Archard Wear Calculator — Wear Volume, Wear Depth, Wear Coefficient & Hertz Yield Check
Predict sliding wear with the Archard equation, calibrate the wear coefficient from test data, estimate sliding distance to a wear-depth limit, or screen a known Hertz contact pressure against yielding.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Archard wear inputs
Wear test data
Wear limit definition
Hertz normal-contact screen
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Archard wear prediction
The calculator predicts steady sliding-wear volume using the Archard equation:
V = K · F · s / H
- V — predicted wear volume [m3]
- K — dimensionless Archard wear coefficient [-]
- F — normal load [N]
- s — accumulated sliding distance [m]
- H — indentation hardness [Pa]
If an effective wear area A is provided, the calculator also estimates average wear depth:
h = V / A
- h — average wear depth [m]
- A — effective wear area [m2]
The specific wear rate is reported as:
ks = V / (F · s)
The displayed specific wear rate is converted to mm3/(N·m).
Archard wear coefficient from measured wear
When measured wear volume is available from a test, the Archard equation is rearranged to calculate the dimensionless wear coefficient:
K = V · H / (F · s)
The resulting coefficient represents the tested material pair and operating regime. It should not be treated as a universal material property.
Sliding distance to an allowable wear depth
The allowable wear volume is calculated from effective wear area and allowable average wear depth:
Vallow = A · hallow
The corresponding sliding distance is then:
sallow = Vallow · H / (K · F)
For this mode, the specific wear rate follows directly from the Archard coefficient and hardness:
ks = K / H
Hertz normal-contact plasticity screen
The contact-plasticity mode does not calculate Hertz contact pressure from geometry. It requires the maximum Hertz contact pressure p0 as an input and estimates the maximum subsurface von Mises stress as:
σvM,max = α · p0
The implemented coefficient is:
- α = 0.620 for Hertz point contact
- α = 0.558 for Hertz line contact
These coefficients represent the implemented smooth, frictionless Hertz screening model for Poisson's ratio approximately equal to 0.3.
If verified yield or proof strength is entered:
σy = entered yield/proof strength
If hardness is used as the strength basis, the calculator applies the screening approximation:
σy,est = H / 3
Plastic utilization is:
Uy = σvM,max / σy
The corresponding yield safety factor and estimated Hertz pressure at initial yield are:
ny = σy / σvM,max
p0,y = σy / α
When to use this calculator
When to use this calculator
Use this calculator for preliminary tribology calculations involving sliding wear and for a simplified yielding screen when a maximum Hertz contact pressure is already known.
Archard wear prediction
Use the wear-prediction mode when the Archard wear coefficient, normal load, accumulated sliding distance and indentation hardness are known. The calculator estimates material loss as wear volume and, when an effective wear area is supplied, average wear depth.
This is useful for preliminary evaluation of sliding interfaces such as bushings, guides, sliding pads, pins, wear surfaces and other contacts where an Archard-type steady-wear model is appropriate.
Wear coefficient calibration
Use the coefficient-calibration mode when a wear test provides measured wear volume together with test load, sliding distance and hardness. The calculated K value can then represent that tested tribosystem in comparable operating conditions.
Wear-depth life estimate
Use the wear-limit mode when a maximum acceptable average material-loss depth is known. From K, load, hardness, effective wear area and allowable depth, the calculator estimates the sliding distance required to reach that limit under the steady Archard model.
Hertz contact plasticity screening
Use the contact-plasticity mode when the maximum Hertz pressure p0 has already been calculated or measured and you need a first screening estimate of subsurface von Mises stress, yield utilization, yield safety factor and pressure at initial yielding.
When not to use this calculator
- Do not use it to calculate Hertz contact pressure from force, radii, elastic modulus or contact geometry. The Hertz pressure must already be known for the plasticity screen.
- Do not treat an Archard prediction as a universal wear-life result when the wear coefficient is not representative of the actual material pair and operating conditions.
- Do not use the Hertz screening result as a rolling-contact fatigue, pitting or spalling-life calculation.
- Do not use the simplified contact screen as a substitute for detailed elastic-plastic contact analysis when friction, tangential traction, coatings, roughness, residual stresses or significant plastic deformation are important.
- Safety-critical or life-critical designs should be supported by representative tribological data, applicable engineering requirements and, where necessary, testing or higher-fidelity analysis.
How to interpret the result
How to interpret the results
Predicted wear volume
V is the total material volume predicted to be removed by the implemented Archard steady sliding-wear model. For fixed hardness, wear volume increases directly with wear coefficient, normal load and sliding distance.
Higher hardness reduces the calculated wear volume when all other entered quantities remain unchanged.
Average wear depth
h is calculated only when an effective wear area is available. It represents V/A and should be interpreted as an average material-loss depth over the entered area, not as the maximum local wear scar depth.
For the same wear volume, increasing the effective wear area reduces the calculated average depth.
Calibrated Archard coefficient
K is calculated from measured wear using K = V·H/(F·s). It characterizes the tested tribosystem and conditions represented by the input data.
A larger calibrated K produces proportionally greater predicted wear in subsequent Archard calculations. The value should therefore be transferred only to sufficiently comparable material pairs and operating conditions.
Allowable sliding distance
sallow is the sliding distance at which the steady Archard model reaches the entered allowable average wear depth.
The calculated distance increases with hardness, effective wear area and allowable depth. It decreases with increasing normal load or Archard coefficient.
Reaching a shorter calculated distance does not itself identify the physical cause of wear or guarantee that the wear coefficient remains constant throughout service.
Hertz plastic utilization
Uy compares the estimated maximum subsurface von Mises stress with the strength used by the screening calculation:
Uy = σvM,max / σy
- Uy < 1 — the estimated subsurface von Mises stress is below the strength used by this screening criterion.
- Uy = 1 — the calculation reaches the implemented initial-yield threshold.
- Uy > 1 — initial yielding is predicted by the implemented smooth Hertz screening model and the result is classified as unsafe.
Yield safety factor
ny = σy/σvM,max is the reciprocal of plastic utilization. A value above 1 means the evaluated stress remains below the strength used by the screen; a value below 1 means the implemented criterion is exceeded.
Estimated Hertz pressure at initial yield
p0,y is the maximum Hertz pressure that corresponds to Uy = 1 within the selected point- or line-contact model:
p0,y = σy/α
The entered p0 can be compared directly with this value for the implemented screening assumptions.
Strength-basis warning
When verified yield or proof strength is used and Uy does not exceed 1, the implemented contact screen returns a safe status.
When strength is estimated from H/3, the calculator returns a warning even when Uy is not greater than 1. This reflects the lower confidence of a hardness-derived strength estimate.
A favorable Hertz yielding result does not verify rolling-contact fatigue life, surface durability, frictional traction effects or complete component safety.
Calculation example
Example: Archard wear volume and average wear depth
A sliding component is evaluated using a calibrated Archard coefficient. The objective is to estimate material loss after 10 km of accumulated sliding.
Input data
- Archard wear coefficient: K = 1.0 × 10−6
- Normal load: F = 1000 N
- Sliding distance: s = 10,000 m
- Indentation hardness: H = 2.0 GPa
- Effective wear area: A = 100 mm2
Convert hardness and area to SI units
H = 2.0 GPa = 2.0 × 109 Pa
A = 100 mm2 = 1.0 × 10−4 m2
1. Calculate wear volume
V = K · F · s / H
V = (1.0 × 10−6 × 1000 × 10,000) / (2.0 × 109)
V = 5.0 × 10−9 m3
Because 1 m3 = 109 mm3:
V = 5.0 mm3
2. Calculate average wear depth
h = V / A
h = (5.0 × 10−9) / (1.0 × 10−4)
h = 5.0 × 10−5 m = 50 µm
3. Calculate specific wear rate
ks = V / (F · s)
ks = (5.0 × 10−9) / (1000 × 10,000)
ks = 5.0 × 10−7 mm3/(N·m)
Interpretation
Under the entered constant-load, constant-hardness and constant-K assumptions, the Archard model predicts 5.0 mm3 of material loss. Distributed uniformly over the entered effective wear area, this corresponds to an average wear depth of 50 µm after 10 km of sliding.
The result is a model estimate rather than a guaranteed service-life value. A different lubrication regime, surface condition, temperature, debris environment or wear mechanism can change the applicable wear coefficient and therefore the predicted material loss.
Assumptions and limitations
Assumptions and limitations
- The wear calculations use the Archard steady sliding-wear relationship V = K·F·s/H.
- The Archard coefficient K is assumed constant over the evaluated sliding distance. Changes in wear regime are not modeled automatically.
- K must be representative of the actual material pair and comparable lubrication, surface, speed, temperature and environmental conditions.
- Normal load and indentation hardness are treated as constant during the evaluated wear interval.
- When average wear depth is calculated, the effective wear area is assumed to represent the area over which the predicted volume loss is distributed.
- Changes in contact geometry caused by progressive wear are not fed back into the Archard calculation.
- Run-in behavior, transitions between mild and severe wear, abrasive-particle effects, oxidation, debris recirculation and other wear mechanisms are not modeled separately.
- The wear-limit result is a sliding-distance estimate under constant model parameters, not a guaranteed component service life.
- The Hertz contact-plasticity mode requires maximum Hertz pressure p0 as an input. The calculator does not derive p0 from load, radii, elastic modulus, Poisson's ratio or contact dimensions.
- The Hertz screen uses fixed coefficients α = 0.620 for point contact and α = 0.558 for line contact, representing the implemented smooth frictionless normal-contact approximation for Poisson's ratio approximately equal to 0.3.
- If hardness is used as the strength basis, the calculator estimates σy = H/3. This is a screening approximation rather than a substitute for verified yield or proof strength, particularly for materials with significant work hardening or other non-ideal behavior.
- Tangential traction, frictional stress, roughness, coatings, residual stress and detailed elastic-plastic contact behavior are outside the Hertz screen.
- Rolling-contact fatigue, pitting, spalling and fatigue-life prediction are not calculated.
- The implemented calculations are engineering screening models and do not by themselves establish compliance with a particular design standard or material specification.
- Final design decisions should use representative material and tribology data and, where required, applicable standards, testing, detailed contact analysis or numerical simulation.