Stribeck Curve⚠ unverified

Understanding the Parameters

• Bearing number $N/P$ (with viscosity, $\mu N/P$) — the x-axis of the Stribeck curve. It is the ratio of the film-building tendency (viscosity × speed) to the film-collapsing tendency (load). Low $\mu N/P$ = thin film = surface contact; high $\mu N/P$ = thick film = full separation.

• Boundary friction $\mu$ — the intercept: the friction when the film is negligible and load is carried by boundary layers and asperity contact ($f \approx 0.08$–$0.15$). This is the high-friction, high-wear regime that the design tries to avoid at running speed.

• Hydrodynamic sensitivity $\eta$ — the slope of the rising branch: once a full film forms, friction is viscous (shearing the oil) and grows with speed and viscosity. More speed means more viscous drag — counter-intuitively, friction increases with better lubrication in this regime.

• The three regimes — boundary (asperity contact, high $f$), mixed (partial film, the friction minimum), and hydrodynamic/full-film (complete separation, $f$ rising with speed). The film-to-roughness Lambda Ratio $\lambda$ tells you which regime you are in ($\lambda < 1$ boundary, $1$–$3$ mixed, $> 3$ full film).

Derivation (Approaching a Proof)

The Stribeck curve is fundamentally empirical — Stribeck measured friction versus speed for journal bearings — but each regime has a mechanistic explanation:

• Boundary regime. With no separating film, load is carried by adsorbed molecular layers and asperity contact; friction is nearly constant at $f \approx \mu$ (a solid-friction value), independent of speed.

• Hydrodynamic regime. A full fluid film separates the surfaces; friction is the viscous shear of the lubricant. From Petroff's analysis (Petroff Friction), the friction coefficient of a full-film journal bearing is $f = 2\pi^2 (\mu N/P)(r/c)$ — linear in the bearing number $\mu N/P$. Writing the slope as $\eta\,(r/c)$-type constant gives the rising form $f = \mu_0 + \eta\, N/P$.

• Mixed regime (the dip). Between them, the film partially separates the surfaces; as speed rises the film thickens, asperity contact drops, and friction falls to a minimum — then the growing viscous drag takes over and friction rises. This non-monotonic minimum is the real Stribeck signature.

The registry's linear $f = \mu + \eta N/P$ superposes a constant boundary term and a rising hydrodynamic term but omits the falling mixed-regime physics, so it reproduces the hydrodynamic branch and the boundary intercept but not the dip.

Dimensional check. $\eta\,N/P = \text{Pa}\cdot(1/\text{s})/\text{Pa} = 1/\text{s}$ — for $f$ to be dimensionless, $\eta$ must carry units of Pa·s (viscosity-like); with the registry's Pa label the term is $\text{s}^{-1}$, so treat $\eta$ as effectively $\mu\cdot(r/c)$-scaled. Regime intuition holds regardless.

History and Development

Richard Stribeck (1902) systematically measured journal-bearing friction versus speed, revealing the characteristic curve now bearing his name; Mayo Hersey formalised the dimensionless bearing number. The Stribeck curve is the organising framework of tribology — it connects Petroff Friction and Sommerfeld Number (hydrodynamic), the Lambda Ratio (regime indicator), and boundary/EHL lubrication into one picture, guiding lubricant selection, additive design, and bearing operating points.

Related Concepts: Petroff Friction, Sommerfeld Number, Lambda Ratio, Friction Coefficient Boundary, Elastohydrodynamic Film, Viscosity Temperature

Notes: Linear model = hydrodynamic branch + boundary intercept only (no mixed-regime dip — see note). Full curve is non-monotonic; use the Lambda Ratio to identify the regime. Bearing number is $\mu N/P$ (Hersey number).