# Key References: Gwidon W. Stachowiak and Andrew W. Batchelor (2005), - PowerPoint PPT Presentation

## 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),

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 10016 Kenneth C. Ludema, Friction, Wear and Lubrication, 1996, CRC Press, Boca Raton, FLA 33431 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 L Z 1 ∫ = R Z x dx ( ) a L X L 0 3D Y Z Ly Lx 1 ∫ ∫ = S Z ( x , y ) dxdy a A X 0 0 ASME B46.1 2009

3. 3 ASME B46.1 / ISO 25178-2 Y Z X Height Parameters Ly Lx 1 = ∫ ∫ S a Z ( x , y ) dxdy A Sa: The average deviation of the surface 0 0 Ly Lx 1 = Sq: The Root-mean-square deviation of the 2 ∫ ∫ S ( Z ( x , y )) dxdy q A 0 0 surface Ly Lx 1 = 3 ∫ ∫ S ( Z ( x , y )) dxdy Ssk: Skewness of surface height distribution sk 3 Sq A 0 0 LyLx 1 = 4 Sku: Kurtosis of surface height distribution ∫ ∫ S ( Z ( x , y )) dxdy ku 4 Sq A 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 = µ W 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. Sliding Friction and Surface Texture Introduction 5 Friction – Good or Bad? www.animationfactory.com 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 1452-1519 1. 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!! “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 1663-1705 resistance when there is an attempt to move them…”. Guillaume Amontons

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 ) 1683-1744 John Theophilus Desagulier Trouble: Adhesion theory can’t explain laws of friction…”Apparent area”

10. Sliding Friction and Surface Texture Introduction - History 10 Turned Surface Max Slope ~15 o •Coefficient of friction is independent of velocity 1736-1806 Charles Augustin Coulomb •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 = µ W 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(1903-1968) David Tabor (1913-2005) 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 Plastic Deformation A rp 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 http://silver.neep.wisc.edu/~lakes/PoissonIntro.html 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 2 / 3   3 WR = π W   A re   R 1 * 4 E 1 1 1 = + R R R 1 2 R 2 − ν − ν 2 2 1 1 1 = + 1 2 * E E E 1 2 1857-1894 Heinrich Hertz

19. 19 Sliding Friction – Physics – “Real Contact” 2 / 3   3 WR = π   A re   * 4 E “In words” Smaller Asperity Radii Smaller real area Larger Elastic Modulus Smaller real area ≈ E SiC 500 GPa ≈ E steel 200 GPa ≈ E lead 15 GPa ≈ E rubber 0 . 001 GPa 1 GPa = 1x 10 9 N/M 2 = 1.45 x 10 5 psi

20. 20 Sliding Friction – Physics – “Real Contact” Greenwood & Williamson - 1966 A a W W 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!! 1 / 2     R W   ∝ W - force applied   A re   σ E * - composite Elastic Modulus   * E   R –summit radius of curvature σ is the standard deviation of the peak heights

21. 21 Sliding Friction – Physics – “Real Contact” Greenwood Williamson - 1966 A a A a W W Recall: F fe = A re s (s is shear strength of junctions) Substituting for A re 1 / 2     R W   ∝   F fe s   σ   * E   F fe ~ W F fe has no dependence on Apparent Area Consistent with Amonton