In order to break the bottleneck of the integer-order transfer function in vehicle ISD (inerter-spring-damper) suspension design, a positive real synthesis design method of vehicle mechatronic ISD suspension based on the fractional-order biquadratic transfer function is proposed. The emergence of the fractional-order components disrupts the equivalence relationship between the passivity of components and the positive realness of integer-order transfer functions in traditional networks. In this paper, the positive real condition of the fractional-order biquadratic transfer function is given. Then, a quarter dynamic model of the vehicle mechatronic ISD suspension is established, and the parameters of the fractional-order biquadratic transfer function and vehicle suspension are obtained by an NSGA-II multi-objective genetic algorithm. Moreover, the structure of the external circuit and the parameters of the electrical components are obtained by the fractional-order passive network synthesis theory. The simulation results show that under the condition of random road input and vehicle speed of 20 m/s, the root-mean-square (RMS) value of the vehicle body acceleration and the dynamic tire load of the fractional-order ISD suspension are reduced by 7.98% and 18.75% compared with the traditional passive suspension, while under the same condition, the integer-order ISD suspension can only reduce by 5.34% and 16.07%, respectively. The results show that employing a fractional-order biquadratic electrical network in the vehicle mechatronic ISD suspension enhances vibration isolation performance compared with the suspension using an integer-order biquadratic electrical network.

An ideal inerter has been applied to various vibration engineering fields because of its superior vibration isolation performance. This paper proposes a new type of fluid inerter and analyzes the nonlinearities including friction and nonlinear damping force caused by the viscosity of fluid. The nonlinear model of fluid inerter is demonstrated by the experiments analysis. Furthermore, the full-car dynamic model involving the nonlinear fluid inerter is established. It has been detected that the performance of the vehicle suspension may be influenced by the nonlinearities of inerter. So, parameters of the suspension system including the spring stiffness and the damping coefficient are optimized by means of QGA (quantum genetic algorithm), which combines the genetic algorithm and quantum computing. Results indicate that, compared with the original nonlinear suspension system, the RMS (root-mean-square) of vertical body acceleration of optimized suspension has decreased by 9.0%, the RMS of pitch angular acceleration has decreased by 19.9%, and the RMS of roll angular acceleration has decreased by 9.6%.

As a two-terminal mechanical element, the inerter has been successfully deployed in various mechanical systems, such as automotives, multi-story buildings, and motorcycles. The introduction of the inerter allows the use of network synthesis to design a passive mechanical network, and can potentially facilitate the identification of practical and high performance mechatronic vibration absorbers. This paper provides an approach for optimal design of both the mechanical and the electrical parts for an inerter-based mechatronic device in vehicle suspension. The system considered includes a mechanical ball-screw inerter alongside an electric motor that is not driven but instead used passively with an electrical load applied across the terminals. The trade-offs in designing the ball-screw inerter and the permanent magnet electric machinery is discussed in detail. Two factors, namely, the coil resistance and the inductor resistance, are taken into account in the performance evaluation. Results show that the improvements in the road holding performance can reach 9.24% for the ideal suspension system with no diverse effect on the ride comfort and suspension travel performance, while a 5.77% improvement can be obtained when the effects of the coil resistance and the inductor are included.

To explore an innovative approach for enhancing the vibration isolation performance of vehicle air suspension systems, this study introduces the inerter element into the vehicle air suspension and investigates the dynamic behavior of the semi-active vehicle air ISD (inerter-spring-damper) suspension. Initially, a dynamic model of the quarter semi-active vehicle air ISD suspension is established, followed by conducting multi-objective optimization of the core parameters using the genetic algorithm. Subsequently, the dynamic performance of the semi-active vehicle air ISD suspension is thoroughly examined through simulations and analyses in both the time and frequency domains. The results demonstrate notable improvements in various aspects: the root-mean-square (RMS) value of the vehicle body acceleration in the semi-active vehicle air ISD suspension is reduced by 12.8%, the RMS value of the suspension working space is decreased by 37.3%, and the RMS value of the dynamic tire load experiences an 8.9% reduction. The findings of this paper indicate that the proposed semi-active vehicle air ISD suspension outperforms both the passive vehicle air suspension and the semi-active vehicle air suspension without an inerter, significantly enhancing the vehicle’s ride comfort, handling stability, and driving safety.