The inerter is a device that produces a force proportional to the relative acceleration of both inerter terminals. When combined with springs and dampers in a vehicle suspension system, it forms an inerter–spring–damper (ISD) suspension. This structure shows significant advantages in improving vehicle ride comfort and road friendliness. This paper systematically reviews research progress on ISD suspension. First, the working principle and structural types of the inerter are introduced. Then, an overview of the breakdown phenomena and nonlinear characteristics of ISD suspension is provided, followed by a systematic analysis of ISD suspension structure designs. Next, the control strategies for ISD suspension are discussed, along with their applications in the automotive field. Finally, the paper outlines the main challenges in current inerter research and explores its potential applications in vehicle suspensions. This work can provide a reference for the development of inerter and ISD suspension technologies.

This study optimizes vehicle suspension dynamics by introducing a controllable degree of nonlinearity, characterized by a parameter ε, into the spring element of Inerter-Spring-Damper (ISD) systems. Quarter-vehicle models for parallel and series ISD configurations are established, and a multi-objective genetic algorithm optimizes the parameters under random road excitation to minimize body acceleration (BA), suspension working space (SWS), and dynamic tire load (DTL). Results demonstrate that optimizing ε brings advantages: compared to a conventional passive suspension, the optimized parallel ISD suspension reduces BA, SWS, and DTL by 7.98%, 8.57%, and 1.69%, respectively, with the BA reduction notably improving from 5.94% (achieved by the linear ISD with ε = 0) to 7.98%. Similarly, the optimized series ISD achieves reductions of 2.53%, 7.62%, and 6.42% in BA, SWS, and DTL, showing a more balanced enhancement over its linear counterpart. The analysis reveals how ε distinctly influences the performance trade-offs, validating that strategically tuning the spring nonlinearity degree, in synergy with the inerter and damper, provides an effective method for superior suspension performance customization.

This paper proposes a dynamic modeling method for heavy dump trucks during lifting operations on sloped terrains. Traditional linear models are limited in capturing system nonlinearities and external disturbances, which are addressed in the proposed approach. Both the rear-dump truck and the side-dump truck are selected as the research objects. A theoretical dynamic model is first established using the Lagrange method, considering the roll motion of the sprung mass and the cargo system as well as the cargo sliding behavior. Subsequently, a multi-body dynamics model is developed, incorporating suspension springs and cargo box torsional stiffness to describe the rigid-flexible coupling characteristics of the vehicle. The discrete element method is employed to calibrate particle contact parameters for different types of cargo, enabling accurate modeling of the unloading process. A co-simulation model under sloped conditions is then established and validated against the theoretical model. Finally, a comparative analysis is conducted under rear-discharge and side-discharge modes. The analysis focuses on centroid height, roll angle, cargo mass, and moment of inertia. The results reveal the influence mechanism of discharge modes on system stability.

In order to prevent the rollover risk of four-axle heavy dump trucks during lifting and unloading, encountering significant road cross slope angle or uneven load distribution, a comprehensive dynamics model for the lifting and unloading on the slope was established. This model consisted of the roll dynamics model, the electrohydraulic servo actuator model, the lifting kinematics model, and the cargo sliding kinematics model. A rollover evaluation index of the energy method was proposed to assess the rollover risk during lifting and unloading. The correctness of the model and the feasibility of the energy method were verified through MATLAB/Simulink simulations. Then, a hierarchical anti-rollover control strategy was designed, and a backstepping sliding mode controller based on the snow ablation optimizer was employed as the upper-level controller to generate the desired force for active suspension actuators, while the proportional integral control served as a bottom controller to track the desired force accurately. The simulation results show that, compared to the no control and backstepping sliding mode control, the roll angles of cargo and cargo box were reduced by 23.70% and 2.28% under a significant road cross slope angle condition, and reduced by 22.74% and 0.19% under a large uneven load distribution condition. The designed control strategy is more effective in preventing the risk of rollover.