Abstract
Several papers have proved that complex eigenvalue analysis (CEA) is an useful to simulate squeal noise. However, it does not directly give informations how to suppress the instability modes. How to improve the design varies depending on engineering knowledge, past experiences and etc. The authors had proposed systematic procedure called modal map approach to reduce instabilities by increasing the gap between frequencies of coupled system modes in the previous study. Generalized coordinates, modal participation factors to system and modal participation factors to component were used. These analyses gave information on contributing modes of the most contributing component in free-free condition. The frequency of a component mode was changed to separate the distance between system modes by changing designs. Although the modal map approach gave the information on the components and the modes to be modified, it still needs a lot of iterations to find the designs for suppressing multiple instabilities. And some modified designs did not reduce the instability at all. This behavior is supposed to be caused by the discrepancies between the system modes and the component modes. Now, a new CAE procedure for reducing squeal instability based on the mass-stiffness relation is proposed in this study. It covers a fundamentally weak point of the modal map approach by handling system modes directly. The mass-stiffness relation was used on the system mode level to describe the effect of a design change on the instabilities. This principle explains the change of system modes that the modal map approach fails to explain. The proposed procedure was applied to a brake squeal model with four instability frequencies. How the mass-stiffness relation worked could be explained on the instability respectively. By mixing and compromising effective designs for each frequency, new housing and bracket derived. The modified design derived from the new procedure made two instabilities vanished and reduced the real part of the eigenvalue of the other two more than 50%. The proposed procedure does not yield perfect countermeasures in one step nor predict all the side effect of a design change. However, it gave a clear explanation of how an instability was affected by a design modification which could save times for design iterations by guiding which design change would be desirable.
KEYWORDS – Brake Squeal, Complex Eigenvalue Analysis, Multiple Instabilities, Mass-Stiffness Relation, Modal Map Approach