A machine part rarely fails the day it's designed. It fails years later, worn thin, when nobody's watching the drawing anymore. Wear is the slowest of the classic failure modes — slower than fatigue, far slower than overload — and that slowness is exactly what makes it dangerous to ignore at the design stage. The Archard wear equation is the closest thing tribology has to a back-of-envelope tool for putting a number on "how long until this surface is gone," and it's simple enough to run in your head once you've done it a few times.
The equation, and why it looks the way it does
Archard's law states that the volume of material removed by sliding wear is proportional to the normal load and the sliding distance, and inversely proportional to the hardness of the softer material:
dV/dt = K * F_N * v / H
Every term earns its place physically. Normal load F_N appears in the numerator because contact pressure — and therefore the severity of asperity contact — scales with load. Sliding speed v appears because wear volume accumulates with sliding distance, and distance is speed integrated over time; rewriting the equation per unit time rather than per unit distance is what pulls v directly into the rate expression. Hardness H sits in the denominator because a harder surface resists the plastic deformation and micro-cutting that actually removes material — double the hardness, and (all else equal) you roughly halve the wear rate.
The one term that isn't a directly measurable material property is K, the Wear coefficient K x10^-6, dimensionless and typically expressed in the 10⁻⁶–10⁻² range depending on the wear regime. This is where Archard's law is honest about its own limits: K isn't a constant of nature, it's an empirically fitted number that bundles up everything the simple load/speed/hardness model can't capture — asperity geometry, lubrication state, third-body debris, oxidation, whether you're in mild or severe wear regime. Two nominally identical steel-on-steel contacts can have K values that differ by two orders of magnitude depending on whether they're dry, boundary-lubricated, or fully flooded. Getting a trustworthy K from a handbook or a short-duration pin-on-disk test is usually the single biggest source of error in a wear life prediction — far bigger than any error in measuring load or speed.
From wear rate to a life prediction
Volumetric wear rate is the fundamental output, but nobody actually cares about volume for its own sake — they care about how long the part lasts, or how much it thins. Converting between the two is where the calculation earns its keep as a design tool rather than a physics curiosity.
Mass wear rate just multiplies by density:
dm/dt = rho * dV/dt
Thinning rate — how fast the surface recedes, in the direction that actually matters for a shaft or a bearing bore — divides the volumetric rate by the nominal contact or wear area:
d(thickness)/dt = (dV/dt) / A
which is why the tool's Thinning rate (A=10 cm^2) stat is normalized to a reference contact area — it lets you compare wear severity across cases without re-deriving the area assumption every time. And Life to V_max = 1 mm^3 just inverts the rate equation against a chosen failure criterion:
t_life = V_max / (dV/dt)
A 1 mm³ threshold is an arbitrary but reasonable stand-in for "enough material has gone that this contact is starting to misbehave" — real wear-out criteria are usually set by a clearance limit or a leak/noise spec, and you'd substitute your own V_max for that limit.
A worked example: a bushing under load
Consider a bronze bushing sliding against a steel shaft, dry-ish with only boundary lubrication — a common industrial scenario. Take Wear coefficient K = 5 (that is, K = 5 x 10^-6, typical for mild, boundary-lubricated sliding of dissimilar metals), Normal load F_N = 200 N, Sliding speed v = 0.5 m/s, and bronze Hardness H = 800 MPa (roughly 80 HB converted to a pressure unit, since Archard's law wants hardness expressed as a pressure — this unit consistency trips people up more than any other step in the calculation).
dV/dt = K * F_N * v / H
= (5e-6) * 200 * 0.5 / (800e6)
= 5e-4 / 8e8
= 6.25e-13 m^3/s
Convert to something more intuitive — mm³ per hour:
6.25e-13 m^3/s * 1e9 mm^3/m^3 * 3600 s/h ≈ 2.25 mm^3/h
At that rate, reaching a Life to V_max = 1 mm³ threshold takes:
t_life = 1 mm^3 / 2.25 mm^3/h ≈ 0.44 h
That's uncomfortably short — under half an hour — which for a real bushing would be a red flag that something in the assumed inputs is off (probably K is too high for the actual lubrication condition, or the contact is running in a more severe wear regime than "mild"). That's actually the useful outcome of running the numbers: a wear-life calculation that spits out "this part dies in 26 minutes" tells you to go re-examine your K value and lubrication assumptions before you cut metal, not after a warranty claim. Rerun the same case with a better-lubricated K = 0.5 (one order of magnitude down) and the life stretches to roughly 4.4 hours — still short for a real design life, which is the honest signal that this contact needs a harder bushing material, a lower load, or genuine oil-film lubrication rather than boundary contact.
Where Archard's simple form stops being trustworthy
The equation is linear in load, which is a reasonable approximation for mild, adhesive/abrasive wear at moderate contact pressures — but it breaks down once contact pressure gets high enough to trigger a transition from mild to severe wear, where wear rate can jump by an order of magnitude or more for a modest increase in Normal load F_N. If your calculated contact pressure is approaching a meaningful fraction of the softer material's hardness, don't trust a linear extrapolation; you're likely near or past that transition.
It's also silent on temperature. Sliding speed generates frictional heat, and at high Sliding speed v that heat can soften the surface (dropping the effective H used in the equation, which the simple form doesn't update dynamically), promote oxidative wear, or in the worst case cause localized melting or seizure — none of which the linear K·F_N·v/H form knows about. And it assumes K is constant over the life of the contact, which is optimistic: real surfaces often run-in over an initial period (wear rate drops as asperities smooth out) before settling into the steady-state rate the equation is meant to describe, so applying it to early-life behavior will generally overpredict wear.
Try it yourself
Hand-calculating wear life is fast once you trust your K, but sanity-checking a design across a range of loads and speeds is where a live tool earns its keep — you can see immediately how sensitive the Volumetric wear rate is to a hardness change versus a load change. Run your own numbers on the Archard wear law simulator here. For the materials side of the same problem — what happens at the interface before wear even starts — the bond wire tool covers a related contact-mechanics case worth comparing against.
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