Abstract
This paper deals with the evaluation of eigenvalues of a linear damped elastic two-degrees-of-freedom system under a non- onservative loading. As a physical interpretation of a proposed mathematical model, a simplified disk brake model is considered. A spectral analysis is performed to predict an eigenvalues bifurcation, known as the Krein collision, leading to double eigenvalues, one of them having a positive real part causing a vibration instability of the mechanical systems. This defective behaviour of eigenvalues is studied with respect to a magnitude of non-conservative Coulomb friction force, through the variation of the friction coefficient. The influence of a proportional versus general damping on the system stability is further analysed. The generalized non-symmetric eigenvalue problem calculation is employed for spectral analyses, while a modal decomposition is performed to obtain a time-domain response of the system. The analyses are compared with an experiment.
Highlights
Brake systems represent one of the most important safety and performance components of vehicles, such as cars, trains, airplanes or industrial machines
In 1952, Ziegler [2], studying a double mathematical pendulum exposed to the non-conservative force, found that the limits of the system stability were reduced by an application of minor damping to the system
This effects can be measured both using accelerometer sensors attached to the flexible structure and a microphone, which directly measures the sound pressure as a side effect of an extensive vibration of the system
Summary
Brake systems represent one of the most important safety and performance components of vehicles, such as cars, trains, airplanes or industrial machines. The non-conservative friction force plays a major role For this reason, the disc brake system is considered as the system with a potential occurrence of the damping destabilization paradox. Analytical and FE studies are mainly based on the complex Eigenvalue Analysis [7] to predict the mode coupling These analyses subsequently allow an optimization of brake systems to avoid a potential brake squeal occurrence. In the process of disc brake development, the complex eigenvalue analysis of finite element model is usually used to perform the modal optimization of the system to reduce any potential system instability [8] In this process, no damping or simple proportional damping is usually considered. Observations are experimentally verified by measurements on an experimental pad-on-disc system
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