Transcript Third Body Modeling Using a Combined Finite Discrete Element Approach Benjamin Leonard Post-Doctoral Research Associate Mechanical Engineering Tribology Laboratory (METL) November 14, 2013

Third Body Modeling Using a
Combined Finite Discrete Element Approach
Benjamin Leonard
Post-Doctoral Research Associate
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
2
Outline
•
•
•
•
•
•
Motivation
Objectives
Combined Finite-Discrete Element Model
Sliding Plates
Fretting Contacts
Summary and Conclusions
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Motivation
• Third body particles play an important role in many industrial applications
– Wear debris
– External objects
• The fretting phenomenon is caused by small scale reciprocating motion leading
to failure from fatigue or wear
– Due to the small scale motions the third body effect is large in fretting
In Situ Photograph of a Fretting Contact
Diagram of Third Body Wear
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Objectives
• Develop a numerical model for fretting wear which
includes third body effects
• Study the effects of various parameters
– Loading
– Surface roughness
– Coatings
• Develop a stress based approach for modeling fretting
wear
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November 14, 2013
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Modeling of the Third Body
• The “third body” is composed of loose wear particles or external
debris inside a contact
• In the FDEM the third body is modeled using loose spherical particles
– Third body particles interact with first bodies
– Third body particles interact with each other
Motion of Third Body Particles in the FDEM
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November 14, 2013
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Compression of the Third Body
k=10
k=15
k=20
k=25
10
Force (mN/ m)
• Shifting particles cause
discontinuities in the forcedeflection curve
• Third body contact stiffness
controls its effective elastic
modulus
12
8
6
4
2
0
0
0.1
0.2
Deflection (m)
0.3
0.4
Reaction Force from Third Body
Compression of a Mass of Third Body Particles
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November 14, 2013
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Friction and the Velocity Gradient
• The velocity
gradient between
two surfaces
depends on their
coefficients of
friction
• By varying the
coefficient of
friction no slip
conditions can be
achieved on each
surface
Y (y/L)
0.3
(a)
0.2
0.1
0
0
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
0.4
0.6
Velocity (V/V 0)
0.8
1
Y (y/L)
0.3
(b)
0.2
0.1
0
0
0.2
Y (y/L)
0.3
0.2
(c)
0.1
0
0
Disposition of Platelets
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
Velocity Gradient
The effect of lower surface coefficient of friction on the
velocity gradient for μ of (a) 0.2, (b) 0.3 and (c) 0.4.
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
Effect of Platelet Length on the
Velocity Gradient
0.3
Y (y/L)
• With unlinked
particles, the third
body behaves as a
Newtonian fluid
• Regions of the third
body clump together
when platelets
interlock
0.2
8
1
0.1
0
-0.2
0
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
1.2
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
1.2
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
1.2
0.2
0.4
0.6
Velocity (V/V 0)
0.8
1
1.2
Y (y/L)
0.3
0.2
2
0.1
0
-0.2
0
0.3
Y (y/L)
– This effect grows
larger as platelets
become longer
– The velocity
gradient is not
constant with time
0.2
4
0.1
0
-0.2
0
Y (y/L)
0.3
0.2
7
0.1
0
-0.2
Disposition of Platelets
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0
Velocity Gradient
November 14, 2013
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The Third Body in a Fretting Contact
• Third body particles can be
introduced into worn fretting
contacts
• Wear particles (individual and
platelets) have been placed into
the worn slip zones at the edge of
the contact
-3
-3
x 10
6
2
0.68
0.685
0.69
X (x/b)
0.695
0.7
0.705
2
-3
6
4
2
0
0.675
0.68
0.685
0.69
X (x/b)
0.695
0.7
0.705
-3
x 10
Y (y/b)
Y (y/b)
6
1
0
0.675
0.68
0.685
0.69
X (x/b)
0.695
0.7
0.705
x 10
4
max
0
0.675
Finite Element Domain
4
, / 
max
Y (y/b)
Y (y/b)
4
x 10
2
0
0.675
0.68
0.685
0.69
X (x/b)
0.695
Variation in Platelet Length
0.7
0.705
P/P
6
0.5
0
-0.5
Normal Load
Displacement
-1
0
0.2
0.4
0.6
time (t/t simulation)
0.8
1
Loading of a Fretting Contact
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
The Effect of Particle Size in a
Fretting Contact
2.5
2.5
(a)
(b)
h
h
Pressure (P/P )
2
1.5
1
0.5
0
-1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1
0
-1.5
1.5
2.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-0.5
0
0.5
Distance (x/b)
1
1.5
2.5
(c)
2
(d)
h
Pressure (P/P )
2
1.5
0.5
h
•
The maximum
pressure and
force carried
by a single
particle
increases with
diameter
The pressure
in the stick
zone does not
vary
significantly
from a single
particle
Pressure (P/P )
•
Pressure (P/P )
2
10
1.5
1
0.5
0
-1.5
1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
0
-1.5
-1
The effect of particle size on the contact pressure for diameters
of (a) 0.1 μm, (b) 0.2 μm, (c) 0.4 μm and (d) 0.6 μm.
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
Effect of A Small Number of Particles
on a Fretting Contact
2.5
2.5
(a)
Pressure (P/P )
2
1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
1
0
-1.5
1.5
2.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-0.5
0
0.5
Distance (x/b)
1
1.5
2.5
(c)
2
(d)
h
h
Pressure (P/P )
2
1.5
0.5
0
-1.5
Pressure (P/P )
•
As the number
of particles
increase, the
maximum
pressure
decreases
The outermost
(4th) particle
does not come
into contact due
to curvature of
the surface
(b)
h
h
Pressure (P/P )
2
•
11
1.5
1
0.5
0
-1.5
1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
0
-1.5
-1
The effect of (a) 2, (b) 4, (c) 6, and (d) 8 of particles with
diameters of 0.6 μm on contact pressure.
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November 14, 2013
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1.5
1.5
1.5
1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
0.5
0
-1.5
1.5
h
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
0.5
0
-1.5
1.5
1
-1
-0.5
0
0.5
Distance (x/b)
1
0
-1.5
1.5
1
1
0.5
0.5
0.5
0.5
-0.5
-1
-1.5
-1
-0.5
0
0.5
Distance (x/b)
1
120 particles
•
•
1.5
0
-0.5
-1
-1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
220 particles
h
h
h
0
Shear Stress (q/P )
1
Shear Stress (q/P )
1
Shear Stress (q/P )
h
Shear Stress (q/P )
0
-1.5
h
h
1
Pressure (P/P )
2
Pressure (P/P )
2
Pressure (P/P )
2
h
Pressure (P/P )
The Effect of Increasing Numbers of
Particles on the Pressure Profile
12
0
-0.5
-1
-1.5
-1
-0.5
0
0.5
Distance (x/b)
1
320 particles
1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
0
-0.5
-1
-1.5
420 particles
Increasing the number of particles has several effects:
– The total force carried by the slip zone increases
– The pressure in the slip zone decreases
Frictional shear stress in the slip zones is not uniform on each side of the contact
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
Wear Particles at the
Stick Zone-Slip Zone Interface
13
Initial disposition of wear particles in the
Hertzian fretting contact (120 particles).
• The normal force (red arrows)
from the first bodies result in a net
lateral force on the third bodies
(blue arrow) pushing them away
from the edge of the stick zone
(green circle)
The stick zone-slip zone
interface in a fretting contact
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
Effect of Platelet Length on
Partial Slip Fretting Contacts
5 particles
14 particles
1.5
1.5
1.5
1.5
0
-1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
0
-1.5
1.5
h
h
h
1
Pressure (P/P )
2
Pressure (P/P )
2
Pressure (P/P )
2
0.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
0
-1.5
1.5
1
0.5
-1
-0.5
Pressure Profile
0
0.5
Distance (x/b)
1
0
-1.5
1.5
0.6
0.4
0.4
0.4
0.4
0
-0.2
-0.4
-1.5
0.2
0
-0.2
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-1.5
0.2
0
-0.2
-0.4
-0.4
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
h
h
h
0.2
Shear Stress (q/P )
0.6
Shear Stress (q/P )
0.6
Shear Stress (q/P )
0.6
h
Shear Stress (q/P )
10 particles
2
h
Pressure (P/P )
2 particles
14
-1.5
0.2
0
-0.2
-0.4
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
-1.5
Frictional Shear Stress
Particle Location After Loading
•
•
Longer platelets lead to formation of a thicker third body mass
Thicker third body masses are pushed further from the stick-slip zone interface
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Wear Particles During Fretting Evolution
120k
80k
160k
1.5
1.5
1.5
1.5
0.5
0
-1.5
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
0
-1.5
h
h
h
1
Pressure (P/P )
2
Pressure (P/P )
2
Pressure (P/P )
2
h
Pressure (P/P )
40k
2
1
0.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
0
-1.5
1
0.5
-1
-0.5
Pressure
0
0.5
Distance (x/b)
1
1.5
0
-1.5
-1
-0.5
0
0.5
Distance (x/b)
1
1.5
Subsurface Stress (σy)
• The wear particles group together due to
the pressure and surface profile shape
• Pressure is not longer uniform in the slip
zone
Groups of Clustered Wear Particles
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013
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Summary and Conclusions
• A model of the third body has been created using the
combined finite discrete element method
• Third body properties can be controlled using size, spring
stiffness and platelet length
• Longer platelets interlock forming thicker third body masses
• The third body supports load and takes the stress off the edge
of the stick zone in fretting contacts
• Loose third body particles tend to clump together in fretting
contacts which may lead to platelet formation
Mechanical Engineering Tribology Laboratory (METL)
November 14, 2013