KEVOS® MAKEOS · Gears
Gear Tooth Bending Stress (AGMA Form)
What bending stress does this tangential load put on the gear tooth root, and is the safety factor enough?
Tooth-root bending stress by the AGMA fundamental rating formula in metric form, from tangential load, face width, module, the bending geometry factor and the application, dynamic, size, load-distribution and rim-thickness factors, compared with your allowable bending stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tangential load at the pitch circle | N | Transmitted tangential force at the operating pitch diameter. |
| Face width | mm | Net face width of the narrower gear. |
| Transverse module | mm | Transverse module (normal module ÷ cos helix angle for helical gears). |
| Bending geometry factor J (Y_J) | Bending strength geometry factor from AGMA 908 or the gear design software. | |
| Overload (application) factor | Application factor for the driving and driven machinery. | |
| Dynamic factor | Dynamic factor for pitch-line velocity and gear accuracy. | |
| Size factor | Size factor (1 unless the standard calls for more). | |
| Load distribution factor | Face load distribution factor for alignment and face width. | |
| Rim thickness factor | Rim thickness factor (1 for solid gears). | |
| Allowable bending stress (adjusted for life and reliability) | MPa | Allowable bending stress for the material, already adjusted for stress cycles, temperature and reliability. |
| Required safety factor | Safety factor your design rule requires. |
Method and formulas
- σ_F = F_t K_o K_v K_s K_H K_B ÷ (b m_t Y_J) — the metric form of the AGMA fundamental bending equation.
- Safety factor = allowable ÷ σ_F; capacity = F_t × safety factor ÷ required factor.
- Example: 3000 N on a 30 mm face, module 2.5, J = 0.35 gives 222.86 MPa.
Limitations
- All factors and the allowable come from AGMA 2001 / 2101 or ISO 6336 data for your gears.
- Pitting resistance is a separate check.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check gear tooth bending strength for a new duty
- Compare face width or module options
- Rate an existing gear pair for a higher load
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Tooth bending stress
- Safety factor
- Load capacity at the required factor
Interpreting the result
- Raising the module raises bending strength fastest; wider faces help only while alignment keeps K_H low.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3304–3320. Topic reference; no source tables or recommended settings are reproduced.
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