Hamrock-Dowson EHL quick calculator

Theory and worked example

The mean entrainment speed is u = (u1 + u2) / 2, with both surface velocities measured relative to the contact along x. The calculator uses this value directly: U = eta0 u / (E’ Rx). It neither doubles nor halves your entry. The sliding velocity u1 – u2 is a different quantity.

E’ = 2 / [(1 – nu1²)/E1 + (1 – nu2²)/E2], G = alpha E’, W = F/(E’ Rx²), and k = 1.03(Ry/Rx)^0.64. The reduced radii satisfy 1/Rx = 1/Rx1 + 1/Rx2, and similarly for y. GPa, inverse GPa and mm are converted to SI before evaluating the correlations shown above.

Example: The defaults represent a 10 mm radius steel ball against a nearly flat steel surface (body 2 uses 1,000,000 mm), under 100 N. Both moduli are 206 GPa and Poisson ratios are 0.29. At u = 1 m/s, viscosity 0.383 Pa s (= 383 mPa s), and alpha = 10 GPa^-1, central film thickness is 745.63 nm and minimum film thickness is 449.15 nm. Use this to compare lubricants at their operating temperature; compare minimum film thickness with combined surface roughness for separation screening.

Reference: Hamrock and Dowson, Applications of film thickness equations, NASA-TM-81701. For more detailed contact analysis, see TriboSolver.

The Hamrock-Dowson correlations are quick screening equations for fully flooded, isothermal, Newtonian elastohydrodynamic contacts. They are useful for lubricant and surface-separation estimates, but they do not model starvation, shear thinning, thermal thinning, transient starts, contamination, or mixed-lubrication asperity contact.

• The x radius is the radius in the entrainment direction. For this quick form, reduced R_x/R_y must be less than or equal to 1.
• Use the minimum film thickness with a lambda-ratio calculation when screening surface separation against roughness.
• Reference: Hamrock-Dowson EHL film-thickness correlation for elliptical contact.

Mean entrainment speed

Measure both velocities along the same direction in the contact frame. For u₁ = 2 m/s and u₂ = 0, enter u = 1 m/s. The input is not the sum or the sliding-speed difference. Arrows and film thickness are schematic, not to scale; this quick model requires positive mean entrainment speed and its stated fully flooded, isothermal assumptions.