Gear Safety Factors Explained: Root (SF) vs Flank (SH)
By Borut Černe ·
Every standards-based gear rating ends in two numbers: the root bending safety factor SF and the flank pitting safety factor SH. They guard against two different ways a tooth can fail — and reading them correctly is the difference between a design you trust and a number you copy into a report.
Two failure modes, two safety factors
A gear tooth has two classic ways to die, and they happen in different places for different reasons:
- Tooth root breakage. The tooth acts as a short cantilever beam. Every mesh cycle bends it, and the bending stress concentrates in the root fillet — the curved transition at the base of the tooth. A fatigue crack that starts there grows until the tooth breaks off. This failure is sudden, and usually terminal for the gearbox.
- Flank pitting. Where the flanks touch, the contact is a narrow, heavily loaded strip with very high local pressure. Repeated contact cycles fatigue the surface material until small pieces flake out, leaving pits. Pitting is progressive: it starts as noise and vibration, degrades the tooth profile, and eventually ends the gear's useful life.
Both are fatigue phenomena — driven by millions of repeated load cycles, not by one overload. That is why both checks have the same shape: compare the stress that occurs in service against the stress the material can endure for the required life, and express the margin as a safety factor.
Root bending and SF
The root check treats the tooth as a loaded cantilever. From the transmitted torque, the standard derives the tangential force at the mesh, then computes the local bending stress in the root fillet — accounting for the tooth's shape, the stress concentration of the fillet radius, and how the load is actually shared and distributed in service.
On the other side of the comparison stands the material's bending fatigue strength, adjusted for the required number of load cycles, the tooth size, the notch sensitivity of the material and the surface condition of the fillet.
SF is the ratio between the two — how much stronger the root is than it needs to be. Because a root crack means sudden tooth loss, engineers typically demand more generous margins here than on the flank. The geometry levers that raise SF are intuitive: a larger module makes the tooth thicker, a fuller root fillet (set by the rack profile, e.g. the ISO 53 variants) softens the stress concentration, positive profile shift thickens the pinion root, and a wider face width spreads the load.
Flank pitting and SH
The flank check is a contact problem. Two curved surfaces pressed together develop a characteristic contact pressure — the standard computes it at the decisive point of the mesh from the gear geometry, the elasticity of both materials, and how many tooth pairs share the load at that instant.
The permissible side is the material's contact fatigue strength, adjusted for life, lubrication conditions, pitch-line velocity, surface roughness, hardness pairing and size.
SH is the margin on that contact stress. One subtlety matters when you read it: contact stress grows much more slowly with torque than bending stress does — roughly with its square root. A given numeric value of SH therefore represents a different torque margin than the same value of SF, and the two numbers should never be compared against each other directly. Judge each against its own target.
Which one governs?
Both checks must pass — the smaller margin governs the design. Which one that is depends mostly on material and heat treatment:
- Surface-hardened gears (case-hardened, nitrided) gain enormously in flank capacity, so the root often becomes the limiting check.
- Through-hardened and structural steels tend to run out of flank capacity first — pitting governs.
- Thermoplastic gears are a special case: per VDI 2736, root bending is the governing failure check, which is why a plastic-gear rating in Zenomiq reports the root safety factor. Temperature-dependent material strength drives the result, so the operating tooth temperature you enter matters as much as the load.
This is also why "just make it stronger" is rarely one change: a lever that helps the root (a fuller fillet) may do little for the flank, and vice versa (a harder surface).
How ISO 6336 Method B derives them
For steel gears, ISO 6336 Method B (2019) is the detailed analytical route. The calculation follows a traceable chain:
- Nominal load — tangential force from torque and geometry.
- Load influence factors — external application effects, internal dynamic effects, and the distribution of load across the face width and between simultaneous tooth contacts. Manufacturing accuracy (the ISO 1328 quality grade) feeds directly into these.
- Local stress — root bending stress and flank contact stress at the decisive points.
- Permissible stress — material fatigue limits adjusted by life, size, roughness, velocity and lubrication factors.
- SF and SH — the ratio of permissible to occurring stress, per gear.
Method B computes each factor from the standard's own formulas rather than lumping them into assumptions — which means every intermediate value can be audited. Zenomiq exposes that full factor chain in the results, so when a reviewer asks where a number came from, you can show them. Try it on the ISO 6336 gear design tool, or read what to do when a safety factor comes back too low.
Frequently asked questions
What is a good gear safety factor?+
There is no universal number. The right margin depends on how well you know the loads, the consequence of a failure, the required life, and your industry's practice or customer specification. What the standard gives you is a consistent way to compute the factor — deciding the target is an engineering judgement.
Why is my SH lower than my SF?+
They measure different stress types and are not directly comparable. SF is a margin on bending stress, which grows roughly in proportion to torque. SH is a margin on contact stress, which grows much more slowly with torque — so a numerically smaller SH can represent a healthy margin.
Does a failing SH mean the gear breaks immediately?+
No. Pitting is a progressive surface fatigue process — it announces itself with noise, vibration and visible pits before the gear stops working. A failing SF is the more dangerous case, because root cracks lead to sudden tooth breakage.
Do plastic gears use SF and SH too?+
Plastic gears are rated per VDI 2736, where root bending is the governing failure check — that's why Zenomiq reports the root safety factor for thermoplastic pairs. Steel gears rated per ISO 6336 get both SF and SH.
How can I raise a safety factor that's too low?+
The main levers are tooth size (module), face width, profile shift, material and heat treatment, and manufacturing quality grade. Each has trade-offs — see our guide on fixing a failing safety factor.