Lambda Ratio Calculator
Estimate lubrication regime from tribological test conditions
Calculates the lambda ratio (λ = hmin / σ) from test configuration, load, entrainment speed, lubricant properties, and surface roughness using EHL theory (Hamrock-Dowson / Dowson-Higginson).
1Select test method
Rotating
Reciprocating
Assumptions & Limitations
- This calculator assumes Newtonian behavior and isothermal conditions. Real lubricants exhibit shear-thinning and temperature/pressure-dependent viscosity, which can significantly alter the actual lambda ratio.
- Film thickness is governed by the entrainment (mean) speed u_e = (u₁ + u₂) / 2. Sliding speed affects film thickness only indirectly, via inlet shear heating.
- Lambda ratio predictions carry inherent uncertainty due to variability in effective viscosity and deformed surface roughness. Use results as a comparative guide, not an absolute prediction.
What is the Lambda Ratio (λ)?
The lambda ratio (λ) is a dimensionless number that characterises the lubrication condition in a tribological contact. It is defined as the ratio of the minimum oil film thickness h_min to the composite surface roughness σ* of the contacting bodies: λ = h_min / σ*. When λ < 1, the asperities of the surfaces are in direct contact (boundary lubrication). For 1 ≤ λ < 3, a mixed regime occurs where partial asperity contact coexists with hydrodynamic pressure. At λ ≥ 3, the surfaces are fully separated by the oil film (full-film or hydrodynamic lubrication), resulting in minimal wear.
Calculation Method
This calculator applies Hamrock–Dowson equations for elastohydrodynamic lubrication (EHL) to estimate h_min for point and line contact geometries. The reduced elastic modulus E' and Hertzian contact parameters (contact radius a, maximum pressure p₀) are computed first. Viscosity at operating temperature is interpolated from tabulated data using the Williams–Landel–Ferry (WLF) model. The resulting λ value classifies the regime and guides lubricant selection or film thickness optimisation.
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