Abstract
In the research into the mechanism of brake squeal, minimal models with two degrees of freedom (DoFs) are widely used. Compared with the finite element method, the minimal model is more concise and efficient, making it easier to analyze the effect of parameters. However, how to accurately determine its kinetic parameters is rarely reported in the literature. In this paper, firstly, the finite element model of a disc brake is established and the complex eigenvalue analysis (CEA) is carried out to obtain unstable modes of the brake. Then, an unstable mode with seven nodal diameters predicted by CEA is taken as an example to establish the 2-DoF model. In order that the natural frequency, Hopf bifurcation point and real parts of eigenvalues of the minimal model coincide with that of the unstable mode with seven nodal diameters, the response surface method (RSM) is applied to determine the kinetic parameters of the minimal model. Finally, the parameter-optimized minimal model is achieved. Furthermore, the negative slope of friction-velocity characteristic is introduced into the model, and transient analysis (TA) is used to study the effect of braking velocity on stability of the brake system. The results show that the brake system becomes unstable when braking velocity is lower than a critical value. The lower the velocity is, the worse the stability appears, and the higher the brake squeal propensity is.
Highlights
Squeal noise of brake system is one of the difficult problems that need to be solved by automobile manufacturers
The results show that the brake system becomes unstable when braking velocity is lower than a critical value
A large number of literatures use a minimal model to study the mechanism of brake squeal, but an accurate determination method of parameters in minimal models is rarely found
Summary
Squeal noise of brake system is one of the difficult problems that need to be solved by automobile manufacturers. It is generally believed that the disc brake squeal is self-excited vibrations induced by friction forces. For the mechanisms of self-excited vibrations, the existing literatures proposed a different hypothesis. The first type of literaturesholds that the variation characteristics of the friction coefficient lead to squeal instability, including mechanisms like stick-slip [1,2,3] and negative friction-velocity relationship [4,5]. The stick-slip mechanism is not sufficient to explain the occurrence of the squeal [6]. As pointed out by Ouyang et al [5], stick-slip occurs only at low speeds of a mass driven across a dry surface, while at a sufficiently high speed the mass will be permanently sliding
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