A rewinding machine for convolutley winding a web material onto a core to is disclosed. The rewinding machine comprises a first winding drum rotatable at a first peripheral velocity, a second winding drum opposed to the first winding drum and rotatable at a second peripheral velocity, and a core support for gripping opposing ends of the core. The core support grips opposing ends of the core during winding of the web material about the core. The core support has first and second rotatable pins each having corresponding first and second ends capable of insertion into a respective end of the core. The first rotatable pin has a channel that provides fluid communication between a source of positive pressure disposed external to the first rotatable pin and the second end of the first rotatable pin to provide positive pressure to the interior portion of the core.