Rotor Inertia Measurement

How do we measure rotor inertia?

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:

1. Main dynamic formula (M_din - dynamic torque, M_t.v. - no load torque).
2. Useful torque.
3. Dynamic Torque equal to No Load Torque.
4. Torque and current link.
5. EMF and angular velocity link.
6. 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.