Transient Squeal Analysis of a Non Steady State Manoeuvre

Brake squeal is one of the main NVH （vibration harshness） challenges in the brake development of passenger cars. The conflict of goals in the development process and the late testability leads to the need of a deeper basic understanding of the squeal phenomenon and definition of design rules. On the other hand, brake squeal is still a very interesting field of research also for the universities because of its combination of different fundamentals, such as friction and stability behaviour of systems with local nonlinearities. Major nonlinearities of the brake system are the joints, especially the contact areas formed by the oscillating brake pad and the caliper. The state-of-the-art calculation method, which still is the ＂complex eigenvalue analysis＂, linearizes these joints, hence, neglecting its nonlinear influence in the stability analysis. Vehicle and bench experiments show that special driving manoeuvres like parking, where the brake pad often leaves the steady state, are likely causing brake squeal. The system in these manoeuvres sometimes behaves opposed to the linearized stability analysis, indicating a limit cycle beyond the Hopf point. Therefore, these states must be investigated more closely. This paper investigates the nonlinear influence of the pad caliper joint in a fixed brake caliper, also called abutment. Bench tests with pressure foils at the abutment of the brake caliper and mode shape analysis were done and a simple FE （finite element） model for a transient simulation is proposed. It is shown that the joint activity varies with driving manoeuvres, leading to different stability behaviours and limiting cycle amplitudes.

Multi-harmonic equivalent modeling for a planar repetitive structure with polynomial-nonlinear joints

How nonlinear joints affect the response of large space structures is an important problem to investigate.In this paper,a multi-harmonic equivalent modeling method is presented to establish a frequency-domain model of planar repetitive structures with nonlinear joints.First,at the local level,the nonlinear joint is modeled by the multi-harmonic describing function matrix.The element of the hybrid beam is obtained by the dynamic condensation of the beam-joint element.Second,at the global level,the displacement-equivalence method is used to model the multi-harmonic Euler continuum beam equivalent to the planar repetitive structure.Then,the pseudo-arc-length continuation method is applied to track the multi-harmonic trajectory of response.Afterwards,an experiment is conducted to validate the correctness of the modeling method,considering the effect of hanging rope and air damping.In the numerical studies,several simulation results indicate the similarity of response between a single-degree-of-freedom system with a single nonlinear joint and the system of the planar repetitive structure with a large number of nonlinear joints.Finally,the component of higher-order harmonics is shown to be important for predicting the resonance frequencies and amplitudes.