# (Lin and Hwang, 2004) 3D Full-Tire Steady State Rolling

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```Prediction of Temperature Distribution
of Steady State Rolling Tires
E. Ledbury, L. Wang, D. Johnson, C. Bouvard, S.D. Felicelli
Mississippi State University
Introduction
Diagram of an example of a coupled thermo-mechanical model including
three modules
Deformation Module
• Use ABAQUS tire analysis
capability
• Hyperelastic material
• Steady-state rolling analysis
• Input: weight, speed, inflation
pressure, road friction
• Output: Strain – Stress
Mechanical Analysis Sequence
Dissipation Module
The energy dissipated in the tire by viscoelastic effects can be obtained
from the hysteresis of the material
H
U loss
U total
H
Hysteresis (obtained from DMA testing)
U total
Total strain energy in tire (obtained from Mechanical Module)
U loss
Strain energy lost by dissipation
Heat generation
q  U loss
VL
D
( H U total )
VL
Vehicle speed
D
Tire diameter
2D Axi-symmetric Tire Model
Tire (185/60 R15) Geometry and Meshing
Material Properties
(Lin and Hwang, 2004)
Components
Material
Apex
Apex
Properties
Hyperelastic
Density (kg/m³) 1200
InnerLiner
InnerLiner
Bead
Rebar
Rubber, Ply
Rubber
Hyperelastic
1200
Elastic
6500
Hyperelastic
1200
SideWall
SideWall
Compound
Hyperelastic
1200
Tread
Tread
Hyperelastic
1200
Poison's Ratio
-
-
0.3
-
-
Young's
Modulus (Pa)
Mooney-Rivlin
Constants
(MPa)
-
-
207×109
-
-
C10 = 118.9
C01= -71.8
D1 = 0.003
C10 = 118.9
C01= -71.8
D1 = 0.01
-
C10 = 118.9
C01= -71.8
D1 = 0.03
C10 = 118.9
C01= -71.8
D1 = 0.01
C10 = 118.9
C01= -71.8
D1 = 0.04
Displacement Contour
Displacement for half-tire static modeling (6 kN, 50 psi)
Displacement vs. Loading
Comparison between model prediction and experiments (Lin and Hwang, 2004)
3D Full-Tire Steady State Rolling
Displacement
Displacement for 3D full-tire steady state rolling modeling (6kN, 50 psi, 80 km/h)
Strain Energy Density
ESEDEN at the cross-section connecting to the road contact for 3D full tire steady state
rolling modeling (6kN, 50 psi, 80 km/h)
Temperature Distribution (50 psi, 60 km/h)
Max Temp. in
Tire Shoulder
```

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