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Spur and helical gear strength: ISO 6336 safety factors explained
A spur or helical pair can mesh perfectly and still pit or break in service. ISO 6336 is the standard that says whether it will carry its load: two safety factors, one for the flank and one for the root, built from the load, a set of factors for how unevenly the load arrives, and the strength of the material. This guide explains them and - measured on one pair - which choices move them most.
Two ways a tooth fails
Pitting is fatigue of the flank surface: where the teeth roll and slide the contact stress is high, and after enough cycles small pieces break out. ISO 6336-2 rates it from the contact stress σH. Tooth root breakage is bending fatigue: each tooth is a short cantilever loaded once a revolution, and a crack from the root fillet on the tension side takes the tooth off. ISO 6336-3 rates it from the root stress σF. ISO 6336-1 supplies the load factors both share, and ISO 6336-5 the strength of the material.
What a safety factor is
| Flank (pitting) | Root (bending) | |
|---|---|---|
| Actual stress | σH | σF |
| Permissible stress | σHP | σFP |
| Safety factor | SH = σHP / σH | SF = σFP / σF |
The permissible stress already contains the life: the material's endurance limit adjusted for the number of load cycles, the lubricant, the roughness and the size. For the example pair the pinion sees σH 1 093 N/mm² against σHP 1 193 - SH 1.09 - and σF 218 N/mm² against σFP 743 - SF 3.40. Pinion and wheel are rated separately; the designer shows the lower of the two. The tooth root is rated at the thinnest tooth the thickness tolerance allows - the smallest generating profile shift xE,min of the DIN 3967 fit, as ISO 6336-3 (6.1) asks when the finished teeth have not been measured.
The minimums: none in the standard
ISO 6336 does not set minimum safety factors: ISO 6336-1 (4.1.11) leaves them to the designer and the customer to agree. The designer's fields start at 1.0, which only means the stress reaches the permissible one - a placeholder, not a recommendation. The root is usually asked for more than the flank: pitting develops gradually and tends to be heard, a broken tooth stops the machine.
The load factors
The nominal tangential force Ft - 3 333 N here - is multiplied by four factors before it reaches the tooth:
| Factor | Example | What it covers |
|---|---|---|
| Application KA | 1.25 | shocks from the driving and driven machine; ISO 6336-1 Table 4 - here a uniform motor and a driven machine with light shocks |
| Dynamic Kv | 1.050 | the pair's own vibration, from the speed (4.6 m/s), the accuracy and the mass; Method B, 6.5 |
| Face load KHβ | 1.643 | uneven load across the face from shaft bending and helix deviations; Method C, 7.5 - needs the shaft and bearing data; here with the contact pattern not verified, (54) |
| Transverse load KHα | 1.000 | uneven sharing between the pairs of teeth in contact, from pitch errors; Method B, (73)–(76) |
KHβ is the largest here, and above 1.5 ISO 6336-1 recommends a contact analysis rather than the simplified method; the designer says so. The face load factor is also the one the designer cannot guess: it needs the pinion shaft's diameter, its bearing span and the pinion's offset from mid-span, and it waits for them.
Why the two respond differently to load
| Pinion torque | SH | SF |
|---|---|---|
| 50 Nm | 1.31 | 5.20 |
| 100 Nm | 1.09 | 3.40 |
| 150 Nm | 0.95 | 2.53 |
| 200 Nm | 0.86 | 2.02 |
Contact stress grows with the square root of the load, root stress in proportion to it. Doubling the torque from 100 to 200 Nm takes SF from 3.40 to 2.02 but SH only from 1.09 to 0.86. The ratios are not exact because the dynamic and face load factors change with the load too. So a large SF beside a modest SH is normal for a hardened pair, and a pair short on pitting needs more than a little extra size.
What moves them most
The example at 100 Nm, one input changed at a time. The base is SH 1.09, SF 3.40.
| Change | SH | SF |
|---|---|---|
| Module mn 2.5 / 3.5 mm | 0.93 / 1.25 | 2.45 / 4.52 |
| Face width 25 / 40 mm | 1.04 / 1.16 | 3.08 / 3.85 |
| Crowned flank (fma only) | 1.20 | 3.93 |
| Pinion 30 mm off mid-span | 1.06 | 3.24 |
| Material quality ML / ME | 0.95 / 1.20 | 2.50 / 4.20 |
| Hardness 660 / 800 HV | 1.09 / 1.09 | 3.40 / 3.40 |
| Nitrided steel, 750 HV | 0.89 | 3.25 |
| Induction hardened, 560 HV | 0.86 | 2.94 |
| Through hardened alloy steel, 300 HV | 0.53 | 2.76 |
| KA 1.0 / 1.5 | 1.17 / 1.03 | 3.95 / 2.99 |
| ISO 1328-1 class 5 / 8 | 1.16 / 0.90 | 3.73 / 2.47 |
| Speed 2 900 min-1 | 1.07 | 3.25 |
| Life 2 000 / 100 000 h | 1.17 / 1.04 | 3.56 / 3.30 |
| Oil ISO VG 46 / 220 (ν40) | 1.05 / 1.15 | 3.40 / 3.40 |
| Kv by Method C instead of B | 1.05 | 3.12 |
- Size first. The module moves both factors furthest. The face width helps less than it promises, because KHβ grows with it.
- The flank's contact pattern is worth as much as a module step. Crowning took SH from 1.09 to 1.20; so did a better accuracy class, almost.
- Material type and quality next. Case hardening gives the flank the most. ML, MQ and ME are ISO 6336-5's grades of how well the material and its heat treatment are controlled, and they matter as much as a material change.
- More hardness is not always more strength. For case hardened steel the permissible stresses ISO 6336-5 gives are flat across the 660–800 HV band.
- Be honest about KA; it moves the result as much as the accuracy.
- The oil acts on the flank only, through the lubricant and speed factors.
- The method matters. ISO 6336-1's simpler Method C for Kv gave 1.184 instead of Method B's 1.050 - pessimistic, as it is on the standard's own worked examples (ISO/TR 6336-30), which is why the designer uses B.
What the rating does not cover
- Scuffing and micropitting. They are in ISO/TS 6336-20, -21 and -22, which the designer does not apply yet. Fast, highly loaded pairs need them.
- Wear. Below about 1 m/s pitch line velocity the capacity is often set by abrasive wear rather than fatigue, which ISO 6336 does not calculate (ISO 6336-1, clause 1).
- Lubrication. ISO 6336-2 is written for oil-lubricated gears; for slow-running grease-lubricated ones it gives approximate values only, as long as there is lubricant in the mesh at all times (clause 1). A coating's effect is not in parts 1 to 3.
- Edition. The designer applies the 2019 editions of parts 1 to 3. Helical root stresses come out lower than in the 2006 edition, mainly through the new helix factor - worth knowing when comparing with older calculations.
Rate your own pair and see both factors against your minimums.
Open the exampleQuestions
What is a good safety factor for spur gears?
ISO 6336 does not give one: ISO 6336-1 4.1.11 leaves the minimums to the designer and the customer. The root is usually asked for more than the flank, because a broken tooth stops the machine at once while pitting develops gradually.
Why is the bending safety factor so much larger than the pitting one?
Root stress grows in proportion to the load but contact stress only with its square root, and case hardened steels are strong in bending. On the example pair S_F is 3.40 and S_H 1.09.
Does ISO 6336 cover helical gears?
Yes. ISO 6336 covers cylindrical gears with straight or helical involute teeth (ISO 6336-1, clause 1); the designer rates external spur and helical pairs with it.
Does a higher oil viscosity help?
On the flank, a little: on the example pair ISO VG 220 instead of VG 46 raised S_H from 1.05 to 1.15. It does not change the root rating.