Method of measuring and compensating roll eccentricity of a rolling mill

In a rolling mill having a top work roll backed with a top backup roller and a bottom work roll backed with a bottom backup roller for rolling a plate, a method of correcting thickness variations of the plate when the plate is being rolled through a gap between the top work roll and the bottom work roll, said method comprising:

• an off-line eccentricity identification method which is performed when there is no plate rolling through the mill and with the top work roll and the bottom work roll in tight contact, said off-line eccentricity identification method determining the eccentricity values of N first points which equally divide a circumference of the top backup roll and N second points which equally divide a circumference of the bottom backup roll, N being a pre-determined integer number;
• and
• an on-line eccentricity compensation method which is performed with a plate being rolled through a gap between the work rolls, said on-line eccentricity compensation method comprising:
• a. determining eccentricity values of a point on the circumference of the top backup roll and a point on the circumference on the bottom backup roll which are in contact with the work rollers by interpolating known eccentricity values determined in said off-line eccentricity identification method;
• b. determining an eccentricity compensation value in accordance with the eccentricity values determined in step a;
• c. converting said eccentricity compensation value of step b into a controlling signal for controlling a position of at least one of the backup rolls relative to the other backup rolls to compensate eccentricities thereof;
• and
• d. deciding if rolling is completed, and if not, repeating steps a through d thereof until the decision of step d is positive, and terminating rolling, and
• wherein said off-line eccentricity identification method determines eccentricity values of said N first points and said N second points by performing 2N times of a measurement utilizing a relationship of:
• E.sub.x +E.sub.y =(1/M)*F,
• where;
• E.sub.x is an eccentricity value of a point x at the circumference of the top backup roll in contact with the top work roll,
• E.sub.y is an eccentricity value of a point y at the circumference of the bottom backup roll in contact with the bottom work roll,
• M is the mill modulus, and
• F is the variation in the rolling force caused by the eccentricity;
• the data from the 2N times of the measurement forming a matrix equation of A'X=Y', where;
• A' is a 2N by 2N square matrix;
• X is a 2N by 1 vector, and
• Y' is a 2N by 1 vector, and
• eccentricity values of said N first points and said N second points being determined by solving the matrix equation for X=A.sup.`-1`.