Study on Repeated-Root Modes in Substructure Modal Composition Analysis

The dynamic properties of disc rotor play important role in the NVH performance of a disc brake system. Disc rotor in general is a centrosymmetric structure. It has many repeated-root modes within the interested frequency range and they may have significant influence on squeal occurrence. A pair of repeated-root modes is in nature one vibration mode. However, in current complex eigenvalue analysis model and relevant analysis methods, repeated-root modes are processed separately. This may lead to contradictory result. This paper presents methods to deal with repeated-root modes in substructure modal composition (SMC) analysis to avoid the contradiction. Through curve-fitting technique, the modal shape coefficients of repeated-root modes are expressed in an identical formula. This formula is used in SMC analysis to obtain an integrated SMC value to represent the total influence of two repeated-root modes. Finally the presented method is applied to analysis a high frequency squeal problem of a disc brake. SMC analysis results are given, where each pair of repeated-roots have one unique SMC. The impacts of these modes on squeal can be clearly examined.