Tribology Reference

Friction data for material pairs and hard coatings, with Archard wear, Hertz contact and lambda ratio calculators.

General material pairs

Unlubricated, at room temperature. Ranges reflect finish, contamination and test method. A starting point: measure under your own conditions.

Material pair	Condition	μ static	μ kinetic	Notes
Steel / Steel	Dry, clean	0.60–0.80	0.50–0.70	Galling risk at high contact pressure
Steel / Steel	Lubricated (mineral oil)	0.09–0.13	0.07–0.11	Boundary lubrication regime
Steel / Cast iron	Dry	0.30–0.45	0.20–0.30	Common in machined components
Steel / Bronze	Dry	0.30–0.40	0.14–0.20	Bronze has natural lubricity
Steel / PTFE	Dry	0.04–0.08	0.04–0.06	Lowest dry μ of common polymers
Steel / UHMWPE	Dry	0.05–0.15	0.04–0.12	Used in bearings and orthopedics
Steel / Nylon (PA)	Dry	0.30–0.40	0.15–0.25	Varies significantly with grade
Aluminum / Steel	Dry	0.55–0.65	0.40–0.55	Adhesion tendency; Al transfer common
Rubber / Concrete	Dry	0.60–0.80	0.50–0.70	Tire-road reference
Rubber / Concrete	Wet	0.40–0.60	0.30–0.50	Aquaplaning risk below ~0.3
Glass / Glass	Dry, clean	0.90–1.00	0.35–0.45	Clean glass is highly adhesive
Wood / Wood	Dry	0.25–0.50	0.20–0.40	Grain direction and species-dependent
Ice / Ice	~0°C	0.03–0.10	0.02–0.06	Pressure-induced melt film; temperature-sensitive

Hard coating tribology

Pin-on-disk values against hardened steel (100Cr6 or equivalent) counterpart unless noted. Coating performance varies strongly with substrate finish, counterpart material, and lubrication. Values are literature ranges for guidance only.

Coating	Dry air / humid	Dry N₂ / vacuum	Typical hardness	Wear rate (mm³/N·m)	Notes
TiN	0.40–0.70	0.30–0.50	~2200–2500 HV	10⁻⁶ – 10⁻⁵	Benchmark PVD coating. Gold color. Adequate tribology; primarily valued for hardness and cost.
TiAlN	0.40–0.70	0.35–0.55	~2800–3500 HV	10⁻⁷ – 10⁻⁶	Superior oxidation resistance (~900°C). Secondary hardening on annealing. Preferred for dry machining.
CrN	0.30–0.55	0.25–0.45	~1700–2000 HV	10⁻⁷ – 10⁻⁶	Best corrosion resistance of the nitrides. Lower μ than TiN. Good for hydraulic and marine applications.
CrAlN	0.35–0.65	0.30–0.55	~2800–3300 HV	10⁻⁷ – 10⁻⁶	Combines corrosion resistance of Cr-based with high-temp stability of Al-based. Excellent for wet machining.
DLC (a-C:H)	0.08–0.25	0.003–0.05	~1500–3000 HV	10⁻⁸ – 10⁻⁷	Friction lowest in dry/vacuum; increases with humidity via OH-passivation of dangling bonds. Best for automotive (dry cam/lifter).
ta-C (DLC)	0.05–0.15	< 0.01	~5000–8000 HV	10⁻⁹ – 10⁻⁸	Tetrahedral amorphous carbon. Superlubricity possible in vacuum. Highest hardness, thinnest required (0.5–2 μm). Made by filtered cathodic arc.
MoS₂	0.06–0.20 (degrades)	0.01–0.05	~200–400 HV	10⁻⁷ – 10⁻⁵	Lamellar structure; easy shear between S–Mo–S planes. Oxidizes in humid air → MoO₃ causes friction rise. Ideal for space/vacuum mechanisms.
WC/C (a-C:H:WC)	0.08–0.20	0.05–0.15	~1000–2000 HV	10⁻⁸ – 10⁻⁷	Nanocomposite DLC with WC inclusions. Works dry and lubricated, and is less sensitive to humidity than pure a-C:H. Common in automotive injection systems.
Al₂O₃	0.30–0.60	n/a	~1800–2200 HV	10⁻⁷ – 10⁻⁶	Hard ceramic; high wear resistance but brittle. Often used as oxidation-resistant top coat over TiAlN for high-temp interrupted cutting.
WC (cemented)	0.10–0.30	n/a	~1400–1800 HV	10⁻⁷ – 10⁻⁶	Substrate or coating material. High stiffness (E ~550 GPa). Co binder content affects both hardness and toughness.

Archard wear

Wear volume from load, sliding distance and a wear coefficient.

Wear coefficient

Given as

Normal force F (N)

Sliding distance L (m)

Hardness H, optional

Hardness unit

Q = k · F · L = K · F · L / H Q wear volume (mm³) k specific wear rate (mm³/N·m) K dimensionless wear coefficient F normal force (N) L sliding distance (m) H hardness of the wearing surface

Hertz contact: sphere on flat

Elastic contact radius, peak pressure, and deflection under normal load.

Ball / sphere radius R (mm)

Normal force F (N)

Sphere material

E₁ (GPa)

ν₁ (Poisson)

Flat material

E₂ (GPa)

ν₂ (Poisson)

a = (3FR / 4E*)^(1/3) p₀ = 3F / (2πa²) δ = a² / R 1/E* = (1−ν₁²)/E₁ + (1−ν₂²)/E₂

Lambda ratio (film parameter)

Minimum film thickness over composite roughness. It sets the lubrication regime.

Minimum film thickness h_min (μm)

Roughness given as

Surface 1 (μm)

Surface 2 (μm)

Λ = h_min / σ σ = √(Rq₁² + Rq₂²) Rq ≈ 1.25 Ra (Gaussian surface) Λ < 1 Boundary lubrication 1 ≤ Λ < 3 Mixed / partial EHD Λ ≥ 3 Full film EHD

Typical Ra values

Process	Ra (μm)
Ground (fine)	0.05–0.20
Ground (rough)	0.20–0.80
Honed	0.05–0.40
Lapped	0.01–0.15
Turned (fine)	0.40–1.60
Milled (fine)	0.40–1.60
Polished	0.005–0.10
PVD substrate	0.01–0.05