A gyratory crusher main shaft sleeve for friction fitting over an uppermost tapered end of a crusher main shaft includes an elongate axial wall extending from an upper end to a lower end and having external and internal facing surfaces aligned transverse so as to taper inwardly towards a central axis. The tapering is defined by a sleeve tapering angle formed between the internal facing surface and an imaginary axis parallel to the central axis. The internal surface of the sleeve has a section in the axial direction with an upper end and a lower end. The sleeve section, from the upper end to the lower end, has a section tapering angle formed between the internal surface and the imaginary axis. The section tapering angle is different from the sleeve angle defining the tapering of the sleeve from the sleeve upper end to the section upper end.