AtlasCalcsUtility Calculation Suite
2026-07-30 11 min

Elastohydrodynamic Lubrication (EHL) Calculator

Calculate elastohydrodynamic lubrication parameters for highly loaded non-conformal contacts like gears, rolling bearings, and cams. Uses Hamrock-Dowson equations.

Calculator

Unit System
Reduced Radius R (m)
Reduced Modulus E'"'"' (Pa)
Viscosity eta0 (Pa-s)
Pressure-Viscosity Coeff (1/GPa)
Speed U (m/s)
Load W (N)

Results

Normal

Central Film Thickness h_c

2.09um

Film thickness at center of EHL contact

Minimum Film Thickness h_min

0.82um

Min film thickness near outlet

Lambda Ratio

1645988.32-

Specific film thickness ratio

Max Hertz Pressure p_H

0.65GPa

Maximum Hertzian contact pressure

Contact Half-Width b

0.017mm

Half-width of Hertzian contact zone

Visualizations

Results Overview

2.1umCentral Film Thickness h_c
0.8umMinimum Film Thickness h_min
1,645,988umLambda Ratio
0.7umMax Hertz Pressure p_H
0umContact Half-Width b

Formula

The Hamrock-Dowson equations predict central and minimum film thickness in EHL point contacts.

h_c = R x [3.06 x (eta0 U / E' R)^0.69 x (alpha E')^0.56 x (W / E' R^2)^-0.10]

Alternative Form

h_min = R x [1.58 x (eta0 U / E' R)^0.69 x (alpha E')^0.49 x (W / E' R^2)^-0.13]

Variables

SymbolNameUnitDescription
h_cCentral Film ThicknessmFilm thickness at contact center
RReduced RadiusmEffective radius of curvature
eta0Atmospheric ViscosityPa-sDynamic viscosity at ambient pressure
alphaPressure-Viscosity CoeffGPa^-1Viscosity increase with pressure

Explanation

EHL occurs in non-conformal contacts where high pressures cause elastic deformation and viscosity increase. Hamrock-Dowson formulas are empirical curve-fits to numerical solutions.

Derivation

Hamrock and Dowson performed extensive numerical solutions of coupled Reynolds, elasticity, and viscosity equations over wide parameter ranges.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Calculate dimensionless parameters.

U* = η₀U / (E'R), G* = αE', W* = W / (E'R²)
Result: Dimensionless parameters
Step 2

Apply Hamrock-Dowson central film formula.

H_c = 3.06 (U*)^0.69 (G*)^0.56 (W*)^-0.10
Result: h_c calculated
Step 3

Apply minimum film thickness formula.

H_min = 1.58 (U*)^0.69 (G*)^0.49 (W*)^-0.13
Result: h_min calculated
Step 4

Calculate lambda ratio and Hertz parameters.

lam = h_min / sigma
Result: Lambda and contact parameters
Final Answer
2.09

Worked Examples

See how the calculator works with different scenarios.

Scenario

R=0.02m, E'=2.1e11, eta0=0.05, alpha=15, U=10, W=5000.

Inputs

R:0.02m
U:10m/s
W:5000N

Calculation

Result

h_c=1.82um, h_min=0.86um, pH=1.26GPa, lam=1.72

Interpretation

Mixed lubrication regime for this moderately loaded bearing.

Understanding Your Result

Your Result: Central Film Thickness h_c: 2.09 um

Typical range: h_c: 0.1-5um. pH: 0.5-4GPa. Lambda: 0.5-10. Mineral oils alpha: 10-25 GPa^-1.

What This Means

EHL describes thin lubricant films (0.1-5um) between non-conformal surfaces where elastic deformation and pressure-viscosity effects dominate.

Why It Matters

Most machine element failures originate from inadequate EHL films. Understanding EHL enables proper lubricant selection and surface finish specification.

Professional Interpretation

The weak load exponent (-0.10) explains why EHL films persist under extreme loads. Speed and pressure-viscosity coefficient are the primary film thickness controls.

Recommendations

  • •Target lambda > 3 for full EHL and maximum bearing life (ISO 281)
  • •Use high-alpha lubricants for low-speed high-load contacts
  • •Ensure EP additives for lambda < 1.5
  • •Account for thermal effects at high speeds

Educational Content

Introduction

Elastohydrodynamic Lubrication (EHL) occurs in highly loaded non-conformal contacts where pressures reach 0.5-4 GPa, causing significant elastic deformation and viscosity increase.

Concept Explanation

EHL involves coupled Reynolds equation, elastic deformation, and piezoviscous effect. The characteristic EHL film is nearly parallel with an outlet constriction and pressure spike.

Applications

▸Rolling element bearings
▸Gear tooth contacts
▸Cam and follower systems
▸Traction drives
▸Metal rolling
▸Human joint lubrication

Benefits

  • •Prevents metal-to-metal contact
  • •Reduces friction and wear
  • •Enables high-load high-speed operation
  • •Extends fatigue life

Limitations

  • •Assumes smooth surfaces
  • •No thermal effects
  • •Fully flooded assumption
  • •Steady-state only

Best Practices

  • •Use lambda ratio as primary criterion
  • •Include thermal correction at high speeds
  • •Consider starvation effects
  • •Verify with experimental methods

Common Misconceptions

Myth: EHL films fully separate surfaces.
Truth: Films are 0.1-5um, similar to roughness. Many EHL contacts operate in mixed lubrication (lambda 1-3).
Myth: Higher load dramatically reduces film.
Truth: Load exponent is only -0.10. Doubling load reduces film by only 7%.

Practical Tips

  • •Alpha is the most influential material property for film thickness
  • •Thermal effects can reduce film by 30-50% at high speeds
  • •Use lambda > 3 for full EHL
  • •Grease-lubricated EHL contacts thin over time
  • •Starvation can reduce film by 50-80%

Common Mistakes

Using kinematic instead of dynamic viscosity
EHL requires dynamic viscosity in Pa-s
Neglecting thermal correction
Apply thermal reduction factor 0.5-0.8 at high speeds
Assuming fully flooded when starved
Check lubricant supply and apply starvation correction
Wrong contact geometry
Use point contact or line contact formulas as appropriate

Assumptions

This calculator makes the following assumptions to provide estimates:

Smooth Surfaces: Formulas assume perfectly smooth surfaces
Fully Flooded: Sufficient lubricant assumed at inlet
Newtonian Fluid: Shear thinning reduces effective viscosity
Steady State: Transient effects not captured

Limitations

Be aware of these limitations when using this calculator:

Empirical Curve-Fit: Accuracy +/-10-20% over fitted range
No Thermal Effects: Thermal reductions of 20-50% common at high speeds
No Roughness: Mixed EHL models needed for rough surfaces
No Transients: Gear meshing has time-varying geometry

Frequently Asked Questions

Answers to common questions about this calculator.

What is EHL?
Elastohydrodynamic Lubrication is the lubrication regime in non-conformal contacts where high pressure causes elastic deformation and viscosity increase.
What is the Hamrock-Dowson equation?
Empirical formulas for EHL film thickness: h_c = R x 3.06 x (U*)^0.69 x (G*)^0.56 x (W*)^-0.10.
What is lambda ratio?
lambda = h_min / sigma where sigma is composite RMS roughness. >3: full EHL, 1.5-3: mixed, <1.5: boundary.
Why is load exponent so small?
Increased load causes more elastic deformation, which helps maintain the film. Exponent -0.10 means 2x load reduces film by only 7%.
What is the Petryusevich spike?
Sharp pressure peak near the EHL contact outlet, reaching 2-3x the maximum Hertz pressure.
What is the pressure-viscosity coefficient?
Alpha describes viscosity increase with pressure: mu(p) = mu_0 exp(alpha p). Mineral oils: 10-20 GPa^-1.
How does speed affect EHL film?
Film thickness increases with speed^0.69. Doubling speed increases film by ~60%.
How does viscosity affect EHL film?
Film increases with viscosity^0.69. Higher viscosity = thicker films but more friction.
What is the reduced modulus?
E' = 2 / ((1-nu1^2)/E1 + (1-nu2^2)/E2). Steel-on-steel: 2.1e11 Pa.
What is thermal EHL?
EHL with energy equation for temperature effects. Thermal reduction can be 20-50%.
How does roughness affect EHL?
Roughness creates local pressure fluctuations. Lambda ratio quantifies significance.
What is starvation?
Insufficient lubricant at inlet reduces film below fully flooded prediction.
EHL vs hydrodynamic lubrication?
Hydrodynamic: conformal, low pressure, no deformation. EHL: non-conformal, high pressure, deformation and piezoviscous effects.
How to calculate composite roughness?
sigma = sqrt(sigma1^2 + sigma2^2). Ground: Ra 0.2-0.8um.
What lubricants for EHL?
Mineral oils ISO VG 68-460, synthetic PAO and esters, appropriate grease.
How to prevent EHL failure?
Ensure lambda > 1.5, proper viscosity, clean lubricant, temperature control, fine surface finish.
What is micropitting?
Surface fatigue from repeated asperity contacts in mixed EHL.
What is grease EHL?
Initially thickener provides thicker films. Over time approaches base oil EHL thickness.
Line contact formula?
H_min = 1.65 x U*^0.71 x G*^0.54 x W*^-0.13 for line contacts.
Reduced radius calculation?
Sphere-on-flat: 1/R = 1/R_s. Crossed cylinders: 1/R = 1/R1 + 1/R2.
Effect of inlet temperature?
Higher temperature reduces eta0 and film thickness by 50%+.
EHL with water?
Water has very low viscosity and negligible alpha. True EHL does not occur with water.
EHL and bearing fatigue life?
Adequate EHL (lambda>3) extends bearing life 10-100x vs boundary lubrication.
How to measure EHL film?
Optical interferometry (nm resolution), ultrasonic, capacitance methods.
Future of EHL?
Thermal EHL, mixed EHL with 3D roughness, transient EHL, ML surrogates, nano-additives.
Ellipticity in Hamrock-Dowson?
Formulas include ellipticity ratio k = a/b. Circular contacts (k=1) use standard coefficients.
EHL and friction relationship?
Friction depends on shear stress. At high pressure, limiting shear stress dominates. Traction curves describe friction vs slide-roll ratio.
What is the minimum film in EHL?
Minimum film occurs near the outlet constriction. Formula: h_min = R x 1.58(U*)^0.69(G*)^0.49(W*)^-0.13.
What affects the pressure spike?
Spike magnitude depends on load, speed, and pressure-viscosity coefficient. Higher alpha increases the spike.
Can EHL occur in soft contacts?
Yes, soft EHL occurs in elastomers and human joints with lower pressures but significant deformation.
What is the EHL film shape?
Nearly parallel central region, slight inlet constriction, and sharp outlet constriction with pressure spike.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Barus Equation
Exponential viscosity-pressure: mu(p) = mu_0 exp(alpha p).
Central Film Thickness
Film thickness in the central parallel region of an EHL contact.
EHL
Elastohydrodynamic Lubrication - regime with elastic deformation and piezoviscous effects.
Hamrock-Dowson
Empirical EHL film thickness formulas from numerical solutions.
Hertz Pressure
Maximum contact pressure from Hertz elastic contact theory.
Lambda Ratio
h_min / sigma, the specific film thickness ratio.
Non-Conformal Contact
Contact between surfaces with different curvatures.
Piezoviscous Effect
Viscosity increase with pressure, key to EHL film formation.
Reduced Modulus
E' - effective elastic modulus of the contact.
Starvation
Insufficient lubricant at inlet reducing film thickness.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 281ISO 76ISO 15243DIN ISO 281AGMA 925-A03ASTM D2782

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.