Can the motor control the reflected load?

Inertia reflects through a reduction by the square of the ratio. A load of 10 000 g·cm² on the output shaft of a 10:1 gearhead appears to the motor as 100 g·cm². The square is what makes gearing such an effective way to make a large load controllable, and it is also what makes the ratio value worth getting right: a ratio taken from a rounded catalog label carries its error into this number squared.

Three inertias have to be handled separately because they sit in different places. The mechanism inertia is measured at the output shaft and divides by the ratio squared. The gearhead's own inertia does not: it is dominated by the first stage, which turns at motor speed, so it is entered already referred to the motor shaft. The rotor inertia is the motor's own, and it is the reference everything else is compared against. Adding a load inertia to a rotor inertia without reflecting it first is the most common error in this calculation, and it is wrong by orders of magnitude.

The number that matters is the ratio between the driven inertia and the rotor inertia. At or below 5:1 the motor dominates and the axis is easy: a simple controller settles it and a move does not ring. Between 5:1 and 10:1 is workable with a slower ramp or a tuned loop. Above 10:1 the mechanism dominates the motor, and torsional wind-up in the gear train, the coupling and the shaft starts to set the settling time instead of the controller. Above about 30:1, treat any positioning requirement as unproven until it has been measured on the real mechanism.

High ratios are not automatically wrong. A conveyor, a pump, a fan or any constant-speed drive can run happily at a mismatch that would make a point-to-point positioner unusable, because nothing is asking the axis to settle. The requirement decides, not the number.

Backlash interacts with all of this and is not in the arithmetic. A gear train with backlash and a mismatched load behaves as two masses connected by a spring with a dead band in the middle: the motor accelerates into the gap, meets the load, and the axis oscillates at a frequency the controller cannot see because the encoder is on the motor. This is the usual reason a mechanism that computes well positions badly.

Linear mechanisms have to be converted before they come here. A mass on a lead screw, a belt or a rack has an equivalent rotational inertia derived from the mass and the travel per revolution, and that equivalent value is what gets entered as the mechanism inertia. A linear axis also carries friction that this calculation says nothing about: inertia sets the acceleration torque, friction sets the continuous torque, and a mechanism can be dominated by either.