Best to keep the drill rotating about a fixed axis and feed the workpiece toward the drill. That nicely separates the two motions. You can use a Translational Joint or a combination of displacements to move the workpiece.
Rotational Velocity is a load that applies an acceleration that has a radius squared field about an axis, it does not rotate bodies.
I don't have much experience with LS-Dyna so I can't give you more specific advice on that.
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