The quality of a wound roll is highly dependent upon the in-roll stress distribution, which is controlled by the operating parameters of center torque, nip and tension. With increasing demands for higher performance of paper winding machines in terms of higher speed of winding, wider width of web and larger diameter of wound rolls, it becomes of vital importance to determine the optimum operating conditions of the machines.

In this paper, a numerical formulation for estimating the in-roll stress of a wound roll is proposed taking account of the effect of nonlinearity in web compressibility, air-entrainment and permeance. The proposed theory of winding is based on the assumption that the accumulation of the in-roll stress by a wound-in layer can be expressed as the superposition of the stress increments calculated from a mechanical model of a pressured thick cylinder. The theory of elasto-hydrodynamic lubrication with the compressibility of air is introduced to evaluate the effect of air-entrainment at the roll-inlet. Permeance of air is newly incorporated into the winding model, which is expressed under the assumption that permeance is proportional to the pressure difference of both sides of a web.

Winding tests were conducted in order to assure the applicability of the proposed theory by usage of the dry-end section of the paper-making pilot machine under the operating conditions of 200 - 2000m/min in winding speed, 765mm in web width and 1200mm in diameter of the wound roll. The numerical analysis and experimental observation shows the significant effect of the air-entrainment and permeance upon the in-roll stress.