Gear Scoring Index⚠ unverified
Mechanical / Gears · Compute a gear scoring index as a flash-temperature proxy
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Wt | Wt | N | 1.0 | Transmitted tangential load |
| v | v | m/s | 1.0 | Pitch-line velocity |
| F | F | — | 1.0 | Face width of the tooth, in length units |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | index | — | Scoring index proportional to flash temperature rise |
The science & history
Understanding the Parameters
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Tangential load $W_t$ — higher load raises the contact pressure and the friction force, generating more heat. The index is proportional to load.
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Velocity $v$ — faster sliding/rolling generates frictional heat faster (heat rate ≈ friction force × sliding speed) and gives less time for it to conduct away, so the flash temperature rises with $v$. The load-times-velocity product $W_t v$ is essentially a frictional power — the classic "PV" concept behind surface-distress limits.
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Face width $F$ — spreads the load over a longer contact line, lowering the load per unit length and the temperature; hence $F$ is in the denominator. A wider face runs cooler.
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Reading the index — it has no absolute failure threshold here; compare it between design options or against a validated limit. A high index flags a scoring risk, calling for extreme-pressure (EP) lubricants, better surface finish, lower load/speed, or profile modification.
Derivation (Approaching a Proof)
Scoring is triggered when the total contact temperature (bulk oil temperature plus the transient "flash" temperature rise at the instant of contact) exceeds the lubricant's breakdown limit. Blok's flash- temperature theory models the moving heat source of a sliding Hertzian contact and gives a flash temperature that grows with the frictional heat generated and falls with the contact's ability to conduct it away.
The frictional heat generated per unit contact is proportional to the friction force times the sliding speed — a frictional power ≈ $\mu W_t v$ — and the temperature rise scales with that power spread over the contact. Dropping the (constant) friction coefficient and normalising by the face width (which sets the load per unit length) gives the crude proxy
$$\text{index} \propto \frac{W_t v}{F}.$$
This captures the correct directions — hotter with more load, more speed, less face — but omits the surface curvature, sliding-vs-rolling split, friction coefficient, and thermal properties that a real flash-temperature calculation includes. It is therefore a first-order screening tool: useful to rank designs, not to certify one.
Dimensional check. $\dfrac{W_t v}{F} = \dfrac{\text{N}\cdot(\text{m/s})}{\text{m}} = \text{N/s} = \text{W/m}$ (frictional power per unit face) — a heat-rate-like quantity, consistent with a temperature-rise proxy. ✓
History and Development
Scuffing/scoring analysis rests on Harmen Blok's flash-temperature theory (1937) and was developed into the AGMA and ISO scuffing (flash-temperature) methods for high-speed, heavily-loaded gears (aerospace, turbine drives). Load–velocity ("PV") indices are common first-order surface-distress screens across gears, bearings, and cams. This calculator is a simplified member of that family.
Related Concepts: Gear Contact Stress, Gear Power Capacity, Gear Mesh Stiffness, Stribeck Curve, Gear Bending Stress Lewis
Notes: Heuristic PV-type flash-temperature proxy — screening only; use Blok/AGMA flash-temperature for design. $F$ is a length (see note). High index ⇒ scoring risk ⇒ EP lubricant, better finish, lower load/speed.