Editorial Type:
Article Category: Research Article
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Online Publication Date: 02 Oct 2018

Finite Element Based Analysis of Reinforcing Cords in Rolling Tires: Influence of Mechanical and Thermal Cord Properties on Tire Response

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Page Range: 294 – 327
DOI: 10.2346/tire.18.4604010
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ABSTRACT

Tires of passenger cars and other special tires are made of rubber compounds and reinforcing cords of different type to form a composite with distinct mechanical and thermal properties. One of the major load cases is the steady state rolling operation during the tire's service.

In this contribution, attention is paid to the strain and force state as well as the temperature distribution in the carcass cord layer of a steady state rolling tire. A simple benchmark tire geometry is considered, which is made of one rubber compound, one carcass cord layer (textile), and two belt cord layers (steel). From the given geometry, two tire designs are derived by using two distinct types of reinforcing cords (polyester and rayon) for the carcass cord layer. Subsequently, the two tire designs are subjected to three load cases with different inner pressure, vertical force, and translational velocity. The strain and the force state as well as the temperature distribution in the cords are computed via a thermomechanically coupled finite element simulation approach for each tire design and load case. To realistically capture the thermomechanical behavior of the cords, a temperature- and deformation-dependent nonlinear elastic cord model is proposed. The cord model parameters can be directly derived from data of cord tensile tests at different temperatures. Finally, cord design parameters (minimum and maximum strains and forces in the cords, maximum strain and force range per cycle, and maximum cord temperature) are summarized and compared. Additionally, the global vertical stiffness and the rolling resistance for each tire design are addressed.

Keywords: reinforcing cords; tire; thermal-mechanical properties; finite element method; steady state rolling; cord strain; cord force; cord temperature; rolling resistance
FIG. 1
FIG. 1

Large principal stretches of a cord: (a) undeformed configuration; (b) deformed configuration.

FIG. 2
FIG. 2

Force-strain relation for cord model with distinct tension-compression behavior.

FIG. 3
FIG. 3

Overview on the thermomechanical tire simulation approach for steady state rolling tires [15] (tire temperature in circumferential direction is constant, i.e., 3D tire model with axisymmetric temperature profile).

FIG. 4
FIG. 4

FE discretization of the tire cross-section.

FIG. 5
FIG. 5

Simplified representation of discrete cords as smeared layer within the numerical simulation approach: (a) layer j of discrete cords; (b) corresponding smeared layer j with equivalent layer thickness t (including orthotropic properties).

FIG. 6
FIG. 6

FE discretization of the tire in circumferential direction (segmentation).

FIG. 7
FIG. 7

Thermal boundary conditions in terms of heat exchange coefficients and reference temperatures.

FIG. 8
FIG. 8

Rheological representation of the isochoric and volumetric part of the material model for rubber compounds.

FIG. 9
FIG. 9

Small strain rheology of a nonequilibrium branch.

FIG. 10
FIG. 10

Stress-strain relation of rubber compound (ground state elastic response) at different temperatures.

FIG. 11
FIG. 11

Constructed force-strain relation for PET 1670 × 2 370 at different temperatures.

FIG. 12
FIG. 12

Constructed force-strain relation for RY 1840 × 2 480 at different temperatures.

FIG. 13
FIG. 13

Carcass layer with cord direction (sequence of layer points in cross-sectional direction).

FIG. 14
FIG. 14

Load case A (statics): Force and strain state in circumferential direction within the carcass cord layer after static loading (inner pressure and vertical force) and before start of rolling; plotted for a discrete number of circumferential streamlines; see Fig. 13.

FIG. 15
FIG. 15

Load case A: Force and strain state in circumferential direction within the carcass cord layer after 1800 s of free rolling.

FIG. 16
FIG. 16

Load case B: Force and strain state in circumferential direction within the carcass cord layer after 1800 s of free rolling.

FIG. 17
FIG. 17

Load case C: Force and strain state in circumferential direction within the carcass cord layer after 1800 s of free rolling.

FIG. 18
FIG. 18

Load case A: Temperature profile of the carcass cords in radial direction (within the cross-section; see Fig. 13) after 1800 s of free rolling.

FIG. 19
FIG. 19

Load case B: Temperature profile of the carcass cords in radial direction (within the cross-section; see Fig. 13) after 1800 s of free rolling.

FIG. 20
FIG. 20

Load case C: Temperature profile of the carcass cords in radial direction (within the cross-section; see Fig. 13) after 1800 s of free rolling.

Contributor Notes

2 Corresponding author. Email: michael.kaliske@tu-dresden.de
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