Numerical control device and numerically controlled machining system

An NC machining system includes a feed that clamps a workpiece; a first rotational axis, which is located opposite the feed, which rotates as a main axis; a second rotation axis that rotates around its center at the first axis of rotation; a numerical control device, which outputs in accordance with pre-programmed machining instructions rotation instructions for the first and second axis of rotation; and a tool that is moved along a peripheral surface of the workpiece by rotation of the first axis of rotation which is fixed to the second axis of rotation, and whose radius is determined by processing a rotation of the second axis of rotation.