Minimum Film Thickness⚠ unverified
Mechanical / Lubrication · Compute the minimum film thickness in a journal bearing
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| c | c | m | 1.0 | Radial clearance |
| eccentricity | eccentricity | — | 1.0 | Eccentricity ratio of the journal within the bearing (dimensionless), ranging from 0 (concentric) to 1 (contact) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | hmin | m | Minimum film thickness, in metres (m) |
The science & history
Understanding the Parameters
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Radial clearance $c$ — the gap between journal and bearing when the shaft is centred; it is the maximum possible film thickness on any side. Everything scales with it.
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Eccentricity ratio $\varepsilon = e/c$ — how far off-centre the shaft sits, from 0 (perfectly centred, uniform film) to 1 (shaft touching the bearing wall, $h_{min} = 0$). It is the geometric fingerprint of load: a lightly loaded bearing runs nearly centred ($\varepsilon \to 0$, thick minimum film), while a heavily loaded one is pushed hard to one side ($\varepsilon \to 1$, vanishing film). Eccentricity is read off the Raimondi–Boyd charts as a function of the Sommerfeld Number.
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The trade-off — load capacity comes from eccentricity (the off-centre position creates the converging wedge that generates pressure), yet too much eccentricity leaves too little film. Design targets an $\varepsilon$ (often 0.6–0.8) that carries the load while keeping $h_{min}$ above the roughness limit.
Derivation (Approaching a Proof)
The journal (radius $r$) sits inside the bearing bore (radius $r + c$) with its centre displaced from the bore centre by the eccentricity $e$. The oil film thickness varies around the circumference; at any angular position $\phi$ measured from the line of centres, geometry gives
$$h(\phi) \approx c\,(1 + \varepsilon\cos\phi), \qquad \varepsilon = \frac{e}{c}.$$
The film is thickest where the journal is farthest from the wall ($\phi = 0$, $h_{max} = c(1+\varepsilon)$) and thinnest diametrically opposite, at the point of closest approach ($\phi = \pi$):
$$h_{min} = c\,(1 - \varepsilon).$$
So the minimum film is simply the clearance reduced by the fractional off-centre displacement. At $\varepsilon = 0$ (centred) the film is uniform at $c$; at $\varepsilon = 1$ (metal-to-metal) it vanishes. The converging region between $h_{max}$ and $h_{min}$ is the wedge that generates the hydrodynamic pressure supporting the load (Hydrodynamic Film Pressure) — which is why load and eccentricity are inseparable.
Dimensional check. $(1 - \varepsilon)$ is dimensionless, so $[h_{min}] = [c] = \text{m}$. ✓
History and Development
The eccentric-journal film geometry is the core of Reynolds' (1886) and Sommerfeld's (1904) hydrodynamic bearing theory. The minimum-film-thickness ratio $h_{min}/c = 1 - \varepsilon$ versus Sommerfeld number is a key Raimondi–Boyd (1958) design curve, standard in Shigley and ISO 7902. Comparing $h_{min}$ against the surface roughness (the Lambda Ratio) determines whether the bearing runs safely in full-film or risks mixed-lubrication wear.
Related Concepts: Sommerfeld Number, Lambda Ratio, Hydrodynamic Film Pressure, Journal Bearing Load Capacity, Petroff Friction
Notes: Eccentricity $\varepsilon = e/c$ (0 centred → 1 contact); read from Raimondi–Boyd vs Sommerfeld number. Check $h_{min}$ against combined roughness via the Lambda Ratio. Load capacity requires eccentricity (the wedge), so $h_{min}$ trades off against load.