Air springs play a pivotal role in modern vehicle suspensions by influencing roll stability, ride comfort, and lateral load transfer. Although extensive research has focussed on their vertical stiffness, the torsional characteristics—crucial for cornering dynamics—remain inadequately understood. This study introduces a novel coupled modelling and simulation framework that bridges the material-scale mechanics of reinforced rubber with full-vehicle dynamic responses. A high-fidelity finite element (FE) model of a diaphragm-type air spring is developed, integrating nonlinear hyper elasticity, cord anisotropy, and gas–structure coupling to capture torsional stiffness variations under combined loads. A new analytical torsional stiffness formulation is derived, explicitly linking cord angle to the air spring’s macroscopic stiffness and revealing nonlinear dependencies neglected in previous models. Furthermore, a three-degree-of-freedom (3-DOF) suspension model is implemented in Simulink to quantify the effects of torsional–roll coupling on roll angle and yaw rate during cornering manoeuvres. The results show that decreasing the cord angle from 64° to 44° increases torsional stiffness by 20%–35%, enhancing roll stiffness proportionally and reducing the roll angle and yaw rate by up to 21.9% and 19.7%, respectively. The proposed framework provides a theoretical and computational foundation for optimising air spring geometry and improving vehicle handling, stability, and ride performance.
AtindanaVAXuXNyedebAN, et al. The evolution of vehicle pneumatic vibration isolation: a systematic review. Shock Vib2023; 2023: 1–23. https://doi.org/10.1155/2023/1716615
2.
VanLVTungNT. Application of air suspension system on multi-purpose forest fire fighting vehicle for reducing dynamic load. J Vib Eng Technol2024; 12: 7219–7230. https://doi.org/10.1007/s42417-023-01069-2
3.
WongPKXieZZhaoJ, et al. Analysis of automotive rolling lobe air spring under alternative factors with finite element model. J Mech Sci Technol2014; 28: 5069–5081. https://doi.org/10.1007/s12206-014-1128-9
4.
GaoPGaoQAnC, et al. Analytical modelling for offshore composite rubber hose with spiral stiffeners under internal pressure. J Reinforced Plast Compos2021; 40: 352–364. https://doi.org/10.1177/0731684420962577
5.
HuYZhangJLongJ. Influence of rubber’s viscoelasticity and damping on vertical dynamic stiffness of air spring. Sci Rep2023; 13: 9886. https://doi.org/10.1038/s41598-023-36904-9
HanYDuanJWangS. Benchmark problems of hyper-elasticity analysis in evaluation of FEM. Materials2020; 13: 885. https://doi.org/10.3390/ma13040885
8.
TuDHuangCWChenMQ, et al. ABAQUS-based study of the effect of cord parameters on the vertical stiffness of automotive air springs. Automot Technol2011; 34: 10–13.
9.
LinGYLiuSYXuHB. Finite element analysis and experimental study of automotive air spring based on ABAQUS. Rubber Industry2015; 62: 363–366.
10.
ChunyanKJieXMingkunY, et al. Analysis of static and dynamic characteristics of membrane air springs for small passenger cars. J Braz Soc Mech Sci Eng2024; 46: 682. https://doi.org/10.1007/s40430-024-05244-8
11.
van DijkRvan KeulenFSterkJC. Simulation of closed thin-walled structures partially filled with fluid. Int J Solids Struct2000; 37: 6063–6083. https://doi.org/10.1016/s0020-7683(99)00287-5
12.
QiZLiFYuD. A three-dimensional coupled dynamics model of the air spring of a high-speed electric multiple unit train. Proc Inst Mech Eng F-J Rail Rapid Transit2017; 231: 3–18. https://doi.org/10.1177/0954409715620534
13.
ZhangGShenG. Study on dynamic air spring model with connecting pipe. J China Rail Soc2005; 27: 36.
14.
ZhangMLuoSGaoC, et al. Research on the mechanism of a newly developed levitation frame with mid-set air spring. Veh Syst Dyn2018; 56: 1797–1816. https://doi.org/10.1080/00423114.2018.1435892
15.
LiM. Study on the dynamic characteristic mechanism of air spring system with auxiliary chamber. Doctoral Thesis, Jiangsu University Papers, 2012.
16.
ZhangM. Research on the influence of torsion characteristics of air spring on vehicle dynamic performance. Master’s Thesis. Southwest Jiaotong University, 2017.
WeiDAnCGaoS, et al. Theoretical investigation on ultimate bearing capacity of offshore floating hoses under internal pressure. Mar Struct2025; 104: 103898. https://doi.org/10.1016/j.marstruc.2025.103898
20.
LeeHKimCS. Prediction of ply angles of air springs according to airbag positions and their effects on lateral and torsional stiffness. Appl Sci2022; 12: 11815. https://doi.org/10.3390/app122211815
21.
ChenJJYinZHYuanXJ, et al. A refined stiffness model of rolling lobe air spring with structural parameters and the stiffness characteristics of rubber bellows. Measurement2021; 169: 108355. https://doi.org/10.1016/j.measurement.2020.108355
22.
WuMWangSTongH, et al. Investigation of the nonlinear dynamic stiffness of rolling-lobe air springs considering rubber Payne effect. Rubber Chem Technol2022; 95: 671–688. https://doi.org/10.5254/rct.22.77996
23.
ChenJJYinZHRakhejaS, et al. Theoretical modelling and experimental analysis of the vertical stiffness of a convoluted air spring including the effect of the stiffness of the bellows. Proc Inst Mech Eng D J Automobile Eng2018; 232: 547–561. https://doi.org/10.1177/0954407017704589
24.
JiangRCWangDF. Optimization of vehicle ride comfort and handling stability based on TOPSIS method. SAE Paper 0148-7191, 2015.
25.
ZhangLLiuJPanF, et al. Multi-objective optimization study of vehicle suspension based on minimum time handling and stability. Proc Inst Mech Eng D J Automobile Eng2020; 234: 2355–2363. https://doi.org/10.1177/0954407020909663
NabagłoTJurkiewiczAKowalJ. Modelling verification of an advanced torsional spring for tracked vehicle suspension in 2S1 vehicle model. Eng Struct2021; 229: 111623. https://doi.org/10.1016/j.engstruct.2020.111623
28.
ShenCLuC. A refined torsional-lateral-longitude coupled vehicular driveline model for driveline boom problems. Appl Math Model2021; 90: 1009–1034. https://doi.org/10.1016/j.apm.2020.10.009
29.
DuYFWangGHZhangC, et al. Applicability and temperature dependence of different constitutive models for rubber materials used in seismic isolation bearings at low temperatures. Cailiao Gongcheng-J Mater Eng2025; 53: 192–202. https://doi.org/10.11868/j.issn.1001-4381.2023.000399
30.
ZhouZWangYZhouG, et al. Vehicle lateral dynamics-inspired hybrid model using neural network for parameter identification and error characterization. IEEE Trans Vehicular Technol2024; 73: 16173–16186. https://doi.org/10.1109/tvt.2024.3416317
31.
ZhouZWangYLiuX, et al. Hybrid of neural network and physics-based estimator for vehicle longitudinal dynamics modelling using limited driving data. IEEE Trans Intell Transp Syst2025; 26: 16735–16746. https://doi.org/10.1109/tits.2025.3585346
32.
ChenJYuCWangY, et al. Hybrid modelling for vehicle lateral dynamics via AGRU with a dual-attention mechanism under limited data. Control Eng Pract2024; 151: 106015. https://doi.org/10.1016/j.conengprac.2024.106015
33.
GhaemiHBehdinanKSpenceA. On the development of compressible pseudo-strain energy density function for elastomers. J Mater Process Technol2006; 178: 307–316. https://doi.org/10.1016/j.jmatprotec.2006.04.014
34.
WangZGaoDDengK, et al. Robot base position and spacecraft cabin angle optimization via homogeneous stiffness domain index with nonlinear stiffness characteristics. Robot Comput Manuf2024; 90: 102793. https://doi.org/10.1016/j.rcim.2024.102793
35.
ChengYQHeLShuaiCG, et al. An integrated structure of air spring for ships and its strength characteristics. Sci Eng Compos Mater2023; 30: 0221. https://doi.org/10.1515/secm-2022-0221
36.
ChengYQHeLShuaiCG, et al. Free vibration characteristics of cord-reinforced air spring with winding formation under preload conditions. AIP Adv2023; 13: 035230. https://doi.org/10.1063/5.0137600
37.
ZhangZ. Research on distributed electric drive vehicle yaw stability control method considering time delay. Master’s Thesis, Hanzhou Electronic Science and Technology University, 2025.
