Rolling Friction. Jayadeep U.B. PhD (MED) IISc. Outline. Introduction Case Studies “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
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Rolling Friction Jayadeep U.B. PhD (MED) IISc
Outline • Introduction • Case Studies • “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
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…
v ω 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 W N Free body diagram
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 = μW cosθ • f=μ N leads to slipping • r f= Iα • No Rolling Friction ω,α v,a θ W f N Free body diagram
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 v,a F W F f N Free body diagram
Continuum assumption Rigid Cylindrical Roller Deformable Horizontal Surface Velocity decreases FBD gives: N cosβ = W N sinβ = ma d N cosβ – rN sinβ = I α No Sliding Friction Rolling with Deformation ω v α a W d ~ r β N Free body diagram
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.
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
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
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.
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
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
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.
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.
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.
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.
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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