Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 09 Nov 2023

Rubber Comprehensive Constitutive Equation and the Prediction of Tire Temperature and Rolling Resistance

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Page Range: 162 – 181
DOI: 10.2346/TST-21-012
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ABSTRACT

Cooler running tires with a reduced rolling resistance is a consideration for both tire makers and automotive original equipment manufacturers. To investigate the mechanics of energy loss and temperature rise, a nonlinear viscoelastic model suitable for numerical analysis of rolling tires is developed and demonstrated. The rubber compounds are represented as nonlinear viscoelastic materials with temperature and frequency, strain, and strain history–dependent response. Several applications to different tire designs are provided to demonstrate the impact of this new material constitutive law in improving the quality of the numerical predictions over other methods. One application is a rolling tire model that was used to delineate the tire temperature distribution and the resultant rolling resistance for different three-dimensional tread patterns.

Keywords: tires; rubber constitutive law; rolling resistance; temperature; viscoelasticity
FIG. 1
FIG. 1

Frequency sweep data as function of temperature.

FIG. 2
FIG. 2

Master curve used to calculate the WLF shift factor.

FIG. 3
FIG. 3

Oscillatory strain sweep.

FIG. 4
FIG. 4

Stress softening (Mullins) effect under shear and tensile deformation modes.

FIG. 5
FIG. 5

Nonlinear strain measure.

FIG. 6
FIG. 6

Summary of the calibration procedure.

FIG. 7
FIG. 7

Machine learning approach for parameters initial guess.

FIG. 8
FIG. 8

Example of comparison between the predicted results and the measured values. (a) Iso-thermal frequency sweep. (b) Iso-frequency strain sweep. (c) Tension and shear loading-unloading strain–stress curves.

FIG. 9
FIG. 9

Analysis flow used in SST modeling.

FIG. 10
FIG. 10

Improved accuracy with the new constitutive equation and improved parameters fits.

FIG. 11
FIG. 11

Analysis flow used in the non-axisymmetric steady-state modeling.

FIG. 12
FIG. 12

Operating temperature of 3-D treaded rolling OTR tire.

FIG. 13
FIG. 13

Predicted temperatures slightly lower than measured values.

FIG. 14
FIG. 14

Predicted RR for different IST models matches trends of measured values.

FIG. 15
FIG. 15

Thermal SST used to provide close start for thermal/mechanical explicit dynamics.

FIG. 16
FIG. 16

Coupled transient thermal-structural multiphysics analysis.

FIG. 17
FIG. 17

Transient thermal-mechanical of slip sweep analysis.

FIG. 18
FIG. 18

Predicted average temperature inside all four grooves.

FIG. 19
FIG. 19

Measured average temperature inside all four grooves.

Contributor Notes

1 The Goodyear Tire & Rubber Company, 200 Innovation Way, Akron, OH 44316, USA
2 Corresponding author: Email: t410e56@hotmail.com
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