Mechanics of rotating wound rolls

In this paper, we investigate the effect of rotation on the internal loads in a wound roll and the dynamics of a fully wound roll under angular acceleration. Two different types of winding are distinguished: constant transport speed and constant rpm. The original scheme proposed by Benson accounted for large deformation, and used a nonlinear elastic constitutive law; in this paper, the Benson model is first expressed in dimensionless form and extended to account for roll rotation in both cases: constant rpm and constant transport speed. Additionally, tangential dynamics are considered to account for angular acceleration of a fully-wound roll. In general, it is seen that the inclusion of angular velocity in the Benson model alters the lap deformation, interlayer pressure and lap tension profiles compared to the case with no rotation, to an extent determined by the magnitude of angular velocity. A direct consequence of this is that there is now an upper bound on the number of laps that can be safely wound onto the core without loss of contact between the outermost laps, and this is a function of rotational speed and wrapping tension, among other parameters. A numerical algorithm is then described to account for angular acceleration due to a constant core torque applied after the roll has been completely wound. This allows one to determine the slip profile through the roll at various instants during the motion.