Uncertainty quantification of squeal instability via surrogate modelling

• Squeal noise of a real disc brake is studied using complex eigenvalue analysis.
• A realistic detailed finite element model is used.
• Uncertainty in the several most influential parameters is examined.
• A Kriging predictor for the full finite element model of the brake is constructed.
• The established surrogate model can be used for reliability analysis to predict the likelihood of squeal noise.

One of the major issues that car manufacturers are facing is the noise and vibration of brake systems. Of the different sorts of noise and vibration, which a brake system may generate, squeal as an irritating high-frequency noise costs the manufacturers significantly. Despite considerable research that has been conducted on brake squeal, the root cause of squeal is still not fully understood. The most common assumption, however, is mode-coupling.Complex eigenvalue analysis is the most widely used approach to the analysis of brake squeal problems. One of the major drawbacks of this technique, nevertheless, is that the effects of variability and uncertainty are not included in the results. Apparently, uncertainty and variability are two inseparable parts of any brake system. Uncertainty is mainly caused by friction, contact, wear and thermal effects while variability mostly stems from the manufacturing process, material properties and component geometries. Evaluating the effects of uncertainty and variability in the complex eigenvalue analysis improves the predictability of noise propensity and helps produce a more robust design.The biggest hurdle in the uncertainty analysis of brake systems is the computational cost and time. Most uncertainty analysis techniques rely on the results of many deterministic analyses. A full finite element model of a brake system typically consists of millions of degrees-of-freedom and many load cases. Running time of such models is so long that automotive industry is reluctant to do many deterministic analyses. This paper, instead, proposes an efficient method of uncertainty propagation via surrogate modelling. A surrogate model of a brake system is constructed in order to reproduce the outputs of the large-scale finite element model and overcome the issue of computational workloads. The probability distribution of the real part of an unstable mode can then be obtained by using the surrogate model with a massive saving of computational time and cost. The established model can be used subsequently for design, reliability analysis and optimisation.