Film Thickness Ratio or Lambda Ratio

The film thickness ratio or lambda ratio gives the relationship between minimum film thickness in a contact and the composite surface roughness.  The following equations give the film thickness ratio, often referred to as lambda, and the composite surface roughness, which combines the roughness of both contacting surfaces into an equivalent value.
Different sources give different guidelines for the film thickness ratio.  On this page I have compiled several of these criterion:

Fundamentals of Fluid Film Lubrication by Hamrock, Schmid and Jacobson

1. Hydrodynamic Lubrication (HD), 5 < Λ < 100
2. Elastohydrodynamic Lubrication (EHL or EHD), 3 < Λ < 10
3. Partial Lubrication or Mixed Lubrication, 1 < Λ < 5
4. Boundary Lubrication, Λ < 1

Principles of Tribology by Shizhu and Ping

1. Wear controlled within a slight range for reasonable life, Λ > 1.5
2. For low speed or surface roughness, Λ > 0.5 – 1
3. For high speed or roughness, Λ > 2
4. For a run-in surface, Λ > 0.5 – 1
5. For a non-run in surface, Λ > 2
6. For a cylindrical or flat surface (possibly greater to account for waviness and shape error), Λ = 2 – 5
7. For an unstable load, make Λ larger

Tribology in Manufacturing Technology by Jackson, Whitfield, Robinson, Morrell and Davim

1. Boundary Lubrication, Λ < 1
2. Mixed Lubrication, 1 < Λ < 3
3. Hydrodynamic Lubrication, 3 < Λ < 10

Synthetics, Mineral OIls and Bio-Based Lubricants by Grega, Kurosky, Lesinski, Raab and Tahir

1. Doubling Λ leads to a reduced wear rate by a factor of 3

Physical Analysis for Tribology by Quinn

1. No-contact time fraction is the percentage of time in a contact when no contact occurs.  This was measured in a one ball to ball contact.
2. Mass wear rate in a four ball test.
3. Time until the first pit occurs

 

Lambda ratio and and the percentage of time with surface to surface contact.

Lambda ratio and the mass wear rate.

Lambda ratio and the time until initial pitting.

 

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