Stress–Strain State of Coiled Steel

Abstract

In a new mathematical model of the stress–strain state of steel strip in the course of cooling, the nonplanarity, surface roughness, and transverse thickness variation (convexity of the cross section) are taken into account. The stress–strain state of a coil of thin steel sheet has a significant influence on factors such as the temperature distribution in the coil; the scale formation on cooling in the course of hot rolling; the adhesion of adjacent turns in the annealing of cold-rolled strip; and the shape of the coil itself. The mathematical model is based on representation of the coil as individual nested hollow cylinders of finite length. The cylinders are divided into sections over the width. The sum of solutions of the Lame equation for individual sections is shown to converge to the solution for the cylinder as a whole. The model permits calculation of the coil’s stress–strain state, taking account of gap formation between adjacent turns as a result of the transverse variation in strip thickness. The modeling results show how the radial and tangential stress formed in strip winding is distributed within the coil. The model permits calculation of the stress–strain state of the coil in the winding of even strip; in the winding of convex even strip with no tension; in the loose winding of convex even strip with tension less than that in tight winding; in tight winding of even convex strip with the correct tension; and in the winding of convex uneven strip without tension. The decrease in distance between contacting rough surfaces is calculated on the basis of a probabilistic approach. An algorithm is presented for calculation of the coil’s stress–strain state. The result obtained for the stress distribution in the coil is typical for the winding of steel strip. The model is verified for the winding of hot-rolled strip, in terms of the size of the region with tight contact of adjacent turns. The tightness of contact is assessed on the basis of the temper color on the edges of the hot-rolled strip. The discrepancy between the calculated and measured size of the region with tight contact is 3%.