Friction - Wikiparency

# Friction **Friction** is the force that resists relative motion between two surfaces in contact, acting along the contact plane and opposing whichever way one surface tends to slide over the other. It is not a fundamental interaction but the summed effect of adhesion, deformation and interlocking across the small patches where two rough bodies actually touch, and for that reason it is described by empirical laws rather than derived from first principles. The engineering description reduces to two numbers: a surface will hold without sliding as long as the required force stays below `f_s ≤ μ_s N`, and once it slides it resists with `f_k = μ_k N`, where N is the [[Normal_force|normal force]] pressing the surfaces together.[^up6-2] Two features of that description do most of the work in design. The friction available is proportional to the load and very nearly independent of the apparent area of contact, so a narrow tyre and a wide one of the same weight hold about the same; and the kinetic coefficient is usually smaller than the static one, so a joint that has just broken loose is easier to move than it was to start. The gap between the two coefficients is not a detail. It is the reason a dragged object judders instead of gliding, the reason [[Brake|brakes]] can grab, and the reason machine slides are designed with stiffness and [[Damping|damping]] in mind. Friction is also the largest single cost in most machinery, dissipated as heat and paid again in [[Wear|wear]], and the whole discipline of [[Tribology|tribology]] exists to manage it. The framework microsim *Friction: static holds until it does not, kinetic is less* puts a block on a tilting plane and draws the free body: the weight, its component down the slope, the normal force and the friction that answers it. The reader raises the angle and watches static friction supply exactly what equilibrium demands, right up to `μ_s N`, then sees the block let go and only `μ_k N` remain; a second scene swaps the ramp for a block towed through a spring, where the same two coefficients make a sawtooth of stick and slip. ## Types Friction is classified by what is sliding and what lies between. **Dry friction**, also called Coulomb friction, acts between solid surfaces in direct contact and divides into the static case, which prevents motion, and the kinetic case, which resists it. **Fluid friction** is the internal resistance of a [[Viscosity|viscous]] fluid to shear, and **lubricated friction** is the intermediate case in which a fluid film carries all or part of the load between two solids. **Skin friction** is the drag a fluid exerts on a surface moving through it, and **internal friction** is the dissipation inside a solid as it is deformed and released. The sections below take these in the pair's order, and the classification matters because the governing law changes with it: dry friction is proportional to load and almost independent of speed, while fluid friction is roughly proportional to speed and independent of load. [[Rolling_resistance|Rolling resistance]], braking, [[Belt_friction|belt drives]] and the [[Triboelectric_effect|triboelectric effect]] are treated separately as special cases of contact. ## History Leonardo da Vinci investigated friction in the 1490s and appears to have found the load-proportional and area-independent behaviour, but his notebooks were unpublished and had no effect on later work, so the laws had to be discovered again.[^dowson] Guillaume Amontons restated them to the French Academy in 1699: the friction force is proportional to the load pressing the surfaces together, and it is independent of the apparent area of contact.[^amontons1699] Charles-Augustin de Coulomb's prize memoir of 1785 added the distinction the modern model rests on, separating the force needed to start motion from the smaller force needed to maintain it, and reporting that the sliding resistance depends only weakly on speed.[^coulomb1785] The three statements together are what engineers still mean by the Coulomb model, and they are what the microsim computes. The explanation came much later. Frank Philip Bowden and David Tabor argued from the 1930s onward that two nominally flat surfaces touch only at the summits of their [[Surface_roughness|roughness]], that those summits deform until the real area of contact is proportional to the load, and that friction is the force needed to shear the junctions formed there.[^bowden1950] That account makes Amontons's two laws consequences of one fact rather than coincidences, it founded modern [[Tribology|tribology]], and it is why the apparent area drops out: pressing harder does not make the contacts stronger, it makes more of them. ## Dry friction Dry friction is the resistance between solid surfaces with no deliberate [[Lubrication|lubricant]] film between them, and it is the case the primary microsim models. It is described by two inequalities rather than one equation, because the force is not determined by the surfaces alone: while the contact is stuck, friction is whatever equilibrium requires, and it is bounded rather than fixed. The subsections below take the two regimes in turn, then the two variables that set the boundary between them, the [[Normal_force|normal force]] and the angle of the surface. ### Static friction Static friction is the force that prevents two surfaces from beginning to slide. Its defining property is that it is a constraint force: it takes whatever value [[Statics|equilibrium]] demands, up to a maximum proportional to the load, `f_s ≤ μ_s N`.[^up6-2] A block resting on a level floor with nothing pushing it sideways experiences no friction at all; push it gently and friction pushes back exactly as hard; push harder and it still pushes back exactly as hard, until the demand exceeds `μ_s N` and the contact fails. The microsim's default makes the arithmetic visible. A 5 kg block on wood, on a plane tilted 20°, presses with a normal force `N = m g cos θ` = 5 × 9.80665 × cos 20° = 46.1 N, and gravity pulls it down the slope with `m g sin θ` = 16.8 N. Static friction supplies 16.8 N — not the 23.0 N that `μ_s N` would allow with `μ_s` = 0.5, and not zero, but precisely the amount needed for equilibrium. The on-screen trace shows a flat line at 16.8 N sitting well below its ceiling, and the gap between the two is the margin against slipping. This is why static friction cannot be measured by watching a stationary block: it reveals only the force it happens to be carrying. The coefficient is found instead by increasing the demand until the contact fails, which is what the [[Inclined_plane|tilting plane]] does and what the *Measurement* section below describes. ### Kinetic friction Once sliding begins, friction stops being a constraint and becomes a definite force, `f_k = μ_k N`, directed opposite the sliding velocity and, to a good first approximation, independent of how fast that sliding is.[^up6-2] Because `μ_k` is usually smaller than `μ_s`, the resistance drops at the instant of breakaway. In the microsim at 20°, the 16.8 N the block needed becomes 13.8 N once it moves, so the moment the contact lets go there is surplus force and the block accelerates. The acceleration follows from [[Newton's_laws_of_motion|Newton's second law]] along the slope: `a = g (sin θ − μ_k cos θ)`. At 40° with `μ_k` = 0.3, the normal force falls to `N` = 5 × 9.80665 × cos 40° = 37.6 N and kinetic friction to 11.3 N, while the driving component has risen to 31.5 N, giving `a` = 9.80665 × (sin 40° − 0.3 cos 40°) = 4.05 m/s². The sim's readout reports 11.3 N against a 16.8 N static trace at the shallower angle, and the drop between them is the whole of the effect.[^pack-mu] The independence from speed is an approximation that holds over a limited range and fails in both directions, as the *Breakdown of the Coulomb model* section sets out. The sim integrates the switch between the two regimes at eight substeps per display frame, holding kinetic friction for as long as the block is moving, so a block released on a steep [[Inclined_plane|slope]] does not re-stick until the angle falls below `arctan μ_k` rather than `arctan μ_s`.[^pack-mu] ### Role of the normal force The normal force is the component of contact force perpendicular to the surface, and it is the only thing in the Coulomb model that sets the size of friction. On a horizontal surface it equals the weight; on an inclined plane it is reduced to `N = m g cos θ`; and anything that presses the surfaces together — a clamp, a [[Spring_(device)|spring]], aerodynamic downforce, the weight of a load — adds to it directly. The proportionality has a consequence that surprises people: friction does not depend on the apparent contact area. Doubling the footprint halves the pressure, so each patch of real contact carries half as much and there are twice as many of them, and the product is unchanged.[^bowden1950] The independence is why [[Brake|brake]] pads are sized for heat and wear rather than for grip, and why the friction force on the microsim's block is the same whether it lies flat or on edge. The proportionality also fails when the real area of contact stops growing with load — under very high pressure, when the contacts merge and the real area saturates at the apparent area, or with soft elastic solids such as rubber, where [[Adhesion|adhesion]] adds a load-independent term. Those cases need [[Contact_mechanics|contact mechanics]] rather than a coefficient. ### Role of angle Tilting the surface changes both sides of the inequality at once, and that is what makes the [[Inclined_plane|inclined plane]] the classical way to measure friction. The demand is `m g sin θ` and the ceiling is `μ_s m g cos θ`; setting them equal, the mass cancels and the condition for slipping is simply `tan θ = μ_s`.[^up6-2] Any block of any mass on the same pair of surfaces slips at the same angle, which is why the measurement is so robust. For the microsim's default pair, wood on wood with `μ_s` = 0.5, that angle is arctan 0.5 = 26.6°, and the notes under the floor say the block lets go past 26.6°. Once it slides, the same reasoning with `μ_k` = 0.3 gives a stopping angle of arctan 0.3 = 16.7°: below that the block comes to rest again. The 10-degree band between the two is a region where the block will stay put if it is placed there gently and will keep sliding if it arrives there moving — the simplest possible example of a system whose state depends on [[Hysteresis|its history]]. Nothing in the sim's physics is simplified and nothing in it is marked ILLUSTRATIVE. The normal force, the slip test, both slip angles and the friction force each substep come straight from the portal's mechanics library, and the coefficients are the textbook table's.[^pack-mu] The only liberties are display conventions, stated in the sim's own notes: the weight arrow is drawn at a fixed length of 1.4 world units, the scene is scaled at 2.1 units to the metre so the arrows stay legible as the load changes, and the block is re-released from the top of the ramp when it reaches the bottom. *Try: raise the ramp angle past 26.6° and watch the friction arrow stop growing at 23.0 N, the block let go, and the trace fall from 16.8 N to the 11.3 N kinetic line; bring the angle back down and see it keep sliding until 16.7°, not 26.6°; switch the contact to ice on ice and both angles collapse toward the floor while the arrows shrink with them.* ## Coefficient of friction The coefficient of friction is the dimensionless ratio of friction force to normal force, `μ = f / N`, quoted separately for the static and kinetic cases. It is a property of a pair of surfaces, not of either material alone, and it depends on finish, cleanliness, the presence of oxide films and adsorbed water, temperature and the history of the contact. Quoted values are therefore approximate, which is why they are given to one or two significant figures and why a design that depends on a precise coefficient is a design in trouble. Values for dry contacts run from about 0.04 for [[Polytetrafluoroethylene|polytetrafluoroethylene]], one of the lowest of any solid pair, to 1.0 and above for clean rubber on dry concrete, where the rubber deforms into the road's texture and adds a [[Hysteresis|hysteresis]] term to the adhesive one. A coefficient above 1 is perfectly ordinary and simply means the surfaces hold more than their own weight pressed sideways. In lubricated contacts the effective coefficient falls by one to two orders of magnitude, to a few thousandths, which is the point of [[Lubrication|lubrication]]. ### Approximate coefficients of friction The portal's mechanics text tabulates representative dry values, and the microsim's contact list is drawn from that table.[^up6-2][^pack-mu] | Surfaces (dry) | μ_s | μ_k | |---|---|---| | Rubber on dry concrete | 1.0 | 0.7 | | Rubber on wet concrete | 0.7 | 0.5 | | Steel on steel | 0.6 | 0.3 | | Wood on wood | 0.5 | 0.3 | | Ice on ice | 0.1 | 0.03 | | Polytetrafluoroethylene on steel | 0.04 | 0.04 | Two rows deserve notice. Ice on ice is low but not zero, and its kinetic value is a third of its static one, which is why a car that starts to slide on ice is so much harder to recover than one that has not. [[Polytetrafluoroethylene|Polytetrafluoroethylene]] is the row where the two coefficients are equal, and in the microsim's spring-pulled scene that equality shows itself directly: the [[Stick–slip_phenomenon|sawtooth]] disappears and the force trace runs flat, because there is no drop in resistance at breakaway to feed it. ## Sources of friction Two surfaces that look flat touch only at the summits of their roughness, and the sum of those patches — the real area of contact — is a small fraction of the apparent area. Under load the summits deform, plastically at first, until the real area is just large enough to carry the load at the material's flow pressure. That makes the real area proportional to the load and independent of the apparent area, and if friction is the force needed to shear the junctions formed at those patches, Amontons's two laws follow at once.[^bowden1950] Three mechanisms contribute in practice. **Adhesion** at the junctions is the dominant term for clean metals, where contacting summits weld and must be sheared apart; it is strongly affected by oxide films and adsorbed layers, which is why a freshly cut metal surface in vacuum can seize while the same metal in air slides freely. **Deformation**, or ploughing, is the work done when a harder asperity furrows a softer surface, and it is the main term for rubber on rough road and for abrasive contacts. **Interlocking** of surface features contributes at large roughness scales. [[Surface_roughness|Surface roughness]], [[Adhesion|adhesion]] and the mechanical properties of the softer member therefore all enter a coefficient that the Coulomb model treats as a single constant, and [[Asperity_(materials_science)|asperity]] models are what connect the two descriptions. Because the work done against friction goes almost entirely into heat at these junctions, sliding contacts run hot locally even when the bulk stays cool, and the flash temperatures at individual asperities can be far above the average. That local heating drives oxidation, softening and, in the limit, seizure and [[Galling|galling]]. ## Breakdown of the Coulomb model The Coulomb model is an excellent approximation and an incomplete description, and the places it fails are where most of the interesting engineering lives. Four failures matter. The coefficients are not constants of the materials. They drift with contamination, humidity, temperature and the running-in history of the surfaces, and the same pair of surfaces measured on two days can differ by tens of per cent. The one- and two-figure precision of the table above is not conservatism; it is the real reproducibility. Kinetic friction is not independent of sliding speed. In dry contacts it typically falls slightly as speed rises over the low range and can rise again at high speed as the contact heats; in [[Lubrication|lubricated contacts]] it varies strongly and non-monotonically with speed, as the *Lubricated friction* section shows. Static friction is not a single number either. The force needed to break a contact loose grows slowly with how long it has been sitting, because the junctions creep and the [[Contact_mechanics|real area of contact]] grows with time under load. The rate-and-state friction laws used in seismology were developed to capture exactly this dependence on dwell time and sliding history. Finally, the sharp switch between `μ_s` and `μ_k` is an idealisation of a continuous transition that occurs over a small but finite sliding distance. The microsim implements the idealised switch — that is what makes the drop at breakaway so visible — and the smooth version would round the corner of the sawtooth without changing its height. Where the distinction matters, in [[Stick–slip_phenomenon|stick–slip]] and in precision positioning, the finite-distance model is what is used. ## Dry friction and instabilities The difference between the two coefficients is not merely a bookkeeping detail; it makes sliding contacts unstable under a compliant drive. If a block is towed not by a rigid rod but through a spring, the force in the spring rises while the block sticks, breaks the contact loose at `μ_s N`, and then finds itself larger than the `μ_k N` needed to keep the block moving. The surplus accelerates the block, it overshoots, the spring force falls, and the block stops and sticks again. The result is a sawtooth of load and a juddering, noisy motion: the [[Stick–slip_phenomenon|stick–slip phenomenon]], heard in a squealing [[Brake|brake]], a creaking door, a chattering machine slide and the note of a bowed string. The microsim's second scene draws this directly. On level ground the 5 kg block presses with `N = m g` = 49.0 N, so the spring force climbs to `μ_s N` = 24.5 N before breakaway and the sliding resistance is `μ_k N` = 14.7 N. During the slip the block overshoots symmetrically about the position where the spring force equals `μ_k N`, so the force falls as far below that value as it started above it and the contact re-sticks at `(2 μ_k − μ_s) N` = 4.9 N. The extension released in one slip is therefore `2 (μ_s − μ_k) N / k`, which for the default spring of 300 N/m is 65 mm.[^pack-mu] The tooth height depends only on the two coefficients and the load; the width and the rate depend on the [[Spring_(device)|spring]]. The See-also variant built on this scene tows at 0.04 m/s through a 250 N/m spring, releasing 78 mm per slip and repeating roughly every two seconds. Stiffening the spring makes the teeth shorter and more frequent, and a rigid drive removes the instability altogether — which is the standard cure: stiffen the drive, close the gap between the coefficients, or [[Damping|damp]] the loop. Isolating a vibrating machine from its floor is the related problem, treated under [[Vibration_isolation|vibration isolation]]. *Try: set the scene to spring-pulled and watch the force climb to 24.5 N, snap down to 4.9 N and flatten at 14.7 N; raise the spring rate and the teeth shrink and crowd together; switch to polytetrafluoroethylene, where the two coefficients are equal, and the sawtooth flattens into a steady line.* ## Friction at the nanoscale At the scale of a single contact the averaged picture no longer applies, and friction is studied one asperity at a time. [[Atomic_force_microscopy|Atomic force microscopy]] with a lateral-force detector drags a tip of nanometre radius across a surface and measures the force directly, which turns the proportionality between friction and real contact area into something that can be tested rather than inferred. At that scale friction is found to track the true contact area rather than the load as such, so the Coulomb proportionality emerges only once many contacts are averaged. The regime also includes [[Superlubricity|superlubricity]], in which two crystalline surfaces slid out of registry show a friction force orders of magnitude below the ordinary value, and the mechanisms of energy dissipation into lattice vibrations that set the floor on how low friction can go. This section of the pair collects those results; the engineering sections above treat the averaged behaviour they explain. ## Fluid friction Fluid friction is the resistance a fluid offers to being sheared, and it obeys a different law from dry friction. For a Newtonian fluid the shear stress is proportional to the rate of shear through the dynamic [[Viscosity|viscosity]] η, so the resisting force grows with sliding speed and with contact area and does not depend on the normal load at all — the exact opposite of the Coulomb model on every count. Water at 20 °C has a viscosity near 1.0 mPa·s and air near 18 μPa·s, a ratio of about 55, which is why moving through water is so much more costly than moving through air at the same speed. Whether the resistance rises linearly or as the square of speed depends on the [[Reynolds_number|Reynolds number]], which compares inertial to viscous effects. At low Reynolds number the flow is orderly and drag is linear in speed; at high Reynolds number the wake dominates and drag goes as speed squared, the familiar case of [[Drag_(physics)|drag]] on vehicles and projectiles. Fluid friction is what makes [[Lubrication|lubrication]] possible: a film that shears instead of two solids that rub replaces a coefficient of 0.5 with one of a few thousandths. ## Lubricated friction Lubricated friction is the middle ground, in which a fluid film separates surfaces that would otherwise rub. How completely it separates them decides everything, and the standard map is the Stribeck curve, which plots the friction coefficient of a [[Plain_bearing|plain bearing]] against the bearing parameter `η N / p` — [[Viscosity|viscosity]] times shaft speed divided by projected pressure.[^stribeck1902] The curve falls steeply, reaches a minimum and rises again; its three parts are three physical situations. At low values of the parameter the film is too thin to carry the load, asperities touch through it, and behaviour is close to dry friction with a coefficient of order 0.1: the **boundary** regime, where only adsorbed additive layers protect the surfaces. At high values the film separates the surfaces completely and the only resistance is shearing the oil: the **hydrodynamic** regime, where Petroff's equation gives `μ = 2π² (r/c)(η N / p)` for a lightly loaded journal, `r/c` being radius over radial clearance.[^shigley] Between them lies the **mixed** regime containing the minimum, where part of the load rides on the film and part on the asperities. The See-also variant built on this curve opens in the hydrodynamic branch, at a bearing parameter of 9 × 10⁻⁷ and a coefficient of 0.018 — what Petroff's form returns for `r/c` = 1000, since 2π² × 1000 × 9 × 10⁻⁷ = 0.018. Its companion variant for [[Lubrication|lubrication]] opens in the mixed band instead — 10 mPa·s, 5 revolutions per second, 2 MPa — giving 2.5 × 10⁻⁸ and a coefficient of 0.06. The curve both variants draw is an illustrative fit, not measured data for any particular [[Bearing_(mechanical)|bearing]]: a boundary coefficient of 0.1 blended into that same Petroff form, and the chart is labelled ILLUSTRATIVE on its face.[^pack-stribeck] The lesson is the shape, not the values. A bearing designed for the hydrodynamic regime passes through the boundary and mixed regimes at every start and stop, which is when almost all of its [[Wear|wear]] occurs; a machine that idles too slowly never reaches the film it was designed for. *Try: in the plain-bearing variant, drag the bearing parameter down from 9 × 10⁻⁷ and watch the operating dot slide off the hydrodynamic branch, through the mixed band into boundary contact while the coefficient climbs from 0.018 toward 0.1; thin the oil or slow the shaft and the dot travels the same way, as on every start-up.* ## Skin friction Skin friction is the tangential force a moving fluid exerts on a surface it flows over, transmitted through the [[Boundary_layer|boundary layer]] in which the flow speed rises from zero at the wall to the free-stream value. It is one of the two components of total [[Drag_(physics)|drag]], the other being pressure or form drag, and for slender well-streamlined bodies it is the larger of the two: for a ship's hull or a long aircraft fuselage, [[Skin_friction_drag|skin friction drag]] dominates the resistance budget. Because it depends on the state of the boundary layer, a laminar layer producing markedly less of it than a turbulent one, much of the effort in low-drag design goes into delaying transition and into keeping surfaces smooth and clean. ## Internal friction Internal friction is dissipation inside a solid as it deforms, rather than between two bodies. A material cycled elastically does not return quite all the work put into it: the stress–strain loop encloses an area, and that [[Hysteresis|hysteresis]] is the energy lost per cycle. The mechanisms are internal — drag on moving [[Dislocation|dislocations]], grain-boundary motion, and the relaxation processes that make polymers [[Viscoelasticity|viscoelastic]] — but the engineering consequence is the same as external friction: work becomes heat. Internal friction is what makes a struck bell eventually fall silent, what heats a flexed tyre sidewall, and what supplies the material damping that limits the resonance of a structure; the same quantity appears in [[Damping|damping]] and is the resource a rubber isolator uses. ## Radiation friction Radiation friction is resistance that arises from the exchange of momentum with radiation rather than from contact. A body that absorbs, emits or scatters radiation asymmetrically because it is moving experiences a net retarding force: [[Radiation_pressure|radiation pressure]] acting through the body's own motion. The canonical case is orbital dust, which absorbs sunlight radially and re-emits it isotropically in its own frame, losing angular momentum and spiralling inward. The effect is negligible in machinery and decisive over astronomical times and for very small bodies, and the pair treats it as the limiting case where friction requires no contact at all. ## Other types of friction Several everyday cases combine the mechanisms above in ways that earn their own names and their own design rules. ### Rolling resistance [[Rolling_resistance|Rolling resistance]] is the force resisting a wheel's rolling motion, and it does not arise from sliding. Its main source is [[Hysteresis|hysteresis]]: the tyre and the surface are compressed at the leading edge of the contact patch and relax at the trailing edge, and because the material does not return all the energy, the pressure distribution is shifted forward and produces a retarding moment. It is quoted as a coefficient defined the same way as a friction coefficient, but with values one to two orders of magnitude lower — a car tyre on asphalt sits near 0.01 against a sliding coefficient near 0.7. That ratio of roughly seventy to one is the entire case for the wheel, and it is why replacing sliding with rolling is the first move of friction reduction. ### Braking friction A [[Brake|brake]] is a machine for converting kinetic energy into heat through dry friction on purpose, and it is sized by heat rather than by grip. The stopping distance of a vehicle braking at the limit of tyre [[Adhesion|adhesion]] follows from the work-energy theorem as `d = v² / (2 μ_k g)`: from 30 m/s on dry concrete with `μ_k` = 0.7 that is 65.6 m, and on the same road wet, with `μ_k` = 0.5, it is 91.8 m — half as far again for the same speed, from a change in the coefficient alone. The quadratic in speed is the reason speed limits do what they do. Because the tyre's own limit falls once it slides, the shortest stop is made just short of lock-up, which is the control problem anti-lock braking solves. ### Triboelectric effect The [[Triboelectric_effect|triboelectric effect]] is the transfer of electric charge between two materials brought into contact and separated, familiar as the shock from a door handle after crossing a carpet. It accompanies dry sliding contact rather than causing it, but it matters in engineering: charge accumulation on belts and in powder handling is an ignition hazard, and electrostatic discharge damages semiconductors. The sign and size of the transfer are tabulated as a triboelectric series, which orders materials by the charge they tend to acquire. ### Belt friction [[Belt_friction|Belt friction]] is the case in which the normal force is not given but generated by the tension itself, as a flexible band wraps a cylinder. Integrating the equilibrium of an element around the wrap gives the [[Capstan_equation|capstan equation]], `T1 / T2 = e^(μ θ)`, where θ is the wrap angle in radians. The exponential is the striking part: with `μ` = 0.3, one full turn of rope around a bollard multiplies the holding force by `e^(0.3 × 2π)` ≈ 6.6, and three turns by a factor of about 290, so a person holding a few hundred newtons can restrain tens of kilonewtons. The same relation sets the power a flat [[Belt_(mechanical)|belt drive]] can transmit before it slips, and it is treated in its own right in the portal's section on belts and chains. ## Friction reduction Reducing friction means attacking one of its terms: reduce the [[Contact_mechanics|real area of contact]], weaken the junctions formed there, or replace sliding with [[Rolling_resistance|rolling]]. Every practical method is one of these three. The engineering payoff is large — friction and the [[Wear|wear]] that follows it consume a substantial share of the energy used by machinery, and wear ends component life long before any static strength limit is reached. Archard's law gives the standard estimate of how much material a sliding contact loses: the wear volume is `V = K F s / H`, proportional to the load F and the sliding distance s, and inversely proportional to the hardness H of the softer surface, with the dimensionless wear coefficient K carrying everything else.[^archard1953] The See-also variant built on this relation makes the scale concrete: with `K` = 10⁻⁴, a 100 N load, 1 km of sliding and a hardness of 2 GPa, the volume lost is 5 mm³ — which over a contact patch of 1 cm² is a depth of 50 μm. It is a small number that accumulates, and halving the load or doubling the hardness halves it directly. ### Devices The most effective device is the one that stops surfaces from sliding at all. A [[Rolling-element_bearing|rolling-element bearing]] interposes balls or rollers between the shaft and its housing so that the relative motion becomes rolling, exchanging a sliding coefficient of a few tenths for an effective coefficient of a few thousandths. A [[Plain_bearing|plain bearing]] takes the other route, generating a fluid film that separates the surfaces entirely. Both are treated as machine elements under [[Bearing_(mechanical)|bearings]], and both are selected by life rather than by friction. Rolling bearings are rated by the dynamic load rating C, defined so that the basic rating life in millions of revolutions is `L10 = (C/P)^p`, with P the equivalent load and the exponent p equal to 3 for [[Ball_bearing|ball bearings]] and 10/3 for roller bearings.[^iso281] The See-also variant draws both on a logarithmic scale: at `C/P` = 5 a ball bearing rates 125 million revolutions, which at 1500 rpm is 1,389 hours, while a roller bearing at the same ratio rates 214 million. Raising `C/P` to 7.5 moves the pair to 422 and 826 million revolutions.[^pack-bearing] The steep exponent is the practical point — halving the load multiplies ball-bearing life by eight — and L10 is a statistical life at which one bearing in ten is expected to have failed, not a guarantee for any individual bearing. *Try: in the bearings variant, switch the element from ball to roller at `C/P` = 5 and watch the life bar jump from 125 to 214 million revolutions while the exponent in the readout changes from 3 to 10/3; push `C/P` out to 7.5 and both bars move to 422 and 826 million, the ball bar gaining more than threefold from a 50 per cent load reduction.* ### Lubricants A [[Lubrication|lubricant]] works by interposing a material that shears more easily than the surfaces would. Liquid lubricants do it by forming a film thick enough to separate the asperities, so the design question is film thickness rather than chemistry, and the Stribeck curve above is the map. Greases carry the same oils in a thickener so they stay where they are put. Solid lubricants work where oil cannot survive — high temperature, vacuum, or a contact too lightly loaded to build a film — and rely on materials that shear easily along one plane: [[Graphite|graphite]] and molybdenum disulfide, whose layered crystal structures slide over themselves, and [[Polytetrafluoroethylene|polytetrafluoroethylene]], which transfers a low-shear film onto the counterface. Boundary additives form adsorbed or chemically bonded layers that protect the surfaces exactly in the regime where the film has failed, which is why they matter most at start-up and under shock load. ## Applications Friction is designed for as often as it is designed against, and the two cases use the same two coefficients in opposite directions. ### Transportation Every vehicle that starts, stops or turns does so through the friction between its tyres and the road; the available acceleration in any direction is bounded by `μ g`, so `μ` = 0.7 permits about 6.9 m/s² and no more, however much power or braking force is available. The same coefficient appears in the stopping-distance calculation above, and its collapse on ice — from 0.7 to a few hundredths — is the whole of winter driving. Inside the vehicle, friction is wanted in the [[Brake|brakes]] and the [[Clutch|clutch]] and unwanted in every bearing and seal, and the two requirements are kept apart by design. Rail transport makes the opposite trade: steel on steel gives a coefficient near 0.2, too low for steep grades and short stops, but a [[Rolling_resistance|rolling resistance]] far below a tyre's, which is why trains are efficient and slow to stop. ### Measurement The simplest instrument for measuring a static coefficient is the [[Inclined_plane|inclined plane]], because at the slip angle the mass cancels and `μ_s = tan θ`.[^up6-2] Placing a sample on a surface and tilting it until it slides therefore gives the coefficient from a protractor alone, with no force measurement at all — and the microsim's first scene is this experiment, with the slip angle marked. Kinetic coefficients are harder, since they require measuring force during steady sliding: a [[Tribology|tribometer]] tows a specimen against a counterface at a controlled speed and load and records the tangential force, most often in a pin-on-disc geometry. Because the answer depends on speed, temperature, humidity and running-in, standardised test conditions matter more here than the resolution of the instrument. ### Household usage Friction is the reason ordinary objects behave at all. A knot holds because rope on rope obeys the [[Capstan_equation|capstan relation]]; a nail holds because the wood grips its shank; a ladder stands because the friction at its foot supplies the horizontal force the wall's reaction demands, and slips when the angle makes that demand exceed `μ_s N` — the same inequality as the microsim's block, applied to a different geometry. Walking is a static-friction problem in which the foot does not slide, and the difference between a floor at `μ_s` = 0.5 and one at 0.1 is the difference between a corridor and a hazard. ## See also - [[Tribology]] - [[Stick–slip_phenomenon]] - [[Bearing_(mechanical)]] - [[Plain_bearing]] - [[Rolling-element_bearing]] - [[Lubrication]] - [[Wear]] - [[Contact_mechanics]] - [[Galling]] - [[Triboelectric_effect]] - [[Belt_friction]] - [[Rolling_resistance]] - [[Vibration_isolation]] (section 15) ## References [^up6-2]: OpenStax (2016). *University Physics Volume 1*. Ling, S. J.; Sanny, J.; Moebs, W. Rice University. Chapter 6 "Applications of Newton's Laws," §6.2 "Friction," Eq. 6.1 (`f_s ≤ μ_s N`) and Eq. 6.2 (`f_k = μ_k N`), Table 6.1 "Approximate Coefficients of Static and Kinetic Friction" (p. 279), the block on an incline and the slip condition `tan θ = μ_s` (pp. 283, 287); pp. 277–287. https://openstax.org/details/books/university-physics-volume-1 (Portal Books 077). [^pack-mu]: Portal engineering pack, `mech.dynamics.MU`, `mech.dynamics.inclinedPlane(m, θ, {s, k})` and `mech.dynamics.frictionSwitch(applied, N, μs, μk, moving)`, with the sim spec `specs/sims/Friction.json` and the sub-manual `02_mechanics` §6.3. The coefficient set is Table 6.1 at one to two significant figures for dry contacts; the stick/slip state and the friction force are evaluated at eight substeps per display frame, and kinetic friction is held while the block moves. Nothing in the physics is ILLUSTRATIVE; the sim's own notes record the display conventions (weight arrow 1.4 world units, scene scale 2.1 units per metre, block re-released at the foot of the ramp). Build report, engineering run, September 18, 2026. [^dowson]: Dowson, Duncan (1998). *History of Tribology*, 2nd ed. London: Professional Engineering Publishing. (The standard history of the subject; edition and publisher as recalled, no page pinned for this article.) [^amontons1699]: Amontons, Guillaume (1699). "De la résistance causée dans les machines." *Mémoires de l'Académie Royale des Sciences*, Paris. (Pages as recalled; the year and the two laws are standard in histories of tribology.) [^coulomb1785]: Coulomb, Charles-Augustin de (1785). "Théorie des machines simples, en ayant égard au frottement de leurs parties et à la roideur des cordages." *Mémoires de Mathématique et de Physique de l'Académie Royale des Sciences*, vol. 10. (Prize memoir of 1781, published 1785; volume and pages as recalled.) [^bowden1950]: Bowden, Frank Philip; Tabor, David (1950). *The Friction and Lubrication of Solids*, Part I. Oxford: Clarendon Press. (The real-area-of-contact and adhesion account of Amontons's laws; no page pinned for this article.) [^stribeck1902]: Stribeck, Richard (1902). "Die wesentlichen Eigenschaften der Gleit- und Rollenlager." *Zeitschrift des Vereines Deutscher Ingenieure* 46. (Volume as recalled; pages not re-checked for this article. The curve named for this work is the standard regime map of lubricated contact.) [^shigley]: Budynas, Richard G.; Nisbett, J. Keith. *Shigley's Mechanical Engineering Design*. McGraw-Hill. Journal-bearing chapter, Petroff's equation `μ = 2π² (r/c)(η N / p)` for a lightly loaded journal (named textbook form; edition and pages not pinned for this article). [^pack-stribeck]: Portal engineering pack, See-also variants `Plain_bearing` and `Lubrication` (`specs/variants/`), built on the `Friction` sim. The Stribeck relation is not in the library (recorded library gap); the chart applies a one-line fit — a boundary coefficient μ_b = 0.1 blended into the Petroff form with `r/c` = 1000 — and is labelled **ILLUSTRATIVE** on the chart. Operating points as built: 9 × 10⁻⁷ → μ = 0.018 (hydrodynamic); 10 mPa·s, 5 rev/s, 2 MPa → 2.5 × 10⁻⁸, μ = 0.06 (mixed). Build report, engineering run, September 18, 2026. [^archard1953]: Archard, J. F. (1953). "Contact and rubbing of flat surfaces." *Journal of Applied Physics* 24. (Volume and pages as recalled; DOI not re-checked for this article. The relation `V = K F s / H` is standard.) [^iso281]: International Organization for Standardization. ISO 281, *Rolling bearings — Dynamic load ratings and rating life* (the basic rating life `L10 = (C/P)^p` in millions of revolutions, with p = 3 for ball bearings and 10/3 for roller bearings; L10 is the life reached by 90 per cent of a population). [^pack-bearing]: Portal engineering pack, See-also variants `Bearing_(mechanical)` and `Rolling-element_bearing` (`specs/variants/`), built on the `Friction` sim. No bearing-life function exists in the design library (recorded library gap); the ISO 281 form is applied in the variant's code append. Values as built: `C/P` = 5 → 125 Mrev (ball, 1,389 h at 1500 rpm) and 214 Mrev (roller); `C/P` = 7.5 → 422 and 826 Mrev. Build report, engineering run, September 18, 2026.  **Microsim — three.js (Wikitube framework):** *Friction* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/engineering/Friction.html" data-title="Friction"></div> *Built from `MICROSIM_GUIDE/specs/sims/Friction.json`; part of the [[PORTAL_Engineering|Engineering portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Friction) : [Wikitube](https://en.wikitube.io/wiki/Friction) - skeleton pinned to revision 1372943918 (2026-09-18).