PARAMETRICAL MODEL OF STRESS-STRAIN STATE OF THE ROLL ON A COILER

The article presents a mathematical model of stress-strain state of the roll in the process of coiling at the simultaneous action of nonflatness, surfaces’roughness and gage transverse variation (a convexity of the cross-sectional profile). The stress-strain state of a thin steel strip roll has a significant effect on the distribution of temperature in the roll and the formation of scale during cooling at hot rolling, the weldability of the turns during annealing of the cold-rolled strip, the shape of the coil itself, etc. The mathematical model is based on representation the roll as separate embedded hollow cylinders of finite length. Cylinders are divided into separate sections in width. It is shown that, in this case, the sum of the solutions of the Lamé equation for individual sections converges with the solution for the cylinder as a whole. The model makes it possible to calculate the stress-strain state of a roll taking into account the formation of a gap between adjacent turns due to the transverse strip thickness. The distribution in the roll of the radial and tangential stresses formed when the strip is under coiling is shown. The developed model makes it possible to calculate the stress-strain state of a roll when coiling an even strip, when coiling a convex flat strip without tension, when coiling a convex flat strip with a tension, less than tight tension, when coiling a convex flat strip with a tight tension, and also when coiling a convex uneven strip without tension. The calculation of convergence of the contacting surfaces taking into account the roughness is based on a probabilistic approach. The article presents an algorithm for calculating the stress-strain state of a roll. The present distribution of stresses in the roll is characteristic of coiling steel strips. Distribution in a roll of the radial and tangential tension created when coiling a strip is shown. Adequacy of this model in a case of coiling of a hot-rolled strip is checked by means of size of a zone of dense pressing of adjacent rounds. An estimation of density of pressing of rounds in a roll was evaluated by means of tarnishing on edges of a hot-rolled strip. The discrepancy between the measured and calculated areas of dense pressing is about 3 %.

thin sheet rolling, coiling, stress-strain state of the coil, gage variation, roughness, flatness

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