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Modelling of disc in brake squeal analysis is complicated because of the rotation of disc and the sliding contact between disc and pads. Many analytical or analytical numerical combined modeling methods have been developed considering the disc brake vibration and squeal as a moving load problem. Yet in the most common used complex eigenvalue analysis method, the moving load nature normally has been ignored. In this paper, a new modelling method for rotating disc from the point of view of modal is presented. First finite element model of stationary disc is built and modal parameters are calculated. Then the dynamic response of rotating disc which is excited and observed at spatial fixed positions is studied. The frequency response function is derived through space and time transformations. The equivalent modal parameter is extracted and expressed as the function of rotation speed and original stationary status modal parameters.

Modelling of disc is crucial in analyzing brake squeal since the disc rotates past the non-rotating pads and the pads are coupled with different areas of the disc at different times. However, in most of the complex eigenvalue analysis of brake squeal, the effect of disc rotation was ignored. This paper proposes a closed-loop coupling model for brake squeal analysis. A modal parameter-based rotating disc model, whose dynamic behavior is represented by rotation speed-dependent equivalent modal parameters, is built through space and time-frequency transformation between reference and moving coordinate systems. The orthogonality of the equivalent modal parameters in state-space is derived. By performing modal synthesis in state-space, the rotating disc is incorporated into brake squeal closed-loop coupling model with other stationary components. Dynamic instability of the system is solved through complex eigenvalue analysis in state-space.

In this paper, analysis methods for brake squeal including substructure modal composition analysis and substructure modal parameters sensitivity analysis are presented. These methods are based on a new closed-loop coupling disc brake model, where the coupled nodal pairs in each coupling interface are connected tightly. This assumption is different from other existing models in literatures, where the interface nodes are coupled through assumed springs. Based on this new model, two analysis methods are derived: Substructure modal composition analysis indicates the contribution of modes of each substructure to the noise mode; Substructure modal parameters sensitivity analysis indicates the sensitivity of the real part of system’s eigenvalue to component’s modal frequency and shape. Finally, the presented analysis methods are applied to analyse a high frequency squeal problem of a squealing disc brake.