“…According to the above shape control mechanism, the shape control is actually to continuously control the lateral distribution of roll gap for adjustment of strip metal flow law which is very important to improve the shape control accuracy [1–3,10]. For the large width–thickness ratio cold rolling strip, it must combine the strip metal deformation model with the elastic deformation model of roll system to complete the coupling calculation of the lateral thickness
of strip and the theoretical tensile stress
respectively.
where
is the pre-setting value of initial roll gap,
is the axis displacement of work roll,
is the roll profile of work roll,
is the sum of rigid displacements of the upper backup roll and the lower backup roll,
is the average value of front tensile stress,
is the elastic modulus,
is the Poisson ratio,
,
,
are respectively expressed as strip thicknesses at the entrance and the exit of mill and their average values,
,
are the entrance length of strip and its mean value respectively,
is the lateral displacement of strip, B is the strip width.…”