The radial tire belt is composed of multi-layered fiber-reinforced cords with a very complex structure. Restricted by the computing speed, the simplified finite element (FE) tire model with equivalent belt is usually applied in the vehicle dynamic simulation. However, it is always difficult to obtain the material parameters of the equivalent belt. In this paper, a calculation method of equivalent belt material parameters for the simplified FE tire model is proposed based on the three-dimensional (3-D) anisotropic elasticity of the cord reinforced composites. The simulation results of the static radial stiffness, modal characteristics, and dynamic responses for the simplified FE tire model with parameters obtained by the calculation method were compared with experiment results. The results show that the deviation between the experiment and simulation is acceptable, and the validity of the calculation method is verified.
YangJJacobsGKramerA, et al. Investigation of the tire in-plane vibration property using an improved ring model. J Sound Vib2020; 478: 115350.
2.
BaranowskiPMalachowskiJJaniszewskiJ, et al. Detailed tyre FE modelling with multistage validation for dynamic analysis. Mater Des2016; 96: 68–79.
3.
GuoHBastienCBlundellM, et al. Development of a detailed aircraft tyre finite element model for safety assessment. Mater Des2014; 53: 902–909.
4.
NevesRRMicheliGBAlvesM. An experimental and numerical investigation on tyre impact. Int J Impact Eng2010; 37: 685–693.
5.
ZhangYZhouTYangX, et al. Transient dynamic behavior of tire traversing obstacles in full vehicle scenario. Proc IMechE, Part D: J Automobile Engineering2020; 234(7): 2001–2013.
6.
ChoJRKimKWJeonDH, et al. Transient dynamic response analysis of 3-D patterned tire rolling over cleat. Eur J Mech A Solids2005; 24: 519–531.
7.
BaranowskiPMalachowskiJMazurkiewiczL. Numerical and experimental testing of vehicle tyre under impulse loading conditions. Int J Mech Sci2016; 106: 346–356.
8.
KorunovićNFragassaCMarinkovićD, et al. Performance evaluation of cord material models applied to structural analysis of tires. Compos Struct2019; 224: 111006.
9.
YanjinGGuoqunZGangC. 3-Dimensional non-linear FEM modeling and analysis of steady-rolling of radial tires. J Reinforced Plast Compos2011; 30(3): 229–240.
10.
SladeJEl-GindyMLescoeR, et al. Off-road tire-soil modeling using finite element analysis technique. In: ASME international design engineering technical conferences computers and information in engineering conference, CA, USA, 30 August–2 September 2009, paper no. IDETC/CIE2009, pp.815–829. New York: ASME.
11.
HernandezJAAl-QadiIL. Tire–pavement interaction modelling: hyperelastic tire and elastic pavement. Road Mater Pavement Des2017; 18(5): 1067–1083.
12.
WeiCOlatunbosunOA. Transient dynamic behaviour of finite element tire traversing obstacles with different heights. J Terramechanics2014; 56: 1–16.
13.
PalaniveluSNarasimha RaoKVRamarathnamKK. Determination of rolling tyre modal parameters using finite element techniques and operational modal analysis. Mech Syst Signal Process2015; 64–65: 385–402.
14.
GuoKHQiuEC. Finite element analysis of tire rolling contact based on ring supported on elastic foundation model. J Jilin Univ Eng Technol Ed2011; 41(3): 597–601.
15.
KindtPSasPDesmetW. Development and validation of a three-dimensional ring-based structural tyre model. J Sound Vib2009; 326: 852–869.
16.
BozdogDOlsonWW. An advanced shell theory based tire model. Tire Sci Technol2005; 33(4): 227–238.
17.
ReidaJDBoeschDABielenbergRW. Detailed tire modeling for crash applications. Int J Crashworthiness2007; 12(5): 521–529.
18.
ShiraishiMYoshinagaHNaoakiI, et al. Making FEM tire model and applying it for durability simulation. In: Proceedings of the 6th international LS-DYNA users conference, Detroit, MI, 9–11 April 2000, pp. 221–241. Livermore, CA: Livermore Software Technology Corporation.
19.
HaSZhuLShiQ, et al. Optimization of finite element modeling of tire and simulation of its stiffness characteristics. J Hefei Univ Technol Nat Sci2015; 38(7): 944–948.
20.
ShokouhfarSRakhejaSGindyME. Development of a computationally efficient rolling truck tyre model using part-composite approach and its verification. Int J Veh Syst Model Test2016; 11(2): 142–164.
21.
ShiraishiMIwasakiNSaruwatariT, et al. Developing FE-tire model library for durability and crash simulations. In: Proceedings of the 7th international LS-DYNA users conference, Dearborn, MI, 19–21 May 2002, pp. 1329–1335. Livermore, CA: Livermore Software Technology Corporation.
22.
ZuLWangJLiS. Analysis of multi-layered thick-walled filament-wound hydrogen storage vessels. Int J Hydrogen Energy2014; 39(36): 21083–21096.
23.
ChenYGWuGZ. Effect of belt structure on footprints and braking performance of high speed PCR tire. Tire Ind2011; 31(9): 525–533.
YuQDengJPGuXF, et al. Determination of elastic constants for tire cord/rubber composite. Tire Ind2001; 21(4): 195–200.
26.
XiaMTakayanagiHKemmochiK. Analysis of multi-layered filament-wound composite pipes under internal pressure. Compos Struct2001; 53: 483–491.
27.
BakaiyanHHosseiniHAmeriE. Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations. Compos Struct2009; 88(4): 532–541.
28.
LvXQ. Derivation and applicable conditions of strength calculation formula for pipes and thin walled cylindrical vessels. Process Equip Piping1977; 1: 38–47.
29.
WangCJ. Numerical investigation of hydroplaning characteristics of 3D complex-patterned tire. Master’s Thesis, South China University of Technology, China, 2012.
30.
ZhangLWangSHWangB, et al. Research on equivalent model of TBR tire. J Mech Strength2019; 41(3): 647–652.
31.
QiaoJF. Study on modal parameter tire model. Master’s Thesis, Tsinghua University, China, 2013.
32.
Gonzalez DiazCKindtPMiddelbergJ, et al. Dynamic behaviour of a rolling tyre: Experimental and numerical analyses. J Sound Vib2016; 364: 147–164.
33.
JiangHH. Study on dynamic load characteristics of wheel under the impact of road. Master’s Thesis, Jilin University, China, 2017.
