Gear parameters
mm
For b/m ratio check only
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Recommended z₁ ≥ 17 (α = 20°)
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Results
| Parameter | Value | Unit | Formula |
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| Parameter | Value | Unit | Formula |
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Formulas & design notes
Basic diameters
d = m · z (pitch circle)da = m · (z + 2 + 2x) (tip)
df = m · (z − 2.5 + 2x) (root)
db = d · cos α (base)
Centre distance
a = m·(z₁+z₂)/2 (standard)a' = m·(z₁+z₂)/2 · cosα/cosα'
inv(α') = inv(α) + 2(x₁+x₂)·tanα / (z₁+z₂)
inv(φ) = tan(φ) − φ [rad]
Contact ratio
εα = (√(da1²−db1²) + √(da2²−db2²) − 2a'sinα') / (2π·m·cosα)εα ≥ 1.0 required; εα ≥ 1.2 recommended for smooth running.
Undercut & profile shift
z_min = 2 / sin²α ≈ 17 (α=20°)x_min = 1 − z·sin²α/2
Positive x increases tip and root diameter, shifts tooth toward tip — avoids undercut on small pinions.
Circular & base pitch
p = π · m (circular pitch)pb = p · cos α (base pitch)
Base pitch must be equal for both gears — automatically satisfied when module and pressure angle are shared.
Design recommendations
- Gear ratio i = z₂/z₁ ≤ 5…6 for single stage
- Face width b = (6…12)·m typical
- z₁ ≥ 17 avoids undercut at α = 20° without profile shift
- Contact ratio εα ≥ 1.2 for quiet running
- Tip clearance c* = 0.25·m (standard)