Journal Bearing Film Thickness Calculator

What happens in a plain bearing?

In a plain bearing a shaft turns inside a slightly larger bore, the bearing bush, with oil in between. When the shaft turns fast enough it drags oil into the narrowing gap and builds up pressure that carries the shaft. Shaft and bush then do not touch; they slide on a very thin oil film.

What is the minimum film thickness h_min?

h_min is the smallest radial distance between the journal surface and the bore wall, i.e. the thinnest point of the oil film for the given eccentricity. It is where the load pushes the journal closest to the bore. Typical values are a few micrometres (1 µm = 0.001 mm), far thinner than a human hair. If h_min is smaller than the roughness peaks of the surfaces, the parts touch: mixed friction with wear and heating results.

What is the radial clearance c?

The bore is minimally larger than the journal. The difference in diameters is the bearing clearance or diametral clearance s. If the journal sat exactly in the centre, there would be an equal gap on every side: the radial clearance c = s/2. Example: bore 50.05 mm, journal 50.00 mm, so s = 0.05 mm and c = 0.025 mm = 25 µm. The relative clearance ψ = s/d expresses the same independently of size (here 0.001).

What does the eccentricity ratio ε mean?

Under load the journal does not sit centred but is pushed off centre. The distance between bore centre and journal centre is the displacement e. The eccentricity ratio ε = e/c says what share of the radial clearance the journal has used up: ε = 0 means centred, ε = 0.7 means 70 % of the clearance used, ε = 1 would mean contact. It follows directly that h_min = c − e = c·(1 − ε).

Where do I get the inputs?

Journal diameter d: nominal size from the drawing. Relative clearance ψ: from the fit dimensions of bore and journal or with the Plain bearing operating clearance calculator, ideally for the operating temperature. Eccentricity ratio ε: do not estimate it; take it from a hydrodynamic calculation that uses load, speed, oil viscosity and bearing width. On this website the journal bearing calculator to DIN 31652 returns ε as a result; alternatively ε is determined from the Plain bearing Sommerfeld number and the ISO 7902-2 characteristic functions.

What do I need the results for?

h_min is the key value: it is compared with the roughness of journal and bush and with a permissible minimum from a standard or manufacturer to check that the bearing runs safely on oil. The radial clearance c is a check on the inputs and the upper bound for h_min. The displacement e shows how far the journal moves off centre in absolute terms, for example for alignment or seal-gap considerations. h_max is the widest point of the gap, where the oil is usually supplied.

Formula

h_min = 0.5 * d * psi * (1 - epsilon) = c * (1 - epsilon)

With the journal displaced eccentrically in the bearing (eccentricity epsilon, 0 = concentric, near 1 = almost touching), the film narrows on the loaded side. Minimum film thickness follows geometrically from the radial clearance c = s/2 = 0.5*d*psi, multiplied by (1-epsilon).

What this model does not show

Eccentricity epsilon is normally the OUTPUT of a full hydrodynamic calculation per ISO 7902-2 (depending on the Sommerfeld number and the width-to-diameter ratio) -- it must not be freely estimated or assumed. This calculator takes epsilon as a known input and only returns the geometric consequence of it. No permissible minimum h_lim is invented either; such a limit must come from surface roughness, misalignment and an actual standard or manufacturer figure for the application.

Worked example

d = 50 mm, psi = 0.001, epsilon = 0.7 (assumed known from a prior hydrodynamic design). Radial clearance c = 0.5 x 50 mm x 0.001 = 0.025 mm = 25 um. Minimum film thickness h_min = 25 um x (1 - 0.7) = 7.5 um. At epsilon = 0.9 (more eccentric, same geometry), h_min would be only 25 um x 0.1 = 2.5 um -- notably more critical regarding mixed friction.

Common mistakes

• Plugging in an eccentricity 'by feel' or from a mismatched source instead of determining it from the Sommerfeld number and the ISO 7902-2 characteristic functions.
• Confusing radial clearance c with diametral clearance s (a factor-of-2 difference).
• Interpreting h_min without reference to surface roughness -- a geometrically positive h_min alone says nothing about actual mixed friction if it is of the same order as the roughness.