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.

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

• f 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).

dxdy y x Z A S

Lx Ly a

∫ ∫

= ) , ( 1

L

R L Z x dx

a L

=

∫

1 ( )

2D 3D

ASME B46.1 2009

X Z

3

dxdy Ly Lx y x Z A q S ∫ ∫ = 0 0 2 )) , ( ( 1

Sq: The Root-mean-square deviation of the surface

X Y Z Height Parameters

Ssk: Skewness of surface height distribution

dxdy Ly Lx y x Z A Sq sk S ∫ ∫ = 0 0 3 )) , ( ( 3 1

Sku: Kurtosis of surface height distribution

dxdy LyLx y x Z A Sq ku S ∫ ∫ = 0 0 4 )) , ( ( 4 1

Sa: The average deviation of the surface dxdy Ly Lx y x Z A Sa ∫ ∫ = 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

www.animationfactory.com

6

Sliding Friction and Surface Texture

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 force required to lift interlocking asperities

1663-1705 Guillaume Amontons

Sliding Friction and Surface Texture Introduction History

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

Ff = W(s/H)

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

ν = - εtrans / εlongitudinal ε = ∆L/L

http://silver.neep.wisc.edu/~lakes/PoissonIntro.html

18

Sliding Friction – Physics – “Real Contact” – Hertz 1880’s

R1 R2 W

‘Elastic” Real Area of Contact, Are

3 / 2 *

4 3       = E WR Are π

2 1

1 1 1 R R R + =

2 2 2 1 2 1 *

1 1 1 E E E ν ν − + − =

1857-1894 Heinrich Hertz

19

Sliding Friction – Physics – “Real Contact”

3 / 2 *

4 3       = E WR Are π

“In words” Smaller Asperity Radii Smaller real area Larger Elastic Modulus Smaller real area

GPa Esteel 200 ≈

1 GPa = 1x 109 N/M2 = 1.45 x 105 psi

GPa Elead 15 ≈ GPa ESiC 500 ≈ GPa Erubber 001 . ≈

20

Sliding Friction – Physics – “Real Contact” Greenwood & Williamson - 1966

W

Aa – Apparent Area

Aa W

Asperities of same radii Asperities of random distribution of heights (e.g. Gaussian, exponential etc..) Asperities separated – “no interaction”

Exponential Distribution – success!!

2 / 1 *

              ∝ σ R E W Are

W - force applied E* - composite Elastic Modulus R –summit radius of curvature σ is the standard deviation of the peak heights

21

Sliding Friction – Physics – “Real Contact” Greenwood Williamson - 1966

W Aa W

Recall: Ffe = Ares (s is shear strength of junctions) Substituting for Are Ffe ~ W Ffe has no dependence on Apparent Area Consistent with Amonton

2 / 1 *

              ∝ σ R E W s Ffe

Aa

22

2 / 1 *

              ∝ σ R E W Are

Dry Friction – Physics – “Real Contact” Greenwood Williamson - 1966

“In Words”

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 *

              ∝ σ R E W Are

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

...) , ( W f A A

re rp

Ψ =

2 1 *

              = Ψ R H E σ

Plasticity Index (very weak dependence on W)

H- hardness of lowest hardness surface at interface

25

2 1 *

              = Ψ R H E σ r

A

2 / 1 *

              ∝ σ R E W Are

Arp = W/H

1.0 0.6

Sliding Friction – Physics – “Elastic and Plastic” Greenwood Williamson – 1966

Ψ<0.6 elastic regime Larger Ar higher friction (“Too Smooth”) Ψ>1.0 plastic regime, lower Ar,but…..

……deformation, wear etc. eventually back to elastic regime or ………….scoring scuffing galling failure etc..

26

Sliding Friction – Physics – “Elastic and Plastic” Greenwood Williamson – 1966

2 1 *

              = Ψ R H E σ

σ ∼ 160 nm R ∼ 10 um σ ∼ 100 nm R ∼ 70 um

“Likely - Elastic Deformation” “Likely - Plastic Deformation”

27

Sliding Friction – Physics – “Reset” –Real Area of Contact

2 / 1 *

              ∝ σ R E W Are

Arp = W/H

Elastic Mode Plastic Mode

2 1 *

              = Ψ R H E 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):

2 / 1 *

              ∝ σ R E W Are

sW E R Ffe

2 / 1 2 *

      ≈ σ

2 / 1 2 *

      ≈ σ µ E R s

ae

28

Dry Friction – Physics – “Elastic and Plastic” - Models

AF- Abbot Firestone – 1933 – Pure Plastic – (Truncation Model) GW – Greenwood and Williamson – 1966- Elastic only – spherical contacts etc. CEB – Cheng, Etsion, Bogy – 1987 – Elastic/Plastic KE – Kogut and Etsion – 2004 - Elastic/Plastic and tangential loading effects Jamari and Schipper – 2006 – Elastic/Plastic – Ellipsoids asperities

• J. Jamari and D.J. Schipper, An elastic-plastic contact model of ellipsoid bodies, Tribology Letters, Vol. 21 No. 3 march 2006.

F=external Load P=Aspertiy Contact Force Fs=Total Adhesive Force Qmax-Static Friction Force

29

Friction – Physics – Rough Surface Contacts

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

Friction Coefficient

30 2 1 *

              = Ψ R H E σ r

A

2 / 1 *

              ∝ σ R E W Are

Arp = W/H

1.0 0.6

Unworn “high friction” - deformation Worn- “run-in” “Minimal friction” Very worn “high friction” – larger Ar adhesion

Sliding Friction -- Engine- Valve Train Components

31

Sliding Friction Transmission Components

2 / 1 *

              ∝ σ R E W Are

32

Sliding Friction – Physics –Plowing Term

θ

π θ µ ) tan( 2 =

d Assumes isotropic material

Gear Surface θ∼ 6 deg µd ∼ 0.06

Bharat Bhushan, (2002), Introduction to Tribology, John Wiley & Sons, New York

100:1 Vertical Magnification

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 µd ∼ 0.36 Also --Sandpaper, brake pads etc…

34

Sa: In spec Sdq: Low Sa: In spec Sdq: High

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?)

Glenn R. Weier, Kelsey Hayes 1995

Sliding Friction – Physics –Plowing Term

dydx y y x Z Ly x y x Z Lx A Sdq 2 ) , ( 2 ) , ( 1         ∂ ∂ ∫ +       ∂ ∂ ∫ =

Sdq: Root-Mean Square Surface Slope

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

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”

Sliding Friction – Physics – Surface Texture Parameters

Ssk Sku

Sku=3.0 Ssk=0.0

Ssk<<0.0 Ssk>> 0.0 Sku< 3.0 Sku> 3.0

37

“Functional” Bearing Area Parameters .. Spk, Sk Svk....

D C B A

tp

=100% x (A + B + C + D )/L

Spk = “Peak Height” .. First Region of contact Sk = “Core Height”... “working” Region ..”Base” Svk = “Valley Depth” ... “Lubricant Retention Region”

tp

Peaks

“

Core

”

Valleys

100% 50% 0% Min Ht Max Ht

40% Svk Sk Spk

Mr1 Mr2

mr

Friction – Physics – Surface Texture Parameters

Abbott and Firestone (1933)

38

Cylinder Bore Finishes and Their Effect on Oil Consumption Stephen H. Hill, SAE, 2001-01-3550

LD=Production Gasoline Auto Engines Units in um unless specified

Cylinder Bore Best predictor of Oil Consumption, Vo,

Vo = Svk(100-Mr2)/200

“Careful of Vo units etc.

39

Sliding Friction – Physics – Surface Texture Parameters

“Functional” Bearing Area Parameters .. Spk, Sk, Svk....

40

K S S S S S S S SI

z a sk sm vk pk k

+      

• −

     

• =

1 log

SI = Surface Index for TFM

SIW – SI for Optical Profiler SIT – SI for Stylus Profiler Largest SI – Worst TFM K for optical or stylus

Tribology Transactions, 51: 784-789, 2008

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
• 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

u u

∞ = γ = γ

h

Friction

43

Cross Hatch Angle Analysis

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.