Gear calculation (ISO 6336)

Q: What minimum safeties should I use?

ISO 6336 leaves them to the user. The defaults are SHmin 1.0 and SFmin 1.4: a root breakage usually ends the gearbox, while initial pitting may be tolerable. Because σH grows with the square root of the load, SH = 1.2 means only 1.44 times the load to the pitting limit.

ISO 6336 rates cylindrical involute gears against the two fatigue failures that end most gearboxes: pitting of the flanks, driven by the contact stress, and breakage of the tooth root, driven by the bending stress in the fillet. Each starts from a nominal stress, raises it by load factors for shocks, dynamics and uneven load, and compares it with the strength of the material corrected for the actual gear.

Axomek rates external and internal spur and helical pairs generated by a basic rack. It gives the involute geometry with profile shift, the load factors, the pitting and root safety of pinion and wheel and, when you ask for it, scuffing, a load spectrum and a loaded tooth contact with flank modifications. Mounted on two shafts, the pair loads both shafts and their bearings with its tooth forces; the two-stage helical gearbox example shows such a gearbox whole, its three shafts set round each other by the mesh angles in the assembly view, coloured by their checks.

ISO 6336-1:2006
ISO 6336-2:2019
ISO 6336-3:2019
ISO 6336-5:2016
ISO 6336-6
ISO/TS 6336-20:2022
ISO/TR 13989-2:2000
ISO/TR 14179-1

Try this example in the app

The Gears module with the spur gear pair template open: the drawn mesh of a 20-tooth pinion and a 60-tooth wheel and the safety factor bars for pitting and tooth root.

What Axomek calculates

You enter

Tooth numbers, normal module, face width, pressure angle, helix angle and profile shifts; internal (ring) wheels with their shaper cutter
Pinion torque in N·m, speed in rpm, application factor K_A, ISO 1328 grade and required life in h
Face load factor K_Hβ, or the pinion shaft layout for method C (bearing span, offset, shaft diameter, constant K′)
Materials with σ_Hlim and σ_Flim from ISO 6336-5:2016, oil viscosity and flank and fillet roughness
Rim thickness, tip relief, rack dedendum and root radius, and the edition of ISO 6336-2/-3 (2019 or 2006)
Optional: scuffing (oil temperature, FZG load stage, lubrication), a load spectrum, flank modifications and misalignment
Minimum safeties S_H, S_F, S_intS and S_B

It calculates

Geometry: centre distance, working pressure angle, diameters and contact ratios
Load factors K_v, K_Hβ, K_Fβ, K_Hα and the Z and Y factors
Contact stress σ_H and pitting safety S_H of pinion and wheel
Tooth root stress σ_F and root safety S_F of pinion and wheel
Scuffing safeties S_B (flash temperature) and S_intS (integral temperature)
Tooth forces on the shafts, mesh loss and efficiency
Safeties over a load spectrum with the damage sums, and the loaded tooth contact with transmission error

Method and standards

ISO 6336-1:2006: K_v by method B from the resonance ratio, K_Hβ by method C from the shaft layout or as given, K_Hα by method B
ISO 6336-2 method B: σ_H = Z_B (or Z_D)·σ_H0·√(K_A·K_v·K_Hβ·K_Hα), with Z_NT, Z_L, Z_v, Z_R and Z_W in the permissible stress
ISO 6336-3 method B: the root stress with the load at the outer point of single pair contact, Y_F, Y_S, Y_β, Y_B and Y_DT
The 2019 edition of parts 2 and 3 by default, or the 2006 edition as ISO/TR 6336-30 uses; the 2006 rating is checked against the eight worked examples of ISO/TR 6336-30:2017
Load spectra by ISO 6336-6 with Palmgren–Miner, each bin at K_A = 1
Scuffing by the flash temperature of ISO/TS 6336-20:2022 (Annex A) and the integral temperature of ISO/TR 13989-2:2000; mesh loss by ISO/TR 14179-1

Limits

Micropitting (ISO/TS 6336-22), tooth flank fracture (ISO/TS 6336-4) and wear are not rated.
The size factor Z_X is taken as 1.
No-load losses (churning, windage) are not part of the mesh loss.
In a gearbox the mesh misalignment from shaft and housing deflection is not fed into K_Hβ automatically; enter it as a misalignment or through the shaft layout.
The loaded tooth contact leaves out bending coupling between slices, edge effects and dynamics.

Worked example

The spur gear pair template: 20/60 teeth, m_n 3 mm, b 30 mm, 150 N·m at 1500 rpm, K_A 1.25, K_Hβ 1.2, case-hardened 18CrNiMo7-6 for 20 000 h, with a scuffing check added at 70 °C oil and FZG stage 10.

Result	Value
Contact stress σ_H, pinion	1,082 MPa
Pitting safety S_H, pinion (min 1.0)	1.377
Pitting safety S_H, wheel	1.484
Root stress σ_F, pinion	236.3 MPa
Tooth root safety S_F, pinion (min 1.4)	4.205
Tooth root safety S_F, wheel	4.467
Scuffing safety S_B, flash temperature (min 2.0)	3.995
Scuffing safety S_intS, integral temperature (min 1.8)	2.952

All checks pass. Pitting of the pinion is the closest; the tooth root and scuffing have wide margins.

The numbers come from the engine: the same commands, run with the axm command line, give them.

The same with the axm command line

axm new ex.axm.json --template gear-pair
axm gear update ex.axm.json G1 --patch {"scuffing":{"oilTemperature":70,"fzgStage":10}}
axm solve ex.axm.json --json

Open the example in the app

Questions

Which edition of ISO 6336 is used?

ISO 6336-1 in its 2006 edition, and parts 2 and 3 in the 2019 edition by default. You can switch parts 2 and 3 to the 2006 edition, the one the worked examples of ISO/TR 6336-30 use.

What minimum safeties should I use?

ISO 6336 leaves them to the user. The defaults are S_Hmin 1.0 and S_Fmin 1.4: a root breakage usually ends the gearbox, while initial pitting may be tolerable. Because σ_H grows with the square root of the load, S_H = 1.2 means only 1.44 times the load to the pitting limit.

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