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 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
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
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
Sinature Multi-Echelles Multi Scale Information Decomposition Decomposition Multi Echelles
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
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: 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
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) 0.4 0.3 0.2 0.1 0 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 Wavelengths (mm)
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
2D Multi Scale Decomposition 2D Decomposition Multi Scale Morphology Multi Scale Decomposition
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
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)
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 ( )
0.019 Échelles X Y Quantitative Decomposition SMa ( a ) M N = = = x 1 y 1 f x, y a ( ) MN Spectre de rugosité SMa 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 2.048 1.498 1.095 0.801 0.586 0.428 0.313 0.229 0.167 0.122 0.090 0.065 0.048 0.035 0.026 Macro Scale Echelles (mm) Micr Scale Ra (µm)
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
Transfer Function of Polishing Before Polishing Multi Scale SMa Après 120s after 90s 30s 3.0 Transfer Function of Polishing 2.5 2.0 1.5 1.0 nm 0.5 0.0 100% 80% 0.12 0.2 0.35 0.6 1.02 1.75 2.99 5.12 8.75 15 25.6 60% Echelle (mm) 40% 30 s 30 s 90 30 s 90 120 s 20% 0% 0.12 0.12 0.17 0.2 0.24 0.35 0.35 0.5 0.6 0.72 1.02 1.46 1.75 2.09 2.99 4.28 5.12 6.12 8.75 12.5 15 17.9 25.6-20% -40% -60% -80% Multi Scale SMa -100% 3.0 Echelle (mm) 2.5 2.0 1.5 nm 1.0 0.5 0.12 0.12 0.2 0.2 0.35 5.12 8.75 15 25.6 0.0 0.6 1.02 1.75 2.99 Echelle (mm)
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
Signature Multi-Echelles de la Finition par Toialage a b c Grains abrasifs Liant Sous-couche adhésive Papier support Abrasive Particules
Finition Multi Echelles -9.63 0 5.27 Z µm Original workpiece Average grits size (µm) 9, 15, 30, 40, 80. -13.1 0 10 22.7 Z µm -20.8 0 28.7 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 -27 0 38.2 Z µm Cycle time Inserts hardness 12 s 95 Shores -49.9 0 76.5 Z µm -25.1 64.8 Z µm Lubrication fluid Strict Oil
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 389 272 190 133 93 65 45 32 22 16 Scale(µm) 9µm 30µm 80µm 61% 58% Y mm Y mm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.87 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.87 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 X mm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 X mm -6.31-5 -4-3 -2-1 0 1 2.37-4.13-3 -2-1 0 1 2 2.78 Zµm Zµm Ra = 0.37 µm
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% 389 272 190 133 93 65 45 32 22 16 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
Effect assessment of the abrasive grits size Roughness Attenuation (%) 100% 80% 60% 40% 20% 0% 9µm 15µm 30µm 40µm 80µm Optimal grits size 389 272 190 133 93 65 45 32 22 16 P=0.3 MPa Scale (µm) Average attenuation 100% Roughness Attenuation (%) 80% 60% 40% 20% 0% 389 272 P=0.8 MPa 190 133 93 65 45 Scale (µm) 32 22 16 9µm 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
Cylinder Liner Wear Signature
Wear Signature Before Wear Worn Cylinder Wear
Wear Signature Before Wear Multi Scale Decomposition CWT Worn Cylinder CWT
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% 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 Wear -40% -60% -80% -100% -60 % Echelle (mm)
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