Planetary gear with fixed ring

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)

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.