KEVOS® MAKEOS · Gears
Gear Tooth Bending Stress (Lewis)
What bending stress does the tooth load cause at the tooth root, by the Lewis equation?
Lewis tooth bending stress with the Barth velocity factor for the manufacturing method, compared with an allowable stress, as a first check before a full gear rating.
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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). |
| Module | mm | Module. |
| Face width | mm | Face width in contact. |
| Lewis form factor Y | Lewis form factor for the tooth count and pressure angle, from a form factor table (based on module, not diametral pitch). | |
| Pitch diameter | mm | Pitch diameter, for pitch-line velocity. |
| Speed | rpm | Gear speed. |
| Tooth manufacture | choice | How the teeth are produced; this sets the Barth velocity factor. |
| Allowable bending stress | MPa | Allowable bending stress for the gear material and heat treatment from your design data. |
Method and formulas
- V = π d n ÷ 60 000 (m/s).
- Velocity factor Kv: cast (3.05 + V)/3.05; cut (6.1 + V)/6.1; hobbed (3.56 + √V)/3.56; ground √((5.56 + √V)/5.56).
- σ = Kv Ft ÷ (b m Y).
- Example: 3000 N on a module 3, 35 mm wide tooth with Y = 0.32 gives σ = 142.81 MPa.
Limitations
- The Lewis equation ignores stress concentration, load sharing and many rating factors; use ISO 6336 or AGMA 2001 for design.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Quickly size the module and face width
- Screen a gear for tooth breakage
- Compare materials and widths
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch-line velocity and velocity factor
- Lewis bending stress
- Ratio to allowable
Interpreting the result
- Treat the result as a screening value; a full rating will usually give a higher stress.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
