A centrifugal compressor adapted to be used in a chiller, the centrifugal compressor comprising: a casing having an inlet portion and an outlet portion; an inlet guide vane disposed in the inlet portion; an impeller disposed downstream of the inlet guide vane, the impeller being attached to a shaft rotatable about a rotation axis; a diffuser disposed in the outlet portion downstream from the impeller; and a motor arranged to rotate the shaft in order to rotate the impeller, the motor including a rotor mounted on the shaft and a stator disposed radially outwardly of the rotor to form a gap between the rotor and the stator; a cooling medium delivery structure including an inlet conduit located to supply a cooling medium to the motor and an outlet conduit located to discharge the cooling medium from the motor, characterised in that the shaft has an external shape different than an internal shape of the rotor to form at least one axial passageway between the shaft and the rotor along an axial length of the shaft at least as long as an axial length of the rotor, and the inlet conduit is located to supply the cooling medium through the gap and the at least one axial passageway to cool the rotor, and the outlet conduit is located to discharge the cooling medium from the gap and the at least one axial passageway, wherein the external shape of the shaft is different than the internal shape of the rotor to form a plurality of axial passageways between the shaft and the rotor along the axial length of the shaft at least as long as the axial length of the rotor, wherein the external shape of the shaft includes an annular section and a plurality of grooves extending radially inwardly from the annular section, wherein each of the grooves includes a first sidewall, a second sidewall circumferentially spaced from the first sidewall and a trough wall connecting radially inner ends of the first and second sidewalls, wherein the first sidewall of each groove is substantially parallel to the second sidewall of the groove as viewed in axial cross section and each groove has a centerline equally spaced from the first and second sidewalls as viewed in axial cross section, and the centerline of each groove is inclined relative to a radial direction of the shaft. a casing having an inlet portion and an outlet portion; an inlet guide vane disposed in the inlet portion; an impeller disposed downstream of the inlet guide vane, the impeller being attached to a shaft rotatable about a rotation axis; a diffuser disposed in the outlet portion downstream from the impeller; and a motor arranged to rotate the shaft in order to rotate the impeller, the motor including a rotor mounted on the shaft and a stator disposed radially outwardly of the rotor to form a gap between the rotor and the stator; a cooling medium delivery structure including an inlet conduit located to supply a cooling medium to the motor and an outlet conduit located to discharge the cooling medium from the motor, characterised in that the shaft has an external shape different than an internal shape of the rotor to form at least one axial passageway between the shaft and the rotor along an axial length of the shaft at least as long as an axial length of the rotor, and the inlet conduit is located to supply the cooling medium through the gap and the at least one axial passageway to cool the rotor, and the outlet conduit is located to discharge the cooling medium from the gap and the at least one axial passageway, wherein the external shape of the shaft is different than the internal shape of the rotor to form a plurality of axial passageways between the shaft and the rotor along the axial length of the shaft at least as long as the axial length of the rotor, wherein the external shape of the shaft includes an annular section and a plurality of grooves extending radially inwardly from the annular section, wherein each of the grooves includes a first sidewall, a second sidewall circumferentially spaced from the first sidewall and a trough wall connecting radially inner ends of the first and second sidewalls, wherein the first sidewall of each groove is substantially parallel to the second sidewall of the groove as viewed in axial cross section and each groove has a centerline equally spaced from the first and second sidewalls as viewed in axial cross section, and the centerline of each groove is inclined relative to a radial direction of the shaft.