In this paper the elongation of a core in a roll bottom is studied experimentally and theoretically. The CD elongation effects are of interest especially because they are known to contribute prominently to a two-drum winder vibration or roll instability phenomenon called bouncing in the paper industry.Analytical and numerical calculation models are used to study the effect of different geometrical, material, etc., parameters on the core and paper CD elongation. If the free lateral elongation and rotation is allowed and the friction between paper and the core is neglected, the radial and tangential stresses of the core are due to the radial pressure only. The lateral and shear stresses are equal to zero and the elongation depends on the pressure, Poisson's ratios in the thickness-machine and thickness-cross directions, elastic modulus in the thickness and tangential directions and the geometry. If the lateral frictional farces between the paper and core are also taken into account, another, equally effective elongation mechanism is introduced.The measurements of the paper and core elongation are in accordance with the calculated results. In practice, cores expand typically +/-1 mm/m depending on the tightness of the roll bottom and core properties. This study shows that the core elongation increases linearly with the radial pressure. Small diameter cores lengthen less than large cores. Cores with thicker wall thickness lengthen less than thinner cores, and cores with a bigger winding angle lengthen less than cores with a smaller winding angle (conventional cores).The radial moduli of paper and the core wall also play an important role in the elongation of the core. Preliminary studies suggest that the softer the paper the more it tends to widen. According to paper stack modulus measurements, the radial modulus of paper layers in the roll bottom can be less than 100 MPa, even with high winding pressures. The radial elastic modulus of the core wall is usually 100 - 200 MPa or even greater depending on the core type. It is possible that the frictional force between the core and paper could force the core to elongate more than it would without paper
