Hydrodynamic design

Minimum journal-bearing film thickness

Calculates the geometric minimum film thickness of a plain bearing from journal diameter, relative clearance and a given eccentricity -- explicitly not the eccentricity itself, which must come from a full hydrodynamic design.

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Inputs

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Film thickness result

ƒ(x)

Set the inputs and run the calculation.

Technical article

Minimum journal-bearing film thickness

Calculates the geometric minimum film thickness of a plain bearing from journal diameter, relative clearance and a given eccentricity -- explicitly not the eccentricity itself, which must come from a full hydrodynamic design.

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.

Frequently asked questions

Where do I get the eccentricity epsilon?

From a full hydrodynamic calculation per ISO 7902-2, which evaluates the characteristic functions depending on the Sommerfeld number (calculator 58) and the width-to-diameter ratio -- not by free estimation.

What do epsilon = 0 and epsilon near 1 mean?

Epsilon = 0 means the journal sits concentrically in the bearing (no load-bearing wedge, practically only at standstill or theoretically at zero load). Epsilon near 1 means the journal is almost touching the bush; h_min then approaches zero.

Is a positive h_min value automatically safe?

No. h_min must be clearly above the combined surface roughness of journal and bush, plus any misalignment, otherwise mixed friction occurs despite a computed positive h_min.

Why doesn't the calculator invent an h_lim limit?

A sensible minimum film thickness depends on manufacturing roughness, alignment, material pairing and the applicable standard or manufacturer figure -- a blanket value would be wrong for many applications.

What's the difference between radial clearance c and diametral clearance s?

Radial clearance c = s/2 is the one-sided gap between journal and bush; diametral clearance s is the full value across the diameter. h_min refers to the radial clearance.

What comes after film thickness?

With a known friction coefficient mu for the achieved lubrication state, friction power (calculator 60) can be calculated; the thermal effect of friction heat on viscosity should also be considered.

Sources

  • ISO 7902-2:2020 -- Hydrodynamic plain journal bearings, part 2: functions.
  • Roloff/Matek Maschinenelemente Formelsammlung, 15th ed. 2019, Ch. 15 Plain bearings.
  • Niemann/Winter/Höhn Maschinenelemente Band 1, Ch. 15-16.