A turbomachine is made by first providing a stepped shaft having a large-diameter cylindrical portion, an intermediate-diameter cylindrical portion, and a small-diameter cylindrical portion all centered on a common axis. A separately manufactured a one-piece and annular first impeller wheel is then permanently mounted on the large-diameter portion with a back face of the first wheel facing axially toward the intermediate-diameter portion and carrying a rotor bearing half of an axial magnetic bearing. A rotor ring of a radial bearing is then detachably mounted on the intermediate-diameter portion of the shaft, and finally a one-piece and annular second impeller wheel is detachably mounted on the small-diameter portion of the shaft with a back face of the second wheel facing axially toward the first wheel and carrying a rotor bearing half of another axial magnetic bearing.