Tribology & Mechanical Engineering
Dowson-Higginson EHL Line-Contact Minimum Film Thickness Formula
Calculate elastohydrodynamic lubrication (EHL) dimensionless speed U, materials G, load W, and minimum film thickness h_min = 2.65 * R_eq * U^0.70 * G^0.54 * W^(-0.13) in microns.
Why rolling speed governs EHL oil-film thickness 5x more strongly than load
In heavily loaded spur gears and cylindrical roller bearings, gigapascal contact pressures elastically flatten steel surfaces AND piezoviscously solidify lubricant viscosity by orders of magnitude! Dowson and Higginson proved that dimensionless minimum film thickness H_min = h_min / R_eq obeys H_min = 2.65 * U^0.70 * G^0.54 * W^(-0.13), where dimensionless speed U = (eta_0 * u_roll) / (E_prime * R_eq), materials G = alpha_pv * E_prime, and line load W = w_line / (E_prime * R_eq).
Audit the exponents before trusting intuition: because load carries exponent -0.13 while entraining speed carries +0.70, doubling line load w_line from 220,000 N/m to 440,000 N/m trims h_min by only 8.6% (from 1.0261 um to 0.9377 um), whereas doubling entraining speed u_roll from 5 m/s to 10 m/s thickens the lubricant film by +62.45% to 1.6669 um!
| Dowson-Higginson Dimensionless Group | Definition | Sample Value |
|---|---|---|
| Speed Parameter U | (eta_0 * u_roll) / (E_prime * R_eq) | 4.5455E-11 (Exponent +0.70) |
| Materials Parameter G | alpha_pv * E_prime | 4,400 (Exponent +0.54) |
| Load Parameter W | w_line / (E_prime * R_eq) | 5.0000E-5 (Exponent -0.13) |
| Minimum Film Thickness h_min | 2.65 * R_eq * U^0.70 * G^0.54 * W^(-0.13) | 1.0261 microns |
Dowson-Higginson Minimum Film Thickness in Microns (h_min_um) Formula
Keep all inputs in coherent SI units (meters, Pa*s, m/s, Pa, Pa^-1, N/m) inside LET and multiply dimensionless H_min * R_eq by 1,000,000 to report microns directly for Tallian lambda comparison.
=LET(r_eq, B2, eta_0, B3, u_rl, B4, e_pr, B5, alp_p, B6, w_ln, B7, IF(OR(r_eq <= 0, eta_0 <= 0, u_rl <= 0, e_pr <= 0, alp_p <= 0, w_ln <= 0), "Invalid EHL Input", LET(u_nd, (eta_0 * u_rl) / (e_pr * r_eq), g_nd, alp_p * e_pr, w_nd, w_ln / (e_pr * r_eq), h_nd, 2.65 * POWER(u_nd, 0.7) * POWER(g_nd, 0.54) * POWER(w_nd, -0.13), ROUND(h_nd * r_eq * 1000000, 4))))Load-Doubling vs Speed-Doubling Film Retention Ratio Check
Verify POWER(2, -0.13) = 0.9138 and POWER(2, 0.70) = 1.6245 directly by testing changed inputs in B7 and B4.
=LET(g_nd, B6 * B5, IF(g_nd <= 0, "Invalid EHL Input", ROUND(g_nd, 1)))Try the example
Use the original values or change them to test your understanding.