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Brake squeal is a complex dynamics instability issue for automobile industry. Closed-loop coupling model deals with brake squeal from a perspective of structural instability. Friction characteristics between pads and disc rotor play important roles. In this paper, a closed-loop coupling model which incorporates negative friction-velocity slope is presented. Different from other existing models where the interface nodes are coupled through assumed springs, they are connected directly in the presented model. Negative friction slope is taken into account. Relationship between nodes’ frictional forces, relative speeds and brake pressure under equilibrant sliding and vibrating states is analysed. Then repeated nodal coordinate elimination and substructures’ modal coordinate space transformation of system dynamic equation are performed. It shows that the negative friction slope leads to negative damping items in dynamic equation of system.

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.

The study of mechanical properties special in the characteristics of elastic element is a challenging task for vehicle industry. Since torsion bar spring acts as an important part of elastic element, and improves performance of torsion bar spring is of great concern. The effects of the torsion bar spring pre-setting precision on the presetting performance are presented. Based on elastic-plastic theories, the algebraic model of torsion bar spring is established to analyze the stress, torque and residual stress under the yield and plastic conditions in pre-setting process. Then, the stress and strain states of various torsion bar springs in different conditions are simulated using the validated finite element model in ABAQUS software. The simulation results show the effects of torsion error on the pre-setting performance are less than 5% in the pre-setting process.

Closed-loop coupling model, based on complex eigenvalue analysis, is one of the most popular and effective methods for brake squeal analysis. In the model, imaginary coupling springs are used to represent the normal contacting force between coupled nodes. Unfortunately, the physical meaning of these coupling springs was seldom discussed and there’s no systematic method to determine the value of spring stiffness. Realizing this problem, this paper, based on finite element model and modal synthesis technique, develops a new closed-loop coupling disc brake squeal model without introducing imaginary coupling springs. Different from the traditional model where two nodes at coupling interface are connected through a spring, these node-pairs in the new model are assumed to remain in tight contact during vibration. Details of the model, including force analysis, coordinate reduction and transformation and complex eigenvalue decomposition are given in this paper.

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.

The study and prevention of unstable vibration is a challenging task for vehicle industry. Improving predicting accuracy of braking squeal model is of great concern. Closed-loop coupling disc brake model is widely used in complex eigenvalue analysis and further analysis. The coupling stiffness of disc rotor and pads is one of the most important parameters in the model. But in most studies the stiffness is calculated by simple static force-deformation simulation. In this paper, a closed-loop coupling disc brake model is built. Initial values of coupling stiffness are estimated from static calculation. Experiment modal analysis of stationary disc brake system with brake line pressure and brake torques applied is conducted. Then an optimization process is initiated to minimize the differences between modal frequencies predicted by the stationary model and those from test. Thus model parameters more close to reality are found.