Procedure for determining the stress state of a work roll by the boundary-elements method

This article examines a loading scheme for a sheet-mill work roll that places the roll in a plane stress state. This state is completely determined by the stresses in a ring that represents the intersection of the roll’s cross section by a plane which is perpendicular to its axis. As part of preparing data for calculation, the circumferences of the ring are divided into individual elements and the normal and shear stresses acting on these elements are calculated. Formulas are proposed for dividing the arcs that comprise the outer circumference of the ring into discrete sections and determining the average normal and shear stresses for rectilinear boundary elements. Replacing the inner and outer circumferences of the ring by polygons does not violate the conditions required for static equilibrium. An example is given to illustrate preparation of the data and its use in calculations.