Hamrock–Dowson
EHL film thickness
From contact geometry and inlet oil properties to minimum and central film thickness. Calculate in SI, inspect the dimensionless groups, and check the geometry assumptions.
Contact & lubricant
Live calculationEnter values in the units shown. Results update as you type.
Film thickness
Awaiting calculationIsothermal, fully flooded estimate. Review the geometry warnings and assumptions below.
Calculation details
SI-based groups and effective geometry
| Elasticity & geometry | |
|---|---|
| Reduced modulus, Er (GPa) | — |
| Rolling radius, Rₓ (mm) | — |
| Across radius, Rᵧ (mm) | — |
| Radius ratio, Rᵧ/Rₓ | — |
| Ellipticity parameter, k | — |
| Dimensionless groups | |
| Speed, U | — |
| Material, G | — |
| Load, W | — |
| Minimum film, Hmin | — |
| Central film, Hc | — |
A film formed under pressure
In an elastohydrodynamic lubrication (EHL) contact, pressure deforms the surfaces and raises the oil viscosity. The Hamrock–Dowson formulas estimate minimum and central lubricant film thickness for point and elliptical contacts using the dimensionless speed U, material G and load W groups.
Hamrock and Dowson fitted these formulas in 1977 to isothermal, fully flooded numerical solutions. The fitted geometry range extends from k = 1, a ball on a flat, to k = 8, close to a line contact.
How to use the calculator
- Set the load and speeds. Enter the normal load in N and both rolling-direction surface speeds in m/s.
- Describe both surfaces. Enter rolling and across-direction radii in mm. Use zero for flat surfaces and negative values for concave surfaces.
- Enter material and oil properties. Supply both elastic moduli and Poisson ratios, then viscosity at the inlet temperature and the pressure–viscosity coefficient.
- Review the result. Read minimum and central film thickness in µm and nm. Inspect Rᵧ/Rₓ, k and any geometry warnings before using the estimate.
Convert to SI first
The calculation uses metres, pascals, pascal-seconds and inverse pascals. Input values are converted before evaluating the formulas.
Modulus: GPa × 109 = Pa
Viscosity: mPa·s × 10−3 = Pa·s
Coefficient: 1/GPa × 10−9 = 1/Pa
A zero surface radius contributes zero curvature. A zero or negative combined curvature in either direction is treated as a conforming-surface error.
The formulas used
1/Rₓ = 1/rₓ₁ + 1/rₓ₂
1/Rᵧ = 1/rᵧ₁ + 1/rᵧ₂
U = η₀u / (ErRₓ) · G = αEr
W = w / (ErRₓ²)
k = 1.0339(Rᵧ/Rₓ)0.636
hmin = HminRₓ
hc = HcRₓ
Hmin and Hc are dimensionless. Multiplying by Rₓ in metres gives film thickness in metres; × 106 gives µm and × 109 gives nm.
Understanding the estimate
What is the difference between minimum and central film thickness?
The calculator reports minimum film thickness as hmin and central film thickness as hc. Each is calculated with its own Hamrock–Dowson formula and displayed in micrometres and nanometres.
How do I enter a flat surface or a concave groove?
Enter 0 mm for a flat surface and a negative radius for a concave surface, such as a bearing groove. A flat surface contributes nothing to the curvature sum. The combined curvature must be positive in both directions.
Why does the calculator warn about the contact geometry?
The formulas assume rolling along the minor axis of the contact ellipse and were fitted for k from 1 to 8. The calculator warns when Ry is below Rx or when k is outside that range, while still displaying the calculated result.
Which inlet conditions do these formulas assume?
The formulas assume smooth surfaces and an isothermal, fully flooded inlet. They do not model inlet heating, starvation or roughness. Use the oil dynamic viscosity at the inlet temperature.
Preliminary estimate only. Not a substitute for a qualified engineer. This calculation assumes smooth surfaces and an isothermal, fully flooded inlet, and does not model inlet heating, starvation or roughness.