BIZOMAT MAKEOS · Gears
Planetary Gear Train
What ratio, output speed and torque does this planetary (epicyclic) gear set give?
Ratio, output speed and torque of a simple planetary gear set with the ring, sun or carrier held, the planet tooth count and the equal-spacing assembly check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sun teeth | teeth | Teeth on the sun gear. |
| Ring teeth | teeth | Teeth on the internal ring gear. |
| Number of planets | planets | Number of equally spaced planets. |
| Arrangement | choice | Which member is held, which is the input and which is the output. |
| Input speed | rpm | Input speed. |
| Input torque | N·m | Input torque. |
| Efficiency | % | Overall efficiency of the stage. |
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: Sun teeth
- What it is
- The number of teeth on the sun gear, the central gear meshing with all the planets.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 24 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With the ring fixed, fewer sun teeth give a higher reduction ratio.
What this means: Ring teeth
- What it is
- The number of teeth on the internal ring gear that surrounds the planets.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 12 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 72 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ring teeth minus sun teeth must be a positive even number so the planets come out as whole gears.
What this means: Number of planets
- What it is
- The number of planet gears spaced equally around the sun, sharing the load between them.
- Units and format
- Enter a number in planets: planets. The form accepts 1 planets to 12 planets. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 planets as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Sun plus ring teeth must divide exactly by the number of planets for equal spacing.
What this means: Arrangement
- What it is
- Which member of the set is held still, which is driven and which delivers the output; it decides the ratio and whether the output reverses.
- Units and format
- Choose one of 3 options from the list: Ring fixed · sun in · carrier out; Sun fixed · ring in · carrier out; Carrier fixed · sun in · ring out.
- Example
- The form opens with “Ring fixed · sun in · carrier out” selected as a worked example. Choose the option that matches your case.
- Get it right
- Holding the carrier makes the ring turn the opposite way to the sun.
What this means: Input speed
- What it is
- The rotational speed of the input member, for example the motor speed driving the sun or ring.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed is the input speed divided by the ratio.
What this means: Input torque
- What it is
- The torque delivered to the input member by the motor or previous stage.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output torque is input torque times the ratio times the efficiency.
What this means: Efficiency
- What it is
- The share of input power that reaches the output after gear mesh and bearing losses in this stage.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 97% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output torque rises in direct proportion; output speed does not change.
- Get it right
- Type the percentage (97 for 97 %). Take it from the gearbox supplier or your own test data.
Method and formulas
- Planet teeth = (Zr − Zs) ÷ 2 (standard gears, same module).
- Ring fixed: i = 1 + Zr/Zs. Sun fixed: i = 1 + Zs/Zr. Carrier fixed: i = −Zr/Zs (output reverses).
- Equal spacing requires (Zs + Zr) ÷ number of planets to be a whole number.
- Example: sun 24, ring 72 with the ring fixed gives 4:1 and 375 rpm.
Limitations
- Standard, unshifted gears of one module; profile-shifted sets can break the planet-count rule.
- Load sharing between planets is assumed equal.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design or check a planetary reduction
- Choose tooth counts that assemble
- Find speed and torque at the output
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Planet teeth
- Ratio and direction
- Output speed and torque
- Assembly check
Interpreting the result
- Check each mesh (sun–planet and planet–ring) for strength with its own tangential force.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2211, 2122–2160. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Design printed gears that mesh
In Printed Mechanisms That Run
What it covers: Choose module and tooth counts a printer can make, lay out a planetary stage that assembles, check tooth bending against measured coupon strength and add the backlash printing needs.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.