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
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Total at motor
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Inertia ratio
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Optimal ratio
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Accel torque
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Total motor torque
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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.