Tribology: Friction, Wear, and Lubrication

Why tribology matters

Nearly every machine loses energy and life at its sliding and rolling interfaces. Studies attributed to Jost and later expanded by Holmberg and Erdemir estimate that friction and wear consume on the order of 23% of total world energy — about one-fifth burned overcoming friction and the rest spent remanufacturing worn parts. Cutting friction and wear by even a few percent across transport, industry, and power generation would save hundreds of billions of dollars and gigatonnes of CO₂ annually.

• Bearings and gears. Rolling-contact fatigue and lubricant film thickness set the L10 life of every ball and roller bearing.
• Engines. Piston rings, cam-followers, and journal bearings each run in a different lubrication regime; ring-liner friction alone is a few percent of fuel energy.
• Brakes and clutches. These use friction on purpose — µ must stay stable and high while dissipating megawatts as heat.
• Tires and rail. Grip is friction; wheel-rail contact stress and creep govern railway wear and adhesion.
• Prosthetics and implants. Hip and knee joints wear microscopically; debris particles drive the biological failure of implants.
• Micro/nano devices. At MEMS scale, surface forces dominate volume forces and stiction can weld parts shut.

How friction really works — step by step

The classical picture of "roughness snagging on roughness" is wrong. Modern tribology explains friction through real contact area and adhesion:

1. Surfaces are rough at the microscale. Even a mirror-polished bearing race has asperities tens of nanometres tall. When two bodies are pressed together, they touch only at the tallest peaks.
2. Real contact area is set by load, not footprint. Each asperity carries so much local pressure that it yields plastically. The junctions grow until the mean contact pressure equals the material's hardness H (roughly three times the yield strength). So the total real contact area is A_r = N / H — proportional to load and completely independent of the apparent area.
3. Junctions adhere. Clean metal-to-metal asperity contacts cold-weld. To slide, you must shear these welds. If the interfacial shear strength is τ, the friction force is F = τ · A_r.
4. Combine the two. Substitute A_r = N/H to get F = (τ/H)·N. Matching this to Amontons' F = µN gives the adhesion model of friction: µ ≈ τ/H. The ratio of a junction's shear strength to the softer surface's hardness is the coefficient of friction.
5. Add plowing. Hard asperities on the harder body also plow furrows in the softer one. Total friction is the sum of the adhesion term and this deformation (plowing) term; in abrasive situations plowing dominates.
6. Sliding tears material away. Every time a welded junction shears, it sometimes fractures below the original surface rather than at the interface, transferring a fragment to the other body or releasing a wear particle. Friction and wear are two consequences of the same asperity contacts.

This adhesion-plus-deformation model, developed by Bowden and Tabor at Cambridge in the 1940s-50s, explains why Amontons' 300-year-old empirical law holds: A_r ∝ N makes F ∝ N automatically, and because A_r ignores the apparent footprint, so does friction.

Lubrication regimes and the Stribeck curve

A lubricant works by making the surfaces shear a weak film instead of welding to each other. Which regime you are in depends on the Hersey number (dynamic viscosity η × sliding speed U ÷ load per unit width W). Plotting µ against this parameter traces the classic Stribeck curve:

Lubrication regimes, film thickness, and typical friction

Regime	Film vs. asperities	Film thickness	Typical µ	Example
Boundary	Adsorbed molecular layers only; asperities touch	1–10 nm	0.08–0.15	Startup, cam nose, cold engine
Mixed	Part fluid film, part asperity contact	0.01–0.1 µm	0.02–0.08	Piston ring mid-stroke
Elastohydrodynamic (EHL)	Full film; surfaces elastically deform	0.1–1 µm	0.001–0.01	Gears, rolling bearings
Hydrodynamic (HL)	Full film; pressure wedge separates surfaces	1–100 µm	0.001–0.005	Journal bearing at speed

The curve dips to a minimum: as speed rises from rest, friction first falls as a fluid film builds and lifts the asperities apart, reaches a minimum at the transition to full-film, then rises again as viscous shear of the thick film takes over. Bearings are designed to sit just to the right of this minimum for stability.

Common misconceptions and failure modes

• "Rougher means more friction." Not necessarily — very smooth surfaces can adhere more (larger real contact) and even seize. There is an optimum finish.
• "A bigger contact patch grips harder." For dry Amontons friction it does not — µN is set by load, not area. (Tires bend the rule because rubber is viscoelastic and its µ genuinely depends on pressure.)
• "µ is a material property." It is a property of the pair, the film, and the conditions. Steel has no single µ; steel-on-steel does, and only for a given finish and lubricant.
• "Kinetic friction depends strongly on speed." For dry metals it is nearly speed-independent; the strong speed dependence appears in lubricated (Stribeck) and viscoelastic contacts.
• Galling and seizure. When adhesive junctions grow faster than they shear — common with like-on-like metals such as stainless-on-stainless or aluminium-on-aluminium — material transfers, roughens, and can weld the parts solid.
• Fretting. Tiny oscillatory slip (microns) at "fixed" joints — bolted flanges, splines, press fits — traps oxide debris and initiates fatigue cracks.
• Stick-slip. Because µ_s > µ_k, a slowly driven contact grips, stores elastic energy, then jumps — producing brake squeal, chatter, and earthquakes.

The three wear mechanisms

Dominant wear mechanisms with typical Archard wear coefficients k

Mechanism	How material is removed	Typical k (unlubricated)	Where it dominates
Adhesive	Welded junctions shear below the surface; fragments transfer	10⁻⁴–10⁻²	Dry metal sliding, galling, seizure
Abrasive	Hard asperities/particles plow grooves (2-body / 3-body)	10⁻³–10⁻¹	Digging tools, slurries, grit-contaminated oil
Surface fatigue	Cyclic sub-surface stress cracks, pits, spalls	—	Rolling bearings, gear teeth

Archard's wear equation ties adhesive and abrasive wear to a single relation for the worn volume:

V = k · (N · s) / H

where V = volume of material removed (m³), k = dimensionless wear coefficient (a severity index for the pair and lubrication, 10⁻⁸ to 10⁻²), N = normal load (N), s = total sliding distance (m), and H = hardness of the softer surface (Pa, i.e. N/m²). Wear volume scales linearly with both load and sliding distance and inversely with hardness — which is exactly why we case-harden gear teeth, nitride cams, and coat tools with hard films.

Worked example — will this bushing survive?

A bronze bushing carries a steel shaft with normal load N = 500 N. The shaft turns a bore of diameter d = 25 mm at n = 300 rpm for a required life of 2,000 hours. The bronze hardness is H = 800 MPa = 8 × 10⁸ Pa, and for lubricated bronze-on-steel the wear coefficient is k ≈ 1 × 10⁻⁷. How much depth wears away, and does it fit a 100 µm allowance?

Step 1 — sliding distance. Surface speed = π·d·n = π × 0.025 m × (300/60 rev/s) = 0.393 m/s. Over 2,000 h = 7.2 × 10⁶ s, s = 0.393 × 7.2 × 10⁶ ≈ 2.83 × 10⁶ m.

Step 2 — wear volume. V = k·N·s / H = (1 × 10⁻⁷ × 500 × 2.83 × 10⁶) / (8 × 10⁸) = 1.77 × 10⁻⁷ m³ ≈ 177 mm³.

Step 3 — wear depth. Spread over the projected bearing area A ≈ d × length. For a 25 mm-long bushing, A = 25 × 25 = 625 mm² = 6.25 × 10⁻⁴ m². Depth h = V / A = 1.77 × 10⁻⁷ / 6.25 × 10⁻⁴ ≈ 2.8 × 10⁻⁴ m = 283 µm.

Verdict: 283 µm exceeds the 100 µm allowance — this bushing would wear nearly three times its budget. Fixes: raise hardness H (harder bronze or a steel-backed liner), lower k with a better lubricant or a PTFE-lined bearing (k can drop 100×), reduce sliding distance (lower speed), or share the load over a larger area. Archard's equation lets you trade all four before cutting metal.