BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Module
- What it is
- The module of the gear pair, pitch diameter divided by number of teeth; the internal gear and its pinion share it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4.2333 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All diameters, the centre distance and the tooth thicknesses scale in proportion.
- Get it right
- To convert from diametral pitch, module = 25.4 ÷ diametral pitch.
What this means: Internal gear teeth
- What it is
- The number of teeth cut on the inside of the ring (internal) gear. It must exceed the pinion teeth by at least the minimum difference for the tooth form.
- Units and format
- Enter a plain number with no unit. The form accepts 20 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 72 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pinion teeth
- What it is
- The number of teeth on the external pinion that meshes inside the ring gear.
- Units and format
- Enter a plain number with no unit. The form accepts 8 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The enlargement rules are stated for pinions of 16 teeth or more; the tool warns below that.
What this means: Tooth form
- What it is
- The tooth system of the pair. In this tool it sets only the minimum difference in tooth numbers needed to avoid interference; the diameters and thicknesses follow the 20° full-depth rules.
- Units and format
- Choose one of 3 options from the list: 20° full depth; 20° stub; 14½° full depth.
- Example
- The form opens with “20° full depth” selected as a worked example. Choose the option that matches your case.
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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