KEVOS® MAKEOS · Gears
Helical Gear Pair Geometry
What diameters, centre distance and contact ratios does this helical gear pair have?
Transverse module, pitch and tip diameters, centre distance, transverse pressure angle, virtual teeth, axial pitch and overlap ratio for a standard (unshifted) parallel-axis helical gear pair.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal module | mm | Normal module (the hob or cutter module). |
| Helix angle | ° | Helix angle at the pitch diameter (0 for spur gears). |
| Normal pressure angle | ° | Normal pressure angle (20° is standard). |
| Pinion teeth | teeth | Number of teeth on the pinion. |
| Gear teeth | teeth | Number of teeth on the gear. |
| Face width | mm | Face width in mesh. |
Method and formulas
- mt = mn ÷ cos β; d = z mt; tip diameter = d + 2mn (standard addendum); a = (d₁ + d₂) ÷ 2.
- αt = atan(tan αn ÷ cos β); base diameter = d cos αt.
- Virtual teeth zv = z ÷ cos³β; axial pitch = π mn ÷ sin β; overlap ratio εβ = b sin β ÷ π mn.
- Example: mn 3, 15°, 20/45 teeth give a centre distance of 100.94 mm and an overlap ratio of 0.82385.
Limitations
- Standard, unshifted gears; profile shift changes the centre distance and tip diameters.
- Strength and contact ratio in the transverse plane need a gear rating method (ISO 6336 or AGMA 2001).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a helical gear pair
- Check centre distance for a replacement pair
- Find axial thrust direction and overlap
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Transverse module and pressure angle
- Pitch, tip and base diameters
- Centre distance and ratio
- Virtual number of teeth
- Axial pitch and overlap ratio
Interpreting the result
- An overlap ratio of 1 or more gives smooth, quiet running.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2210. Topic reference; no source tables or recommended settings are reproduced.
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