Abstract: A new complex warping deformation defects are appeared in the ultra-thin strip steel (tin plating) cold-rolled production. This paper focus on this issue, we name it reverse C-warped defect through the modal analysis of its warping displacement and comparing with some common simple warping defects such as C-warped and L-warped defect. Through mechanical modeling and simulation calculation, we propose the forming mechanism of reverse C-warped defect, and point out that it is caused by the difference of longitudinal extension along the thickness direction on the cross section of strip steel and this difference is unevenly distributed along the width direction of strip steel. Based on the research of C-warped defect, through establishing the mechanical model of the reverse C-warped deformation caused by initial strain on the strip steel, we establish the analytical model and the spline finite element model of the reverse C-warped deformation and get the corresponding algorithm. The calculation results from two methods can checked with each other and are consistent with the actual reverse C-warped defect in manufacturing procedure. This paper reveals the laws of C-warped deformation and the factors that influence them, and get the distribution (along the width direction of strip steel) of the difference between the longitudinal extension along the thickness direction of the strip steel and C-warped defect. When the difference distribution is uniform or symmetric parabolic along the width direction of strip steel, the C-warped defect with different curvature and height will be generated accordingly; when the difference distribution is linear or monotone nonlinear along the width direction of strip steel, the reverse C-warped defect with different curvature and height will be generated accordingly; and when the difference distribution is a more complex curve along the width direction of strip steel, the more complicated C-warped defect will be generated accordingly. Three kinds of symmetric periodic C-warped defect models are presented, resulting from the typical symmetric complex difference distribution. In this paper the reverse C-warped defect in industry and the C-warped defect from simulation prediction will combine with the strip steel flat defects from our previous research, to propose a new classification.

Key words: complex warping, periodic C-warped, reverse C-warped, steel flat defects