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 Large gamme d’échelles ≈ Nano-échelle mm Echelles des longueurs d’onde 10 -9 m 10 -3 m Fonctionnalités Mécanique et Tribologie Propriétés Optiques - Lubrification - Contact & Etanchéité Diffusion - Réduction du frottement - Peinture- Aspect - Adhésion Planéité - Usure

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

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

Sinature Multi-Echelles Multi Scale Information Decomposition Decomposition Multi Echelles

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

Generation of Wavelet Family x Mother Wavelet x/a i 0.04mm 0.09mm 0.19 mm 0.40mm 0.86mm 1.86mm Wavelets Family

Local Detection Signal Decomposition Second Detection First detection

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

Multi-Scale Arithmetic Mean value: Ma (Ra, Wa) Ra(a i ) Scales N 1 ( ) ∑ = Ma ( a ) f a x N = x 1 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 PROCESS ( ) ( ) x x f G I F • Manufacturing • Finishing • Wear Ma G a ( ) Ma ( a ) f I F Transfer Function: − Ma Ma ( ) a ( ) a ( ) = G f h a F I x Ma ( ) a f I

2D Multi Scale Decomposition 2 D D e c o m p o s i t i o n Multi Scale Morphology Multi Scale Decomposition

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

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

Inverse Transform { } % − = ψ 1 f % f ( , ) x y TF W ( w w , ) ( aw aw , ) ψ a , a x y x y ( ) df − ∞ Ψ 2 1 dadb ( ) f ∫∫ % = ψ ∫ f = f x y , W ( , ) a b ( , ) x y C g Avec ψ a a b , 2 C a f − ∞ g Wavelets Spectrum Multi Scale Decomposition Scales Scales Wavelets ⊗ Bank (Dual) ฀ ( ฀ ( ) ψ ) ( ) a b x y , f f x y , W a b , ψ , a

Quantitative Decomposition ( ) = ∑∑ f x y , M N a SMa a ( ) MN = = x 1 y 1 Échelles Spectre de rugosité SMa 0.35 0.30 0.25 0.20 (µm) Ra 0.15 0.10 0.05 0.00 X 8 8 5 1 6 8 3 9 7 2 0 5 8 5 6 9 4 9 9 0 8 2 1 2 6 2 9 6 4 3 2 1 0 4 0 8 5 4 3 2 1 1 0 0 0 0 0 0 . . . . . . . . . . . . . . . . 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 Y Echelles (mm) Macro Micr Scale Scale

2D Transfer Function PROCESS ( ) ( ) f x y , G x y , I F • Manufacturing • Finishing SMa ( a ) SMa • Finition G a ( ) f I F − SMa ( ) a SMa ( ) a ( ) = G f h a F I ( , ) x y SMa ( ) a f I

Transfer Function of Polishing Before Polishing Multi Scale SMa 3.0 2.5 2.0 nm 1.5 Transfer Function of Polishing 1.0 0.5 100% 100% 100% 0.0 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12 80% 80% 80% Echelle (mm) 60% 60% 60% 40% 40% 40% 20% 20% 20% 30 s 30 s 0% 0% 0% 90 s 30 s 90 s 25.6 25.6 25.6 17.9 17.9 15 12.5 12.5 8.75 8.75 8.75 6.12 6.12 5.12 4.28 4.28 2.99 2.99 2.99 2.09 2.09 1.75 1.46 1.46 1.02 1.02 1.02 0.72 0.72 0.6 0.5 0.5 0.35 0.35 0.35 0.24 0.24 0.2 0.17 0.17 0.12 0.12 0.12 120 s -20% -20% -20% Après 90s Après 30s 120s after -40% -40% -40% -60% -60% -60% Multi Scale SMa -80% -80% -80% 3.0 3.0 3.0 -100% -100% -100% 2.5 2.5 2.5 Echelle (mm) Echelle (mm) Echelle (mm) 2.0 2.0 2.0 nm nm nm 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 25.6 25.6 15 15 8.75 8.75 5.12 5.12 2.99 2.99 1.75 1.75 1.02 1.02 0.6 0.6 0.35 0.35 0.2 0.2 0.12 0.12 25.6 15 8.75 5.12 2.99 1.75 1.02 0.6 0.35 0.2 0.12 Echelle (mm) Echelle (mm) Echelle (mm)

Signature Multi-Echelles de la Finition par Toilage M. El Mansori Mansori M. El H. Zahouani Zahouani H. Incidence de la Finition par Toilage sur les Echelles des Etats de Surface Φ with tolerance intervals << 10µm Φ with tolerance intervals << 10µm Form performance with an accuracy < 2µm Form performance with an accuracy < 2µm Journ al Ra < 0.04µm Ra < 0.04µm Crank Crank pin 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 Original workpiece Original workpiece Average grits size (µm) – – 9, 15, 30, 40, 80. 9, 15, 30, 40, 80. Average grits size (µm) -9.63 0 5.27 Z µm -13.1 0 10 22.7 Z µm -20.8 0 28.7 Z µm Working conditions Working conditions Workpiece rotation speed Workpiece rotation speed 100 rpm 100 rpm -27 0 38.2 Z µm Oscillation frequency of Oscillation frequency of 2,5 Hz 2,5 Hz shoes shoes Belt grinding tests Oscillation amplitude of Oscillation amplitude of 1 mm 1 mm shoes shoes Cycle time 12 s Cycle time 12 s -49.9 0 76.5 Z µm -25.1 64.8 95 95 Z µm Inserts hardness Inserts hardness Shores Shores Strict Strict Lubrication fluid Lubrication fluid Oil Oil

Why the use multiscale approach is relevant ? As well known, the surface roughness is function and scale dependent dent : : As well known, the surface roughness is function and scale depen Ra = 0.32 µm 1.87 2.37 1.6 1 1.4 0 The effect of the abrasive belt grits size 1.2 -1 Z µm Y mm 1 -2 0.8 Roughness attenuation (%) 100% -3 0.6 -4 0.4 80% -5 0.2 9µm -6.31 61% 60% 0 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 30µm 40% 1.87 2.78 80µm 58% 2 1.6 20% 1.4 1 1.2 0% 0 Z µm Y mm 1 389 272 190 133 93 65 45 32 22 16 -1 0.8 Scale(µm) 0.6 -2 0.4 -3 0.2 -4.13 0 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 Ra = 0.37 µm

Effect assessment of the abrasive grits size 100% Roughness Attenuation (%) Gs=30µm Optimum 80% 9µm 60% 15µm 30µm Gs ≤ 30µm No scale dependent 40% 40µm 80µm 20% Gs>30µm Scale dependent 0% 389 272 190 133 93 65 45 32 22 16 Scale (µm) P=0.8 MPa The choice of the optimal grain size is a function of the spatial morphology of l morphology of The choice of the optimal grain size is a function of the spatia the workpiece workpiece surface surface the

Effect assessment of the abrasive grits size 100% Roughness Attenuation (%) Optimal grits size 80% 9µm 60% 15µm 30µm 40% 40µm 80µm 20% 0% 389 272 190 133 93 65 45 32 22 16 P=0.3 MPa Scale (µm) Average attenuation 100% Roughness Attenuation (%) 80% 9µm 60% 15µm 30µm 40% 40µm 80µm 20% No scale Scale 0% 389 272 190 133 93 65 45 32 22 16 dependent dependent P=0.8 MPa Scale (µm) The choice of the optimal grain size seems to be independent of the contact the contact The choice of the optimal grain size seems to be independent of pressure between abrasive belt and workpiece workpiece surface surface pressure between abrasive belt and

Wear Signature Cylinder Liner

Worn Cylinder Wear Signature Wear Before Wear

Multi Scale Decomposition Wear Signature CWT CWT Worn Cylinder Before Wear

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