Yuewei Ma, Valeri Markine
(Yuewei.Ma@tudelft.nl, V.L.Markine@tudelft.nl)
A Numerical Procedure for
Analysis of W/R Contact Using
Explicit Finite Element Methods
Delft
University of Technology
Outline
Parametric studies
Research Motivation
W/R Contact FE Model & Results
Research Motivation
Background
V
Head Check
b)
Fig 1. Typical defects on a shallow curve
Two commonly used approaches
Wheel and Rail (W/R) contact analysis.
a)
Short wave corrugation
Thermal weld
c)
Wear
d)
Research Motivation
Challenges in FE Modelling
Reality
Rolling frictional
Efficiency & Accuracy
Flexibility
Number of element
Element quality
Track conditions (straight, curve)
Loading conditions (braking ,accelerating)
Realistic geometries
An
efficient & flexible
numerical procedure for W/R
rolling
Outline
•
Refining Method
Research Motivation
W/R Contact FE Model & Results
•
Contact set-up
•
Indicative results
Fig.2 wheel-rail contact model. a) Schematic diagram; b) FE model – side view;
1640
Z
Y
90
60
O
M
90
solution area
dynamic relaxation area
coarse meshed area
further rolling area
a)
b)
W/R contact FE model:
Axle load: 10 t
Train speed: 140km/h
More details can be found from paper.
Primary
suspension
Lumped
Mass
W/R contact FE model:
Refining efficiency
Conventional
New developed –
Nested transition mapped hexahedral refining method
Free refining method
Easy-implemented
Poor quality, large quantity
Complicated-control
High quality, small quantity
a)
b)
c)
Number of
elements
200,000
Warning element
25%
Number of
elements
110,000
Warning element
<5%
b)
a)
c)
d)
W/R contact FE model:
Refining flexibility
Parametric studies >> Contact point location variation.
Fig.3 Contact points variation. a) 5.5mm; b) 2.0mm; c) -3.5mm; d) -5.5mm.
Flexible enough
1) Gauge corner
2) Tread center etc.
Outline
•
Refining Method
Research Motivation
W/R Contact FE Model & Results
•
Contact set-up
•
Indicative results
W/R contact FE model:
Contact compatibility
Contact body Target body Springs Target body Contact body0
s
l k
i i iif l
i
f
n
il
in
Fig.4 schematic graph of contact interaction
Low stiffness >>
large penetration
High stiffness >>
Numerical instability
Relationship between contact force and penetration
is contact force.
sf
Where:.
is contact stiffness.
i2 i i i i
K
A
k
V
where
: interface stiffness scale factor;
K
i: bulk modulus;
i
A
:element face area;
i
V
:element volume;
W/R contact FE model:
Contact stiffness
Question:
How deeply are the W/R interaction influenced by
and
element size ?
W/R interaction
Element size
Material properties
W/R contact FE model:
Varying stiffness scale factor
more stable response.
1.0
Fig.6 Resulting force variation under different interface scale factor
Element size = 1.0mm.
By default:
Notation:
10 scale factors range from 0.3 to 10
0.1
W/R contact FE model:
Varying element size
a) Element size =
db) Element size =
x d d d d d d d sf
sf
1
x
x d
Notation:
Fig.7 Schematic graph of element size variation.
a)
b)
2 i i i iK
A
k
V
f
s
l k
i in
i 2 2 3((
) )
(
)
i iK
k
x d
x d
Contact compatbility function:
x x
f
s
l
xdx
k
i
n
xd
d
l
x
l
Penetration depth:
a)
W/R contact FE model
Varying elemen size
2.0
Notation:
Fig.8 Reaction force variation under different element size.
a) 1.5*1.5*1.5mm; b) 1.0*1.0*1.0mm; c) 0.5*0.5*0.5mm.
b)
c)
Smaller element size >> high contact stiffness >> Stable W/R interaction.
6 mesh sizes range from 1.7 to 0.5mm
Outline
•
Refining Method
Research Motivation
W/R Contact FE Model & Results
•
Contact stiffness
•
Indicative results
Element size = 1mm
2.0
Interface Scale factor
Friction coefficient = 0.5
Traction coefficient = 0.5
Fig.2 wheel-rail contact model – side view;
Indicative Results:
Normal pressure
(a)
(b)
Fig. 9 Rail surface normal contact pressure distribution at origin Z = 0.
a) 3D shaded surface plot; b) 2D Contour plot.
“Realistic” W/R contact pressure
Comparable with literature [1]
Indicative Results:
Shear pressure
Fig. 10 Rail surface shear pressure distribution and slip-stick area distribution at
origin Z = 0mm. a) 3D shaded surface plot ; b) 2D Contour plot;
a)
b)
The surface shear pressure is mainly distributed at the trailing edge of the contact patch.
Logical !
Indicative Results:
Slip-Stick area
Fig.11 Rail surface shear pressure distribution and slip-stick area
distribution at origin Z = 0mm. a) Quiver plot; b) Slip-stick area plot.
a)
b)
The observed
slip-adhesion phenomenon
is consistent with the analytical results presented in
[Ref].
Indicative Results:
Sub-surface stress
Fig.12 Stress distribution in longitudinal-vertical plane at origin Z = 0mm. a) Cutting surface on X-Y Plane; b)
Von-Mises stress on A-A Cutting plane; c) Shear stress on A-A cutting plane; d) Cutting surface on Y-Z Plane;
e) Von-Mises stress on B-B Cutting plane; f) Shear stress on B-B cutting plane
A
B
B
A
a)
d)
b)
e)
c)
f)
W/R contact FE model
Summary
The developed refining method can significantly reduce the number of both total elements and
warning elements. Meanwhile, flexible enough to account contact point variation(Conformal
contact at gauge corner).
Default contact setting in FE model should be tuned to fit the case of W/R interaction. (
Interface scale factor >1.0; Elemen size <1.0mm )
Realistic W/R contact geometries, rolling frictional interactions .has been considered in
the Dynamic FE model.
Surface pressure distribution, slip-adhesion phenomenon and sub-surface stress/strain
reponse can all be captured.
Outline
Parametric studies
Research Motivation
W/R Contact FE Model & Results
• Contact point variation
-5.5mm
-3.5mm
0.0m
m
2.0m
m
5.5m
m
Fig. 14. Resultant interface force variation w.r.t rolling
distance. (Solid line: FY; Dash-dot line: FX; Dashed line FZ).
Parametric study:
Contact point variation
a) -5.5mm
b) -3.5mm
c) 2.0mm
d) 5.5mm
1393.5 1063.5 962.8 975.6 1066.3 915.9 898.0 867.7 890.6 Maximum normal pressure [MPa]
La te ra l co or dina te [mm ] -5.5 -3.5 -2.0 -1.0 0.0 1.0 2.0 3.5 5.5 Lateral displacement [mm] 709.0 525.4 423.3 432.4 491.9 421.7 385.6 372.4 363.8 Maximum shear pressure [MPa]
La te ra l co or dina te [mm ]
