This paper describes the theoretical modeling for the prediction of slippage onset condition between the paper web and steel roller with experimental verifications. For the first step of modeling, the occurrence of slippage is observed for the cases of uncoated paper (newsprint) and coated paper, and the relation between the slip ratio and roller velocity is measured by changing web tension. Two kinds of theoretical model are proposed, and the applicability of the models is confirmed experimentally. List of symbolsB web wrap angle (rad) d shape function (m) F friction force between web and roller (N) f traction force at bearing (N) h entrained air film thickness (m) k web permeability (m 2 ) L web width (m) M b bearing torque (Nm) p air film pressure (Pa) p a ambient pressure (Pa) R roller radius (m) r bearing radius (m) s slip ratio T web tension (N/m) t w web thickness (m) U total velocity (= U r + U w ) (m/s) U r roller velocity (m/s) U slip slip onset velocity (m/s) U w web velocity (m/s) w web deflection (m) x coordinate in the web transport direction (m) x e outlet position of web wrap angle (m) x s inlet position of web wrap angle (m) z coordinate in the cross machine direction (m) g air viscosity (Pa s) l traction coefficient between web and roller l bbearing friction coefficient l l local traction coefficient r rms composite roughness (m) r r rms roughness of roller surface (m) r w rms roughness of web surface (m)

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Many kinds of defects occurring at winding process such as telescoping and starring have been recognized. Their main cause is internal stress of a wound roll. Thus, understanding internal stress of a wound roll is necessary to prevent these defects. In the field of web handling, analytical models have been developed to figure out radial and circumferential stress of a wound roll. So far, models have been built based on an assumption that web has uniform thickness. However, actual web thickness is not uniform. We have faced defects caused by non-uniform thickness across widthwise direction. We use modified Hakiel's model with air entrainment effects. As the non-uniform web is wound, radius across widthwise direction also becomes non-uniform. The main characteristic of this model is that it distributes the winding tension across widthwise direction based on non-uniform radius. The model has a problem that it does not consider the radial compression of a wound roll when the most outer layer is added. Because of this, the tension applied to the thick web area tends to be higher at the time of tension distribution. Experimental coefficient is applied to the tension to correct this effect. Experimental verification has been performed on this model. Quantitative agreement between the calculated and measured results is confirmed. We explain both theoretical concept and experimental method of its verification.

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