Critical thresholds for mode-coupling instability in viscoelastic sliding contacts

Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoelastic dissipation in the substrate, adhesive friction at the interface and nonlinear normal contact stiffness as derived from numerical simulations based on a boundary element method capable of accounting for linear viscoelastic effects. The linear stability boundaries are analytically estimated in the limits of very low and very high substrate velocity, while in the intermediate range of velocity the eigenvalue problem is solved numerically. It is shown how the system stability depends on externally imposed parameters, such as the substrate velocity and the normal load applied, and on contact parameters such as the interfacial shear strength $$\tau _{0}$$ τ 0 and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength $$\tau _{0,crit}$$ τ 0 , c r i t and normal load $$F_{n,crit}$$ F n , c r i t , which trigger mode-coupling instability: for shear stresses larger than $$\tau _{0,crit}$$ τ 0 , c r i t or normal load smaller than $$F_{n,crit}$$ F n , c r i t , self-excited vibrations have to be expected.

Squeal Noise Analysis Using A Combination of Nonlinear Friction Contact Model

Squeal noise is generated by an unstable friction-induced vibration in a mechanical structure with friction load. Nonlinear mechanisms like sprag-slip, stick-slip, and negative frictions damping are believed in contributing to generate this kind of noise. However, the prediction of its occurrence still counts on the analysis of complex-linear eigenvalue, which may underpredict the number of unstable vibration modes. The structure also is found to seem to generate squeal noise randomly. In this paper, nonlinear analysis of a squeal noise is investigated. The study is conducted numerically by a simple two-degree of freedom model and an experimental observation using a circular and slider plate with a friction contact interface. The friction force is modeled as a function cubic nonlinear contact stiffness and nonlinear negative velocity function of friction coefficient. It is found that mode coupling instability will occur if the normal contact stiffness and friction coefficient exceed the bifurcation point to generate a couple-complex conjugate eigenvalue and eigenvector. However, when the system is stated linearly stable, instability still can appear because of increasing the nonlinear contact stiffness and coefficient of friction. The instability is affected significantly by relative velocity and pressing force. Both parameters dynamically change depending on the vibration response of the structure. Furthermore, it is also found the stick-slip phenomenon interacted with mode coupling instability to generate squeal noise. It contributes to supply energy to increase the response caused by instability of mode coupling.

Effect of high-frequency excitation on friction induced vibration caused by the combined action of velocity-weakening and mode-coupling

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.

A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

This paper presents a new metamodel approach based on nonstationary kriging and a support vector machine to efficiently predict the stochastic eigenvalue of brake systems. One of the difficulties in the mode-coupling instability induced by friction is that stochastic eigenvalues represent heterogeneous behavior due to the bifurcation phenomenon. Therefore, the stationarity assumption in kriging, where the response is correlated over the entire random input space, may not remain valid. In this paper, to address this issue, Gibb’s nonstationary kernel with step-wise hyperparameters was adopted to reflect the heterogeneity of the stochastic eigenvalues. In predicting the response for unsampled input, the support vector machine-based classification is utilized. To validate the performance, a simplified finite element model of the brake system is considered. Under various types of uncertainties, including different friction coefficients and material properties, stochastic eigenvalue problems are investigated. Through numerical studies, it is seen that the proposed method improves accuracy and robustness compared to conventional stationary kriging.