Clutch Wear Volume⚠ unverified
Mechanical / Clutches Brakes · Compute an estimate of clutch facing wear volume
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| V | V | — | 1.0 | Wear coefficient (volume per unit pressure-velocity-time, dimensionless scaling factor) |
| p | p | Pa | 1.0 | Contact pressure |
| v | v | m/s | 1.0 | Sliding velocity |
| t | t | s | 1.0 | Sliding duration |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | wear | m**3 | Estimated wear volume, in cubic metres (m**3) |
The science & history
Understanding the Parameters
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Contact pressure $p$ — higher pressure presses asperities together harder, increasing the material removed. Archard wear is proportional to the normal load (here, pressure × area), so heavily-loaded facings wear faster.
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Sliding velocity $v$ and time $t$ — their product $v\,t$ is the sliding distance. Wear is proportional to how far the surfaces rub, so a clutch that slips a long way (soft engagements, hill starts) wears more than one that engages crisply. The combination $p\,v$ is the PV product — the same quantity that governs frictional heating and scoring (Gear Scoring Index) — and lining materials are rated by a maximum allowable PV.
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Wear coefficient $V$ — the material property that sets how fast a given PV·time wears the lining. It bundles the material's hardness and adhesion behaviour; harder, more wear-resistant linings have a smaller $V$ (and usually a lower, more stable $\mu$ — a trade-off with grip).
Derivation (Approaching a Proof)
The Archard wear equation (1953) states that the volume of material worn is proportional to the normal load $F_N$ and the sliding distance $s$, and inversely proportional to the material hardness $H$:
$$\text{wear volume} = k\,\frac{F_N\, s}{H},$$
where $k$ is a dimensionless wear coefficient. The physical picture: real contact occurs at asperity tips whose true contact area is proportional to load/hardness; a fraction $k$ of the asperity junctions shed a wear particle per unit sliding.
Recast for a clutch facing of area $A$: the normal load is $F_N = p A$, and the sliding distance is $s = v\,t$. Substituting,
$$\text{wear volume} = k\,\frac{(p A)(v t)}{H} = \left(\frac{k A}{H}\right) p\, v\, t.$$
Grouping the material and area constants into a single specific wear coefficient $V = kA/H$ gives the registry form
$$\text{wear} = p\, v\, t\, V.$$
So $V$ carries the hardness, the wear-coefficient $k$, and the contact area — which is why it is dimensional (m²/Pa), not truly dimensionless. The law is an empirical engineering model (real wear also depends on temperature, third-body debris, and lubrication regime — see Stribeck Curve), best used for relative life estimates with a material-specific $V$.
Dimensional check. With $V$ in m²/Pa: $p\,v\,t\,V = \text{Pa}\cdot(\text{m/s})\cdot\text{s}\cdot(\text{m}^2/\text{Pa}) = \text{m}^3$. ✓
History and Development
The Archard wear law (J. F. Archard, 1953) is the foundational quantitative model of sliding wear, underpinning life prediction for brakes, clutches, bearings, and cams. The PV limit (pressure × velocity) it implies is a standard rating for friction and bearing materials. Real clutch/brake wear is more complex (thermal, oxidative, and third-body effects), so $V$ is calibrated from tests; the law remains the standard first-order life estimate in Shigley and tribology practice.
Related Concepts: Clutch Facing Pressure, Clutch Slip Power, Gear Scoring Index, Stribeck Curve, Friction
Notes: Archard-type wear ($V$ = specific wear rate, units m²/Pa — see note; not dimensionless). $p\,v$ is the PV product (also a rating limit); $v\,t$ is the sliding distance. Empirical — calibrate $V$ per material; use for relative life estimates.