Gear scuffing (flash and integral temperature)

Scuffing is the sudden welding and tearing of gear flanks when the lubricant film breaks down. Unlike pitting or root breakage it is not a fatigue failure: a single overload at high sliding speed can damage the flanks so badly that the gears are no longer fit for use. Both methods in the app treat it as a temperature problem. Friction in the sliding contact heats the surfaces for the instant they are in contact; when the temperature reached exceeds what the oil and the steel can bear, the film fails.

Add a scuffing input to a gear pair (oil temperature, FZG load stage of the oil, lubricant base, lubrication method) and the app rates it by both criteria.

axm gear update drive.axm.json G1 --patch '{"scuffing":{"oilTemperature":70,"fzgStage":10}}'

Contact temperature

The temperature of a flank point in contact is the sum of two parts (ISO/TS 6336-20, 5.1, formulas (1) and (2)):

• The bulk temperature θM is the temperature of the tooth body immediately before it enters the mesh. It changes slowly and is set by the balance of frictional heat and cooling.
• The flash temperature θfl is the short temperature rise in the moving Hertzian contact band. It varies along the path of contact: zero sliding at the pitch point means no flash there, and it peaks near the start or end of contact where sliding is fastest.

The flash temperature method (ISO/TS 6336-20:2022)

Blok's flash temperature, in the closed form for cylindrical gears of Annex A, formula (A.5), is

The app evaluates it at each point of the path of contact:

• μm, mean coefficient of friction by method C, formula (23): from the transverse unit load, the sum of tangential velocities, the relative curvature, the lubricant factor XL (by base oil and its dynamic viscosity at the oil temperature) and the roughness factor XR (from the mean Ra).
• XM, thermo-elastic factor (A.13): the materials' moduli and thermal contact coefficients $B_M=\sqrt{\lambda \cdot \rho \cdot c}$.
• XJ, approach factor (clause 8): raises the flash temperature in the approach path, where the driven gear's tip meets the driver, because the contact is less favourable there.
• XG, geometry factor (A.6, A.7): the curvature and sliding at that point.
• XΓ, load sharing factor (clause 9): how the load is shared between the tooth pairs along the path, which depends on the accuracy grade, buttressing of helical gears and above all on tip relief. With loadSharing auto the app judges the reliefs from the flank modifications or tipRelief against the optimal tip relief Ceff and the equivalent tip reliefs of Annex B.
• wBt, transverse unit load, formula (11), with the load factors and the multiple path factor Kmp for planetary branches.

The bulk temperature follows the approximation of 5.5, formula (20): ${\theta }_M={\theta }_{\mathrm{oil}}+0.47\cdot X_S\cdot X_{mp}\cdot {\theta }_{flm}$, with the mean flash temperature θflm along the path (22), the lubrication factor XS (1.2 spray, 1.0 dip, 0.2 immersed with sufficient cooling) and the factor Xmp for a pinion meshing with several gears.

The scuffing temperature θS is a property of the oil–steel system. From the oil's failure stage SFZG in the FZG A/8.3/90 test, formula (77) gives ${\theta }_S=80+(0.85+1.4\cdot X_W)\cdot X_L\cdot S_{\mathrm{FZG}}^2$, with the structural factor XW of Table 3 and XL taken for the test oil at 90 °C. The TS allows one load stage less than the oil's specification, since test results scatter by about one stage. For oils with anti-scuff additives (antiScuff), θS rises at contact exposure times below 18 µs (10.3).

The safety, formula (78), is a ratio of temperature rises above the oil:

The TS itself warns that a quotient of temperatures is a poor measure of load safety, and suggests instead requiring a minimum margin between θS and θBmax, for example 50 K (10.5). The app reports that margin as temperatureMargin and checks SB against limits.minFlashSafety, 2.0 by default; the TS sets no minimum.

The integral temperature method (ISO/TR 13989-2:2000)

The integral temperature criterion, the predecessor of ISO/TS 6336-21, compares a weighted average of the contact temperature over the path with a critical value from the same FZG test. It is simpler and less sensitive to local peaks:

• The flash temperature at the pinion tip θflaE (6.1.4) is computed in closed form with μmC (5.1, with KBγ, XR and ηoil), XM, the geometry factor at the pinion tip XBE (formula (22)), the pressure angle factor Xαβ, the run-in factor XE (runIn), the approach factor XQ (formulas (25) to (29)) and the tip relief factor XCa.
• The mean flash temperature is ${\theta }_{fla,\mathrm{int}}={\theta }_{flaE}\cdot X_{\epsilon }$, with the contact ratio factor Xε (6.1.13).
• The bulk temperature is ${\theta }_M={\theta }_{\mathrm{oil}}+0.7\cdot X_{mp}\cdot X_S\cdot {\theta }_{fla,\mathrm{int}}$.
• The integral temperature, formula (17), weights the flash part by C2 = 1.5 for spur and helical gears: ${\theta }_{\mathrm{int}}={\theta }_M+1.5\cdot {\theta }_{fla,\mathrm{int}}$.
• The scuffing integral temperature ${\theta }_{\mathrm{int}S}={\theta }_{MT}+X_W\cdot 1.5\cdot {\theta }_{fla,\mathrm{int},T}$ comes from the bulk and flash temperatures of the FZG test gears at the failure stage (pinion torque $T_{1T}=3.726\cdot S_{\mathrm{FZG}}^2$ N·m).

The safety, formula (14), is $S_{\mathrm{int}S}={\theta }_{\mathrm{int}S}/{\theta }_{\mathrm{int}}$. ISO/TR 13989-2, 6.1.1, describes values below 1 as a high scuffing risk, 1 to 2 as a critical range in which roughness, running-in, the accuracy of the load factors and the oil decide, and above 2 as a low risk. The app checks SintS against limits.minIntegralSafety, 1.8 by default. The TR also gives an approximate load safety $S_{Sl}=\frac{{\theta }_{\mathrm{int}S}-{\theta }_{\mathrm{oil}}}{{\theta }_{\mathrm{int}}-{\theta }_{\mathrm{oil}}}$, formula (15), reported as loadSafety.

A worked example

The Spur gear pair template (20/60 × m3, 150 N·m at 1500 rpm, mineral oil ISO VG 220 by default) with "scuffing":{"oilTemperature":70,"fzgStage":10}:

Both checks pass with a wide margin. The run also notes that the Péclet number is 1.7 where the flash temperature is largest, below the value of 5 that Blok's formula assumes (ISO/TS 6336-20, 5.2): at low sliding speeds the flash temperature formula is used outside its range of validity, so treat the flash result of a slow pair with care.

Raising the scuffing safety

• An oil with a higher FZG stage, or with anti-scuff additives at short contact times.
• A lower oil temperature, or spray or better cooling (lower θM).
• Tip relief, which unloads the tooth tips where sliding is fastest (XΓ, XCa).
• Profile shifts that balance the sliding between approach and recess.
• Finer flanks (lower μm through XR) and running-in.

What is not covered

• Bulk temperatures from a heat balance of the gearbox: both methods use their approximation from the oil temperature.
• Bevel, worm and plastic gears: the scuffing check is offered for cylindrical gear pairs.
• Cold scuffing at very low speeds and wear are not rated.

Related

• Gear rating (ISO 6336)
• Gear pairs
• Lubrication: viscosity, film and κ
• Tutorial: spur gear pair