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.