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

Transcription

1 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

2 Caractère Multi-Echelles des Surfaces Procédés de de Finition des des Surfaces Large gamme d échelles Nano-échelle 10-9 m Echelles des longueurs d onde mm 10-3 m Fonctionnalités Propriétés Optiques Diffusion - Peinture- Aspect Planéité Mécanique et Tribologie -Lubrification - Contact & Etanchéité - Réduction du frottement - Adhésion -Usure

3 Métrologie Multi-Echelles 10mm Z TRIANGULATION LASER 6mm RUGOSIMÈTRE TACTILE LARGE ÉCHELLE 1mm INTERFÉROMÈTRIE LARGE ECHELLE MICROSCOPIE CONFOCALE 50µm INTERFÉROMÈTRIE CLASSIQUE DEFLECTOMETRIE 3D Joint d étanchéité 5µm 0 AFM 100µm 500µm 50mm X,Y

4 Identification Multi-Echelles des Procédés de Finition f I ( x) PROCESS Manufacturing GF ( x) Finishing Wear G F ( x) = T( a) fi( x) Multi- Sacle Transfer Fonction

5 Sinature Multi-Echelles Multi Scale Information Decomposition Decomposition Multi Echelles

6 Decomposition by Continuous Wavelet Function ψba x x b, ( ) = ψ( ) a a 1 With a i = [a 1,a 2...a n ] the scales of analysis in mm & b the spatial parameter of translation. ψ( x) is a wavelet if : continuous, with finite energy + ( ) ψ 2 xdx< + ( ) = 0 ψ xdx

7 Generation of Wavelet Family x Mother Wavelet x/ai 0.04mm 0.09mm 0.19 mm 0.40mm 0.86mm 1.86mm Wavelets Family

8 Local Detection Signal Decomposition First detection Second Detection

9 Wavelet Transform Mathematical Procedure: F(x) Convolution of the Signal with different scales of Mother Wavelet ψ ( x) = ψ( a ) b, a i 2 a L Modulus b mm fb a Phase θ W, ( x) Signal Wavelet Family mm

10 Scales Multi-Scale Arithmetic Mean value: Ma (Ra, Wa) Ra(a i ) Ma ( a ) = 1 N N x = 1 ( ) f a x Wa(a i ) Micro-Scale: Ra Waviness: Wa Ma(µm) Wavelengths (mm)

11 Multi Scale Signature f I Ma f I ( x) (a) PROCESS Manufacturing Finishing Wear GF ( x) F ( ) Ma G a Transfer Function: h x ( a) Ma ( a) Ma ( a) GF fi = ( a) Ma f I

12 2D Multi Scale Decomposition 2D Decomposition Multi Scale Morphology Multi Scale Decomposition

13 Multi Scale Decomposition by Wavelet Transform f ( x, y ) L 2( R ), 1 x b y b x y Cwt( a, b) = f ( x, y) ψ (, ) dxdy a a a x y ψ 2D Wavelet ( ) ( 2 2, = 2 ) xy x y e 2 2 ( x y ) + 2

14 Mathematical Procedure: Wavelets Bank Surface Multi scale Spectrum f ( x, y ) ψ a*,b ( x, y ) Wψf (b, a) = f ( x, y ) ψ a,b* ( x, y)

15 Inverse Transform f% (, x y) = TF W ( w, w )%( aw, aw ) 1 { f } ψ, ψ a a x y x y 1 f% a x y = W a b x y C f (, ) ψ (, ) ψ a, b(, ) 2 g dadb a Avec C g = Ψ 2 ( f ) df f Wavelets Spectrum Scales Wavelets Bank (Dual) Multi Scale Decomposition Scales W f ψ ( a, b) ψ ab, ( xy, ) fa x, y ( )

16 0.019 Échelles X Y Quantitative Decomposition SMa ( a ) M N = = = x 1 y 1 f x, y a ( ) MN Spectre de rugosité SMa Macro Scale Echelles (mm) Micr Scale Ra (µm)

17 f I ( x, y) SMa f I (a) 2D Transfer Function PROCESS Manufacturing Finishing Finition GF ( x, y) SMa G a F ( ) h ( xy, ) ( a) SMa ( a) ( ) G SMa a F fi = ( a) SMa f I

18 Transfer Function of Polishing Before Polishing Multi Scale SMa Après 120s after 90s 30s 3.0 Transfer Function of Polishing nm % 80% % Echelle (mm) 40% 30 s 30 s s s 20% 0% % -40% -60% -80% Multi Scale SMa -100% 3.0 Echelle (mm) nm Echelle (mm)

19 Signature Multi-Echelles de la Finition par Toilage M. El Mansori H. Zahouani Incidence de la Finition par Toilage sur les Echelles des Etats de Surface Φ with tolerance intervals << 10µm Form performance with an accuracy < 2µm Ra < 0.04µm Journ al Crank pin

20 Signature Multi-Echelles de la Finition par Toialage a b c Grains abrasifs Liant Sous-couche adhésive Papier support Abrasive Particules

21 Finition Multi Echelles Z µm Original workpiece Average grits size (µm) 9, 15, 30, 40, Z µm Z µm Working conditions Workpiece rotation speed 100 rpm Oscillation frequency of shoes Oscillation amplitude of shoes 2,5 Hz 1 mm Belt grinding tests Z µm Cycle time Inserts hardness 12 s 95 Shores Z µm Z µm Lubrication fluid Strict Oil

22 Why the use multiscale approach is relevant? As well known, the surface roughness is function and scale dependent dent : Ra = 0.32 µm Roughness attenuation (%) 100% 80% 60% 40% 20% 0% The effect of the abrasive belt grits size Scale(µm) 9µm 30µm 80µm 61% 58% Y mm Y mm X mm X mm Zµm Zµm Ra = 0.37 µm

23 Effect assessment of the abrasive grits size 100% Roughness Attenuation (%) 80% 60% 40% 20% 9µm 15µm 30µm 40µm 80µm Gs=30µm Optimum Gs 30µm No scale dependent 0% Gs>30µm Scale dependent P=0.8 MPa Scale (µm) The choice of the optimal grain size is a function of the spatial l morphology of the workpiece surface

24 Effect assessment of the abrasive grits size Roughness Attenuation (%) 100% 80% 60% 40% 20% 0% 9µm 15µm 30µm 40µm 80µm Optimal grits size P=0.3 MPa Scale (µm) Average attenuation 100% Roughness Attenuation (%) 80% 60% 40% 20% 0% P=0.8 MPa Scale (µm) µm 15µm 30µm 40µm 80µm No scale dependent Scale dependent The choice of the optimal grain size seems to be independent of the contact pressure between abrasive belt and workpiece surface

25 Cylinder Liner Wear Signature

26 Wear Signature Before Wear Worn Cylinder Wear

27 Wear Signature Before Wear Multi Scale Decomposition CWT Worn Cylinder CWT

28 Multi Scale Signature of Wear: Transfer Function Before Wear Transfer Function of Wear SMa (a) {Worn Cylinder} T(a) = SMa (a) {Before Wear} SMa (a) {Before Wear} Worn Cylinder 100% 80% 60% 40% 20% 0% 160 µm -20% Wear -40% -60% -80% -100% -60 % Echelle (mm)

29 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