Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping (original) (raw)
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Effects of damping on mode-coupling instability in friction induced oscillations
ZAMM, 2003
The mode-coupling instability has generally been acknowledged as one of the most prominent mechanisms leading to selfexcited oscillations in sliding friction systems. The influence of structural damping on this type of instability mechanism however has not yet been fully clarified. The objective of the present work therefore is to investigate qualitative and quantitative aspects of the mode-coupling instability in the presence of structural damping, which will be assumed as linear viscous. For the sake of simplicity a two-degree-of-freedom minimal model is set up and analyzed. It is shown that under specific conditions the mode-coupling instability may be regarded as a viscous instability in the sense that an increase in structural damping may render a stable system unstable. An explanation for this behavior is given by two lines of argument: First a description and explanation is given in terms of eigenvalue-analysis. Due to the mathematical formality of this approach, the insight gained remains phenomenological. Second, a feedback-loop formalism is developed that allows a more detailed understanding of the underlying mechanical processes. Based on this formalism, necessary and in sum sufficient conditions for the onset of instability can be deduced and also the role of damping can be clarified.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2019
Finite Element Method (FEM) is proposed to model the friction-induced vibration in the gear system with a lead screw and nut. In order to validate it, the experiment was conducted by using the lead screw test setup. In the frequency spectrogram, there were two distinctively different patterns of the unstable modes: a mode where the frequency significantly changed and another where the frequency remained almost unchanged. Under a constant friction coefficient, the complex eigenvalue analysis in the FE model demonstrated that the system frequencies altered with respect to the transfer distance of the nut. The unstable modes were found to occur due to mode-coupling between the paired bending modes of the screw. Meanwhile, an unstable mode in which the frequency showed little changes in relation to the translation distance of the nut, was found to be an unstable torsion mode, which was caused by the negative friction-velocity slope.
Journal of Sound and Vibration, 2021
Brake squeal is a major issue for car manufacturers as it is the reason for the return of many vehicles to customer services, representing high costs for the companies. To meet customer's expectations, squeal must be accurately predicted during the design process. In the context of the automotive industry, squeal usually refers to friction-induced vibrations that generate noise. The main methodology employed nowadays for friction-induced vibrations prediction of industrial systems is the well-known complex eigenvalue analysis (CEA) despite its limitations. The latter suffers from an under-or over-predictive aspect and the vibration amplitudes cannot be estimated. A recent approach, called the generalised modal amplitude stability analysis (GMASA), has been developed as a complementary approach of the CEA to identify the modes involved in the nonlinear dynamic response of systems subjected to friction-induced vibrations and to approximate the quasi-periodic oscillations. The objective of this paper is to predict the nonlinear dynamic response of a full industrial automotive brake system. The GMASA is employed to predict its nonlinear dynamic response. It is demonstrated that when the CEA predicts a single unstable mode, two are actually involved in the nonlinear dynamic response. The quasi-periodic oscillations are analysed, as well as the evolution of the contact conditions at the pad/disc interface and exhibits the presence of micro-impacts.
International Journal of Mechanical Sciences, 2006
Friction-induced vibrations are a major concern in a wide variety of mechanical systems. This is especially the case in aircraft braking systems where the problem of unstable vibrations in disk brakes has been studied by a number of researchers. Solving potential vibration problems requires experimental and theoretical approaches. A non-linear model for the analysis of mode aircraft brake whirl is presented and developed based on experimental observations. The non-linear contact between the rotors and the stators, and mechanisms between components of the brake system are considered.Stability is analyzed by determining the eigenvalues of the Jacobian matrix of the linearized system at the equilibrium point. Linear stability theory is applied in order to determine the effect of system parameters on stability.
Numerical investigation on the mode coupling contact dynamic instabilities
2013
When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in the dynamic behavior of systems. The presence of frictional contact can give rise to mode-coupling instabilities that produce harmonic "friction induced vibrations". Unstable vibrations can reach large amplitude that could compromise the structural integrity of the system and are often associated with annoying noise emission. The study of this kind of dynamic instability has been object of many studies ranging from both theoretical and numerical study of simple lumped models to numerical and experimental study on real mechanical systems, such as automotive brakes, typically affected by such issue. In this paper the numerical analysis of a lumped system constituted by several degrees of freedom in frictional contact with a slider is presented, where the introduction of friction gives rise to an unstable dynamic behavior. Two different approaches are used to invest...
Journal of Vibroengineering
In certain industrial applications with frictional interfaces such as brake systems, the friction-induced vibrations created by coupled modes can lead to a dynamic instability and thus to an important deterioration in the operating condition. As a result, they are considered as a source of critical engineering problem. In addition, the presence of the nonlinearity makes necessary the consideration of the nonlinear dynamic analysis in order to explain clearly the complexity of the contribution of different frequency components due to unstable modes in the self-excited friction-induced vibrations, to get a design as reliable as possible and to avoid catastrophic failure during the operation phase of the mechanism. The present paper is based on previous works of Sinou and Jézéquel and extends them to include a developed damped four-degree-of-freedom system with frictional contact and spring cubic nonlinearities. Its essential goals are to analyze numerically the mode-coupling instability of the four-degree-of-freedom system owing to the friction between the surfaces of contact and to predict its nonlinear dynamic behavior. The numerical study of stability for the static solution of the mechanical system is performed by applying the complex eigenvalue analysis of the linearized differential equations of motion and by identifying the Hopf bifurcation points as a function of the coefficient of kinetic friction. Depending on the Runge-Kutta time-step integration scheme and the fast Fourier transforms, quantitative and qualitative nonlinear phenomena related to self-excited friction-induced oscillations and limit cycle evolutions are observed and discussed for various friction coefficients.
Transient Friction-Induced Vibrations in a 2-DOF Braking System
World scientific series on nonlinear science, series A, 2017
Non-stationary effects in the friction-induced dynamics of a two-degree-of-freedom brake model are examined in this paper. The belt-spring-block model is designed to take into account variations of the normal load during the braking process. It is shown that due to the adiabatically slowing down velocity of the belt, the system response experiences specific qualitative transitions that can be viewed as simple mechanical indicators for the onset of squeal phenomenon. In particular, the creep-slip leading to a significant widening of the spectrum of the dynamics is observed at the final phase of the process. & 2015 Elsevier Ltd. All rights reserved. phases [25]. This leads to widening spectrum of the dynamics, which can provide the possibility of interaction with acoustical modes in real brake systems. Such effects obtained experimental proof based on the rig designed in [9,21], however, theoretical considerations of the present work are conducted on a new model, which accounts for the influence of gravity and geometrical nonlinearity. Friction-induced vibrations in physical systems based on the mass-damper-spring modeling have been widely considered in the literature for many years. In particular, such models have been used extensively as deterministic Contents lists available at ScienceDirect
Journal of Vibration and Control, 2020
The present article studies the effects of both tangential and normal high-frequency excitations on a two-degree-of-freedom moving-mass-on-belt which represents a minimal model incorporating both velocity-weakening instability (so-called Stribeck effect) and mode-coupling instability (so-called binary flutter). The method of direct partition of motion is employed for studying the characteristics of the system in slow time scale. Linear stability analysis is performed near the equilibrium point of the system for both with and without sinusoidal high-frequency excitation. It is observed that the instability can be suppressed by the tangential high-frequency excitation only for a specific range of strength of excitation. However, stability does not improve under normal high-frequency excitations, though amplitude of the self-excited oscillation can be controlled to some extent. Direct numerical simulations are carried out in MATLAB SIMULINK to validate the analytical predictions.
Investigation of the relationship between damping and mode-coupling patterns in case of brake squeal
Journal of Sound and Vibration, 2007
Brake squeal is a friction induced instability phenomenon that has to be addressed during the development process. The mechanism is considered a mode coupling phenomenon also referred to as coalescence. The system eigenvalues have been computed using a technique based on the finite element method. The coalescence patterns were then determined in relation to the friction coefficient. The effects of damping on the coalescence patterns have been investigated. If the two modes involved in the coalescence are equally damped, a “lowering effect” that tends to stabilize the system is observed. If the two modes are not equally damped, both “lowering” and “smoothing” effects occur. If the “smoothing effect” prevails, added damping may act in an unintuitive way by destabilizing the system. To further study this point, stability areas have been plotted and a metric is proposed to find the most stable configuration in terms of damping distribution. In the squeal frequency range, coalescence patterns often involve more than two modes. In this case, the effect of damping is far more complicated since several modes are coupled both in terms of friction and damping.