Engineering
Archard Sliding Wear Equation: Wear Volume & Linear Depth (Tribology)
Calculate mechanical sliding wear volume V = (K * F_N * s) / H (mm^3) and bushing/brake-pad linear wear depth h = (K * P * s) / H from Archard's dimensionless wear coefficient K, load F_N, sliding distance s, and hardness H.
Predict brake-pad, gear-tooth, and hip-implant wear life from Archard's Law!
Formulated by British tribologist John F. Archard (1953) from microscopic asperity junction theory, Archard's Wear Equation is the foundational law of sliding mechanical wear in FEA (ANSYS/Abaqus), prosthetic joints, clutches, and sleeve bushings: Wear Volume V = (K * F_N * s) / H, where K is the dimensionless Archard Wear Coefficient, F_N (N) is normal contact load, s (m) is cumulative sliding distance, and H (Pa) is the softer mating surface's indentation hardness!
Look at the dramatic lubrication effect captured by K: unlubricated dry metal-on-metal sliding has K ~ 2e-4 (removing 400 mm^3 of steel over 10 km under 500 N load at H = 2.5 GPa), whereas boundary lubrication drops K by 200x down to 1e-6 (losing just 2.00 mm^3)! Dividing both sides by apparent contact area A (m^2) yields Linear Wear Depth h = V / A (in mm)!
| Tribology Regime (F_N = 500 N, s = 10,000 m, H = 2.5e9 Pa, Area = 400 mm^2) | Wear Coeff K | Wear Volume V (mm^3) | Linear Wear Depth h (mm) |
|---|---|---|---|
| Dry Unlubricated Steel Sliding | K = 2.0e-4 | 400.00 mm^3 | 400 / 400 = 1.000 mm |
| Boundary-Lubricated Sliding | K = 1.0e-6 | 2.00 mm^3 (-99.5% wear!) | 2 / 400 = 0.005 mm (5 um) |
| Zero/Invalid Hardness Guard | H <= 0 | IF(B5 <= 0, ...) | "Invalid Surface Hardness" |
Archard Wear Volume V in Cubic Millimeters (mm^3)
Evaluates ((K * F_N * s) / H) * 1e9 to convert SI m^3 directly into mm^3.
=IF(OR(B2 < 0, B3 < 0, B4 < 0, B5 <= 0), "Invalid Wear Input", ROUND(((B2 * B3 * B4) / B5) * 1E9, 2))Linear Surface Recession / Wear Depth h = V_mm3 / ContactArea_mm2 (mm)
Divides wear volume (mm^3) by nominal pad/bearing contact area B6 (mm^2).
=ROUND((((B2 * B3 * B4) / B5) * 1E9) / B6, 4)Try the example
Use the original values or change them to test your understanding.