We can calculate it out of free run.

**Method:**

- Connect motor to the battery;
- Measure no-load current;
- Connect oscilloscope to the terminals;
- Disconnect the battery;
- Let the single measurement appear in the oscilloscope.

**Results:**

We measured free run BEMF dynamic process, which is equivalent for speed.

We can approximate the achieved graph to linear, which will allow us to use approximated differential dynamics:

- Main dynamic formula (M_din - dynamic torque, M_t.v. - no load torque).
- Useful torque.
- Dynamic Torque equal to No Load Torque.
- Torque and current link.
- EMF and angular velocity link.
- Voltage balance equation.

Moment of inertia is equal to:

Where I_t.v. - no load current, k - motor constant, T - time, E_bat - battery EMF, r_a - armature resistance, r_bat - battery resistance.

**Simulation:**

Simscape electrical in Matlab, helps us to have this approximated dynamic process and calculate the rotor inertia, which is equal to 1,081e-4 kgm^2:

**Conclusion:**

This is quite accurate method for rotor inertia calculation, if the gearmotor has static load (friction), which linearised the exponential graph of the speed.

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