Gear Stress Analysis
Lewis bending stress & Hertz contact stress with safety factor check — AGMA / ISO 6336
Module (m) — ISO standard
Pinion Teeth (z₁)
teeth
Gear Teeth (z₂)
teeth
Face Width (b)
mm
Pressure Angle (α)
Transmitted Power (P)
kW
Pinion Speed (n₁)
RPM
Pinion Material
Gear Material
Dynamic Factor (Kᵥ)
—
Application Factor (Kₐ)
—
Gear Forces
Pinion Torque (T₁)
—N·m
Tangential Force (Fₜ)
—N
Radial Force (Fᵣ)
—N
Normal Force (Fₙ)
—N
Design Force (Wₜ)
—N
Pitch Line Velocity
—m/s
Lewis Bending Stress — Pinion
Lewis Form Factor (Y₁)
—
Bending Stress (σ₁)
—MPa
Allowable Bending (σP₁)
—MPa
Bending Safety Factor (S₂)
—
Lewis Bending Stress — Gear
Lewis Form Factor (Y₂)
—
Bending Stress (σ₂)
—MPa
Allowable Bending (σP₂)
—MPa
Bending Safety Factor (S₂)
—
Hertz Contact Stress
Elasticity Factor (Zₑ)
191√MPa
Contact Stress (σℋ)
—MPa
Allowable Contact (Pinion)
—MPa
Allowable Contact (Gear)
—MPa
Contact Safety Factor Sℋ₁
—
Contact Safety Factor Sℋ₂
—
Stress Formulas
Design tangential forceWₜ = Fₜ × Kₐ × Kᵥ
Lewis bending stressσ = Wₜ / (b × m × Y)
Hertz contact stressσℋ = Zₑ √(Wₜ × (u+1) / (b × d₁ × u))
Bending safety factorS₂ = σP / σ ≥ 1.5
Contact safety factorSℋ = σℋP / σℋ ≥ 1.2
Lewis Form Factor Y (20° pressure angle)
| Teeth | Y | Teeth | Y |
|---|---|---|---|
| 12 | 0.245 | 50 | 0.371 |
| 14 | 0.276 | 60 | 0.378 |
| 17 | 0.303 | 75 | 0.390 |
| 20 | 0.320 | 100 | 0.399 |
| 25 | 0.333 | 150 | 0.408 |
| 30 | 0.346 | 200 | 0.414 |