1 The Connection between Surface Texture and Sliding Friction by Donald K. Cohen, Ph.D. 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. Key References:
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1
The Connection between Surface Texture and Sliding Friction by
Donald K. Cohen, Ph.D.
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.
Key References:
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…”
X
Y Z
“Surface Roughness”, Ra (2D), Sa (3D) is the average of the absolute value of profile heights over a given length (area).
dxdyyxZA
SLxLy
a ∫∫=00
),(1
L R
LZ x dxa
L
= ∫1
0
( )2D
3D
ASME B46.1 2009
X
Z
3
dxdyLy Lx
yxZAqS ∫ ∫=0 0
2)),((1Sq: The Root-mean-square deviation of the surface
X
Y Z
Height Parameters
Ssk: Skewness of surface height distribution
dxdyLy Lx
yxZASqskS ∫ ∫=
0 03)),((3
1
Sku: Kurtosis of surface height distribution
dxdyLy Lx
yxZASqkuS ∫ ∫=
0 04)),((4
1
Sa: The average deviation of the surface dxdy
Ly LxyxZASa ∫ ∫=
0 0),(1
ASME B46.1 / ISO 25178-2
Ssk<<0.0 Ssk>> 0.0 Sku< 3.0 Sku> 3.0
4
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)
Ff = µW µ is the coefficient of friction “Friction is NOT strictly a property of the material – “its a system response”
Sliding Friction and Surface Texture Introduction
F Ff
W
F Ff
W
Sliding Friction Rolling Friction
5
Friction – Good or Bad?
Sliding Friction and Surface Texture Introduction
Application Specific: Sometimes need friction sometimes want it to be zero
Ernest Rabinowicz, Friction and Wear of Materials, John Wiley & Sons, 1995, New York, NY
θ
7 Sliding Friction and Surface Texture Introduction
History
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
Leonardo da Vinci
8
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 resistance when there is an attempt to move them…”.
Considered the fundamental cause of friction being surface roughness
9 Sliding Friction and Surface Texture Introduction - History
Does friction primarily comes from surface roughness..?
1683-1744
John Theophilus Desagulier
“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)
Trouble: Adhesion theory can’t explain laws of friction…”Apparent area”
10 Sliding Friction and Surface Texture Introduction - History
1736-1806 Charles Augustin Coulomb
•Coefficient of friction is independent of velocity
•Considers Ff ~ “Adhesion” + Roughness
Turned Surface Max Slope ~15o
Frank Phillip Bowden and David Tabor (1982), Friction An Introduction to Tribology,
11 Sliding Friction and Surface Texture Introduction - History
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
“Refresh”!!
So which is it? Roughness?, Adhesion?, Shearing of Asperities (Lesile, Phillipe de la Hire)?
Ff = µW
12 Sliding Friction and Surface Texture Introduction - History
Frank Phillip Bowden(1903-1968)
Abbott and Firestone (1933) ( U of Michigan)-Invent Profilometer
David Tabor (1913-2005)
“…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)
13 Sliding Friction – “Strength of Materials –Review”
Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York
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)
14 Sliding Friction- Physics
Bowden/Tabor revisit adhesion theory....why? Asperity slopes << 15o, also - Smooth metals – increase in friction, lubricants
Consider the Real Area (Arp) of contact vs Apparent Area Aa of contact
Plastic Deformation
Assume plastic flow – at the asperity – “mini hardness test” Form enough junctions to support the applied force (W)
W=ArpH (H~3Y) (Y is the yield strength) W/Aa = (Arp/Aa)H Arp/Aa = (W/Aa)/H
Steel Y~ 105 PSI , so 200 psi load on 1in2 steel Arp/Aa~0.05% Aluminum Y~3000 PSI, so 200 psi load on 1in2 Arp/Aa~2%
W Aa
Arp
15 Sliding Friction - Physics
Bowden/Tabor – key point Arp = 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 (Ff) 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…
Ffp = Arps (s is shear strength of junctions) Recall (pure plastic): Arp = W/H so Ffp = W(s/H)… µ=s/H metals, s~0.5Y=H/6 So µ=1/6 (~0.2)
16 Sliding Friction - Physics
•Bowden/Tabor: Ffp proportional to normal force Ffp not dependent on the apparent area of contact Ffp will be reduced by lubricants that lower shear strength of asperities
Ffp (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 Sliding Friction – “Strength of Materials – Review “again”
Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York
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
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)*
Ffe = Ares
Friction ~ shear strength of the real regions of contact
* elastic domain
23 Sliding Friction – Physics – “Real Contact”
Greenwood Williamson – 1966
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”
“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*
(σ3R)1/2)
“Good News”
“Bad News”
24 Sliding Friction – Physics – “Elastic and Plastic”
Greenwood & Williamson – 1966
2/1
*
∝
σR
EWAre
Arp = W/H
Pure Elastic 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
...),( WfAA
re
rp Ψ=
21
*
=Ψ
RHE σ Plasticity Index
(very weak dependence on W)
H- hardness of lowest hardness surface at interface
27 Sliding Friction – Physics – “Reset” –Real Area of Contact
2/1
*
∝
σR
EWAre
Arp = W/H
Elastic Mode
Plastic Mode 21
*
=Ψ
RHE σ
Plasticity Index - Predicts Elastic or Plastic
Friction relates to the Adhesion between surfaces at the real area of contact.
Adhesion – chemical bonds, mechanical, etc…”totally different/new field”
Ffp = Arps (s is shear strength of junctions) Recall (pure plastic): Arp = W/H so Ffp= W(s/H)… µap=s/H Ffe = Ares (s is shear strength of junctions) Recall (pure elastic):
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?)
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
Kotwal, C.A. and Bhuhsan, B. (1996) “Contact Analysis of Non-Gaussian Surface for Minimum Static and Kinetic Friction and Wear Tribol. Trans. 39, 890-898 “elastic limit”
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 697-704
…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 Modeling and Optimizing Honing Texture for Reduced Friction in Internal Combustion Engines
Jeffrey Jocsak, Yong Li, Tian Tain and Victor K. Wong SAE, 2006-01-0647 •MIT-Ring-Pack Simulation Program
Sliding Friction – 3D Texture Directional Analysis
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 57-76 1992 Kluwer Academic Publishers, Netherlands.