A magnetically levitated high-speed spindle assembly (20) is provided for forming non-circular holes (22) in workpieces (24) or non-circular surfaces on pins. The non-circular holes (22) can be formed with dimensionally varying axial trajectories at high speeds and with great accuracy. This is accomplished by supporting a rotating spindle (26) between first (58) and second (60) magnetic bearing clusters and independently controlling these bearing clusters (58, 60) to move a shaping tool (32) at the end of the spindle (26) in a predetermined orbital path (B). A multiple input-multiple output control strategy is used to control spindle (26) movements in the X and Y axes. The tilt angle between the cutting edge (34) of the shaping tool (32) and the orbital path (B) is maintained perpendicular under this multiple input-multiple output control of the magnetic bearing clusters (58, 60) to further improve shaping precision and spindle (26) stability during high-speed operations.