Gear rating (ISO 6336)

ISO 6336 rates cylindrical involute gears against two fatigue failures: pitting of the flanks, driven by the Hertzian contact stress, and tooth root breakage, driven by the bending stress in the root fillet. Both ratings follow the same pattern: a nominal stress for a perfect gear pair under the nominal torque, multiplied by load factors for everything that makes the real load larger, compared with a permissible stress derived from test gears and corrected for the actual gear. The app implements method B for external and internal spur and helical gears generated by a basic rack.

Nominal load and the load factors

The nominal tangential load at the reference circle is $F_{t} = 2000 \cdot T_{1} / d_{1}$ (T1 in N·m, d1 in mm). ISO 6336-1 multiplies it by four factors, in this order:

KA, application factor: load peaks from the driving and driven machines (shocks, torque fluctuation) that the nominal torque does not contain. It is an input (applicationFactor); 1.0 for uniform drive and load, 1.25 to 2 or more for shock loads are common choices.
Kv, dynamic factor: internal dynamic loads from the mesh's own vibration, by method B from the resonance ratio $N = n_{1} / n_{E 1}$ (the speed relative to the mesh's main resonance), with separate expressions for the subcritical range, the main resonance and the supercritical range. Accuracy grade, pitch deviations, tip relief and mesh stiffness enter.
KHβ, face load factor: uneven load across the face width from helix deviations and from shaft deflection. Method C computes it from the pinion shaft layout (bearing span, offset, shaft diameter and the constant K′), with the manufacturing misalignment fma and running-in; otherwise the given value (1.15 by default) is used. For the root, $K_{F β} = K_{H β}^{N_{F}}$ .
KHα and KFα, transverse load factors: uneven sharing of the load between the tooth pairs in contact, from pitch deviation, by method B.

The mesh load factor Kγ, which shares the load between several power paths, is 1 for a single mesh; planetary sets apply their own.

Contact stress

ISO 6336-2:2019 writes the nominal contact stress at the pitch point, formula (3), and the contact stress of pinion and wheel, formulas (4) and (5), as

\begin{matrix} σ_{H 0} & = Z_{H} \cdot Z_{E} \cdot Z_{ε} \cdot Z_{β} \cdot \sqrt{\frac{F_{t}}{d_{1} \cdot b} \cdot \frac{u + 1}{u}} \\ σ_{H} & = Z_{B} (or Z_{D}) \cdot σ_{H 0} \cdot \sqrt{K_{A} \cdot K_{γ} \cdot K_{v} \cdot K_{H β} \cdot K_{H α}} \end{matrix}

with the zone factor ZH (curvature at the pitch point, clause 6), the elasticity factor ZE (moduli and Poisson's ratios, clause 7), the contact ratio factor Zε (clause 8), the helix angle factor $Z_{β} = 1 / \sqrt{\cos β}$ (clause 9), the face width b, the gear ratio $u = z_{2} / z_{1}$ , and the single pair contact factors ZB and ZD, which move the stress from the pitch point to the inner point of single contact of pinion or wheel when that is more severe.

Permissible contact stress

The permissible contact stress of method B, formula (6), starts from the allowable stress number σHlim of ISO 6336-5 (1500 MPa for the case-hardened steel of the template below):

σ_{H P} = \frac{σ_{H \lim} \cdot Z_{N T} \cdot Z_{L} \cdot Z_{v} \cdot Z_{R} \cdot Z_{W} \cdot Z_{X}}{S_{H \min}}

ZNT, life factor (clause 11): above 1 for limited life, 1 at the endurance knee, optionally declining towards 10¹⁰ cycles (enduranceLifeFactor below 1).
ZL, Zv, ZR, lubricant film factors (clause 12): oil viscosity, pitch line velocity and flank roughness.
ZW, work hardening factor (clause 13): a hard pinion running with a through-hardened wheel raises the wheel's strength.
ZX, size factor (clause 14): 1 in the app.

The app reports the safety as the pitting stress limit over the stress, $S_{H} = σ_{H G} / σ_{H}$ (formulas (1) and (2)), so σHP is shown without dividing by SHmin, and the check compares SH with your minimum.

Tooth root stress

ISO 6336-3:2019 method B assumes the decisive load acts at the outer point of single pair tooth contact. Formulas (3) and (4) give

\begin{matrix} σ_{F 0} & = \frac{F_{t}}{b \cdot m_{n}} \cdot Y_{F} \cdot Y_{S} \cdot Y_{β} \cdot Y_{B} \cdot Y_{D T} \\ σ_{F} & = σ_{F 0} \cdot K_{A} \cdot K_{γ} \cdot K_{v} \cdot K_{F β} \cdot K_{F α} \end{matrix}

YF, form factor (clause 6): the bending lever and root thickness at the 30° tangent to the fillet.
YS, stress correction factor (clause 7): the stress concentration of the fillet.
Yβ, helix angle factor (clause 8).
YB, rim thickness factor (clause 9): above 1 for a rim thinner than 1.2 tooth depths (a ring gear's 3.5 modules).
YDT, deep tooth factor (clause 10), for virtual contact ratios between 2 and 2.5.

The permissible root stress, formula (5), uses the nominal bending stress number σFlim of ISO 6336-5 (500 MPa in the template):

σ_{F P} = \frac{σ_{F \lim} \cdot Y_{S T} \cdot Y_{N T} \cdot Y_{δ rel T} \cdot Y_{R rel T} \cdot Y_{X}}{S_{F \min}}

with YST = 2 (the stress correction of the test gear), the life factor YNT (clause 12), the relative notch sensitivity YδrelT (clause 13), the relative surface factor YRrelT (clause 14) and the size factor YX (clause 15). The tooth root safety is $S_{F} = σ_{F G} / σ_{F}$ .

Safeties and typical minima

ISO 6336 leaves the minimum safeties to the user and refers to ISO 6336-1:2019, 4.1.11, for guidance. The app's defaults are SHmin = 1.0 and SFmin = 1.4 (limits.minContactSafety, limits.minBendingSafety). Because σH grows with the square root of the load, SH = 1.2 means only 1.44 times the load to the pitting limit; σF grows in proportion to the load, so SF = 1.4 means 1.4 times the load to the root limit. A tooth breakage usually ends the gearbox's life while initial pitting may be tolerable, which is why SFmin is higher.

A worked example

The Spur gear pair template: 20/60 teeth, mn = 3 mm, b = 30 mm, 150 N·m at 1500 rpm, KA = 1.25, KHβ = 1.2, case-hardened 18CrNiMo7-6 (σHlim 1500 MPa, σFlim 500 MPa), 20 000 h.

Quantity	Value
Ft	5000 N
Kv (N = 0.0733, subcritical)	1.042
KHβ / KFβ	1.2 / 1.154
KHα	1.0
ZH, ZE, Zε	2.495, 189.8 √MPa, 0.881
σH0	802.9 MPa
ZB (pinion)	1.078
σH pinion / wheel	1082 / 1004 MPa
ZL · Zv · ZR	1.020 · 0.981 · 0.993
σHG (ZNT = 1)	1490 MPa
SH pinion / wheel	1.377 / 1.484
YF · YS pinion	1.542 · 1.835
σF pinion / wheel	236.3 / 223.6 MPa
σFG pinion	993.5 MPa
SF pinion / wheel	4.205 / 4.467

By hand:

\begin{matrix} σ_{H 0} & = 2.495 \cdot 189.8 \cdot 0.881 \cdot \sqrt{\frac{5000}{60 \cdot 30} \cdot \frac{4}{3}} = 802.9 MPa \\ σ_{H 1} & = 1.078 \cdot 802.9 \cdot \sqrt{1.25 \cdot 1.042 \cdot 1.2 \cdot 1.0} = 1082 MPa \end{matrix}

With 1.8·10⁹ pinion load cycles over 20 000 h both life factors are 1.

The 2019 and 2006 editions

The edition input selects ISO 6336-2 and -3 in their 2019 edition (default) or their 2006 edition, which ISO/TR 6336-30's worked examples use. ISO 6336-1 is applied in its 2006 edition either way. The 2019 edition:

multiplies YF by the load distribution factor fε (for helical gears with εβ ≥ 1, $1 / \sqrt{ε_{α n}}$ ) and divides Yβ by $\cos^{3} β$ ;
gives helical gears the contact factors $Z_{B} = Z_{D} = \sqrt{f_{Z C a}}$ (1.0 with load-distribution-based modifications, 1.07 with modifications from experience, 1.2 without);
takes Zv at the working pitch circle and widens the work hardening factor ZW.

axm verify checks the 2006 rating against the eight worked examples of ISO/TR 6336-30:2017.

Load spectra (ISO 6336-6)

A gear that runs at varying torque is rated over its loadSpectrum: bins of torque, speed and share of the life. Each bin is solved on its own with KA = 1, because the spectrum itself is the load variation. The damage Σ n/N is summed by Palmgren–Miner on S–N curves made of the rating's permissible stresses at the life curve's knee points, at each bin's speed (ZNT or YNT with the lubrication and roughness factors running to their static values in the limited life range). The safety over the spectrum is the factor on all stresses that makes the damage sum 1.

With 250 N·m for 5 %, 180 N·m for 35 % and 120 N·m for 60 % of the life on the same pair, the pinion's safeties over the spectrum are SH = 1.196 and SF = 3.173. The 250 N·m bin, with 9·10⁷ pinion cycles, is already past the knee of the pitting curve, so it governs: 1490/1246.0 = 1.196.

What is not covered

Micropitting (ISO/TS 6336-22), tooth flank fracture (ISO/TS 6336-4) and wear are not rated.
The size factor ZX is 1.
No-load losses (churning, windage) are not part of the mesh loss.
In a gearbox model the mesh misalignment from shaft and housing deflection is not fed into KHβ automatically; enter it as misalignment or through the shaft layout.

Scuffing is rated separately: see Gear scuffing.