KEVOS® MAKEOS · Gears
Internal Gear and Pinion Proportions
What diameters, centre distance and tooth thicknesses do this internal gear and pinion need, and do the tooth numbers interfere?
Proportions of an internal spur gear and its pinion by the handbook rules for 20° full-depth teeth: pitch diameters, enlarged internal diameter and pinion outside diameter to avoid interference, conventional diameters, centre distance, arc tooth thicknesses and the tooth-number difference check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module (25.4 ÷ diametral pitch). |
| Internal gear teeth | Number of teeth in the internal gear. | |
| Pinion teeth | Number of teeth in the pinion. | |
| Tooth form | choice | Tooth system, which sets the minimum tooth-number difference. |
Method and formulas
- Pitch diameters = m Z; centre distance = m (Z_g − Z_p) ÷ 2.
- Enlarged internal diameter = m (Z_g − 1.2) for pinions of 16 teeth or more (conventional: m (Z_g − 2)).
- Enlarged pinion outside diameter = m (Z_p + 2.5) (conventional: m (Z_p + 2)).
- Arc tooth thickness at the pitch circle: internal gear 1.3888 m, enlarged pinion 1.7528 m (20°).
- Tooth-number difference at least 12 (20° full depth), 7–8 (stub) or 15 (14½°).
- Example: 72 teeth with a 18-tooth pinion: internal diameter 299.72 mm and pinion outside diameter 86.783 mm.
Limitations
- Rules for 20° full-depth teeth with pinions of 16 teeth or more; thicknesses apply to 20° with the enlarged diameters.
- Check tip interference and trimming with gear design software for unusual ratios.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out an internal gear drive
- Check tooth-number combinations for interference
- Size a ring gear blank
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch diameters and centre distance
- Internal diameter and pinion outside diameter
- Tooth thicknesses and interference check
Interpreting the result
- A tooth-number difference below the minimum causes interference; add teeth to the gear or remove them from the pinion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2170–2171. Topic reference; no source tables or recommended settings are reproduced.
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