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This paper presents a new FEA approach for brake squeal simulation, the energy flow analysis. It demonstrates that under certain conditions, two system normal modes with equal or close frequencies may start injecting vibration energy into each other, from dynamic friction mechanism. The vibrations, therefore, can “self-grow” (limited cycle), resulting in system instability, such as brake squeal and brake moan. The theoretical conditions for such positive energy flows to occur are discussed. Test examples and application case studies are presented, along with comparison with, and linkage to, complex eigenvalue analysis.

Lining life numerical evaluation is getting increasingly popular. Through numerical simulation, the impacts on lining life due to design changes can be easily evaluated. The numerical approach usually predicts rotor temperature first, and then uses the lining wear versus rotor temperature data derived from physical testing to further assess lining life. Therefore, the success in predicting lining life largely relies on the accuracy of predicted rotor temperature as well as the lining wear versus rotor temperature data incorporated afterwards. In this paper, a 1-D rotor thermal model is presented, which intends to better predict rotor temperature while not dramatically increasing computational time. Furthermore, the inputs that would greatly affect simulation results are discussed. After that, two lining life evaluation examples, which employ the 1-D rotor thermal model, are presented. Finally, the applicability of lining wear versus rotor temperature data is discussed.

Recently the ALCO (Anisotropic Lining elastic Constants Optimization) method for acquiring NAO material elastic constants is introduced by the authors [1]. In this paper, further development and application of ALCO method is discussed. First, two newly incorporated optimization methods are introduced, along with examples of using different optimization methods. The effect of different starting points is then discussed. Finally, a case study is provided to examine whether the elastic constants acquired from one pad assembly are still applicable to other pad and pressure plate shapes (same friction material).

In this paper, a Frequency Response Function (FRF) measurement based ALCO (Anisotropic Lining elastic Constants Optimization) method is introduced. ALCO is an extension of one popular dynamic response based measurement method - the Resonant Ultrasound Spectroscopy (RUS) method. The ALCO method provides a practical alternative to the ultrasonic measurement (e.g. ETEK) for acquiring friction material elastic constants, especially for NAO (Non-Asbestos, Organic) materials. The method requires verifications of pad assembly modal information (frequencies and mode shapes) of all modes between FEA and measurement, under same load condition (free-free). Therefore, it ensures a well correlated NVH simulation model, at least at the component level.

The direct finite element analysis (FEA) approach for disc brake squeal prediction is presented in this paper. A linear model is developed to include the impact of negative μ-v slope on brake systems noise performance. The recently-developed iterative algorithm - ABLE, is used to solve the resulting large-scale complex eigenvalue problems on a PC. Efficiency and effectiveness of the algorithm are discussed. Good correlations are achieved between simulation and measurement, both in squeal frequencies and corresponding unstable modal shapes. Initial study has also validated the conventional wisdom that negative μ-v slope can cause more system instabilities.

This paper expands the oral presentation the authors made at 2000 Brake Colloquium [1], and publishes, for the first time, the key concept and procedures of applying an advanced component mode synthesis method, the MacNeal method, in brake squeal simulations. The effectiveness and the efficiency of the overall approach are demonstrated and verified by direct FEA. In addition to squeal propensities and the unstable complex mode shapes, this paper also investigates different mode participation factors (MPF) - Component MPF and System MPF, and component participation factors (CPF). The paper also introduces Acoustic Component Participation Factors (ACPF). Application case studies are presented to demonstrate the commonalities and differences of those factors.