The invention relates to an exchangeable cylinder jacket-shaped cover made of pile whose threads radially project outward. The aim of the invention is to provide a cover of this type, which has a high cohesive strength both in the axial as well as radial direction and which also has an outer and inner cylindrical contour that is as continuous as possible. To this end, the invention provides that the cover consists of an endless helically wound pile strip whose edges are interconnected by an endless helically running seam without forming a step that disrupts the cylindrical outer contour.