Elaboration of a mathematical model of parameters calculation for section bars leveling at a roller leveling machine

Abstract

During rolling and cooling at cooling beds, section bars get general and local curvatures, to correct which, leveling at roller leveling machines (RLM) is used. Calculation of leveling parameters of section bars at RLM is based on hypothesis of isotropy and homogeneity of the deformed metal. Besides the calculation is based also on assumptions of a linear distribution of penetration coefficient of plastic deformation along the rolled product thickness at alternating bending, point character of roller and rolled product surface contact, vertical direction of leveling force for all rollers of RLM. Application of those hypothesizes considerably deteriorates the accuracy of technological parameters calculation for rolling and leveling operations. A mathematical model presented for leveling parameters of section bars at RLM calculation. The novelty of the model is an accurate determination of the border between elastic and plastic zone Z0, which is accomplished by an iterative method. The information about exact value of Z0 is necessary for calculation of stress distribution along the piece section, as well as sag and curvature calculation after the leveling. In traditional models the Z0 value is determined approximately and does not meet the today’s requirements. Stress distribution diagrams along the rolled product section at bending under RLM rollers presented for rectangular, square, channel, Z-section profiles of rolled products, as well as for I-beam and rail, necessary for calculation of residual stresses. The comparison was done of P65 rail sag in the plane of maximum rigidity at the six-roller RLM of Kuznetsk steel-works and their value, obtained by the mathematical model application. The discrepancy between actual and calculated data is only 4.5%, which speaks about conformity of the elaborated mathematical model.