Analytical method for use in optimizing dimensional quality in hot and cold rollling mills

A device for rolling metal strip, said device comprising:

• a strip-conveying member;
• a plurality of rollers cooperative with said strip-conveying member such that upon passage of said metal strip along said strip-conveying member between said plurality of rollers, at least one surface dimension of said metal strip is modified;
• at least one actuator configured to arrange said plurality of rollers relative to one another;
• and
• a controller in signal communication with said at least one actuator, said controller configured such that upon generation of a set of displacement values associated with at least one of said profile and flatness values corresponding to said modified at least one surface dimension, said controller instructs said at least one actuator to arrange said plurality of rollers to such that a deviation from a desired modified surface dimension is reduced without an appreciable change in the speed with which said metal strip is passed through said plurality of rollers, said controller comprising an arithmetic logic unit that is configured to achieve said generation of a set of displacement values by modeling contact between said metal strip and said plurality of rollers as a combination beam elements and continuous elastic foundations coupled between said beam elements.

A method of rolling metal strip, said method comprising:

• passing a metal strip through a rolling mill such that it changes from a first state to a second state that is different from said first state;
• creating a global stiffness-based displacement model that provides a detailed assessment of said second state, said model comprising:
• (a) building a nodal representation of said first state through a combination of beam elements and continuous elastic foundations coupled between said beam elements;
• (b) assigning input parameters to a plurality of nodes within said nodal representation, at least one of said input parameters corresponding to at least one load representative of at least one force imparted to said first state by at least one roller within said rolling mill;
• (c) determining beam Euler-Bernoulli or Timoshenko element shape functions;
• (d) generating a custom element stiffness matrix based upon a summation of a beam element stiffness matrices and a foundation element stiffness matrix;
• (e) assembling global matrices;
• (f) repeating steps (c) through (e) until all said at least a portion of said plurality of nodes have been analyzed;
• and
• (g) solving nodal displacements for said second state;
• and
• outputting a result corresponding to said global stiffness-based displacement model such that said creating said global stiffness-based displacement model does not appreciably change the speed with which said metal strip is changed from said first state to said second state.