1. Jayadeep U.B. PhD (MED) IISc
Rolling Friction
Jayadeep U.B.
PhD (MED) IISc

2. Outline Introduction Case Studies Mechanisms of Rolling Friction
“Free” or “Inertial” Rolling
Accelerated Rolling
Rolling with Deformation
Mechanisms of Rolling Friction
Interfacial slip in the Contact Area
Adhesion Hysteresis
Effect of Surface Roughness
Elastic and Plastic Deformation
Electric Double Layer
Concluding Remarks
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3. Introduction
Invention of Wheel – Difference between Rolling and Sliding Friction
Energy loss is much higher for sliding friction compared to rolling friction, when the components are reasonably rigid.
Highly counter-intuitive: static friction has almost no effect on rolling friction!
Combined effect of a number of energy dissipating effects
We do not generally talk about a “rolling friction force”!
Rolling friction could be a misnomer; Resistance to Rolling is much better…
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4. I: Free Rolling or Inertial Rolling
Continuum assumption
Rigid Cylindrical Roller
Rigid Horizontal Surface
Velocity remains constant
FBD gives:
N = W
No Frictional Force
No Rolling Friction v ω W N
Free body diagram
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5. II-A: Accelerated Rolling – down an incline
Continuum assumption
Rigid Cylindrical Roller
Rigid Inclined Surface
Velocity increases
FBD gives:
N = W cosθ
f ≤ μ N = μ W cosθ
f = μ N leads to slipping
r f = I α
No Rolling Friction
ω,α
v,a θ W f N
Free body diagram
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6. II-B: Accelerated Rolling – on a Horizontal Surface
Continuum assumption
Rigid Cylindrical Roller
Rigid Horizontal Surface
Velocity increases
FBD gives:
N = W
F – f = m a
r f = I α
f ≤ μ N
f = μ N leads to slipping
No Rolling Friction
ω,α F
v,a W F f N
Free body diagram
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7. Rolling with Deformation
Continuum assumption
Rigid Cylindrical Roller
Deformable Horizontal Surface
Velocity decreases
FBD gives:
N cosβ = W
N sinβ = ma
d N cosβ – r N sinβ = I α
No Sliding Friction ω v α a W d
~ r β N
Free body diagram
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8. Mechanisms of Rolling Friction: Coulomb Laws & Interfacial Slip
In case of hypothetical continuum, the only mechanism for rolling resistance is what we discussed…
Coulomb (1781): For same materials, resistance to rolling is proportional to weight and inversely proportional to diameter.
Reynolds (1876): Slipping & friction at the contact (due to deformation) is the reason for Rolling Friction (Hence so-called!) and Heathcote (1921):
Explained difference in rolling resistance in hard and soft materials
But, lubrication never significantly reduces rolling friction!
It was explained that reducing friction increases slip, and slipping area.
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9. Molecular Adhesion Hysteresis
Tomlinson (1929):
Micro-slip suggested by Reynolds is extremely small to account for experimental values of rolling friction.
Reynolds type micro-slip should have produced fretting, which was not observed.
Surface atoms are pulled away from equilibrium position; exceeding a critical distance they flick back.
Hysteresis during this process leads to energy dissipation, accounting for rolling friction
Insignificant influence of lubricant films on rolling friction can not be explained
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10. Adhesion Hysteresis – An illustration
Hysteresis Loop F F x
Motion K
Magnet x r
Ignoring gravity, force is given by:
Steel Surface
F = Kδ ≤ C/r2
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11. Effect of Surface Roughness
Bikerman (1949):
Based on experiments by rolling stainless steel balls on a brass plate
For the roughness values considered (0.02 – 3 microns), higher surface roughness increases rolling friction.
Balls can rest on hills, while tilting the plate.
Other effects like elastic deformation, adhesion, capillary forces etc. found to be negligible.
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12. Elastic & Plastic Deformation
Eldredge & Tabor (1955), Tabor (1955):
For metals, plastic deformation is the predominant mechanism during initial traversals.
Plastic deformation, and hence rolling friction, reduces on repeated traversals on same track.
Elastic hysteresis accounts for the rolling friction in later traversals
Rolling friction is independent of presence of lubricants/greases – effect of slip is “minute”
Work hardening promotes the change of mechanism from plastic deformation to elastic hysteresis
Elastic hysteresis is the major mechanism of rolling friction of elastomers like rubber
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13. Elastic Hysteresis Greenwood, Minshall, Tabor (1961):
Hysteresis loops from more complicated stress cycles required for rolling friction
Obtained expressions, which correctly predicted dependence of rolling friction on load, diameter and elastic constants of rubber
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14. Effect of Electric Double Layer
Derjaguin & Smilga (1963):
When dielectric/semi-conductor cylinder rests on a metal surface (or vice versa), electric double-layer is created.
While rolling, electric double-layer is not symmetric about mid-point.
This asymmetry leads to a moment on cylinder, leading to rolling friction.
Reduction in surface conductivity and gas pressure increases rolling friction.
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15. Crack Propagation (Peel Adhesion)
Kendall (1975):
Rolling is similar to two cracks propagating in same direction & same speed – one opening and another closing – for smooth roller & surface.
Force required can be calculated from fracture mechanics.
Rolling friction shown to be connected to peel adhesion – dwell time (speed) affects friction.
Energy required for breaking bonds is much higher than that obtained while making the bond.
Explains unexpectedly high rolling friction in rolling smooth glass cylinder over a smooth rubber surface, drastic reduction due to contamination in this case & static rolling friction, and predicts stick-slip in rolling at high speeds giving noise.
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16. Concluding Remarks
Rolling Friction is used to account for a number of energy dissipation mechanisms
Rolling Friction might be a misnomer; “resistance to rolling” is a better terminology
From a pure continuum mechanics perspective, rolling friction can be explained using deformations.
Physical mechanisms of rolling friction include:
Plastic deformation
Elastic Hysteresis
Adhesion Hysteresis
Electrostatic (Electric Double layer) effects
Interfacial slip and many others
Coulomb’s law is only very approximately true.
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17. References
Shames, I.H.: Engineering Mechanics – Statics and Dynamics, Prentice Hall of India
Reynolds, O.: On Rolling Friction, Phil Trans 166 (1876),
Tomlinson, G.: A Molecular Theory of Friction, Phil. Mag. 7 (1929), 905
Eldredge K.R., Tabor, D.: Mechanism of Rolling Friction – I. The Plastic Range, Proc. R. Soc. Lond. A (1955) 229,
Tabor, D.: Mechanism of Rolling Friction – I. The Elastic Range, Proc. R. Soc. Lond. A 229 (1955),
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18. References
Derjaguin B.V. Smilga V. P.: Prog. Surf. Sci. 45 (1994) 108.
Kendall, K.: Rolling Friction and Adhesion between Smooth Solids, Wear 33 (1975)
Bikerman, J.J.: Effect of Surface Roughness on Rolling Friction, J. Appl. Phys. 20 (1949)
Greenwood, J.A., Minshall, H., Tabor, D.: Hysteresis Losses in Rolling and Sliding Friction, Proc. R. Soc. Lond. A 259 (1961),
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19. Thank You...
Questions???
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