Application Limits of the Complex Eigenvalue Analysis for Low-Frequency Vibrations of Disk Brake Systems

Complex Eigenvalue Analysis (CEA) is widely established as a mid- to high-frequency squeal simulation tool for automobile brake development. As low-frequency phenomena like creep groan or moan become increasingly important and appropriate time-domain methods are presently immature and expensive, some related questions arise: Is it reasonable to apply a CEA method for low-frequency brake vibrations? Which conditions in general have to be fulfilled to evaluate a disk brake system’s noise, vibration and harshness (NVH) behavior by the use of CEA simulation methods? Therefore, a breakdown of the mathematical CEA basis is performed and its linear, quasi-static approach is analyzed. The mode coupling type of instability, a common explanation model for squeal, is compared with the expected real world behavior of creep groan and moan phenomena. Problems of the CEA regarding the context of stick-slip vibrations, non-linear stiffness and local damping behavior of elastomer bushings and joints are discussed. Their importance for low-frequency phenomena and evolving oscillation limit cycles is evaluated, leading to the statement of an application limit for disk brake related CEA usage in Finite Element (FE) environments. Especially the linearization of frictional forces in the brake disk/pad contact is identified as an important limitation. A FE-model of a vehicle’s front corner was used for low-frequency CEA simulations and parameter studies. Experiments with a corresponding setup have been performed on a drum-driven suspension and brake test rig in order to evaluate theoretical considerations as well as vibration characteristics of creep groan and moan. Both the simulative and experimental investigations show the importance of modelling parameters, linearization methods and physical limitations for the application of CEA methods on low-frequency vibration analyses of disk brake systems.