equipped with a check valve the air source can be disconnected and the mandrel will remain in the expanded condition it can then be lifted out of the core box and placed in a winding machine with the end journals rotatably supported in bearings ready for the winding operation from the foregoing description and the drawings it will be apparent that the differential winding air shaft or mandrel of the present invention has a number of features and advantages first of all it is simple excluding the rubber hose assembly and the screws there are only seven different parts required all of the parts can be fabricated by relatively simple machining operations secondly the design has an inherently high bending strength because the tubular portion of the shaft is close to the maximum diameter of the unexpanded mandrel and the longitudinal bars compensate for strength lost by the annular grooves in the outer surface of the tubular portion these grooves are shallow in any event because they need only to accommodate the shells which can be relatively thin since the external flanges 24 along each circumferential edge of the shells provide stiffness as well as an axial locating function for the cores the shells can be made of a suitable thermosetting plastic material such as a phenolic material or they can be made out of metal such as aluminum a particularly effective material is aluminum that has been surface coated or impregnated with a fluorocarbon plastic such as polytetrafluoroethylene the various parts of the hollow shaft can.