tribology on mechanical engineering - wide project whirling speed of a shaft is almost constant, and...
TRANSCRIPT
2013/01/16
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22001122 School of Internet
Tribology on Mechanical Engineering
Iwamoto Katsumi Tokyo University of Marine Science and Technology
<Tribology> Research Field : Lubrication, Friction and Wear in machines and instruments.
The failures of machines and instruments might be caused by the friction or wear.
The solutions of tribological problem are basic key technology which affect the performance of machines and instruments.
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<Contents of Lecture>
1. Basic Hydrodynamic Lubrication 2. Improvement of Friction Characteristics on Reciprocating Machinery by Micro Texture 3. Guideline of Design on the Coated Film under EHL Condition
I have studied about tribology for thirty years.
Basic Hydrodynamic Lubrication
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Ancient Mural in Egypt
From this mural we can understand people have used the oil and know the usefulness of oil in ancient times.
Experiment by B. Tower
The experiment about Lubrication of support bearing of shaft used in train
cork
B.Tower found high pressure generates in the oil film.
Osborn Reynolds formulated a theory of lubrication in 1886. (Reynolds’ Theory)
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Reynolds’ Assumption
In deriving Reynolds’ equation, some assumptions are given as follows: 1. The flow is laminar. 2. The gravity and inertia forces acting on the fluid can be ignored compared with the viscous force. 3. Compressibility of the fluid is negligible. 4. The fluid is Newtonian and the coefficient of viscosity is constant. 5. Fluid pressure does not change across the film thickness. 6. The rates of change of the velocity in the x direction and z direction are negligible compared with the rate of change of the velocity in the y direction. 7. There is no slip between the fluid and the solid surface.
Fig.1 Pressure Distribution
Reynolds’ Equation((PPrreessssuurree EEqquuaattiioonn))
Fig.2 Mechanism of Pressure Generation ・Upward Convex
Average Curvature of Pressure Distribution Surface
・Pressure become positive
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Journal Bearing(schematically)
Cross Section of the Journal Bearing and Pressure Distribution
Wedge Effect
Positive Pressure
Negative Pressure
Spring Force Damping Force
Springlike Resistance Dependent on journal displacement relative to the bearing.
Spring force is not linearly related to the displacement of the journal.
The stability of journal bearing is an important consideration. Behavior of the vibration
The equations of motion of a rotating shaft are given by these equation.
Rotating Shaft
Diagonal Terms
Coupling Terms
The existence of a coupling term causes the unstable vibration.
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At twice the critical speed
Newkirk and Taylor found a severe vibration under certain condition
Unstable Vibration
The vibration disappeared when the oil supply to the bearings was stopped and it resumed when the oil was supplied again.
Resonant vibration
A large vibration occurs at the critical speed.
A large vibration appear again when the rotation speed reach to the twice the critical speed.
The unstable vibration of the rotating shaft supported by the journal bearing is called oil whip.
The features of oil whip are summarized as follows:
1. When the rotation speed of a shaft is raised from zero, oil whip starts at twice the critical speed.
2. The whirling speed of a shaft is almost constant, and is almost equal to the critical speed of the shaft. 3. The whirling direction of a shaft is the same as the rotating direction of the shaft. 4. Oil whip occurs easily when the journal floats up easily.
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When a large vibration generates such as the oil whip in the machine, the machine is sometimes broken.
Turbine blade broken by the accident
Several decades ago, in a heavy industry company
In that accident:
Destroyed the wall of building
Flied to the place where is 1500m away from turbine plant
Journal Bearing
The phenomenon of the oil whip has been studied by many researchers
Counterplan to prevent the generation of the oil whip
To use the special bearing having the stability
・Increase the threshold speed of stability
・don’t have the coupling terms
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The lobed bearing and tilting pad bearing are using for the turbine rotor of the generator.
Turbine rotor of generator
Schematic construction of generator
The turbine rotor has low natural frequency because the rotor shaft is long.
Therefore the threshold speed of unstable vibration is low too.
Consequently the shaft of rotor is required to support by stable
From this figure we found the oil film pressure generates at lower three lobe in journal bearing.
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Kind of Bearing
The bearing are classified into journal bearing and ball bearing
The journal bearing has big load capacity. But this bearing needs supply of oil continually.
In the ball bearing the contact parts between inner bush and ball, outer bush and ball are lubricated by the grease.
Experimental apparatus of the ball bearing
I have stayed in Leeds University of England twelve years ago.
I conducted the experiment of EHL.
EHL means elastohydrodynamic lubrication. In the condition of EHL, sliding surfaces deform by high oil film pressure.
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Schematic apparatus of elastohydrodynamic lubrication.
This experiment simulates the lubrication between bush and ball in ball bearing. The oil film thickness formed between the ball and the disk is measured by this apparatus.
Light up the contact point between the ball and glass disk
The reflect of light is measured by the microscorp and CCD camera.
Ball used in the experiment
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Data of these colors become standards of judging the oil film thickness.
In the experiment of EHL, at first, the gap between the ball and the disk is measured when the ball press to the glass disk and the ball and the disk don’t rotate.
The gap increase
These colors indicate the gap dimension.
From this situation, the ball or the disk start to rotate, oil film is formed.
Sliding (X) direction
Y direction
X axis
Smallest value of oil film thickness
((--)) ((++))
((--))
((++))
[nm]
[nm]
These pictures show the variation of oil film thickness.
These oil film thickness include the deformation of sliding surfaces.
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No.1 No.2
No.3 No.4
Speed Increase
Oil Film Increase
These pictures show the variation of oil film thickness. From these pictures we found the oil film thickness increase according to the increase of relative speed on the ball and the disk.
Improvement of friction characteristics on reciprocating machinery
by Micro Grooves
Katsumi Iwamoto Tokyo University of Marine Science and Technology
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Tokyo University of Marine Science and Technology
Background
In the reciprocating machinery, the lubricating condition between the slider and liner become the mixed lubrication.
Mixed lubrication Friction force increases rapidly
Damage of surface
Shift from Mixed lubrication to Hydrodynamic lubrication to prevent the failure of sliding surfaces
0
max
0Velocity
Tokyo University of Marine Science and Technology
Background
Surface Texturing
・Oil reservoir effect ・Expanding the range of the
Hydrodynamic lubrication regime
The pitch, width, and depth of the surface texturing
affect the oil reservoir effect
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Tokyo University of Marine Science and Technology
Present work
• The effect of processing micro grooves
• The optimum design of the micro grooves
Tokyo University of Marine Science and Technology
Experiment apparatus
Reciprocating friction tester
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Tokyo University of Marine Science and Technology
Measurement of friction force
Tokyo University of Marine Science and Technology
Test piece
Liner Slider
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Tokyo University of Marine Science and Technology
Kinds of micro groove patterns
No Width W Depth D Pitch P No groove 0 0 0
1 0.1 0.01 0.6 2 0.1 0.02 0.6 3 0.1 0.03 0.6 4 0.3 0.01 0.6 5 0.3 0.02 0.6 6 0.3 0.03 0.6 7 0.5 0.01 0.6 8 0.5 0.01 0.9 9 0.5 0.02 0.9 10 0.5 0.03 0.9
[mm]
Tokyo University of Marine Science and Technology
Experimental condition
• Lubricating Oil : Marine diesel engine oil
• Viscosity [mPa・s] : 121
• Load [N] : 5, 7.5, 10, 12.5, 15
• Rotational Velocity [rpm] : 0 ~ 60
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Tokyo University of Marine Science and Technology
Experiment
Increase of rotational velocity
(a) Load 10N, 20rpm (b) Load 10N, 41rpm
The rotational velocities of disk are measured when the peak of friction force disappears for each groove patterns. We judge the smaller rotational velocity measured in the experiment means more superior friction characteristics.
Tokyo University of Marine Science and Technology
Influence of groove depth
0 10 2010
20
30
40
Rot
atio
nal V
eloc
ity [r
pm]
Load [N]
D=0.01
No Groove
D=0.02
D=0.03W=0.1P=0.6
0 10 2010
20
30
40
Rot
atio
nal V
eloc
ity [r
pm]
Load [N]
D=0.01
D=0.02D=0.03W=0.3
P=0.6
Influence of groove depth at W=0.1, P=0.6 Influence of groove depth at W=0.3, P=0.6
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Tokyo University of Marine Science and Technology
Influence of groove depth
0 10 20
25
50
Rot
atio
nal V
eloc
ity [r
pm]
Load [N]
D=0.01
D=0.02
D=0.03
W=0.5P=0.9
Influence of groove depth at W=0.5, P=0.9
Tokyo University of Marine Science and Technology
Influence of groove width
0 10 20
25
50
Rot
atio
nal V
eloc
ity [r
pm]
Load [N]
W=0.1
W=0.5
W=0.3
D=0.01P=0.6
Influence of groove width at D=0.01, P=0.9
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Tokyo University of Marine Science and Technology
Influence of groove pitch
0 10 20
25
50R
otat
iona
l Vel
ocity
[rpm
]
Load [N]
P=0.6
P=0.9
W=0.5D=0.01
Influence of groove pitch at D=0.01, W=0.5
Tokyo University of Marine Science and Technology
Analysis
Slider
Liner
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Tokyo University of Marine Science and Technology
Reynolds equation µ:Coefficient of friction U:Velocity p:Pressure h:Oil film thickness x:coordinate in direction of motion z:coordinate in vertical direction of motion
xhBhBhBhBh
hUxpB
⎭⎬⎫
⎩⎨⎧
+
+−= 3
12311
212
2212
21
1)(16)( µ
xhBhBhBhBh
hUxpB
⎭⎬⎫
⎩⎨⎧
−+
+= 1)(6)( 3
12311
212
2211
22
2µ
Area B1
Area B2
∫∫ +=+=21
0 20 121 )()(B
B
B
B dxxpLdxxpLWWWLoad capacity W
Load capacity
dxdhU
xph
dxd 6)(
3
=∂
∂
µ
dxdhU
zph
dzd
xph
dxd 6)()(
33
=∂
∂+
∂
∂
µµthe groove is assumed as infinitely long
Tokyo University of Marine Science and Technology
Friction force
Friction force F
∫ ∫− ∂∂
+=2
2
2
0 21b
b
bdxxphLdx
hULF µ
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Tokyo University of Marine Science and Technology
Calculation conditions
Load [N]
Pitch P [mm]
Width W [mm]
Depth D [mm]
Velocity V [m/sec]
10
0.3 0.05~0.25 each 0.05
0.0025~0.03 each 0.0025
0.233 0.6 0.05~0.55 each 0.05
0.9 0.05~0.85 each 0.05
Velocity when the slider slides onto the micro groove on the liner
Pitch Number of grooves N
0.3 100
0.6 50
0.9 33
Tokyo University of Marine Science and Technology
Oil film thickness
0 0.01 0.02 0.03 0.040
0.005
0.01
Depth of groove [mm]
Oil
film
thic
knes
s [m
m]
W=0.1W=0.15W=0.2W=0.25
0 0.01 0.02 0.03 0.040
0.005
0.01
Depth of groove [mm]
Oil
film
thic
knes
s [m
m]
W=0.1W=0.2W=0.3W=0.4W=0.5
0 0.01 0.02 0.03 0.040
0.005
0.01
Depth of groove [mm]
Oil
film
thic
knes
s [m
m]
W=0.1W=0.2W=0.3W=0.4W=0.5W=0.6
W=0.8W=0.7
P=0.6 P=0.3 P=0.9
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Tokyo University of Marine Science and Technology
Friction force
0 0.01 0.02 0.03 0.040
5
10
Depth of groove [mm]
Fric
tion
forc
e [N
]
W=0.1W=0.15W=0.2W=0.25
0 0.01 0.02 0.03 0.040
5
10
Depth of groove [mm]
Fric
tion
forc
e [N
]
W=0.1W=0.2W=0.3W=0.4W=0.5
0 0.01 0.02 0.03 0.040
5
10
Depth of groove [mm]
Fric
tion
forc
e [N
]
W=0.1W=0.2W=0.3W=0.4W=0.5W=0.6
W=0.8W=0.7
P=0.3 P=0.6
P=0.9
0 0.01 0.020
2
4
6
8
Fric
tion
Forc
e [N
]
Depth of groove [mm]
P=0.6
P=0.9
W=0.5
Tokyo University of Marine Science and Technology
Conclusion Finally, following conclusions are obtained within results of the
experiment and the analysis.
• Generally the groove patterns with smaller depth have more superior friction characteristics.
• The optimum value of the groove depth, which makes the friction
force smallest, exists in case of larger groove width.
• The groove patterns with smaller width have more superior friction characteristics.
• The optimum groove pitch, which makes the friction force smallest, exists according to the width and the depth of groove.
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Tokyo University of Marine Science and Technology
Thank you for your attention!
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Guideline of Design on the Coated Film with Interlayer or Gradient Layer under
EHL Condition
Katsumi Iwamoto (Tokyo University of Marine Science and Technology)
2013/01/16
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Background
• The materials of the coated film are selected by the past knowledges and experiences
• Techniques improving sliding performance have progressed by the coated film
• The design of the coated film is conducted by try and error. It’s not the optimum design
• The optimum design of the coated film is
required
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Previous study
• Evaluation of stress distribution of the coated film in a point contact under EHL condition.
• Guideline of the optimum design of the coated film
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Present work
• There are some cases that Interlayer or gradient layer is bonded between coated film and substrate
• Evaluation of stress distribution • Guideline of the optimum design - on coated film with interlayer or gradient layer
• For design of coated film with interlayer or gradient layer
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical model
ssuubbssttrraattee
ccooaatteedd ffiillmm ooiill ffllooww
iinntteerrllaayyeerr,, ggrraaddiieenntt llaayyeerr
bbaallll llooaadd
Analytical model X
Y Z
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Structure of gradient layer
Lamination layer2
Lamination layer8
Interlayer : Em
Lamination layer1
Substrate: Es
Coated film: Ec
Interlayer homogeneous
in the depth direction
Gradient layer change gradually
in the depth direction
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method
( )XH
YP
YXP
X ∂
∂=⎥⎦
⎤⎢⎣
⎡∂
∂
∂
∂+⎥⎦
⎤⎢⎣
⎡∂
∂
∂
∂ *ρξξ
ληρ
ξ *
3*H=
3
2012apRu
h
x
⋅=
ηλ
0* /ηηη =
ayY /=axX /=0
* / ρρρ = 2/ ahRH x=hppP /=
HP
u*ρ*η
hp
:Dimensionless oil film thickness :Dimensionless oil film pressure
:Mean velocity a:Radius of Hertzian contact region :Dimensionless viscosity :Dimensionless density :Maximum Hertzian pressure
• Dimensionless Reynold’s equation
:Equivalent radius of curvature xR
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method • Dimensionless viscosity
( )( )*0
0exp ln 9.67 1 1 hp P
p
α
η η⎧ ⎫⎛ ⎞⎛ ⎞⎪ ⎪⎜ ⎟= + − + +⎜ ⎟⎨ ⎬⎜ ⎟⎜ ⎟⎝ ⎠⎪ ⎪⎝ ⎠⎩ ⎭
• Dimensionless density )}7.11/(6.0{1* PpPp hh ++=ρ
0.67α =0η =0.0400 [Ns/m2] 0p =1.96×108 [N/m2]
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method
• Dimensionless oil film thickness 2 2
0 2 2 b cX YH H V V= + + + +
: Dimensionless central film thickness 0H: Dimensionless elastic deformation of ball bVcV : Dimensionless elastic deformation of coated film
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method
( ) ( )
( ) ( )
2
2 2
1 ', '' '
' '
b x hb
b
R p P X YV dX dY
E a X X Y Y
ν
π
−=
− + −∫∫
• Dimensionless elastic deformation of ball
:Modulus of elasticity of ball bE:Poisson’s ratio of ball bν
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method • Dimensionless elastic
deformation of coated film The Hertzian contact theory is applied for analysis of the contact pressure and deformations in single material
Elastic deformations of coated film with interlayer or gradient layer can’t be evaluated by the Hertzian contact theory
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Analytical method • Dimensionless elastic
deformation of coated film
r
Unit force
(Xi’ ,,Yj’) (Xi ,,Yj)
Dci,j
The Influence factor Dci,j is
given by the displacement at point (Xi , Yj) in which is located at a distance of r from the point (Xi’ , Yj’) where unit force is applied.
Elastic deformations of coated film are obtained by using the influence factor
The influence factor is calculated by using the three-dimensional axis-symmetrical finite element method
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Calculation conditions : 1.73×10-7
: 8.83×10-12
: 206[GPa] : 0.30 : 206[GPa] : 0.30 : 0.50(soft), 2.00(hard) : 0.30 : 50.0 ~ 100.0[µm] :0.25 ~ 2.50 : 0.30 :12.5 ~ 50.0[µm]
Modulus of elasticity of ball :Eb Poisson’s ratio of ball :νb
Modulus of elasticity of coated film/ Modulus of elasticity of substrate :Ec/Es Poisson’s ratio of coated film :νc
Modulus of elasticity of interlayer or gradient layer/ Modulus of elasticity of sibstrate :Em/Es Poisson’s ratio of interlayer or gradient layer:νm
Modulus of elasticity of substrate : Es
Poisson’s ratio of substrate :νs
Coated film thickness :Tc
Interlayer or gradient layer thickness :Tm
Dimensionless load parameter :W Dimensionless speed parameter :U
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Interlayer
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
X
Y
××
Tc =50.0[µµm] Tm =25.0[µµm] Em / Es=2.00
Stress distribution
Tc =50.0[µµm] Tm =25.0[µµm] Em / Es=1.00
××
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=0.25
××
Tc =50.0[µµm] Tm =25.0[µµm] Em / Es=0.75
Ec/Es=0.50, Tc=50µµm, Tm=25µµm constant
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=0.50
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=1.50
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=2.50
It is preferable that value of Em is given within the range from Ec to Es in cases of Ec/Es=0.50 and 2.00
Ec/Es=2.00, Tc=50µµm, Tm=25µµm constant Stress distribution
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=0.75
××
Tc =50.0[µµm] Tm=20.0[µµm] Em / Es=0.75
××
Tc =50.0[µµm] Tm=5.0[µµm] Em / Es=0.75
Tc =50.0[µµm] Non-Interlayer
××
Ec/Es=0.50, Tc=50µµm, Em/Es=0.75 constant Stress distribution
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
××
Tc =50.0[µµm] Tm=25.0[µµm] Em / Es=1.50
××
Tc =50.0[µµm] Tm=5.0[µµm] Em / Es=1.50
××
Tc =50.0[µµm] Non-Interlayer
Substrate 1. The region of high stress into the substrate become
small with increase of Tm 2. The position of maximum stress move to coated film or
interlayer with increase of Tm
It is preferable to have a larger value of Tm in cases of Ec/Es=0.50 and 2.00
Ec/Es=2.00, Tc=50µµm, Em/Es=1.50 constant Stress distribution
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=0.25
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=0.75
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=1.50
X
Y
Ec/Es=0.50, Tc=100µµm, Tm=50µµm constant Stress distribution
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=0. 50
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=1.50
××
Tc =100.0[µµm] Tm=50.0[µµm] Em / Es=2.50
Ec/Es=2.00, Tc=100µµm, Tm=50µµm constant Stress distribution
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Gradient layer
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Ec:: MMoodduulluuss ooff eellaassttiicciittyy ooff ccooaatteedd ffiillmm
CCooaatteedd ffiillmm
SSuubbssttrraattee
IInn ddeepptthh ddiirreeccttiioonn:: Z
MMoodduulluuss ooff eellaassttiicciittyy ooff ggrraaddiieenntt llaayyeerr:: Em
P1
P2
Ec
P0
Es
P4
P3
Es Ec
Es:: MMoodduulluuss ooff eellaassttiicciittyy ooff ssuubbssttrraattee
Properties of gradient layer
GGrraaddiieenntt llaayyeerr
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Tc=50.0µµm , Ec/Es=0.50
10 20 30 40
Max
imum
von
Mis
es s
tress
, σ
mise
s–m
ax [
GPa
]
Interlayer or Gradient layer thickness, Tm [µm]
Gradient layerInterlayer
0.22
0.24
0.26
0.28
10 20 30 40
Max
imum
shea
r stre
ss, σ m
ises–
max
[G
Pa]
Interlayer or Gradient layer thickness, Tm [µm]
Gradient layerInterlayer
0.38
0.40
0.42
0.44
Tc=50.0µµm , Ec/Es=2.00
Maximum stress (Interlayer and Gradient layer)
Interlayer (Em/Es=0.75) ,, Gradient layer(linealy:P0)
Interlayer (Em/Es=1.50) ,, Gradient layer(linealy:P0)
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
× ×
Tc=50.0µm , Tm=20.0µm , Ec/Es=0.50
Gradient layer(linealy:P0)
The region of high stress at the boundary face between the coated film and the gradient layer disappear
Stress distribution Ec/Es=0.50 (Interlayer and Gradient layer)
Interlayer (Em/Es=0.75)
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Tc=50.0µm , Tm=20.0µm , Ec/Es=2.00 × ×
The stress gradient at the boundary face between the coated film and the gradient layer become small
Gradient layer(linealy:P0) Interlayer (Em/Es=1.50)
Stress distribution Ec/Es=2.00 (Interlayer and Gradient layer)
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Tc=50.0µm, Tm=20.0µm, Ec/Es=0.50
Modulus of elasticity of gradient layer: Em
Coated film
Substrate
In depth direction: Z
P1
P2
Ec
P0
Es
P4
P3
Es Ec
Gradient layer
Max
imum
von
Mis
es s
tress
, σm
ises–
max
[G
Pa]
Type of gradient layerP0 P1 P2 P3 P4
0.38
0.44
0.40
0.42
Tc=50.0µm, Tm=20.0µm, Ec/Es=2.00
Max
imum
von
Mis
es s
tress
, σm
ises–
max
[G
Pa]
Type of gradient layerP0 P1 P2 P3 P4
0.22
0.28
0.24
0.26
Maximum stress (Pattern of Gradient layer)
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Coated film
Gradient layer
Substrate
Coated film
Gradient layer
Substrate
P1
P2
Tc=50.0µµm, Tm=20.0µµm, Ec/Es=0.50
Coated film
Gradient layer
Substrate
P0
Ec Es Interlayer
Coated film
P1
P0 P2
Stress distribution(Pattern of Gradient layer) Ec/Es=0.50
2013/01/16
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Coated film
Gradient layer
Substrate
P0
Coated film
Gradient layer
Substrate
P3
Coated film
Gradient layer
Substrate
P4
Tc=50.0µµm, Tm=20.0µµm, Ec/Es=0.50
Stress distribution(Pattern of Gradient layer) Ec/Es=0.50
P4
P3
Es Ec
Coated film
Interlayer For soft coated film, it is preferable to select the gradient layer varying sharply the modulus of elasticity around the center of gradient layer such as P4
The region of high stress becomes small at the area where the variation in modulus of elasticity into the gradient layer is large
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Coated film
Gradient layer Substrate
P1
Tc=50.0µµm, Tm=20.0µµm, Ec/Es=2.00
Coated film
Gradient layer Substrate
P2 Coated film
Gradient layer Substrate
P0
Stress distribution(Pattern of Gradient layer) Ec/Es=2.00
Ec Es Interlayer
Coated film
P1
P0 P2
2013/01/16
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Coated film
Gradient layer Substrate
P0
Tc=50.0µµm, Tm=20.0µµm, Ec/Es=2.00
Coated film
Gradient layer Substrate
P4
P4
P3
Es Ec
Coated film
Interlayer
P3
Coated film
Gradient layer Substrate
Stress distribution(Pattern of Gradient layer) Ec/Es=2.00
For hard coated film, it is preferable to select the g r a d i e n t l a y e r v a r y i n g linearly the modulus of elasticity around the center of gradient layer such as P0
The stress gradient is large at the area where the variation in modulus of elasticity into the gradient layer is large.
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Conclusions
From the results, the following conclusions are obtained:
• Stresses of the coated film, the interlayer, the gradient layer and the substrate have been numerically evaluated by three dimensional analysis.
• For soft and hard coated film with interlayer, when the thinner coated film are used, it is preferable that interlayer thickness, Tm has the larger value, and that the value of Em is given within the range from Ec to Es.
2013/01/16
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Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Conclusions • The stress gradient at the boundary face between
the coated film and the interlayer, or the interlayer and the substrate become smaller by using the gradient layer. However, the effect of using the gradient layer on the maximum stress is small.
• For soft coated film, it is preferable to select the
gradient layer varying sharply the modulus of elasticity around the center of gradient layer.
• For hard coated film, it is preferable to select the
gradient layer varying linearly the modulus of elasticity into the gradient layer.
Tokyo University of Marine Science and Technology 36th Leeds-Lyon Symposium on Tribology
Thank you for your attention!!