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I am using a stepper motor with a holding torque of x N.m driving a mass with inertia y. will adding a 2:1 gear reduction at the output cause effective holding torque to be 2x AND the inertia of the load to be y/2?

If this is the case, when calculating acceleration torque can I assume the inertia is halved and the torque available is double?

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Moment of inertia, like mass, does not change just because you have more torque or force available. Ultimately, it is acceleration that changes. The 2:1 gearbox causes the load to see double the torque from the motor, and it causes the motor to see half the moment of inertia from the load (as well as other load torques if there are there are any).

If you treat a 2:1 gearbox as doubling the torque AND reducing the moment of inertia you are double-counting the mechanical advantage being provided by the gearbox.

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