A support for endless grinding sleeves for grinding workpieces has a casing which axially running slots or grooves and the support has a round outline in cross section. An axial hole through the support becomes narrower along its length and is designed to receive a wedging cone that is to be drivingly joined with a shaft. The outer surface of the support is made somewhat smaller in size than the inner circumference of the endless grinding sleeve that is to be placed on the support and the cone is driven into the support to radially expand it into engagement with the sleeve.
