Identification Multi-Echelles par Ondelettes Continues de la - - PowerPoint PPT Presentation

Identification Multi-Echelles par Ondelettes Continues de la Signature des Etats de Surface

• H. ZAHOUANI

Laboratoire de Tribologie et Dynamique des Systèmes UMR CNRS 5513 ENISE - ECL

Caractère Multi-Echelles des Surfaces

Procédés de Finition des Surfaces Procédés de Finition des Surfaces Nano-échelle 10-9m mm 10-3m Echelles des longueurs d’onde Large gamme d’échelles

≈

Fonctionnalités Propriétés Optiques Diffusion

• Peinture- Aspect

Planéité Mécanique et Tribologie

• Lubrification
• Contact & Etanchéité
• Réduction du frottement
• Adhésion
• Usure

Métrologie Multi-Echelles

10mm 6mm 1mm 50µm 5µm

TRIANGULATION LASER RUGOSIMÈTRE TACTILE LARGE ÉCHELLE

INTERFÉROMÈTRIE CLASSIQUE

AFM

MICROSCOPIE CONFOCALE

100µm 500µm 50mm Z X,Y

Joint d’étanchéité

INTERFÉROMÈTRIE LARGE ECHELLE

DEFLECTOMETRIE 3D

PROCESS

• Manufacturing
• Finishing
• Wear

( )

x

I

f

( )

F

G x

Identification Multi-Echelles des Procédés de Finition

Multi- Sacle Transfer Fonction

) ( ) ( ) ( x f a T x G

I F

⊗ =

Sinature Multi-Echelles

Decomposition Multi Scale Information

Decomposition Multi Echelles

Decomposition by Continuous Wavelet Function

ψ ψ

b a x

a x b a

, ( )

( ) = − 1

With ai = [a1,a2.....an] the scales of analysis in mm & b the spatial parameter of translation.

is a wavelet if : continuous, with finite energy

• ( )

x ψ

( )

2 xd

x ψ

+ ∞ − ∞

<∞

∫

( )

=

∫

+∞ ∞ −

dx x ψ

Generation of Wavelet Family

x Mother Wavelet x/ai

0.04mm 0.09mm 0.19 mm 0.40mm 0.86mm 1.86mm

Wavelets Family

Local Detection

Signal Decomposition First detection Second Detection

Wavelet Transform

Mathematical Procedure: Convolution of the Signal with different scales of Mother Wavelet

⊗

• Wavelet Family

) ( ) (

, i a b

a x ψ ψ =

F(x) b

mm

) (

,

x f

a b

mm

Modulus

W

Phase θ

a

∆ 2

Signal

L

Multi-Scale Arithmetic Mean value: Ma (Ra, Wa)

( )

∑

=

=

N x a x

f N a Ma

1

1 ) (

Scales

Ra(ai) Wa(ai)

0.1 0.2 0.3 0.4 0.016 0.025 0.04 0.063 0.099 0.156 0.247 0.39 0.615 0.97 1.53 2.414 3.809 6.011 9.484 14.964 23.611

Ma(µm)

Waviness: Wa Micro-Scale: Ra

Wavelengths (mm)

Multi Scale Signature

PROCESS

• Manufacturing
• Finishing
• Wear

( )

x

I

f

( )

F

G x

( )

F

G a

Ma

) (a

Ma

I

f

Transfer Function:

( )

( ) ( ) ( )

F I I

G f f

a a a a

Ma Ma h Ma

=

−

x

2D Multi Scale Decomposition

2 D D e c

• m

p

• s

i t i

• n

Multi Scale Morphology

Multi Scale Decomposition

Multi Scale Decomposition by Wavelet Transform

), ( ) , (

2 R

L y x f ∈

1 ( , ) ( , ) ( , )

y x x y

y b x b Cwt a b f x y dxdy a a a ψ − − = ∫∫

2D Wavelet

( ) (

)

( )

2 2

2 2 2

, 2

x y

x y x y e ψ

− +

= − −

Mathematical Procedure:

Wavelets Bank

⊗

Surface Multi scale Spectrum

( )

* ,

( , ) , ( , )

f a b

W b a f x y x y

ψ

ψ = ⊗

( )

y x f ,

( )

y x

b a

,

* ,

ψ

{ }

1 ,

( , ) ( , ) ( , )

f a a x y x y

f x y TF W w w aw aw

ψ

ψ

−

= % %

Inverse Transform

( )

, 2

1 , ( , ) ( , )

f a a b g

dadb f x y W a b x y C a

ψ

ψ =

∫∫

%

( ) df

f f C g

∫

∞ − ∞ −

Ψ =

2

Avec

Wavelets Spectrum

⊗

Wavelets Bank (Dual)

฀

( )

,

,

a b x y

ψ

( )

,

f

W a b

ψ

Multi Scale Decomposition Scales

฀ (

)

,

a

f x y

Scales

Quantitative Decomposition

Échelles

( )

1 1

, ( )

M N a x y

f x y SMa a MN

= =

= ∑∑

X Y

Spectre de rugosité SMa

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 2 . 4 8 1 . 4 9 8 1 . 9 5 . 8 1 . 5 8 6 . 4 2 8 . 3 1 3 . 2 2 9 . 1 6 7 . 1 2 2 . 9 . 6 5 . 4 8 . 3 5 . 2 6 . 1 9

Echelles (mm)

Micr Scale

Macro Scale

Ra (µm)

• Finition

( )

,

I

f x y

( )

,

F

G x y

) (a

SMa

I

f

( )

( , )

( ) ( ) ( )

F I I

G f x y f

a a a a

SMa SMa h SMa

=

−

( )

F

G a

SMa

PROCESS

• Manufacturing
• Finishing

2D Transfer Function

Transfer Function of Polishing

Before Polishing Après 30s Après 90s 120s after Multi Scale SMa Multi Scale SMa

• 100%
• 80%
• 60%
• 40%
• 20%

0% 20% 40% 60% 80% 100% 25.6 17.9 12.5 8.75 6.12 4.28 2.99 2.09 1.46 1.02 0.72 0.5 0.35 0.24 0.17 0.12

Echelle (mm)

30 s

• 100%
• 80%
• 60%
• 40%
• 20%

0% 20% 40% 60% 80% 100% 25.6 17.9 12.5 8.75 6.12 4.28 2.99 2.09 1.46 1.02 0.72 0.5 0.35 0.24 0.17 0.12

Echelle (mm)

30 s 90 s

• 100%
• 80%
• 60%
• 40%
• 20%

0% 20% 40% 60% 80% 100% 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12

Echelle (mm)

30 s 90 s 120 s 0.0 0.5 1.0 1.5 2.0 2.5 3.0 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12

Echelle (mm) nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12

Echelle (mm) nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12

Echelle (mm) nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12

Echelle (mm) nm

Transfer Function of Polishing

Signature Multi-Echelles de la Finition par Toilage

Incidence de la Finition par Toilage sur les Echelles des Etats de Surface

Φ Φ with tolerance intervals << 10µm with tolerance intervals << 10µm Ra < 0.04µm Ra < 0.04µm

Journ al Crank Crank pin pin

Form performance with an accuracy < 2µm Form performance with an accuracy < 2µm

• M. El
• M. El Mansori

Mansori H.

• H. Zahouani

Zahouani

Signature Multi-Echelles de la Finition par Toialage

Papier support

Sous-couche adhésive

Liant Grains abrasifs a b c

Abrasive Particules

• 13.1

Finition Multi Echelles

Z µm

• 9.63

5.27

Original Original workpiece workpiece Average grits size (µm) Average grits size (µm) – – 9, 15, 30, 40, 80. 9, 15, 30, 40, 80.

• 20.8

• 49.9

Working conditions Working conditions Workpiece Workpiece rotation speed rotation speed 100 rpm 100 rpm Oscillation frequency

• f

Oscillation frequency

• f

shoes shoes 2,5 Hz 2,5 Hz Oscillation amplitude

• f

Oscillation amplitude

• f

shoes shoes 1 mm 1 mm Cycle time Cycle time 12 s 12 s Inserts hardness Inserts hardness 95 95 Shores Shores Lubrication fluid Lubrication fluid Strict Strict Oil Oil

• 25.1

• 27

Belt grinding tests

Why the use multiscale approach is relevant ?

The effect of the abrasive belt grits size

0% 20% 40% 60% 80% 100% 389 272 190 133 93 65 45 32 22 16 Scale(µm) Roughness attenuation (%)

9µm 30µm 80µm

61% 58%

Z µm

• 6.31

2.37

• 5
• 4
• 3
• 2
• 1

1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 X mm 1.87 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Y mm Z µm

• 4.13

2.78

• 3
• 2
• 1

1 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 X mm 1.87 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Y mm

As well known, the surface roughness is function and scale depen As well known, the surface roughness is function and scale dependent dent : :

Ra = 0.32 µm Ra = 0.37 µm

Effect assessment of the abrasive grits size

0% 20% 40% 60% 80% 100% 389 272 190 133 93 65 45 32 22 16

Scale (µm) Roughness Attenuation (%)

9µm 15µm 30µm 40µm 80µm

Gs=30µm Optimum Gs≤30µm No scale dependent Gs>30µm Scale dependent

P=0.8 MPa

The choice of the optimal grain size is a function of the spatia The choice of the optimal grain size is a function of the spatial morphology of l morphology of the the workpiece workpiece surface surface

Effect assessment of the abrasive grits size

0% 20% 40% 60% 80% 100% 389 272 190 133 93 65 45 32 22 16 Scale (µm) Roughness Attenuation (%)

9µm 15µm 30µm 40µm 80µm

Average attenuation

0% 20% 40% 60% 80% 100% 389 272 190 133 93 65 45 32 22 16 Scale (µm) Roughness Attenuation (%)

9µm 15µm 30µm 40µm 80µm

P=0.3 MPa P=0.8 MPa

No scale dependent Scale dependent Optimal grits size The choice of the optimal grain size seems to be independent of The choice of the optimal grain size seems to be independent of the contact the contact pressure between abrasive belt and pressure between abrasive belt and workpiece workpiece surface surface

Wear Signature

Cylinder Liner

Wear Signature

Before Wear Worn Cylinder

Wear

Wear Signature

Multi Scale Decomposition Worn Cylinder Before Wear

CWT CWT

Multi Scale Signature of Wear: Transfer Function

Transfer Function of Wear T(a) = SMa (a) {Worn Cylinder} SMa (a) {Before Wear} SMa (a) {Before Wear}

• 100%
• 80%
• 60%
• 40%
• 20%

0% 20% 40% 60% 80% 100% 3.84 2.81 2.05 1.50 1.10 0.80 0.59 0.43 0.31 0.23 0.17 0.12 0.09 0.07 0.05 0.04

Echelle (mm)

Wear

160 µm

• 60 %

Worn Cylinder Before Wear

Conclusions L’analyse multi échelles par ondelettes continues est outil robuste pour identifier:

• La signature des process de finition dans une large gamme

de longueurs d’onde

• les échelles liées à l’usure
• les échelles mises en jeu dans le contact, l’adhérence, le bruit

de rugosité et l’écoulement de fluide