Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 27 Jan 2023

A Microsphere-Based Rubber Curing Model for Tire Production Simulation

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Page Range: 82 – 113
DOI: 10.2346/tire.23.21018
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ABSTRACT

In this contribution, a constitutive model for rubber is presented that describes the material in its unvulcanized and vulcanized state as well as during its phase transition. The model is based on the microsphere approach to represent the three-dimensional macroscopic behavior by a set of one-dimensional microscopic chains. When the uncured rubber is exposed to large temperature, the polymer chains build-up crosslinks among each other and the material changes its properties from soft viscoplastic to stiffer viscoelastic behavior. The state of cure over time at different temperatures is identified via a moving die rheometer (MDR) test. Based on this experimental data, a kinetic model is fitted to represent the state of cure in the simulation. The material model changes from the description of an unvulcanized state to a vulcanized state based on the current degree of cure in a thermomechanically consistent manner and fulfills the second law of thermodynamics. The curing model framework is suitable to combine any given material models for uncured and cured rubber.

The presented material formulation is applied to an axisymmetric tire production simulation. Therefore, the kinetic state of cure approach is fitted to MDR experimental data. The uncured and cured material model parameters are fitted separately to experiments by a gradient based fitting procedure. The in-molding and curing process of a tire production is simulated by a finite element approach. Subsequently, the simulated footprint of the tire is compared to experimental results. It can be shown that the quality of the footprint could be optimized solely by changing the shape of the green tire.

Keywords: tire production; green tire; rubber curing; finite element method
FIG. 1 —
FIG. 1 —

Comparison of the curing kinetics of a belt rubber compound to experimental results.

FIG. 2 —
FIG. 2 —

The curing kinetics of an inner-liner rubber compound.

FIG. 3 —
FIG. 3 —

Rheological model of the proposed rubber curing formulation.

FIG. 4 —
FIG. 4 —

Simple rubber block at 100% strain in its (a) undeformed configuration; (b) deformed configuration; and (c) in its new equilibrium configuration after curing.

FIG. 5 —
FIG. 5 —

Simple rubber block at 500% strain in its (a) undeformed configuration; (b) deformed configuration; and (c) in its new equilibrium configuration after curing.

FIG. 6 —
FIG. 6 —

Comparison of the free energy of the simple block during curing for (a) 100% strain and (b) 500% strain.

FIG. 7 —
FIG. 7 —

Green tire inside the mold after the contact with the bladder is established.

FIG. 8 —
FIG. 8 —

Green tire after the sidewalls is closed to its final position.

FIG. 9 —
FIG. 9 —

Green tire in the closed mold with a small inner pressure.

FIG. 10 —
FIG. 10 —

Green tire in the closed mold pushed into its final position by an inner pressure of 16 bar.

FIG. 11 —
FIG. 11 —

Comparison of the equilibrium configuration of the green tire and the fully cured tire.

FIG. 12 —
FIG. 12 —

Comparison of (a) experimentally obtained contact pressure to (b) numerical result.

FIG. 13 —
FIG. 13 —

Modified green tire geometry. The edges in the tread compound are moved to match the mold geometry.

FIG. 14 —
FIG. 14 —

Critical contact point of the mold with the modified green tire. The grooves of the mold are matching with the green tire geometry.

FIG. 15 —
FIG. 15 —

Contact pressure distribution of the modified geometry (a) experimentally and (b) simulation result. The footprint pressure distribution is more uniform between the inner circumferential grooves.

Contributor Notes

1 Institute for Structural Analysis (ISD), Technische Universität Dresden, 01062 Dresden, Germany. Email: thomas.berger@tu-dresden.de
2 Hankook Tire, Daejeon, South Korea. Email: kimsanghyub@hankookn.com
3 Corresponding author. Institute for Structural Analysis (ISD), Technische Universität Dresden, 01062 Dresden, Germany. Email: michael.kaliske@tu-dresden.de
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