Archard Wear Rate Calculator

Archard Wear Equation

The Archard equation relates the volume of material removed to the applied load, sliding distance, and hardness of the softer material, scaled by a dimensionless wear coefficient:

Where:

• V = wear volume (typically mm³)
• k = dimensionless wear coefficient (depends on materials, lubrication, and wear mechanism)
• F = normal load (N)
• s = sliding distance (m)
• H = hardness of the softer material (MPa)

The wear coefficient k captures how easily material is removed in a given contact. For example, lubricated steel-on-steel contacts in mild wear may have k around 10⁻⁸ to 10⁻⁶, while severe abrasive wear can reach values near 10⁻³ to 10⁻². Because wear behaviour is highly system-specific, realistic predictions depend on choosing an appropriate value of k from experiments or reliable literature.

Input Parameters and Units

To obtain meaningful results, the inputs must be consistent and physically realistic. The calculator expects:

Wear Coefficient (k)

• Definition: Dimensionless factor representing the severity of wear for a given material pair, lubrication condition, and wear mechanism.
• Typical ranges:
  • Well-lubricated metal contacts (mild adhesive wear): ~10⁻⁸ to 10⁻⁶
  • Moderate adhesive or mild abrasive wear: ~10⁻⁶ to 10⁻⁴
  • Severe abrasive wear or poor lubrication: ~10⁻⁴ to 10⁻²
• Guidance: Use values measured under conditions similar to the application (same materials, load regime, lubrication, temperature, and surface finish).

Normal Load F (N)

• Definition: The total normal force pressing the two surfaces together.
• Unit: Newton (N).
• Example values: Tens to hundreds of newtons for small mechanical components; kilonewtons for large bearings or structural contacts.
• Guidance: Use the maximum or representative service load, not just the nominal design load, especially when peak loads dominate wear.

Sliding Distance s (m)

• Definition: Total relative sliding distance during the time period of interest.
• Unit: Metre (m).
• Example values: From a few metres for one-off tests to 10⁴–10⁷ m for long-life components over their design life.
• Guidance: Convert cycles or rotations into sliding distance using the contact path length per cycle. For rotating parts, this is often the circumference times the number of revolutions.

Hardness H (MPa)

• Definition: Indentation hardness of the softer material in the sliding pair.
• Unit: Megapascal (MPa). 1 MPa = 10⁶ N/m².
• Conversion note: If you have hardness in Vickers (HV) or Brinell (HB), you can convert approximately to MPa using published correlations. Ensure the hardness corresponds to the near-surface region that actually wears (e.g., case-hardened layer).
• Guidance: Use hardness measured at the operating temperature when possible; hardness can drop significantly at elevated temperatures.

How to Use This Calculator

1. Define the operating scenario. Decide the time interval or service life you want to analyse (e.g., 10,000 hours of operation, 1 million cycles, or one year of typical use).
2. Estimate the normal load. Determine the representative or peak load acting on the contact during that period. Use system calculations, manufacturer data, or test measurements where available.
3. Convert motion to sliding distance. For each component, compute the total sliding distance over the chosen life. For example, for a shaft: distance = circumference × number of revolutions.
4. Select an appropriate wear coefficient. Look up k values in tribology handbooks, research papers, or your own test data for the same material pair, surface roughness, and lubrication regime.
5. Enter hardness in MPa. Use the hardness of the softer material, converted to MPa, and reflecting the actual surface condition (heat treatment, coating, etc.).
6. Run the calculation. The calculator computes the wear volume V in mm³ using the Archard equation.
7. Relate volume to wear depth. If you know the apparent contact area, you can convert volume to an approximate wear depth by depth ≈ V / area.

Interpreting the Results

The main output is the estimated wear volume V in cubic millimetres. To decide whether the predicted wear is acceptable, consider:

• Allowable wear depth: Convert volume to an average wear depth and compare it to design tolerances, clearances, or case-hardening depth.
• Functionality: In gears or bearings, excessive wear can lead to misalignment, increased backlash, vibration, or noise even before catastrophic failure.
• Debris generation: In hydraulic systems or biomedical implants, even small wear volumes can be critical if debris causes contamination or biological reactions.
• Time scaling: If the predicted wear over the design life is too high, check how it scales with time. Because V scales linearly with distance s, halving the life or duty can halve the wear, and vice versa.

Always treat the result as an estimate, not an exact prediction. It is most useful for comparing design options (e.g., different materials, surface treatments, or lubrication strategies) and for identifying orders of magnitude rather than precise values.

Worked Example

Consider a steel pin sliding against a hardened steel plate under boundary-lubricated conditions. We want to estimate the wear of the pin over a specific duty cycle.

Given data

• Wear coefficient, k = 2 × 10⁻⁶ (dimensionless) for mild adhesive wear under boundary lubrication.
• Normal load, F = 500 N.
• Sliding distance per hour = 100 m.
• Operating time = 2,000 hours.
• Hardness of the pin surface, H = 600 MPa.

Step 1: Total sliding distance

Total sliding distance over 2,000 hours:

s = 100 m/hour × 2,000 hours = 200,000 m

Step 2: Apply Archard equation

Using V = k F s / H:

V = (2 × 10⁻⁶) × (500 N) × (200,000 m) / (600 MPa)

First compute the numerator:

k × F × s = 2 × 10⁻⁶ × 500 × 200,000 = 2 × 10⁻⁶ × 100,000,000 = 200

Then divide by hardness:

V = 200 / 600 ≈ 0.333 mm³

Step 3: Relate to wear depth

Suppose the effective contact area of the pin is 50 mm². The average wear depth d is approximately:

d ≈ V / area = 0.333 mm³ / 50 mm² ≈ 0.0067 mm (about 6.7 µm)

This very small wear depth over 2,000 hours suggests that, under these assumptions, the design is likely acceptable with respect to wear. However, changes in lubrication, contamination, or misalignment could increase the effective wear coefficient and lead to much higher wear.

Comparison: Mild vs. Severe Wear Conditions

The table below compares typical ranges of wear coefficients and their implications under different wear regimes. Actual values depend strongly on materials and operating conditions.

Assumptions and Limitations

The Archard wear model and this calculator rest on several important assumptions:

• Steady-state sliding wear: The equation assumes a stable wear regime after initial running-in, with a roughly constant wear coefficient.
• Constant normal load and hardness: The load F and hardness H are treated as constant over the analysed period. Significant load variation, thermal softening, or phase changes in the material are not explicitly modelled.
• Uniform contact conditions: It assumes that the contact area and contact pressure distribution do not change dramatically due to wear or deformation.
• Dominant sliding wear mechanism: The equation is most appropriate when sliding wear (adhesive or abrasive) is the main damage mechanism, rather than fatigue, corrosion, fretting, or impact.
• Empirical wear coefficient: The reliability of results is limited by how representative the chosen k value is of the actual system. Small errors in k can change the predicted wear volume by orders of magnitude.

Because of these assumptions, the calculator is best used for:

• Order-of-magnitude estimates of wear volume.
• Comparative studies between design options (e.g., different materials, hardness levels, or lubrication schemes).
• Educational purposes and early-stage feasibility assessments.

It is not a substitute for detailed tribological testing, finite element contact analysis, or safety-critical design verification. For critical components (such as aerospace parts or biomedical implants), always validate predictions with experiments and follow relevant standards and regulations.

Practical Tips for Better Predictions

• Use realistic duty cycles: Account for startup, shutdown, and transient conditions if they contribute significantly to sliding distance or peak loads.
• Consider surface roughness: Rough surfaces can increase wear and effectively raise the wear coefficient. Polishing or superfinishing may reduce k.
• Account for lubrication breakdown: If boundary or mixed lubrication is expected, choose k values appropriate for those regimes rather than ideal hydrodynamic conditions.
• Check sensitivity: Run the calculator with lower and upper bound values of k to understand how uncertainty in the wear coefficient affects predicted wear.

Use the results of this calculator together with engineering judgement, experimental data, and design codes to make informed decisions about material selection, surface treatments, lubrication, and maintenance intervals.