Servo Inertia Match

Load inertia reflects to the motor as J / N² — which is the entire reason gearboxes make big loads drivable. An inertia ratio under about 5:1 tunes easily; above 10:1 the loop gets sluggish and prone to ringing unless the coupling is very stiff.

Reflected load inertia
Total at motor
Inertia ratio
Optimal ratio
Accel torque
Total motor torque

The optimal ratio √(Jload/Jmotor) maximises acceleration but often gives an impractical speed — pick the nearest stock ratio and re-check. Torque here excludes gravity and process load.

A helper, not a substitute for engineering judgment. Verify against the governing standard.