KEVOS® MAKEOS · Gears
Gear Train Tooth Number Planner
What tooth numbers give this reduction ratio in one or two stages, and how close can I get?
Search for spur or helical gear tooth numbers that produce a target reduction in one or two stages within limits on tooth count and stage ratio: the best combination by ratio error, preferring hunting-tooth pairs (no common factor) and the smallest total teeth, with the actual ratio, error, output speed and a table of the five best trains.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Target reduction ratio (input ÷ output speed) | Required overall reduction (for a step-up drive enter the reciprocal and reverse the train). | |
| Input speed | rpm | Input shaft speed. |
| Stages | choice | Number of gear meshes in series. |
| Minimum teeth | Smallest pinion allowed (17 or more avoids undercut at 20°). | |
| Maximum teeth | Largest gear allowed. | |
| Maximum ratio per stage | Largest ratio allowed in one mesh (about 6–8 for spur gears). | |
| Prefer hunting-tooth pairs | choice | Prefer pairs whose tooth numbers share no common factor, so every tooth meets every other tooth (more even wear). |
Method and formulas
- One stage: for each pinion z₁, gear z₂ = round(R z₁) within the limits.
- Two stages: for each first pair z₁/z₂ (ratio r₁ ≤ limit), the second pair z₃/z₄ = round(R ÷ r₁ × z₃).
- Ranked by ratio error, then hunting-tooth pairs (greatest common divisor 1), then fewest total teeth.
- Actual ratio = Π z_driven ÷ Π z_driver; output speed = input ÷ ratio.
- Example: a 23.5:1 reduction in 2 stage(s) is 17/94 × 20/85 (error 0%).
Limitations
- Ratio only; centre distances, strength and space need their own checks.
- Two stages searched exhaustively within the limits; three or more stages are not covered.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Pick tooth counts for a custom reduction gearbox
- Match an odd ratio for a feed or timing drive
- Avoid repeating tooth contact with hunting-tooth pairs
Who it is for
- Gear designers
- Machine designers
- Toolmakers
What you get
- Best tooth numbers
- Actual ratio and error
- Output speed and the five best trains
Interpreting the result
- If the error is too large, widen the tooth range or add a stage.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160, 2043–2047. Topic reference; no source tables or recommended settings are reproduced.
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