Nonlinear Dynamic Behaviour Analysis of a Clutch System with Uncertainties Using Polynomial Chaos and the Constrained Harmonic Balance Method

M.-H Trinh,E Aubry,S Berger

doi:10.1155/2020/8401745

Abstract

The study of the nonlinear dynamic behaviour of friction systems in general and of clutch systems in particular remains an open problem. Noise and vibrations induced by friction in the sliding phase of a clutch are very sensitive to design parameters. The latter have significant dispersions. In the study of the system stability, the problem is not only to know if the parameter values lead to the appearance of unstable equilibrium points; the real challenge lies in estimating the vibration levels when such unstable equilibrium points occur. This estimation is analyzed using the limit cycles. This article aims to study the ability of robust approaches based on developments in nonintrusive generalized polynomial chaos and a constrained harmonic balance method to estimate the vibration levels through the limit cycles of a clutch system in the presence of uncertainty. The purpose is to provide a low-cost, high precision approach, compared to the classic Monte Carlo method.

Highlights

In the sliding phase of clutch systems in vehicles, self-oscillations may be caused by frictional forces and thereby generate noise. ese phenomena can be classified into two main categories depending on whether they are related to tribological aspects or to the geometric and structural characteristics of the systems [1]
Erefore, the main objective of this article is to explore the possibility of an approach combining Nonintrusive Generalized Polynomial Chaos and the constrained harmonic balance method (CHBM) to take into account of the uncertainties in the estimation of limit cycles of a clutch system with an increasing number of uncertain parameters. e results are compared with the classic Monte Carlo approach for validation. e aim is to propose an effective method for determining the dispersion of limit cycles at a low cost and with high accuracy in order to overcome the difficulties of the time integration method and the classic MC method
Some studies are presented in which the limit cycles are determined, on a sample of N 100 parameter sets. e objective is to determine the dispersion of the limit cycles due to the dispersion of the uncertain parameters. is number of sample N was chosen to be sufficiently high so as to provide representative results of the system behaviour, but not too high either, to ensure reasonable calculation time

Summary

Introduction

In the sliding phase of clutch systems in vehicles, self-oscillations may be caused by frictional forces and thereby generate noise. ese phenomena can be classified into two main categories depending on whether they are related to tribological aspects or to the geometric and structural characteristics of the systems [1]. For high-frequency oscillations, such as squeal noise (up to several kHz), the mode coupling instabilities inherent in the structure of the system are more likely to be responsible for this phenomenon [2]. Numerous studies have shown that the dynamic behaviour of dry friction systems in general and clutch systems in particular is very sensitive to design parameters. Ese studies focused on the analysis of the system stability from the eigenvalues. The effects of friction and damping on the phenomenon of mode coupling in a finite element squeal model of a brake were presented in studies by G. It is necessary to take account of the dispersion of uncertain parameters to ensure the robustness of the analysis of the dynamic behaviour of friction systems. The Monte Carlo (MC) method which is conventionally used to achieve this requires prohibitive calculation time, especially for systems with many degrees of freedom (DOF)

Objectives

Methods

Results