Stability Analysis And Optimization Of Uncertain Automotive Disc Brake Systems

With the increasing requirement of consumers on automobile riding comfort, brake noise problem has become one of the major concerns of automakers and consumers. The researches on suppressing brake noise are of great practical significance. At present, the stability analysis and optimization of brake systems are the most direct and effective approaches to control brake noise. The traditional approaches for reducing brake noise are commonly based on the deterministic techniques, which do not take the effects of uncertainties into consideration. However, uncertainties widely exist in the engineering structures and systems, as well as in the automotive disc brake systems. Due to the effects of wear, manufacturing errors, measuring errors and material aging, the uncertainties associated with automotive brake systems are unavoidable. Under uncertain case, those approaches on the basis of the deterministic parameters may lead to unreliable analysis and designs in practice. Thus, in order to evaluate and control brake noise more effectively, it needs to develop a set of practical approaches on the stability analysis and optimization of uncertain automotive disc brake systems.Supported by National Natural Science Foundation(No. 11572121, 11402083), this dissertation focuses on the stability analysis and optimization of an uncertain automotive disc brake system, and tries to conduct a systematic study on brake noise reduction. In order to evaluate and improve the stability of an uncertain disc brake system effectively, practical approaches based on different types of uncertain analysis models should be developed, as well as the specific procedures of the corresponding approaches. The main works and innovative achievements of this dissertation are listed as follows:(1) Both complex eigenvalue analysis and dynamic transient analysis are employed to predict the system stability of an automotive disc brake system. The computational efficience and prediction ability of the two methodologies are investigated and comparised. The investigation results show that complex eigenvalue analysis is very efficient but conservative on the prediction of disc brake system unstable frequencies, when compared to the transient analysis.(2) The stability analysis and optimization of disc brake systems is quite inefficient, while the analysis and optimization are based on detail finite element(FE) model. Aimed at this problem, in conjunction with Latin hypercube method, response surface methodology(RSM) and complex eigenvalue analysis, the surrogate models of the real part, imaginary part and damping ratio of the domain unstable eigenvalue of the brake system are constructed. After the surrogate models are established, their significance and fitting accuracy are tested by F hypothesis testing, the multiple correlation coefficient and the modified multiple correlation coefficient, based on the analysis of variance(ANOVA). The testing results show that the surrogate models have fairly high significant levels and fairly great values of multiple correlation coefficients/modified multiple correlation coefficients. Thus, the surrogate models can be used for the further researches.(3) For the case that the precise distributions of the uncertain parameters can be constructed with sufficient information, a practical approach is proposed for the stability analysis of the disc brake system based on random model. By introducing the proposed approach for the stability analysis and improvement of a disc brake system with random uncertainties, the results demonstrate that the proposed approach is an effective way to obtain the probability distribution information(such as the means, the variances, the coefficients of variation and the confidence intervals, and so on) of the real part, imaginary part and damping ratio of the domain unstable eigenvalue. Based on the obtained information, the stability of the random disc brake system can be assessed and improved effectively.(4) For the case that the precise distributions of the uncertain parameters cannot be constructed due to limited information, practical approaches for the stability analysis of disc brake system with non-probabilistic uncertainties are proposed. In the proposed approaches, three different types of non-probabilistic models, including the interval, the fuzzy and the evidence theory models, are employed to represent the uncertainties of system parameters with limited data. For the case that only the lower and upper bounds of the uncertain parameters can be obtained, an approach for the stability analysis and improvement of the disc brake system based on interval model is proposed; for the case that fuzziness widely exists in the disc brake system, an approach for the stability analysis and improvement of the disc brake system based on fuzzy modle is proposed; for the case that the parameters information of a disc brake system is incomplete or even conflicting, an approach for the stability analysis and improvement of the disc brake system based on evidence theory is proposed. The results of numerical examples indicate that these proposed approaches can effectively analyze and improve the stability of the disc brake system under non-probabilistic uncertainties.(5) For the case that the uncertain parameters of disc brake systems with and without sufficient information may exist simultaneously, or that the key parameters in the distribution functions of the uncertain parameters cannot be determined due to limited data, practical approaches for the stability analysis of the disc brake system with hybrid uncertainties are proposed. In the proposed approaches, the random and interval hybrid model and the interval random hybrid model are employed to deal with the above-mentioned uncertain cases, respectively. Firstly, the uncertain parameters of the disc brake system are treated as random and interval hybrid variables, or interval random variables. Secondly, the reliability analysis is introduced into the stability analysis of the disc brake system, and two stability analysis models with the previous two type of hybrid uncertainties are developed, respectively; Finally, the reliability of the damping ratio of domain unstable eigenvalue meeting the design requirements can be calculated by the reliability analysis models, and the calculated results can be used for the stability assessment and improvement of the disc brake system with hybrid uncertainties. The results of numerical examples demonstrate that the proposed approaches can effectively analyze and improve the stability of a disc brake system under hybrid uncertainties.(6) For the case that the random uncertainties and interval uncertainties exist in a disc brake system simultaneously, practical approaches for the stability optimization of the disc brake system with hybrid uncertainties are proposed. Firstly, two types of reliability-based design optimization(RBDO) models are developed to explore the optimal designs of the disc brake system with hybrid uncertainties for squeal reduction. In the two types of RBDO models, the upper bound of the confidence interval of the damping ratio of domain unstable eigenvalue is taken as the optimization objective for the disc brake system with random and interval variables, and the upper bound of the mean value of the damping ratio of domain unstable eigenvalue are taken as the optimization objective for the the disc brake system with interval random variables. Secondly, the detailed optimization procedures of the two types of RBDO models are presented. Finally, the proposed two types of RBDO models are applied to the stability optimization of the disc brake system under random and interval uncertainties and interval random uncertainties, respectively. The results of numerical examples demonstrate the effectiveness of the proposed approaches on optimizing and reducing brake noise of a disc brake system with hybrid uncertainties.For brake noise suppression, this dissertation conducts a systematic research on the stability analysis and optimization of an uncertain disc brake system. For the different uncertain cases of system parameters, the corresponding practical approaches and their specific procedures are proposed. In actual engineering, which one of these approaches selected to deal with brake noise problem, is mainly depended on the obtained information of the uncertain system parameters. The research ideas and proposed approaches of this dissertation have a good potential guidance and application in the engineering field of brake noise control.