Peripheral rewinding machine and method for producing logs of web material

A peripheral rewinding machine for the production of logs of web material on a core, comprising a first winding roller on which the web material may be wound, the first roller having an axis about which the roller rotates, a second winding roller defining with the first winding roller a gap through which a core may be inserted, a third roller movably mounted to allow the diameter of a log to increase and the log to be discharged at the end of winding, the first, second, and third rollers defining a winding space, means for severing the web material at the end of winding, and means for inserting a new core, characterized in that said means for severing the web material comprises a blade carried by a rotating member pivoted on the axis of said first winding roller and protruding from said first winding roller and in that actuating means are provided for causing the blade to rotate at different speeds in the same direction of rotation as said first winding roller such as to impart a change in speed to the blade when the blade is in contact with the web material in the winding space bed defined by said three rollers.