KEVOS® MAKEOS · Gears
Spur and Helical Gear Contact (Pitting) Stress
What contact stress does this gear mesh run at, compared with the allowable for the material?
Nominal contact (Hertzian) stress at the pitch point of a spur or helical gear pair by the ISO 6336-style relation with elasticity and zone factors, as a screening check against pitting.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tangential force | N | Tangential force at the pitch circle (see the gear tooth forces tool). |
| Pinion pitch diameter | mm | Pitch diameter of the pinion. |
| Face width | mm | Face width in contact. |
| Gear ratio (gear ÷ pinion teeth) | Tooth ratio; use it as negative for internal gears is not supported here. | |
| Pressure angle | ° | Pressure angle. |
| Elastic modulus (both gears) | GPa | Modulus of the gear material. |
| Poisson’s ratio | Poisson’s ratio. | |
| Load factor (application × dynamic × distribution) | Product of application, dynamic and load-distribution factors from your rating method. | |
| Allowable contact stress | MPa | Allowable contact stress for the material and heat treatment (e.g. from ISO 6336-5 or AGMA data). |
Method and formulas
- Elasticity factor ZE = √(E ÷ 2π(1 − ν²)) for equal materials (≈ 189.8 √MPa for steel).
- Zone factor ZH = √(2 ÷ (sin α cos α)) for unshifted spur gears (≈ 2.49 at 20°).
- σH = ZE ZH √(K Ft (u + 1) ÷ (b d₁ u)).
- Example: 3000 N on a 60 mm pinion, 30 mm wide, ratio 3: σH ≈ 864.49 MPa.
Limitations
- Screening relation; a full ISO 6336 or AGMA 2001 rating adds contact ratio, helix, lubrication and life factors.
- Same material for both gears.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Screen gear face width and diameter for pitting
- Compare materials and heat treatments
- Check a gear set after a power increase
Who it is for
- Gear designers
- Design engineers
What you get
- Elasticity and zone factors
- Contact stress
- Ratio to allowable
Interpreting the result
- Contact stress falls with the square root of face width and pinion diameter; doubling width cuts stress by about 30%.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2301–2309. Topic reference; no source tables or recommended settings are reproduced.
- ISO 6336-2 Calculation of load capacity of spur and helical gears — Surface durability (pitting)
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Open the Spur and Helical Gear Contact (Pitting) Stress calculator
