Stribeck Curve Simulator: Lubrication Regime Transitions

simulator intermediate ~10 min
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Λ ≈ 3.2 — transitioning from mixed to full hydrodynamic lubrication

At η=0.05 Pa·s, U=1 m/s, W=10 kN/m, and R_a=0.5 μm, the lambda ratio of ~3.2 indicates the system is at the boundary between mixed and full hydrodynamic lubrication.

Formula

S = η × U / W (Hersey/Sommerfeld number)
Λ = h_min / R_q (lambda ratio, regime indicator)
h_min ∝ (ηU)^0.7 / W^0.13 (Hamrock-Dowson film thickness)

The Stribeck Curve

In 1902, Richard Stribeck published his landmark study of bearing friction, revealing a characteristic curve that remains the cornerstone of lubrication engineering. By plotting friction coefficient against a parameter combining speed, viscosity, and load, Stribeck showed that friction passes through a minimum as conditions change — high in boundary lubrication, dropping through a minimum in the mixed regime, then rising again in the viscous hydrodynamic regime.

Three Regimes of Lubrication

Boundary lubrication occurs at low speeds, high loads, or low viscosity: the oil film is thinner than surface roughness, and asperities contact directly. Mixed lubrication is the transition zone where partial film supports some load while asperity contacts carry the rest. Full hydrodynamic lubrication occurs when the film is thick enough to completely separate surfaces — friction is purely viscous shear, and wear is essentially zero. Each regime demands different design strategies.

The Lambda Ratio

The lambda ratio Λ = h_min/R_q provides a quantitative criterion for lubrication regime. When the minimum film thickness h_min exceeds about three times the composite surface roughness R_q, surfaces are fully separated. Modern surface metrology and elastohydrodynamic (EHL) film thickness calculations allow engineers to predict Λ for any operating condition, enabling rational lubricant and surface finish selection.

Design Implications

Understanding the Stribeck curve is essential for machine design. Engine bearings must operate in the hydrodynamic regime during normal running but survive boundary conditions at startup. Gears often operate in mixed or EHL regimes, demanding robust additive packages. The trend toward lower-viscosity lubricants for fuel efficiency pushes systems closer to the mixed regime, requiring better surface engineering. This simulation lets you explore how each parameter shifts the operating point on the Stribeck curve.

FAQ

What is the Stribeck curve?

The Stribeck curve plots friction coefficient against the Hersey number (a dimensionless group ηN/P combining lubricant viscosity, speed, and pressure). It reveals three distinct lubrication regimes: boundary (high friction, surface contact), mixed (intermediate, partial film), and hydrodynamic (low friction, full film separation). It is the most important diagram in lubrication engineering.

What is the lambda ratio?

The lambda ratio Λ = h_min/R_q compares minimum film thickness to composite surface roughness. Λ < 1 indicates boundary lubrication (asperity contact), 1 < Λ < 3 indicates mixed lubrication, and Λ > 3 indicates full-film hydrodynamic lubrication. It is the primary criterion for predicting lubrication regime.

What is boundary lubrication?

In boundary lubrication, the oil film is too thin to separate surfaces. Friction and wear are controlled by thin molecular films (physisorbed or chemisorbed layers) on the surfaces, not by bulk lubricant viscosity. Anti-wear additives like zinc dialkyldithiophosphate (ZDDP) form protective tribofilms that prevent metal-to-metal contact.

Why does friction increase at high speeds?

In the hydrodynamic regime, the full oil film separates surfaces completely (no wear), but viscous shear of the lubricant causes friction proportional to η×U/h. Higher speed means more viscous dissipation. This is why high-performance applications use the lowest viscosity lubricant that still maintains adequate film thickness.

Sources

Embed

<iframe src="https://homo-deus.com/lab/tribology/lubrication-regimes/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub