Static Lewis-type screen
Gear tooth root stress
Inputs
Select the narrow static spur or parallel-axis helical first-estimate relation.
Known static tangential mesh load; this workspace does not derive or select it.
Nominal loaded face width for the stated spur-gear tooth.
Nominal metric module for the stated spur-gear geometry.
User-entered tooth count used only to expose the helical virtual-tooth arithmetic.
Use 0° for a spur gear; the helical first-estimate relation is limited to a positive angle through 45°.
User-entered dimensionless form factor for the declared tooth geometry; it is not selected here.
Results
Spur tangential tooth force
1,000
Declared tooth count
20
teethLewis-type loaded section factor
30
Static Lewis-type spur root bending stress
33.333
σF = Ft/(b m Y)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Calculate a basic user-factor Lewis-type spur or parallel-axis helical gear tooth root stress from tangential load, geometry, helix angle, and form factor.
σF = Ft/(b m Y)
When
- Static tangential load
- User-entered Lewis form factor
- Spur or bounded parallel-axis helical first estimate
- Nominal geometry
Don’t
- This is a basic static Lewis-type spur/helical root-bending arithmetic screen using a user-entered form factor. For the parallel-axis helical first estimate it exposes normal force and virtual tooth count, but does not select a form factor or apply rating factors. It does not select module, pressure angle, material, hardness, tooth form, or Lewis factor; calculate dynamic factors, contact stress, AGMA/ISO rating, mesh load distribution, lubrication, life, reliability, gearbox design, or approval.