The Connection between Surface Texture and Sliding Friction by Donald K. Cohen, Ph.D.

Transcription

1 1 The Connection between Surface Texture and Sliding Friction by Donald K. Cohen, Ph.D. Key References: Gwidon W. Stachowiak and Andrew W. Batchelor (2005), Engineering Tribology, Elsevier Butterworth-Heinemann, UK Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York. Duncan Dowson, (1998), History of Tribology, Bookcraft (Bath) Ltd. Great Britain. Peter J. Blau Friction Science and Technology, 1996, Marcel Decker, Inc. New York, NY Kenneth C. Ludema, Friction, Wear and Lubrication, 1996, CRC Press, Boca Raton, FLA Ernest Rabinowicz, Friction and Wear of Materials, John Wiley & Sons, 1995, New York, NY Frank Phillip Bowden and David Tabor (1982), Friction, An Introduction to Tribology, Robert E. Kreiger. Floriday, USA.

2 2 Surface Texture - Basics Surface: The boundary that separates an object from another object, substance, or space Texture: The composite of certain deviations that are typical of the real surface. It includes roughness and waviness Surface Roughness, Ra (2D), Sa (3D) is the average of the absolute value of profile heights over a given length (area). 2D R a L 1 = L 0 Z ( x ) dx Z X L 3D S a = 1 A Ly 0 Lx 0 Z( x, y) dxdy Z X Y ASME B

3 3 ASME B46.1 / ISO Z Y X Height Parameters Sa: The average deviation of the surface Sq: The Root-mean-square deviation of the surface Ssk: Skewness of surface height distribution Sku: Kurtosis of surface height distribution Ly Lx S a = 1 Z x y dxdy A (, ) 0 0 Ly Lx Sq = 1 Z x y dxdy A ( (, )) Ly Lx S = 1 Z x y dxdy sk ( (, )) 3 Sq3A 0 0 Ly Lx S = 1 Z x y dxdy ku ( (, )) 4 Sq4A 0 0 Ssk<<0.0 Ssk>> 0.0 Sku< 3.0 Sku> 3.0

4 4 Sliding Friction and Surface Texture Introduction What is Friction? Friction is the resistance to motion during sliding or rolling that is experienced when one solid body moves tangentially over another with which it is in contact. The resistive tangential force, which acts in a direction directly opposite to the direction of motion is called the friction force (Bhushan) F f = µw µ is the coefficient of friction Friction is NOT strictly a property of the material its a system response F f F F f F Sliding Friction Rolling Friction W W

5 5 Sliding Friction and Surface Texture Introduction Friction Good or Bad? Application Specific: Sometimes need friction sometimes want it to be zero

6 6 Sliding Friction and Surface Texture θ Ernest Rabinowicz, Friction and Wear of Materials, John Wiley & Sons, 1995, New York, NY

7 7 Sliding Friction and Surface Texture Introduction History Leonardo da Vinci The areas in contact have no effect on friction. 2. If the load (weight) of an object is doubled, its friction will also be doubled

8 8 Sliding Friction and Surface Texture Introduction History Considered the fundamental cause of friction being surface roughness force required to lift interlocking asperities No Picture Exists!! Guillaume Amontons It is impossible that these irregularities shall not be partly convex and partly concave, and when the former enter upon the latter they shall produce a certain resistance when there is an attempt to move them.

9 9 Sliding Friction and Surface Texture Introduction - History Does friction primarily comes from surface roughness..? yet it is found by experience that the flat surface of metals or other bodies may be so far polished as to increase the friction Introduces the concept of cohesion (today we call it adhesion) John Theophilus Desagulier Trouble: Adhesion theory can t explain laws of friction Apparent area

10 10 Sliding Friction and Surface Texture Introduction - History Turned Surface Max Slope ~15 o Charles Augustin Coulomb Coefficient of friction is independent of velocity Considers F f ~ Adhesion + Roughness Frank Phillip Bowden and David Tabor (1982), Friction An Introduction to Tribology,

11 11 Sliding Friction and Surface Texture Introduction - History Refresh!! 1. The apparent area of contact has no effect on friction. 2. If the load (weight) of an object is doubled, its friction will also be doubled F f = µw So which is it? Roughness?, Adhesion?, Shearing of Asperities (Lesile, Phillipe de la Hire)?

12 12 Sliding Friction and Surface Texture Introduction - History putting two solids together is rather like turning Switzerland upside down and standing it on Austria their area of intimate contact will be small (1950) more closely Iowa on top of the Netherlands (Thomas 1973) Frank Phillip Bowden( ) David Tabor ( ) Abbott and Firestone (1933) ( U of Michigan)-Invent Profilometer

13 13 Sliding Friction Strength of Materials Review Stress = Force/area Strain L/L E Young's Modulus of Elasticity Y - Yield Strength H - Hardness Resistance of metal to plastic deformation, usually by indentation H ~ 3Y (metals) Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York

14 14 Sliding Friction- Physics Bowden/Tabor revisit adhesion theory...why? Asperity slopes << 15 o, also - Smooth metals increase in friction, lubricants Consider the Real Area (A rp ) of contact vs Apparent Area A a of contact A a W A rp Plastic Deformation Assume plastic flow at the asperity mini hardness test Form enough junctions to support the applied force (W) W=A rp H (H~3Y) (Y is the yield strength) W/A a = (A rp /A a )H A rp /A a = (W/A a )/H Steel Y~ 10 5 PSI, so 200 psi load on 1in 2 steel A rp /A a ~0.05% Aluminum Y~3000 PSI, so 200 psi load on 1in 2 A rp /A a ~2%

15 15 Sliding Friction - Physics Bowden/Tabor key point A rp = W/H; Real area of contact 1) Proportional to Force 2) Independent of apparent area of contact sounds like friction! Maybe friction will be related to the real area of contact?? Friction (F f ) is the force required to shear intermetallic junctions plus the force required to plow the surface of the softer material by asperities of the harder surface (Bowden/Tabor).Consider the shear term F fp = A rp s (s is shear strength of junctions) Recall (pure plastic): A rp = W/H so F fp = W(s/H) µ=s/h metals, s~0.5y=h/6 So µ=1/6 (~0.2)

16 16 Sliding Friction - Physics F f = W(s/H) Bowden/Tabor: F fp proportional to normal force F fp not dependent on the apparent area of contact F fp will be reduced by lubricants that lower shear strength of asperities F fp (adhesion) not dependent on the surface roughness??? BUT: Are all contacts purely plastic? How about elastic deformation? Typically surface deforms plastically (work hardens?) then stabilizes-elastic support Experience indicates some frictional dependence on surface roughness

17 17 Sliding Friction Strength of Materials Review again ν = - ε trans / ε longitudinal ε = L/L σ Stress = Force/area ε - Strain L/L E Young's Modulus of Elasticity Y - Yield Strength H - Hardness Resistance of metal to plastic deformation, usually by indentation H ~ 3Y (metals) ν - Poisson s ratio Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York

18 18 Sliding Friction Physics Real Contact Hertz 1880 s Elastic Real Area of Contact, A re R 1 W A re = π 3WR * 4E 2/3 1 R = 1 R R 2 R 2 1 E * = 2 1 ν1 1 ν + E E Heinrich Hertz

19 19 Sliding Friction Physics Real Contact A re 3WR = π * 4E 2/3 In words Smaller Asperity Radii Larger Elastic Modulus Smaller real area Smaller real area E SiC 500 GPa E steel 200 GPa E lead 15 GPa E rubber GPa 1 GPa = 1x 10 9 N/M 2 = 1.45 x 10 5 psi

20 20 Sliding Friction Physics Real Contact Greenwood & Williamson W A a A a Apparent Area Asperities of same radii Asperities of random distribution of heights (e.g. Gaussian, exponential etc..) Asperities separated no interaction Exponential Distribution success!! A re W R * E σ 1/ 2 W - force applied E * - composite Elastic Modulus R summit radius of curvature σ is the standard deviation of the peak heights

21 21 Sliding Friction Physics Real Contact Greenwood Williamson A a W A a Recall: F fe = A re s (s is shear strength of junctions) Substituting for A re F fe W R * s E σ F fe ~ W F fe has no dependence on Apparent Area Consistent with Amonton 1/ 2

22 22 Dry Friction Physics Real Contact Greenwood Williamson In Words F fe = A re s Friction ~ shear strength of the real regions of contact A re W R * E σ 1/ 2 Larger the applied force larger real area of contact (friction ) Larger Elastic Modulus smaller area of contact (friction) Larger Summit Radii larger area of contact (friction) Larger the roughness smaller area of contact (friction) * * elastic domain

23 23 Good News Sliding Friction Physics Real Contact Greenwood Williamson 1966 Laws of friction follows since all surfaces have texture The mean asperity real contact area is independent of applied force -Exp dist only Rσ The mean asperity real pressure very weak dependence on applied force -Exp dist only E * (σ/r) 1/2 The number of contacts are proportional to applied force -Exp Dist only W/(E * (σ 3 R) 1/2 ) Bad News 1) Only Exponential law gives Laws of Friction results 2) Other frictional mechanisms (e.g. plowing) not considered 3) Asperity on asperity/ resolution - reality 4) Assumes elastic contact only next step is plasticity

24 24 Sliding Friction Physics Elastic and Plastic Greenwood & Williamson 1966 A re W R * E σ Pure Elastic 1/ 2 A rp = W/H Pure Plastic Plastic deformation will begin when the pressure at the asperity is greater than H. Calculate for various distribution (e.g. Exp) the probability of plastic deformation A A rp re = f ( Ψ, W...) E Ψ = H * σ R H- hardness of lowest hardness surface at interface (very weak dependence on W) 1 2 Plasticity Index

25 25 Sliding Friction Physics Elastic and Plastic Greenwood Williamson 1966 A re W R * E σ 1/ 2 Ψ<0.6 elastic regime Larger A r higher friction ( Too Smooth ) A r Ψ>1.0 plastic regime, lower Ar,but.. deformation, wear etc. eventually back to elastic regime or.scoring scuffing galling failure etc.. A rp = W/H Ψ = E H * σ R 1 2

26 26 Sliding Friction Physics Elastic and Plastic Greenwood Williamson 1966 σ 100 nm R 70 um Likely - Elastic Deformation Ψ = E H * σ R 1 2 σ 160 nm R 10 um Likely - Plastic Deformation

27 27 Sliding Friction Physics Reset Real Area of Contact A re W R * E σ Elastic Mode 1/ 2 E Ψ = H * σ R Plasticity Index - Predicts Elastic or Plastic 1 2 A rp = W/H Plastic Mode Friction relates to the Adhesion between surfaces at the real area of contact. Adhesion chemical bonds, mechanical, etc totally different/new field F fp = A rp s (s is shear strength of junctions) Recall (pure plastic): A rp = W/H so F fp = W(s/H) µ ap =s/h F fe = A re s (s is shear strength of junctions) Recall (pure elastic): A re W R * E σ 1/ 2 F fe R * 2 E σ 1/ 2 sw µ ae s E 1/ 2 R * 2 σ

28 28 Dry Friction Physics Elastic and Plastic - Models AF- Abbot Firestone 1933 Pure Plastic (Truncation Model) GW Greenwood and Williamson Elastic only spherical contacts etc. CEB Cheng, Etsion, Bogy 1987 Elastic/Plastic KE Kogut and Etsion Elastic/Plastic and tangential loading effects Jamari and Schipper 2006 Elastic/Plastic Ellipsoids asperities F=external Load P=Aspertiy Contact Force Fs=Total Adhesive Force Qmax-Static Friction Force J. Jamari and D.J. Schipper, An elastic-plastic contact model of ellipsoid bodies, Tribology Letters, Vol. 21 No. 3 march 2006.

29 29 Friction Physics Rough Surface Contacts Friction Coefficient C.Y. Poon and R. S. Sayles, The Classification of rough surface contacts in relation to tribology, J. Phys D: Appl. Phys. 25 (1992) A249-A256

30 30 Sliding Friction -- Engine- Valve Train Components A re W R * E σ 1/ 2 Very worn high friction larger A r adhesion Worn- run-in Minimal friction A r A rp = W/H Ψ = E H * σ R 1 2 Unworn high friction - deformation

31 31 Sliding Friction Transmission Components A re W * R E σ 1/ 2

32 32 Sliding Friction Physics Plowing Term θ µ d = 2 tan( θ ) π Assumes isotropic material 100:1 Vertical Magnification Gear Surface θ 6 deg µ d 0.06 Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York

33 33 Sliding Friction Physics Plowing Term Plowing Term Not that big for typical machined surface textures But! - debris and wear particles another story Sand Particle (Ottawa 16) Slope ~ 30 deg µ d 0.36 Also --Sandpaper, brake pads etc

34 34 Sliding Friction Physics Plowing Term Problem: Brake Rotor Sa inspec some work..some have NVH issues Solution: Quantify the surfaces Spec additional texture parameters q Solution: Identify cause of texture variation..(materials? tools? setup?) Sdq: Root-Mean Square Surface Slope Sdq = Lx Ly 2 1 Z ( x, y) + A 0 0 x Z ( x, y 2 y) dydx Sa: In spec Sdq: Low Sa: In spec Sdq: High Glenn R. Weier, Kelsey Hayes 1995

35 35 Sliding Friction Physics Surface Texture Bottom Line What is the connection between Surface Texture and Friction? 1) Friction - adhesion at the real area of contact 2) Friction - the deformation of asperities 2) Friction - plowing of the harder asperities into the softer material Other Texture Parameters can relate to the real area of contact/asperity slope..this has been the source of confusion/speculation/empirical work Surfaces are not a nice distribution of asperities of radius R

36 36 Sliding Friction Physics Surface Texture Parameters Sku=3.0 Ssk=0.0 Ssk Sku Ssk<<0.0 Ssk>> 0.0 Sku< 3.0 Sku> 3.0 Kotwal, C.A. and Bhuhsan, B. (1996) Contact Analysis of Non-Gaussian Surface for Minimum Static and Kinetic Friction and Wear Tribol. Trans. 39, elastic limit

37 37 Friction Physics Surface Texture Parameters Functional Bearing Area Parameters.. Spk, Sk Svk... tp =100% x (A + B + C + D )/L A B C D Max Ht Spk Peaks 40% Sk Core Svk Valleys Min Ht 0% Mr1 tp 50% mr Mr2 100% Spk = Peak Height.. First Region of contact Sk = Core Height... working Region.. Base Svk = Valley Depth... Lubricant Retention Region Abbott and Firestone (1933)

38 38 Cylinder Bore Finishes and Their Effect on Oil Consumption Stephen H. Hill, SAE, Cylinder Bore Best predictor of Oil Consumption, Vo, Vo = Svk(100-Mr2)/200 LD=Production Gasoline Auto Engines Units in um unless specified Careful of Vo units etc.

39 39 Sliding Friction Physics Surface Texture Parameters Functional Bearing Area Parameters.. Spk, Sk, Svk...

40 40 Tribology Transactions, 51: , 2008 SI = Surface Index for TFM SI = S pk 1 S a log Sk Ssk + Svk Ssm S z K SIW SI for Optical Profiler SIT SI for Stylus Profiler Largest SI Worst TFM K for optical or stylus

41 41 Effect of Roughness Parameter and Grinding Angle on Coefficient of Friction When Sliding os Al-Mg Alloy over EN8 Steel Pradeep L. Menezes Kishore and Satish V. Kailas, ASME Journal of Tribology, October 2006, Vol 128. p The coefficient of friction and transfer layer formation were observed to depend primarily on the direction of the grinding marks of the harder mating surface and independent of the surface roughness of harder mating surface. Direction of Motion

42 42 Modeling and Optimizing Honing Texture for Reduced Friction in Internal Combustion Engines Jeffrey Jocsak, Yong Li, Tian Tain and Victor K. Wong SAE, MIT-Ring-Pack Simulation Program Reduce Cross Hatch Angle -reduces friction (less asperity contact/more hydrodynamic lift) However, -Tradeoff- As reduce cross hatch angle increase risk of scuffing (TDC) / oil consumption Friction h γ = u γ = 0 u

43 43 Sliding Friction 3D Texture Directional Analysis Cross Hatch Angle Analysis

44 44 Conclusion Sliding Friction and Surface Texture Friction relates to adhesion of surfaces at points of real contact.real area of contact relates to surface texture Friction relates to deformation / plowing asperity shape/slope Asperity Shape/Slope relates to surface texture The challenge is choosing the right lateral/height resolution for measurement and the appropriate texture parameters to relate to friction and then to optimize for desired friction What is clear, is that the study of surface roughness continues to get more complicated and that we are a long way from understanding it. J. A. Greenwood (1992) I.L. Singer and H.M. Pollock (eds.) Fundamentals of Friction: Macroscopic and Microscopic Processes Kluwer Academic Publishers, Netherlands.