To address the contradiction between ride comfort and handling stability, a new vibration-absorbing wheel structure with time-delay feedback control was proposed by applying a time-delay feedback-controlled dynamic vibration absorber to the wheel structure. Using H2 optimization and the particle swarm optimization algorithm (PSO), the design parameters of the time-delay vibration-absorbing wheel structure were obtained with sprung mass acceleration (SMA), suspension deflection (SD) and dynamic tire deflection (DTD) as the optimization objective functions. The stability interval of the system was analyzed using the Routh–Hurwitz criterion and the Sturm criterion. The vehicle vibration reduction performance of the new vibration-absorbing wheel structure was simulated and verified in the time domain under harmonic excitation and random excitation. The simulation results show this new structure can effectively solve the contradiction between the ride comfort and handling stability. It provides a new technical idea for reducing vehicle vibration.

The combination of dynamic vibration absorber and partial state feedback with time-delay is called delayed resonator. In order to suppress the seat vibration caused by uneven road surface and improve ride comfort, the delayed resonator is applied to the seat suspension to realize active control of the seat suspension system. The dynamic model of the half-vehicle suspension system is established, and the time-delay differential equation of the system under external excitation is solved by the precise integration method. The root mean square of the time-domain vibration response of seat displacement, seat acceleration and vehicle acceleration are selected as the objective function. Then, the optimal time-delay control parameters are obtained by particle swarm optimization algorithm. The frequency sweeping method is used to obtain the critical time-delay value and time-delay stable interval of the system. Finally, an active seat suspension model with delayed resonator is established for numerical simulation. The results show that the delayed resonator can greatly suppress the seat vibration response regardless of the road simple harmonic excitation or random excitation. Compared with dynamic vibration absorber, it has a better vibration absorption effect and a wider vibration reduction frequency band.

To reduce seat vibration caused by uneven road surfaces, the time-delay feedback control into the seat suspension system was introduced and an active seat suspension control method based on time-delay feedback was proposed in this paper. A three-degree-of-freedom (3-DOF) suspension model with time-delay feedback control was established. The time-delay independent stability region and critical stability curve of the system were derived using the method of characteristic root and stability switching. The effect of feedback control parameters on system vibration was investigated in the stability region. The seat acceleration (SA), body acceleration (BA), suspension dynamic deflection (SDD), and tire dynamic displacement (TDD) were used as multi-objective optimization functions and the optimal values of feedback control parameters were obtained based on the particle swarm algorithm (PSO) with above optimization functions. The numerical simulation was conducted to validate the proposed model. The simulated results show that the time-delay feedback control can significantly suppress the vibration response of the seat and effectively improve the suspension performance under different road excitation compared with the passive suspension. It can be seen that the active seat suspension with time-delay control significantly improve ride comfort and handling stability of the vehicle, which can be used as a reference for the active control technology of vehicle suspension.

In practical application, the phenomenon of time delay inevitably exists in all kinds of systems. Although the time delay is small, it has a certain influence on the stability and control performance of the control system. In this paper, the rise and development of the time-delay dynamic vibration reduction theory are summarized. Since the time-delay vibration reduction technology was proposed, scholars have conducted a lot of theoretical research, and the research field has expanded from the linear system when it was first proposed to the nonlinear system, and achieved good research results. At present, the main research methods of linear or nonlinear ordinary differential equations with time delay can be divided into time domain method and frequency domain method. The dynamics research of this kind of system mainly focuses on stability analysis, perturbation technology, Holp bifurcation, chaos and so on. The research shows that both linear and nonlinear systems have good application value in vehicle engineering. By selecting reasonable time-delay control parameters, the vehicle body vibration can be greatly suppressed.

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