3-Dimensional non-linear FEM modeling and analysis of steady-rolling of radial tires

Abstract

The 3D finite element method modeling based on MSC.MARC software was studied and a non-linear FEM model was developed. The non-linear mechanical properties of elastomers were described by the Mooney—Rivlin model. The rebar model was employed to simulate complex multilayer rubber—cord composites and directly define the cord directions varying with their positions. The radial tire model was established based on consideration of the geometric non-linearity due to large deformation, the material’s non-linearities of cord—rubber composites, the non-linear boundary conditions from tire—rim contact and tire—road contact. The steady-rolling performance of 195/60R14 radial tire was analyzed numerically. Under free-rolling state, centrifugal force had a certain effect on the contact performance of the radial tire. Under load rating, the stiffness of tire increased with the increase of the rotary speed. Under braking state, high stress region moves to the direction contrary to the running direction. The high stress region moves to the running direction under driving state. Compared with braking condition, the level of normal stress and friction stress in the contact region was higher under the driving conditions. Cord equivalent stress of the tire belt was larger near the tire shoulder, and smaller in the center of contact zone. Cord equivalent stress increased sharply with the rotary speed. Meanwhile, the maximum cord equivalent stress was higher under the driving state. The gradient of strain energy density near the belt end was larger. The strain energy density of the tire shoulder was the largest.

Finite element analysis of a tire using an equivalent cord model

“…This characteristic cannot be reproduced when beam elements are used to represent cords. In other studies [2,3,6,7,8,10,11,12,[20][21][22][23][24][25], rebar elements were used to represent the cords in belts. However, rebar elements cannot duplicate the bending behavior of cords either because rebar elements are used to define uniaxial reinforcement.…”

“…Modeling the belt behavior is also necessary when studying tire structure [1,5], the interaction between the tire and ground [7][8][9][10][11][12], the temperature distribution in the tire [1,9], and the effect of blast waves [13]. Because the cords and rubber that make up the belt have very different Young's moduli, and because anisotropy occurs due to the angles of the cords, constructing a constitutive equation for the belt is difficult.…”

“…When belts are modeled using finite element analysis (FEA), the physical properties of the rubber and cords are combined to yield the resulting physical behavior of the belts [1,5,9,18,19], the internal cords are modeled using beam elements [13] or using rebar elements [2,3,6,7,8,10,11,12,[20][21][22][23][24][25]. Studies that have modeled belts based on a single physical behavior have defined the behavior using isotropic elasticity [1], hyperelasticity [5], the Halpin-Tsai composite equation [9], or theoretically derived belt constitutive equations [18,19].…”

Guidelines for the design of tyre sensor housings

“…The mesh is more refined in the contact zone to improve the computation accuracy. The same procedure has been used to generate a 3D mesh by Yangjin et al in [23], while rebar elements have used to simulate the reinforcing cord.…”

“…Rubber can be defined as a hyper-elastic material by means of a strain-energy density function that can be determined by fitting experimental data. In the FEM modelling of tyre, as was reported by Yangjin et al [23], rubber is usually considered as an isotropic hyper-elastic material, in terms of a proper strainenergy density function, using a simplified form of the Rivlin model, like the Neo-Hookean or Mooney-Rivlin.…”