## Topic:

- Why does gearhead inertia decrease with increasing number of stages?

## Solution:

### Gearhead inertia

The "Mass inertia" (line 10) of the maxon gearhead data sheets is defined as the moment of inertia the motor "sees". This means the motor has to drive the following inertias during acceleration:

- its own rotor inertia (including pinion)
- the load inertia transferred to the motor axis
- the gearhead inertia

### Load inertia

Load inertias are reduced by the square of the gearhead reduction. E.g. assuming a gearhead reduction of 10:1, the motor "sees" a load inertia which is a hundred (100) times smaller. This reduction rule for inertias applies to the inertias of gearhead stages too:

- The motor sees the full inertia of the gearhead input stage.
- The inertia of the next stage is already reduced by the square of the reduction of one stage (typically 3-5:1), hence by a factor of 9 to 25.
- Therefore, each additional stage is increasing the gearhead inertia only by a small amount.
- In most cases, the gearhead output stage has a much higher inertia than the other stages.
- If the gearhead has only one stage, the motor sees this output stage reduced only by the reduction of this stage.
- Increasing the number of stages, the high inertia of the output stage is strongly reduced. The much smaller inertias of the following stages cannot compensate for this reduction.
- As a result, the motor sees a decreasing gearhead inertia with increasing number of stages.

### Model calculation

- Inertia per stage: 5 gcm
^{2} - Inertia of the output stage: 10 gcm
^{2}

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