Contact Mechanics · Lubrication

Lubrication regimes and the Stribeck curve

Start with the first picture: lower the speed and watch the dot slide down the Stribeck curve from a full oil film into mixed and boundary lubrication, where the rough surfaces touch.

1 Stribeck curve 2 EHL film thickness and lambda 3 Hot oil, thin film

What is the Stribeck curve?

A plot of the friction coefficient against the Hersey number, ηN/P: oil viscosity η times shaft speed N (revolutions per second), divided by the bearing pressure P (load over projected area). Speed, viscosity and load all move you along the same curve. On the left the surfaces rub (boundary lubrication). On the right an oil film holds them apart (hydrodynamic lubrication). In between they share the load (mixed).

Left: friction against ηN/P for a 50 mm journal bearing (length 25 mm, radial clearance 25 µm). Top right: the bearing, clearance exaggerated; the journal shifts off centre as the film thins. Bottom right: the surfaces at the thinnest film, oil in blue, touching asperities in red (vertical scale stretched).
Oil (at 40 °C)
Hersey number ηN/P
Friction coefficient f
Thinnest film hmin
λ = hmin/σ
Load on asperities
Pressure P = W/(LD)
Try it: ISO VG 68 at 1500 rpm and 5 kN runs on a 12 µm full film (f about 0.009). Drag the speed down to 10 rpm: the film falls to about 1 µm, only twice the roughness, and the regime turns mixed. At 1 rpm it is boundary and f rises to about 0.03. Now pick water at 1500 rpm: its viscosity is 90 times lower, so the dot lands in the mixed band.

How thick is the oil film in a ball or gear contact?

A ball on a flat or a gear tooth touches on a tiny spot at about 1 GPa. There the oil gets thousands of times more viscous and the steel flattens elastically. This is elastohydrodynamic lubrication (EHL). The film is well under a micrometre, so it must be compared with the roughness: the lambda ratio λ = hmin/√(Rq12 + Rq22).

Top: section along the rolling direction (flow left to right). Film and roughness share one vertical scale in nm; the horizontal scale is in µm, so the shape is stretched upward. Grey curve: Hertz pressure. Bottom left: hc and hmin against speed; shaded bands mark λ < 1 and 1 to 3. Bottom right: the λ gauge.
hc/Rx = 2.69 U0.67 G0.53 W−0.067 (1 − 0.61e−0.73k)
hmin/Rx = 3.63 U0.68 G0.49 W−0.073 (1 − e−0.68k)
U = η0u/(E′Rx), G = αE′, W = w/(E′Rx2), k = 1.03(Ry/Rx)0.64
Materials (sets E′)
Central film hc
Minimum film hmin
λ = hmin/σ
Hertz pmax, radius a
U, G
W, k
Try it: the default is a 19.05 mm steel ball on a steel disc at 30 N and 1 m/s in VG 68: hc is 340 nm, hmin 196 nm and λ about 1.9, so it is mixed. Double the load to 60 N: the film hardly changes (it only drops about 5%). Double the speed to 2 m/s: the film grows about 60%. Polish the flat to Rq2 = 20 nm and λ passes 3.

Why does oil lose its film when it gets hot?

Oil viscosity falls steeply with temperature. An ISO VG 68 oil is about 214 mm2/s at 20 °C and 8.7 mm2/s at 100 °C. Lower viscosity means a lower Hersey number and a thinner film. The viscosity index (VI) says how strongly it thins: the higher the VI, the less the viscosity changes.

Left: viscosity against temperature (ASTM D341 Walther line through the 40 and 100 °C values). Bold: your oil. Dashed: the same grade at VI 0. Blue: water. Right: the bearing of section 1 at 100 rpm and 15 kN (12 MPa). Small dots every 10 °C, labelled every 40 °C.
Oil
Kinematic viscosity ν
Dynamic viscosity η = ρν
ν at 100 °C (from VI)
Hersey number ηN/P
hmin and λ
Friction coefficient f
Try it: VG 68 at VI 100: heat it from 40 °C to 100 °C. The viscosity drops from 68 to 8.7 mm2/s and the dot slides from full film into the mixed band. Keep going to 150 °C and it reaches boundary. Now set 120 °C and compare VI 0 (boundary) with VI 150 (mixed).

What to take away

One number sets the regimeSpeed, viscosity and load act together through ηN/P. Halve the speed or double the load: same dot, same place on the curve.
Friction has a minimumAt high ηN/P friction comes from shearing the oil and rises with speed. At low ηN/P asperities touch and friction climbs to the boundary value near 0.1.
Compare film with roughnessThe regime depends on λ = hmin/σ, not on the film alone. Below 1: boundary. 1 to 3: mixed. Above 3: full film.
EHL films barely feel the loadFilm thickness goes as speed0.67 but load−0.067. Speed, viscosity and smoother surfaces help; less load hardly does.
More detail: the models behind the pictures and where they stop working

The bearing (section 1 and 3). A full journal bearing, D = 50 mm, L = 25 mm, radial clearance c = 25 µm. The eccentricity ratio ε comes from Ocvirk's short-bearing solution, W = (ηUL3/4c2)·ε/(1−ε2)2·√(π2(1−ε2) + 16ε2) with U = πDN. For fixed geometry this makes ε a function of ηN/P alone, which is why all three sliders move the dot along one curve. The thinnest film is hmin = c(1−ε).

Fluid friction. fh = 2π2(ηN/P)(R/c)/√(1−ε2) + cεsinφ/(2R), with the attitude angle tanφ = π√(1−ε2)/(4ε). At small ε the first term is Petroff's law, f = 2π2(ηN/P)(R/c). The shear term is taken over the whole circle, as if the film never cavitates.

Mixed friction. f = φμb + (1−φ)fh, with boundary friction μb = 0.10. φ is the share of load on the asperities. Here it is taken as the Greenwood-Tripp function F5/2(λ) (fit 4.4086×10−5(4−λ)6.804) divided by its value at λ = 0, so φ = (1−λ/4)6.804 for λ < 4. That is a simple sharing rule, not a solved mixed-lubrication model; the film is not recomputed for the load the asperities take.

EHL (section 2). Hamrock and Dowson fitted these formulas to their numerical solutions for isothermal, fully flooded elliptical contacts, k from 1 to 8. E′ = 2/[(1−ν12)/E1 + (1−ν22)/E2], twice the Hertz contact modulus E*. Hertz sizes use the Hamrock-Brewe approximations. The drawn film shape (flat in the Hertz zone, a constriction near the outlet) is a sketch that matches hc and hmin; the inlet gap is the Hertz gap outside a line contact. Real films also thin with inlet shear heating and starvation at high speed, and asperities flatten inside the contact (micro-EHL), so λ is a conservative guide.

Viscosity and temperature (section 3). ASTM D341 (Walther): log log(ν + 0.7) = A − B log T, T in kelvin, drawn through ν40 (the ISO VG number) and ν100. ν100 is found so that the ASTM D2270 viscosity index equals your VI; L and H come from quadratic fits to the D2270 table, which give VI 156 and 92.4 for the two worked examples in the standard. Density: 875 kg/m3 at 15 °C, 0.65 kg/m3 lower per °C (a typical mineral oil). Water: η = 2.414×10−5·10247.8/(T−140) Pa·s, which gives 1.00 mPa·s at 20 °C and 0.65 at 40 °C. The film thickness in section 3 ignores the heat made in the film itself.

Questions people ask

What is a Stribeck curve?

A plot of friction coefficient against ηN/P (or against speed at fixed oil and load). It falls steeply as an oil film forms, reaches a minimum near the start of full-film lubrication, then rises slowly as the oil is sheared faster.

What are the three lubrication regimes?

Boundary: the load is carried by touching asperities and surface films, f about 0.05 to 0.15. Mixed: the load is shared between the oil film and the asperities. Full film (hydrodynamic or EHL): the oil holds the surfaces apart and f can fall to 0.001 to 0.01.

What is the Hersey number?

ηN/P: viscosity in Pa·s times speed in revolutions per second, divided by pressure in Pa. In these units it has no dimension. Hersey showed in 1914 that journal bearing friction falls on one curve when plotted against it.

What is the lambda ratio in lubrication?

The film thickness divided by the combined roughness, λ = hmin/√(Rq12 + Rq22). Below about 1 the surfaces touch a lot; above about 3 they are almost always apart.

What is elastohydrodynamic lubrication?

Film lubrication in concentrated contacts such as ball bearings, cams and gears. The pressure (around 1 GPa) raises the oil viscosity many times over and flattens the solids elastically. Both effects let a film tens to hundreds of nanometres thick survive.

Why does load barely change EHL film thickness?

More load flattens the steel over a larger area, so the pressure rises only slowly and the inlet that builds the film changes little. In the Hamrock-Dowson formula hc goes as w−0.067: doubling the load thins the film by about 5%.

What does viscosity index mean?

A number (ASTM D2270) for how much viscosity changes between 40 and 100 °C. Mineral oils are near 95 to 105; synthetic PAO oils are often 130 to 150. A higher VI keeps more film when the oil is hot.

Why is friction lowest just before full-film lubrication?

At that point the asperities have just stopped touching, but the film is still thin. Go further right and the oil is sheared harder, so viscous friction grows. Go left and asperity contact adds boundary friction.

Related: Asperities and the real area of contact (what touches when λ is small) · Wear mechanisms and wear depth · Wear rate calculator · Flash temperature (heat at the asperity contacts) · Why friction is not a material constant · Fatigue and S-N curves (rolling contact fatigue life depends on λ) · Scratch hardness and regimes · The mountain range you cannot see

References

Show the 10 references
  1. B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, Part III: fully flooded results, Journal of Lubrication Technology 99(2), 264 to 275 (1977). doi:10.1115/1.3453074. Source of the hc and hmin formulas.
  2. R. Stribeck, Die wesentlichen Eigenschaften der Gleit- und Rollenlager, Zeitschrift des Vereines Deutscher Ingenieure 46, 1341 to 1348, 1432 to 1438 and 1463 to 1470 (1902).
  3. M. D. Hersey, The laws of lubrication of horizontal journal bearings, Journal of the Washington Academy of Sciences 4, 542 to 552 (1914).
  4. I. M. Hutchings and P. Shipway, Tribology: Friction and Wear of Engineering Materials, 2nd ed., Butterworth-Heinemann (2017): chapter 4 (lubricants and lubrication, regimes and the lambda ratio).
  5. G. W. Stachowiak and A. W. Batchelor, Engineering Tribology, 4th ed., Butterworth-Heinemann (2014): chapter 2 (viscosity, Walther equation, viscosity index, pressure-viscosity coefficients of mineral oils), chapter 4 (hydrodynamic bearings) and chapter 7 (EHL).
  6. F. W. Ocvirk, Short-bearing approximation for full journal bearings, NACA Technical Note 2808 (1952).
  7. B. J. Hamrock, S. R. Schmid and B. O. Jacobson, Fundamentals of Fluid Film Lubrication, 2nd ed., Marcel Dekker (2004): the short journal bearing load and friction, and the Hamrock-Brewe approximations for elliptical Hertz contacts.
  8. J. A. Greenwood and J. H. Tripp, The contact of two nominally flat rough surfaces, Proceedings of the Institution of Mechanical Engineers 185, 625 to 633 (1970). The F5/2 function used for load sharing.
  9. ASTM D341, Standard Practice for Viscosity-Temperature Equations and Charts for Liquid Petroleum or Hydrocarbon Products, ASTM International.
  10. ASTM D2270, Standard Practice for Calculating Viscosity Index from Kinematic Viscosity at 40 °C and 100 °C, ASTM International. ISO 3448 defines the ISO VG grades by their kinematic viscosity at 40 °C.
Cite this page: Tripathy, Manisha. “Lubrication Regimes and the Stribeck Curve.” untethered atom, 2026, https://untetheredatom.com/tribology/lubrication-regimes-stribeck-curve.
BibTeX 
@misc{tripathy2026stribeck,
  author = {Tripathy, Manisha},
  title  = {Lubrication Regimes and the Stribeck Curve},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/tribology/lubrication-regimes-stribeck-curve}},
  note   = {Interactive web tool}
}
Last updated 24 September 2026.