Simulation processes used in the brake industry for simulating the high-frequency noise events (“squeals”) are in a standard way based on Complex Eigenvalue Analysis (CEA). CEA is a well-known technic which allows to identify brake systems’ unstable modes through the calculation of the real part of their complex eigenvalues, with positive real parts (“negative damping”) indicating unstable modes. Unstable modes correspond to self-excited vibrations which can lead to squeal. However, making assessments regarding the potential criticality in reality of those calculated unstable modes is often difficult, as there is no direct relationship between the value of the real part of one specific unstable mode and the final amplitude reached by the corresponding self-excited vibration. The reason is that those “limit-cycles” are determined by nonlinear phenomena arising in brake systems, and these nonlinear phenomena cannot be taken into account by classical CEA, which is by nature a linear analysis. Moreover, although originally the squeal phenomena are vibrations, they are perceived by drivers and passengers as noises, and CEA gives of course no hindsight regarding the sound level reached by unstable modes, which however would be the most important information. In order to overcome the limitations of the current standard squeal simulation processes, Hitachi Astemo has developed two other types of analyses, which are run just after the CEA and which seamlessly integrate into the existing squeal simulation process. The first type of analysis is so-called Energy Balance Analysis (EBA) and is based on the calculation of the amount of energy “created” and dissipated at the various brake system’ inner contact interfaces : initially, by nature of unstable modes, some energy will be “created” within the brake system because of friction forces at disc-lining interfaces, leading to a self-excited and exponentially rising vibration. But soon, due to nonlinear mechanisms in the brake system, and especially friction forces at the other contact interfaces, a state of equilibrium is reached between the energy “created” and the energy dissipated, leading to a stable “limit-cycle” whose amplitude can be estimated. Then, considering the mode shape of the now stabilized mode, the Equivalent Radiated Power (ERP) for this mode is calculated. ERP is an approximation of the actual acoustic power radiated by the mode, and thus is a valuable output to calculate. The second type of analysis introduced into the Hitachi Astemo’s squeal simulation process is the explicit calculation of the acoustic power radiated by each stabilized mode calculated by EBA. In addition to the brake system’s FE model used for CEA and EBA, it requires to build an acoustic mesh of the air volume surrounding the brake system. This calculation allows to identify the actual critical unstable modes (the potentially noisiest ones) and to make comparison with real-life squeal evaluation tests which measure for each squeal event the Sound Pressure Level of this squeal, which is not possible with classical CEA. The presentation gives details regarding these less common features of the Hitachi Astemo’s squeal simulation processes. Several real study cases are shown, encompassing a wide variety of brakes. ERP results are compared with explicitly-calculated acoustic power results, in order to assess if acoustic radiation analysis is mandatory in the process or if it can be approximated with ERP. Comparisons of simulation results with tests results are done, in order to evaluate the current accuracy of the process.

Mr. Rémi Lemaire, Simulation Development Manager, Hitachi Astemo