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The electromagnetic regenerative suspension has attracted much attention recently due to its potential to improve ride comfort and handling stability, at the same time recover kinetic energy which is typically dissipated in traditional shock absorbers. The key components of a ball-screw regenerative suspension system are a motor, a ball screw and a nut. For this kind of regenerative suspension, its damping character is determined by the motor's torque-speed capacity, which is different from the damping character of the traditional shock absorber. Therefore, it is necessary to establish a systematic approach for the parameter matching of ball-screw regenerative suspension, so that the damping character provided by it can ensure ride comfort and handling stability. In this paper, a 2-DOF quarter vehicle simulation model with regenerative suspension is constructed. The effects of the inertia force on ride comfort and handling stability are analyzed.

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.

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.

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.

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.