Method of controlling an edging opening in a rolling mill

A method of controlling an edging opening in a rolling mill including an edging roll having an inlet and a feedforward control for controlling the edging opening followed by a horizontal roll and then by a succeeding rolling process for finishing, comprising the steps of

• (i) measuring a width distribution W.sub.0 (X) along the full length of a material to be rolled having a leading end part, a trailing end part and an intermediate part extending between the leading end and a trailing end part and effecting the measuring adjacent to and upstream from the inlet of the edging roll from the leading end to the trailing end,
• (ii) calculating an optimum edging opening variation quantity distribution .DELTA.W.sub.1 (x) from a predetermined pass schedule, a target width deviation distribution .DELTA.W.sub.3 (x) of the rolled material required at an outlet of the rolling mill and the width distribution W.sub.0 (x) of the rolled material measured at the inlet of the edging roll, and
• (iii) supplying the optimum edging opening variation quantity distribution to an edging opening setting unit for the feedforward control,
• said pass schedule for calculating the optimum edging opening variation quantity distribution .DELTA.W.sub.1 (x) includes a target plate width value W.sub.0 at the inlet, an edging opening setting value W.sub.1, a plate width W.sub.2 on the supposition that only dogbones or swelling at the ends of the plate produced in the edging rolling process are horizontally rolled, and a plate width W.sub.3 after horizontal rolling,
• said step of calculating said optimum edging opening variation quantity distribution .DELTA.W.sub.3 (x) comprises steps of:
• calculating a width deviation distribution in a moving direction of the plate at an irregular deformation portion produced in the rolling process and a corresponding length of the plate in the moving direction,
• calculating a plate width adjustment efficiency on the basis of the calculated values of the width deviation distribution and the length of the plate in the moving direction, and
• calculating an optimum edging opening variation distribution using the plate width adjustment efficiency,
• said step of calculating the width deviation distribution in the moving direction of the plate at the irregular deformation portion produced in the rolling process includes the following calculations:
• when edging rolling and dogbone rolling are carried out, a width deviation .DELTA.W.sub.T'V produced at the leading edge of the plate and a width deviation .DELTA.W.sub.B'V produced at the trailing edge of the plate are given by ##EQU7## when horizontal rolling is carried out, a width deviation distribution .DELTA.W.sub.T'H (x) produced at the leading edge of the plate and a width deviation distribution .DELTA.W.sub.B'H (x) produced at the trailing edge of the plate are given by ##EQU8## where K.sub.T2, K.sub.B2, K.sub.T4, K.sub.B4 :
• constant determined by plate material
• C.sub.T, C.sub.B :
• constant
• W.sub.0 :
• plate width at inlet before rolling
• W.sub.1 :
• edging opening setting quantity
• t.sub.0 :
• plate width
• L.sub.T, L.sub.B :
• length of width reduction portion
• .DELTA.B.sub.E :
• width restoration quantity of regular deformation portion by dogbone rolling
• x:
• distance from leading edge of plate
• l.sub.T, l.sub.B :
• length of width increasing portion
• .zeta.:
• constant
• r.sub.H :
• horizontal rolling ratio
• g(r.sub.H):
• function having variable of horizontal rolling ratio r.sub.H,
• said step of calculating the length in the moving direction of the plate at the irregular deformation portion produced in the rolling process includes the following calculations:
• lengths L.sub.T and L.sub.B of the width reduction portion and lengths l.sub.T and l.sub.B of the width increasing portion at the irregular deformation portion are calculated in accordance with the following equations:
• ##EQU9## where K.sub.T1, K.sub.B1, K.sub.T3, K.sub.B3 :
• constant determined by plate material a.sub.T1, a.sub.T2, a.sub.B1, a.sub.B2, e.sub.T, .gamma., k, .delta., .beta..sub.T, .beta..sub.B :
• constant
• ld:
• roll contact projection length ##EQU10## D.sub.E :
• diameter of edging roll, said step of calculating the plate width adjustment efficiency on the basis of the calculated values of the width deviation distribution and the length in the moving direction of the plate includes the following calculations:
• plate width adjustment efficiency distribution .eta..sub.T (x) and .eta.(x) at the leading edge and the trailing edge of the plate, respectively, are calculated by the following equations from the above .DELTA.W.sub.T, V and .DELTA.W.sub.B'V :
• ##EQU11## where f(x) is a distribution curve of the width reduction upon edging and dogbone rolling, and .eta..sub.0 is plate width adjustment efficiency at regular deformation portion.