Plain bearing minimum lubricant film thickness

What does this quantity describe?

The minimum film thickness h0 = 0.5·dL·ψ·(1−ε) is the smallest gap between shaft and bearing shell during hydrodynamic operation. Wear-free operation requires h0 to stay above the material-dependent limit h0,allow, which depends on surface roughness, form errors and lubricant cleanliness.

Think of h0 as the thinnest point of an oil film on which the shaft 'floats' inside the bearing, similar to a water skier gliding on a thin film of water over the surface — as long as the film stays thick enough, no solid contact occurs.

Formula and variables

h0 = 0.5 · dL · ψ · (1 − ε)

• h0 = 0.5 · dL · ψ · (1 − ε)
• dL = h0 / [0.5 · ψ · (1 − ε)]
• ε = 1 − h0 / (0.5 · dL · ψ)

Choose the inputs correctly

dL is the bearing bore diameter, ψ the relative clearance (from the corresponding calculator), and ε the relative eccentricity, determined via the Sommerfeld number and TB 15-11.

How to use the calculator

First determine ψ and, via the Sommerfeld number, the relative eccentricity ε, then enter both together with dL to get h0.

Worked example

dL = 50 mm, ψ = 1‰ and ε = 0.7 give h0 = 0.5 · 50 mm · 0.001 · 0.3 = 0.015 mm = 7.5 µm.

Understand the result and units

h0 = 7.5 µm is compared against the allowable value h0,allow from TB 15-14, which depends on surface roughness and lubricant filtration. If h0 falls below it, mixed friction and wear are likely.

dL is given in mm, ψ is dimensionless and ε is dimensionless between 0 and 1; h0 is usually expressed in µm due to its small magnitude.

How the allowable limit h0,allow is determined

The allowable limit h0,allow is approximately based on the sum of the roughness depths of shaft and bearing shell plus an allowance for form deviations: h0,allow ≈ Σ(Rz + Wt) for a shaft without misalignment or deflection. TB 15-14 in Roloff/Matek gives specific experience values, which additionally assume careful assembly and adequate lubricant filtration. Without these boundary conditions, the real limit can be noticeably higher than the pure roughness-based value.

Typical applications

Minimum film thickness is the final check in every plain bearing design, deciding whether a bearing actually operates wear-free in the hydrodynamic regime.

Assumptions, limits and common mistakes

The formula applies to shafts without misalignment or deflection in a full journal bearing. Shaft deflection, alignment errors and form deviations can locally reduce the actual minimum gap below the calculated value.

Common mistake: A common mistake is estimating ε instead of properly determining it via the Sommerfeld number and TB 15-11; an incorrect ε substantially distorts h0, especially near ε = 1.