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To analyze and solve the problem of single-side long edge of hot rolled strip in certain domestic factory, the asymmetrical deformation of rolls and strip in asymmetrical stiffness mill stand based on slit beam model, the strip profile and rolling force distribution at the exit of asymmetric stiffness stand mill were calculated using influence function method. Considering the character of in-site equipment and technology, a scheme of adjusting load distribution in finishing mill was made and the experiment was applied. Comparison of strip profile between new load distribution and the old one shows that the method can solve single-side long edge problem well.

Strip shape including profile and flatness of hot rolled strip is a difficult problem involving extensive and complex influence factors. There are still many unsolved strip shape problems left for the technicians in site, although long-term exploration and experiment have been made. Flatness problem of thin gauge strip is the most difficult one. As the current theory of shape control is proposed under conditions of axial symmetry or point symmetry [1-4] on one side, on the other side the single-side shape problems are lack of theoretical foundation, especially for thin strip, eventually the quality of strip shape is seriously affected. However the steel shape control mechanism for this can not build based on the theory under symmetry condition. In a certain domestic factory, the single-side long edge problem was serious. In order to solve this problem it is necessary to analyze the impact factors on single-side long edge. Therefore, improving the shape control quality has important theoretical and practical value.

The unit of strip shape which is called I Unit was proposed by the Alcan Aluminium Co., defined as the relative length difference between the longest and the shortest longitudinal section in horizontal direction. One I unit is equivalent to the relative length difference is 10^{–5}, as given by Equation (1). I unit is currently widely used to measure the shape of strip, as well as the middle section of the strip is normally used to replace the original definition of the shortest fiber longitudinal section, to make it easier to shape representation and measurement.

where, is the longitudinal stretch difference, mm. is the length of the shortest section, mm.

Strip shape problems present as center wave, edge wave, single-side long edge, side buckle, near-edge buckle, dual buckle and center buckle. When the buckle or wave present in appearance, the internal stress is distributed heterogeneous.

When the uneven distribution of internal stress is sufficient to show the appearance of wave shape, the shape became manifest. When the non-uniform distribution of internal stress does not affect the strip's appearance, a latent wave shape will exist. Long edge wave is a kind of manifest shape existing in the operation or performance of the drive side of the strip as the wave-shaped, while the central and the other side of the strip are straight. The performance of unilateral external waves and the internal stress distribution are shown in

Just as the profile and flatness meter are used for on-line measurement, the concept of steepness is used to express flatness for off-line measurement. The steepness is the ratio of peak-to-peak amplitude and the wave length of a sinusoidal wave, which is given by (2) [

where, is the steepness, %. is the peak-to-peak amplitude. is the wave length.

The reason for single-sidelong wave is that the elongation of one side is larger than the center and other side of the strip, the loose side is limited by geometric condition, then the wave is produced. The reasons which produce non-uniform elongation are complex, such as non-uniform temperature of strip across width, the shape problem of slab, strip off-tracking and plant administration. The wedge of slab and asymmetrical stiffness of mill stand sides may cause single-side long wave and hard to be eliminated by management tool.

The strip and slab wedge before rolling mill stands are hard to be measured. The strip thickness distributions across inter-stand strip width were obtained through an experimental test implemented in certain factory, which are presented in

difference of thickness between both sides of the strip decrease along with mill stand number increasing from F1 stand to F6 stand, with wedge of slab existing.

Single-side long edge is the significant share of strip shape problems, and is hard to be resolved. The strip setup model was bought from a worldwide famous company, the setup strategy is available, and the physical process was described by mathematic model accuracy in detail.

To analyze the reason of single-side long edge, the stiffness of both operation and driving side of mill stand was measured. The data shows that the difference is large enough and should not be eliminated. The difference of mill stand stiffness of both sides can excess 20kN/mm as illustrated in

The stiffness of mill stand can be described as follows: the rolling force increase for unit change of roll gap, which is denoted as the following formula (3).

where, is the disturbance of rolling force, is the according change of roll gap.

The stiffness of mill stand is a function of rolling force and mill stand spring, if the rolling force and according mill stand spring are measured and logged, the spring curve of stand mill can be obtained by fitting method, the stiffness of mill stand can be derived by using interpolative calculation. The asymmetric character of mill stand stiffness is produced not only by the reasons of mill stand itself, but also the stiffness of roll series. The maximum value of mill stand stiffness difference occurs in different stand during multi-time measurements, this shows that the roll series stiffness difference contributes much to the stiffness asymmetric in this factory. Since the mill stands of this factory were built early, as well as the rolls and roll bearing are not exclusively used for

special mill stand, the asymmetrical stiffness can not be eliminated thoroughly, it is necessary to find a way to overcome it and to avoid the single-side long edge produced by it.

The forces loaded on rolls include rolling force, roll bending force and force between work roll and backup roll. While the mill is symmetric about the middle-span of rolls, the load distribution is illustrated in

To analyze lateral distribution of the load distribution and thickness, the effect function method was adopted to construct the model of roll elastic deformation. The effect function method can be denoted as follows: the concept of influence function was induced from the Mathematic Physics, the influence function of work roll deflection effect rate and backup roll effect rate were derived based on the influence function theory. The rolls, load and lateral deformation of roll were scattered with the same elements arrangement away axial direction of work roll. Firstly, the deformation of elements produced by according load was calculated, then, all the deformation of elements was added with the whole load applied, therefore, the deformation of all the elements was calculated. As a result, the distribution of strip thickness in lateral direction can be obtained.

The method of elements’ numbers layout of workpiece and roll are denoted as

rolling force, roll pressure, the deflection of work roll and backup roll, and the strip thickness lateral distribution are scattered by the numbers distribution.

To analyze the deformation of rolls, distribution of force and rolled strip profile, a calculation was made by using a software coded for asymmetrical deformation of roll series [8-10]. The calculation was based on engineering log data gathered in site, due to the F3 mill stand, which has serious asymmetrical stiffness characteristic. For the calculation, supposing that the stiffness of driving side of mill stand is 620 t/mm and the stiffness of operation side is 600 t/mm ~ 620 t/mm (2 t/mm as step length), the rolling force distribution in lateral direction was obtained as shown in

As shown in