Rolling Friction
Jayadeep U.B.
PhD (MED) IISc
Outline
Introduction
Case Studies
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I.
“Free” or “Inertial” Rolling
II. Accelerated Rolling
III. Rolling with Deformation
Mechanisms of Rolling Friction
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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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Introduction
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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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I: Free Rolling or Inertial Rolling
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Continuum assumption
Rigid Cylindrical Roller
Rigid Horizontal
Surface
Velocity remains
constant
FBD gives:
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v
ω
W
N=W
No Frictional Force
No Rolling Friction
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N
Free body diagram
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II-A: Accelerated Rolling – down
an incline
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Continuum assumption
Rigid Cylindrical Roller
Rigid Inclined Surface
Velocity increases
FBD gives:
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N = W cosθ
f ≤ μ N = μ W cosθ
f = μ N leads to slipping
rf=Iα
No Rolling Friction
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ω,α
v,a
θ
W
N f
Free body diagram
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II-B: Accelerated Rolling – on a
Horizontal Surface
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Continuum assumption
Rigid Cylindrical Roller
Rigid Horizontal Surface
Velocity increases
FBD gives:
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N=W
F–f =ma
rf=Iα
f ≤μN
f = μ N leads to slipping
No Rolling Friction
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F
ω,α
v,a
W
F
f
N
Free body diagram
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Rolling with Deformation
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Continuum assumption
Rigid Cylindrical Roller
Deformable Horizontal
Surface
Velocity decreases
FBD gives:
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N cosβ = W
N sinβ = ma
d N cosβ – r N sinβ = I α
No Sliding Friction
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ω
α
v
a
W
d
~r
β
N
Free body diagram
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Mechanisms of Rolling Friction: Coulomb
Laws & Interfacial Slip
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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):
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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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Molecular Adhesion Hysteresis
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Tomlinson (1929):
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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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Adhesion Hysteresis – An
illustration
Hysteresis Loop
F
F
x
Motion
K
Magnet
x
r
Steel Surface
Ignoring gravity, force is
given by:
F = Kδ ≤ C/r2
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Effect of Surface Roughness
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Bikerman (1949):
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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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Elastic & Plastic Deformation
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Eldredge & Tabor (1955), Tabor (1955):
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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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Elastic Hysteresis
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Greenwood, Minshall, Tabor (1961):
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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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Effect of Electric Double Layer
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Derjaguin & Smilga (1963):
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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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Crack Propagation (Peel Adhesion)
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Kendall (1975):
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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 stickslip in rolling at high speeds giving noise.
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Concluding Remarks
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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:
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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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References
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Shames, I.H.: Engineering Mechanics –
Statics and Dynamics, Prentice Hall of India
Reynolds, O.: On Rolling Friction, Phil Trans
166 (1876), 155-174.
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, 181-198
Tabor, D.: Mechanism of Rolling Friction – I.
The Elastic Range, Proc. R. Soc. Lond. A 229
(1955), 198-220.
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References
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Derjaguin B.V. Smilga V. P.: Prog. Surf. Sci. 45
(1994) 108.
Kendall, K.: Rolling Friction and Adhesion
between Smooth Solids, Wear 33 (1975) 351358.
Bikerman, J.J.: Effect of Surface Roughness
on Rolling Friction, J. Appl. Phys. 20 (1949)
285-296.
Greenwood, J.A., Minshall, H., Tabor, D.:
Hysteresis Losses in Rolling and Sliding
Friction, Proc. R. Soc. Lond. A 259 (1961),
480-507.
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