Rolling control method for metal strip, rolling control apparatus, and manufacturing method for rolled metal strip

A rolling control method comprising:

• under conditions in which out-of-plane deformation of a metal strip is restrained, finding a provisional rolling load difference distribution, which is a distribution of differences in rolling load in a strip width direction of the metal strip during rolling under specific rolling conditions, and finding a provisional elongation strain difference distribution, which is a distribution of differences in the strip width direction in elongation strain along a rolling direction of the metal strip during rolling, by using an up-down asymmetrical model that permits displacement of a strip-thickness center of the metal strip within a plane of a reference plane, the reference plane being parallel to a strip surface of the metal strip and passing through a center point of a line that joins respective rotational centers of upper and lower rolls, and does not permit displacement of the strip-thickness center of the metal strip outside of the plane of the reference plane;
• finding a critical buckling strain difference distribution, which is a distribution in the strip width direction of differences in a critical strain at which the metal strip will buckle, based on the provisional elongation strain difference distribution, a strip thickness of the metal strip, a strip width of the metal strip, and tension acting on the metal strip at exit from a rolling mill;
• in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution, finding an out-of-plane deformation load difference distribution corresponding to an out-of-plane deformation strain difference distribution, which is a difference between the provisional elongation strain difference distribution and the critical buckling strain difference distribution, from a correlation between the provisional rolling load difference distribution and the provisional elongation strain difference distribution, deriving a new rolling load difference distribution by superimposing the out-of-plane deformation load difference distribution on the provisional rolling load difference distribution, finding a new elongation strain difference distribution based on the new rolling load difference distribution under the assumption that there is a change in a crown ratio of the metal strip, and further finding a new critical buckling strain difference distribution based on the new elongation strain difference distribution, the strip thickness and the strip width of the metal strip, and tension acting on the metal strip at exit from the rolling mill;
• finding a difference between the new elongation strain difference distribution and the new critical buckling strain difference distribution, and finding a true elongation strain difference distribution by adding this difference to the new elongation strain difference distribution;
• and
• rolling the metal strip without changing the specific rolling conditions in cases in which the provisional elongation strain difference distribution does not exceed the critical buckling strain difference distribution, and rolling the metal strip under rolling conditions that are set based on the true elongation strain difference distribution in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution.

A rolling control method comprising:

• under conditions in which out-of-plane deformation of a metal strip is restrained, finding a provisional rolling load difference distribution, which is a distribution of differences in rolling load in a strip width direction of the metal strip during rolling under specific rolling conditions, and finding a provisional elongation strain difference distribution, which is a distribution of differences in the strip width direction in elongation strain along a rolling direction of the metal strip during rolling, by using an up-down asymmetrical model that permits displacement of a strip-thickness center of the metal strip within a plane of a reference plane, the reference plane being parallel to a strip surface of the metal strip and passing through a center point of a line that joins respective rotational centers of upper and lower rolls, and does not permit displacement of the strip-thickness center of the metal strip outside of the plane of the reference plane;
• finding a critical buckling strain difference distribution, which is a distribution in the strip width direction of differences in a critical strain at which the metal strip will buckle, based on the provisional elongation strain difference distribution, a strip thickness of the metal strip, a strip width of the metal strip, and tension acting on the metal strip at exit from a rolling mill;
• in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution, finding a critical buckling load difference distribution, which is a rolling load difference distribution corresponding to the critical buckling strain difference distribution, from a correlation between the provisional rolling load difference distribution and the provisional elongation strain difference distribution, finding a difference between the provisional rolling load difference distribution and the critical buckling load difference distribution, and finding a true elongation strain difference distribution by adding a strain difference distribution, corresponding to the difference, to the provisional elongation strain difference distribution under the assumption that there is no crown ratio change in the metal strip between exit from and entry to the rolling mill;
• and
• rolling the metal strip without changing the specific rolling conditions in cases in which the provisional elongation strain difference distribution does not exceed the critical buckling strain difference distribution, and rolling the metal strip under rolling conditions that are set based on the true elongation strain difference distribution in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution.

A manufacturing method for a rolled metal strip, the manufacturing method comprising:

• finding a critical buckling strain difference distribution, which is a distribution in a strip width direction of differences in a critical strain at which a metal strip will buckle, based on a strip thickness of the metal strip, a strip width of the metal strip, tension acting on the metal strip at exit from a rolling mill, and a provisional elongation strain difference distribution, which is a distribution of differences in the strip width direction of elongation strain along a rolling direction of the metal strip during rolling under specific rolling conditions, and which is found under conditions in which out-of-plane deformation of a metal strip is restrained by using an up-down asymmetrical model that permits displacement of a strip-thickness center of the metal strip within a plane of a reference plane, the reference plane being parallel to a strip surface of the metal strip and passing through a center point of a line that joins respective rotational centers of upper and lower rolls, and does not permit displacement of the strip-thickness center of the metal strip outside of the plane of the reference plane, and;
• in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution, finding a true elongation strain difference distribution by adding the difference between the provisional elongation strain difference distribution and the critical buckling strain difference distribution to the provisional elongation strain difference distribution;
• and
• rolling the metal strip without changing the rolling conditions in cases in which the provisional elongation strain difference distribution does not exceed the critical buckling strain difference distribution, and rolling the metal strip under rolling conditions set based on the true elongation strain difference distribution in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution.

A rolling controller comprising:

• a computer configured to:
• find a provisional elongation strain difference distribution, which is a distribution of differences in the strip width direction of elongation strain along a rolling direction of the metal strip during rolling, under conditions in which out-of-plane deformation of a metal strip is restrained by using an up-down asymmetrical model that permits displacement of a strip-thickness center of the metal strip within a plane of a reference plane, the reference plane being parallel to a strip surface of the metal strip and passing through a center point of a line that joins respective rotational centers of upper and lower rolls, and does not permit displacement of the strip-thickness center of the metal strip outside of the plane of the reference plane;
• find a critical buckling strain difference distribution, which is a distribution in a strip width direction of differences in a critical strain at which a metal strip will buckle, based on a strip thickness of the metal strip, a strip width of the metal strip, tension acting on the metal strip at exit from a rolling mill, and the provisional elongation strain difference distribution,
• in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution, find a true elongation strain difference distribution by adding the difference between the provisional elongation strain difference distribution and the critical buckling strain difference distribution to the provisional elongation strain difference distribution;
• and
• roll the metal strip, without changing the specific rolling conditions, in cases in which the provisional elongation strain difference distribution does not exceed the critical buckling strain difference distribution, and roll the metal strip under rolling conditions that are set based on the true elongation strain difference distribution in cases in which the provisional elongation strain difference distribution exceeds the critical buckling strain difference distribution.