Determination of geometrical volume of deformation zone during rolling of a strip in smooth rolls

Abstract

The article considers the longitudinal rolling of a thin strip in smooth rolls. The deformation takes place between rolls during their rotation in opposite directions. The process of reduction of metal by pressure is characterized by geometric sizes and shape of the deformation zone. Geometrically, the deformation zone contains elements of a circle, and for the numerical determination of the volume of the deformation zone we used Simpson’s formula with automatic choice of an integration step for a prescribed accuracy. Using the developed computer program we have defined the reduction of a strip for twelve passes and we have investigated the change of the geometric volume of the deformation zone along the rolling mill, from cage to cage. By the methods of correlation and regression analysis we have established the tightness and form of relation between the volume of the deformation zone and the number of a cage for expansion, calculated according to different formulas. It was determined that in all cases there was a steady statistical, nonlinear dependence of the volume of the deformation zone on a number of a cage. The formula was suggested to calculate the volume of deformation zone, which took into account the extension of a strip, determined by theoretical formulas of Zhez, Gubkin, Zibel and Chekmarev. The established rules have expanded the concept of relations of characteristic parameters of the geometric deformation zone.