Product development is frequently carried out on a trial-and-error basis. There is also a limitation on the feasibility of the hardware implementation of ideas. A quietness margin for robust design is usually not found experimentally. Analytical or numerical modeling can simulate different structures, material compositions, operational and environmental conditions of brakes. With these methods, noise performance and improvement measures can be examined conceptually before a prototype is made and tested. Theoretical results can also provide guidance to an experimental set-up and help interpret experimental findings. The conventional numerical methods consist of complex eigenvalue analysis in the frequency domain and transient nonlinear analysis in the time domain. The complex eigenvalue analysis may over-predict or under-predict the number of unstable vibration modes and not all predicted unstable vibration modes will result in troublesome noise. These could be attributed to the inherently high sensitivity of the friction-induced vibration problem to the variation or the small changes of parameters, the uncertainty of the structure, materials and friction parameters, and the unforeseen effects of micro-level interface evaluations on friction. Brake components possess a large range of variations in material properties and sizes. The influence of the variations can be seen from measured and simulated frequencies on system and component levels. The variations present great difficulties in validating a numerical model or a physical design. A robust theoretical model taking into consideration the uncertainties due to material and size variations is needed. It is noted that the repeatability of friction tests and brake noise tests is notoriously poor. Brake noise is a largely elusive phenomenon, partly due to the stochastic features of friction and the relevant time varying factors such as interface profile, wear, interface films. The theoretical stochastic models have been developed to address variability and uncertainty in brakes noise. A typical study is reported in an article, which documented a robust design of a disc brake through structural optimization using the complex eigenvalue approach, considering the variation of friction coefficient, major elastic constants and the effect of material worn-off. The evaluation of robustness can be conducted using commercial available software to give varied statistical measures. It explores the sensitivity and uncertainty of predictions from a dynamics modal point of view. A method for efficiently estimating prediction error bounds is presented and validated using representative parametric uncertainties. It is illustrated that physical effects such as contact stiffness, damping and friction laws can to extreme sensitivity.
Last date updated on April, 2024
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