Specific film thickness

Non-conforming contacts (in which the shapes of the bodies are dissimilar enough that under zero load, they only touch at a point or along a line and the stresses are highly concentrated in this contact area) such as; gear teeth, cam-follower joints and rolling-element bearings (balls, rollers) can operate in three modes of lubrication:

• boundary,
• mixed,
• EHD.

The specific film thickness is a principal factor that determines which of these situations will occur. It is denoted as: Λ.

Λ is defined as the ratio of minimum film thickness at the patch center to the composite rms (root mean square) surface roughness of the two surfaces.

, where

h_c – film thickness at center of contact patch
R_1q, R_2q  – rms average roughness of two contacting surfaces.

Λ<1 – the surfaces are in continuous metal-to-metal contact (i.e. boundary lubrication)

Λ>3÷4 – there is essentially no asperity contact

Figure below shows the experimentally measured frequency of asperity contact. Within an EHD gap as a function of specific film thickness.

Figure 10-13.
Effect of Specific Film Thickness Λ on the Asperity Contacts and Fatigue Life

It also shows the effect of specific film thickness on fatigue life of a rolling bearing.

Reference: Machine Design An Integrated Approach, 4th edition - Robert L. Norton