonlinear structure and can show limits in terms of robustness. No study has yet considered the case of mechanical systems for which several instabilities can coexist with the generation of quasi-periodic transient and stationary self-excited vibrations This aspect of the usefulness and feasibility of an active control to reduce periodic and quasi-periodic vibrations of a mechanical system subjected to friction-induced vibration is one of the first contributions of the proposed study. One of the contributions and novelties of the proposed study is to analyze quantitatively the contribution of linear and nonlinear parts in the control vector when the control is started exactly at the beginning of the self-oscillations

Mechanical System under Study

Active Feedback Linearization

Linear Poles Placement h

Numerical Simulations

Conclusions