Calculation
nC = nS·zS/(zS+zR)
The sun drives, the ring is fixed, and the carrier turns more slowly in the same direction.
Roloff/Matek Umlaufgetriebe
Planetary Gear Calculator with Fixed Ring Gear
The sun drives, the ring is fixed, and the carrier turns more slowly in the same direction.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Carrier speed nC — The speed of the planet carrier at the output. As a result it follows from nS·zS/(zS+zR).
- Sun speed nS — The speed of the driving sun gear (the central gear at the middle of the planetary set). Source: a tachometer or the drive's nameplate.
- Sun teeth zS — The tooth count of the sun gear. Source: drawing, or count them on the part.
- Ring teeth zR — The tooth count of the fixed ring gear – the outer, internally toothed ring surrounding the planetary set, which here does not rotate. Source: drawing, or count them.
Example
nS=1,500 rpm, zS=30 and zR=90 give nC=375 rpm.
Assumptions and limits
Simple lossless planetary set, fixed ring and sun input; verify assembly condition separately.
Understand Planetary Gear Calculator with Fixed Ring Gear
Planetary set with fixed ring is a focused preliminary calculation based on Roloff/Matek. The calculator rearranges the closed-form relationship for every included quantity and deliberately separates this result from a complete component verification.
What does this quantity describe?
For a simple planetary set with fixed ring, driving sun and output carrier, nC=nS zS/(zS+zR).
Formula and variables
nC = nS·zS/(zS+zR)
nC = nS zS / (zS + zR)
| Symbol / input | Meaning |
|---|---|
| Carrier speed nC | The speed of the planet carrier at the output. As a result it follows from nS·zS/(zS+zR). |
| Sun speed nS | The speed of the driving sun gear (the central gear at the middle of the planetary set). Source: a tachometer or the drive's nameplate. |
| Sun teeth zS | The tooth count of the sun gear. Source: drawing, or count them on the part. |
| Ring teeth zR | The tooth count of the fixed ring gear – the outer, internally toothed ring surrounding the planetary set, which here does not rotate. Source: drawing, or count them. |
Choose the inputs correctly
nS is sun speed, zS and zR the sun and ring tooth counts, and nC carrier speed.
How to use the calculator
Select the target, enter all remaining quantities for the actual component, and verify the units. Then compare the result with the stated model limits and with the required strength, safety and operating checks.
Worked example
1,500 rpm, 30 sun and 90 ring teeth give 375 rpm at the carrier.
Understand the result and units
The carrier turns more slowly in the sun direction. The fixed ring carries a reaction torque that its support must withstand.
The calculator converts internally to coherent SI units. Length, force, torque, stress and angle may therefore use the offered units; dimensionless factors are entered as decimals.
What is taken from Roloff/Matek
Only the closed-form relationship from Kapitel 22, Umlaufgetriebe is used. Tabulated data, material limits and detailed design checks are not silently added; they remain explicit inputs or are expressly outside the model.
Typical applications
Planetary set with fixed ring supports option comparison, plausibility checks and early sizing within its machine-element cluster. Releasing a design requires the additional checks described in the cited chapter.
Assumptions, limits and common mistakes
Only a simple ideal planetary set in this exact state; planet tooth count, assembly condition, efficiency, load sharing and strength are excluded.
Common mistake: Typical errors are misreading the effective length or force, entering percentages instead of decimals, and treating a preliminary result as a complete verification. In particular: Only a simple ideal planetary set in this exact state; planet tooth count, assembly condition, efficiency, load sharing and strength are excluded.
Frequently asked questions
Is Planetary set with fixed ring a complete strength verification?
No. Only a simple ideal planetary set in this exact state; planet tooth count, assembly condition, efficiency, load sharing and strength are excluded.
Where do the equation and validity limits come from?
Roloff/Matek, Machine Elements, Kapitel 22, Umlaufgetriebe; the local 21st edition was cross-checked against the available 24th edition.
Can I order the calculated value directly as a nominal size?
Only after matching it to available standard or manufacturer series and completing the additional safety, material and operating checks.