Mixed-Lubrication Stribeck and Load-Sharing Calculator

Equations used

SI units are used internally. The line load q is normal load per contact width; E′ and R′ are reduced modulus and radius. Positive pressures and load fractions are compressive. Component RMS values should be combined before entry as σ = √(Rq₁² + Rq₂²).

Symbols: η₀ is ambient dynamic viscosity; uₑ is entrainment speed; α is the Barus pressure–viscosity coefficient; h_c is central film thickness; λ is film ratio; η_s and R_a are summit density and mean radius; p_a is nominal-area asperity pressure; A_r/A₀ is real-area ratio; b is Hertz half-width; X_a = p_a/p₀; τ₀ is Eyring stress; and μ_b is boundary friction.

Assumptions and limits

The model assumes steady isothermal line contact, Gaussian independent spherical elastic summits, Newtonian inlet viscosity, Barus pressure dependence, and a uniform nominal contact. It does not model starvation, thermal shear thinning, running-in, coatings, debris, non-Gaussian directional texture, transient load, or plastic summit deformation. A measured grid replaces σ only; summit density and radius still require an independent estimate. Do not use this screening result as a lubricant or component qualification.

References

• Greenwood and Williamson (1966), doi:10.1098/rspa.1966.0242.
• Dowson and Higginson (1966), Elastohydrodynamic Lubrication, ISBN 978-0-08-011760-7.
• Bair and Winer (1979), doi:10.1115/1.3453327.

How to use

1. Enter the reduced line-contact radius in mm, line load in N/mm, and reduced modulus in GPa.
2. Enter dynamic viscosity at operating temperature in Pa·s and the pressure–viscosity coefficient in GPa⁻¹.
3. Set minimum and maximum entrainment speeds in m/s and a slide–roll ratio from −2 to 2; the primary result uses their geometric mean.
4. Enter composite RMS roughness in µm plus independently justified summit density in mm⁻² and summit radius in µm.
5. Enter boundary friction and Eyring stress. Results calculate automatically as numeric inputs change.
6. Optionally paste or load a rectangular height grid in µm, enter pixel spacing, and select Apply height grid. The measured RMS then replaces the statistical RMS input; clear the grid and apply again to return to the entered RMS.
7. Read the canonical friction coefficient, regime, film/lambda values, load split, real area, pressure, and convergence residual. The blue chart shows the full speed sweep.
8. Use Reset example to restore all defaults and clear the active measured-grid summary.
9. Correct any red input message before interpreting results. Treat boundary-dominated warnings as high uncertainty.
10. Do not use the model for starved, strongly thermal/non-Newtonian, plastically deforming, transient, debris-contaminated, or safety-critical qualification cases.

Interpretation

• λ < 1: boundary-dominated; asperity interaction is substantial.
• 1 ≤ λ < 3: mixed lubrication; fluid and asperity load paths coexist.
• λ ≥ 3: predominantly full-film under the stated assumptions.
• A convergence residual below 10⁻⁵ confirms the numerical load balance, not physical model suitability.