KEVOS® MAKEOS · Gears
Spur Gear Set Design Check
Will this spur gear set carry the power for bending and pitting, and what face width does it really need?
One-pass design check of an external spur gear pair: geometry, pitch-line speed, torque and tangential load, contact ratio, undercut check, tooth bending stress (AGMA form with geometry factor J) and contact stress (Hertz with elastic and zone factors) against your allowables, with the face width each criterion requires.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Power | kW | Power transmitted. |
| Pinion speed | rpm | Pinion speed. |
| Overload factor | Overload (application) factor for the driver and load. | |
| Load distribution factor | Face load distribution factor for alignment and face width. | |
| Dynamic factor (0 = Barth for cut gears) | Dynamic factor; 0 uses the Barth factor (6.1 + v) ÷ 6.1 for cut gears. | |
| Geometry | ||
| Pinion teeth | Pinion tooth count. | |
| Gear teeth | Gear tooth count. | |
| Module | mm | Module. |
| Face width | mm | Face width in mesh. |
| Pressure angle | ° | Pressure angle. |
| Bending geometry factor J | Bending geometry factor for the pinion (AGMA 908 or software). | |
| Materials | ||
| Elastic modulus (both gears) | GPa | Elastic modulus of the gear materials. |
| Poisson’s ratio | Poisson’s ratio. | |
| Allowable bending stress | MPa | Allowable bending stress adjusted for life and reliability. |
| Allowable contact stress | MPa | Allowable contact stress adjusted for life and reliability. |
| Required bending safety factor | Safety factor required on bending. | |
| Required contact safety factor | Safety factor required on contact. | |
Method and formulas
- d = m z; a = (d₁ + d₂) ÷ 2; v = π d₁ n₁ ÷ 60,000; F_t = 2 T₁ ÷ d₁.
- Contact ratio = [√(r_a1² − r_b1²) + √(r_a2² − r_b2²) − a sin φ] ÷ (π m cos φ); undercut-free pinion needs z₁ ≥ 2 ÷ sin² φ.
- Bending σ_F = F_t K_o K_v K_H ÷ (b m J).
- Contact σ_H = Z_E Z_H √[F_t K_o K_v K_H (u + 1) ÷ (b d₁ u)], with Z_E = √[E ÷ 2π(1 − ν²)] and Z_H = √[2 ÷ (sin φ cos φ)].
- Face width needed: bending ∝ 1 ÷ b, contact ∝ 1 ÷ √b.
- Example: 7.5 kW at 1450 rpm on a module 3, 20/60 pair needs 27.71 mm of face width.
Limitations
- External spur gears of the same material; helical and internal gears need their own factors.
- Factors and allowables come from AGMA 2001 or ISO 6336 for your gears.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a new spur gear pair for a motor and ratio
- Check an existing pair against a power increase
- Decide whether module or face width must grow
Who it is for
- Gear designers
- Design engineers
- Mechanical engineers
What you get
- Geometry, speed, torque and tangential load
- Bending and contact stresses with safety factors
- Face width needed for each criterion
Interpreting the result
- If contact governs, a harder material or larger pinion helps most; if bending governs, a larger module does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2156, 3304–3320. 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.
