Rolling Friction

Jayadeep U.B.PhD (MED) IISc

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Outline Introduction Case Studies

I. “Free” or “Inertial” RollingII. Accelerated RollingIII. 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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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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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

NFree body diagram

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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

v,a

ω,α

W

NFree body diagram

θ

f

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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

Free body diagram

v,aω,α

W

N

F

f

F

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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

vωα a

W

NFree body diagram

β

d~ r

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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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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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Adhesion Hysteresis – An illustration

Magnet

Ignoring gravity, force is given by:

r

x

K

F

Motion

x

F

F = Kδ ≤ C/r2

Hysteresis Loop

Steel Surface

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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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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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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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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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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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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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References 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 Derjaguin B.V. Smilga V. P.: Prog. Surf.

Sci. 45 (1994) 108. Kendall, K.: Rolling Friction and

Adhesion between Smooth Solids, Wear 33 (1975) 351-358.

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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