A Method and Mathematics for Studying Web Feed-up and Tensions in Multi-stage Offset and Gravure Presses

This paper is about web feed-up and interstage tensions in offset and gravure printing presses. In it will be shown a method and the development of simple algebraic equations that may be used to calculate and study steady-state web feed-up and tensions under various web and press conditions. The equations are applicable to single stage and multiple stage presses. In the experimental work and the development of the mathematics these factors of special interest have evolved: First, there is an inherent slippage of the web in the printing nip of presses and this slippage is a function of the tension unbalance across the nip. Second, within the nip, high tension stresses are transmitted to the web which cause a velocity stratification within it and result in the establishment of an effective neutral plane in the web with respect to the impression cylinder. Third, the print length and interstage tensions in a press are dependent upon the tension balances across the printing nips, the elasticity and caliper of the web, the slippage of the web in the nips, and the effective neutral plane of the web on the impression cylinder. In the experimental work and the development of the mathematics these factors of special interest have evolved: First, there is an inherent slippage of the web in the printing nip of presses and this slippage is a function of the tension unbalance across the nip. Second, within the nip, high tension stresses are transmitted to the web which cause a velocity stratification within it and result in the establishment of an effective neutral plane in the web with respect to the impression cylinder. Third, the print length and interstage tensions in a press are dependent upon the tension balances across the printing nips, the elasticity and caliper of the web, the slippage of the web in the nips, and the effective neutral plane of the web on the impression cylinder.