2015/02/05

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
hc – film thickness at center of contact patch
R1q, R2q  – rms average roughness of two contacting surfaces.

Λ<1 – the surfaces are in continuous metal-to-metal contact (i.e. boundary lubrication)
Λ>3÷– 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

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