An assembly for supporting a roll of sheet product with respect to a sheet product dispenser is provided including a mandrel configured to be positioned within a housing of the dispenser and a spindle. The spindle includes a spindle body positioned over the mandrel and configured to be received within a central opening of the roll. The spindle includes first and second sets of friction elements extending away from respective ends of the spindle body. Each friction element is configured to extend radially inward from the spindle body so as to provide a contact force against the mandrel when the spindle is installed on the mandrel. The contact forces applied against the mandrel may be designed to be constant irrespective of whether the roll of sheet product is installed on the spindle and/or if the inner surface of the central opening of the roll of sheet product has any inconsistencies.