Tribology on Mechanical Engineering - WIDE Project whirling speed of a shaft is almost constant, and is almost equal to the critical speed of the shaft. 3. The whirling direction of

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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


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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Present work

•  The effect of processing micro grooves

•  The optimum design of the micro grooves


Experiment apparatus

Reciprocating friction tester

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Measurement of friction force


Test piece

Liner Slider

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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]


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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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.


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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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


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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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


Analysis

Slider

Liner

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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


Friction force

Friction force F

∫ ∫− ∂∂

+=2

2

2

0 21b

b

bdxxphLdx

hULF µ

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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


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


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


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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Friction force

0 0.01 0.02 0.03 0.040

5

10


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


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


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

]


P=0.6

P=0.9

W=0.5


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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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)

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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


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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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


Analytical model

ssuubbssttrraattee

ccooaatteedd ffiillmm ooiill ffllooww

iinntteerrllaayyeerr,, ggrraaddiieenntt llaayyeerr

bbaallll llooaadd

Analytical model X

Y Z

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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


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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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]


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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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


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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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


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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Interlayer


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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××

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


××

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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××

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


××

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


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××

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



Gradient layer

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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


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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× ×

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)


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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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)


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

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Coated film

Gradient layer

Substrate

P0

Coated film

Gradient layer

Substrate

P3

Coated film

Gradient layer

Substrate

P4



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


Coated film

Gradient layer Substrate

P1


Coated film


P2 Coated film


P0


Ec Es Interlayer

Coated film

P1

P0 P2

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Coated film


P0


Coated film


P4

P4

P3

Es Ec

Coated film

Interlayer

P3

Coated film



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.


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.

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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.


Thank you for your attention!!

Documents

Tribology on Mechanical Engineering - WIDE Project whirling speed of a shaft is almost constant, and is almost equal to the critical speed of the shaft. 3. The whirling direction of