Abstract
Roll flattening is an important component in the roll stack elastic deformation, which has important influence on controlling of the strip crown and flatness. Foppl formula and semi-infinite body model are the most popular analytical models in the roll flattening calculation. However, the roll flattening calculated by traditional flattening models has a great deviation from actual situation, especially near the barrel edges. Therefore, in order to improve the accuracy of roll flattening, a new model is proposed based on the elastic half plane theory. The calculation formulas of roll flattening are deduced respectively under the assumptions of plane strain and plane stress. Then, the two assumptions are combined through the method of introducing an transition coefficient, and the distribution rules of roll flattening for different rolling force, flattening width, roll length and roll diameter are analyzed by using the FEM analysis software Marc. Regarding the ratio of the length to roll end and the roll diameter as variable to fit the transition coefficient, the new model of roll flattening is established based on the elastic half plane theory. Finally, the transition coefficient is fitted to establish the model. Compared with the traditional models, the new model can effectively improve the calculation deviation in the roll end, which has important significance for accurate simulation of plate shape, especially for the distribution of rolling force between rolls.
Highlights
The flattening between work roll and strip and the flattening between rolls are important components of the important influence on controlling of the strip crown and flatness [1,2,3,4,5,6,7,8,9,10]
For the flattening between work roll and strip, because of the strip width is shorter than the work roll length more the 200 mm and the contact arc length is far less than roll diameter, the work roll can be seen as semi-infinite body and it’s reasonable to use the elastic half space theory [11, 12] for roll flattening
For the flattening between rolls, because of the length of back up roll is almost equal to the work roll, using the semi-infinite body assumption is obviously unreasonable, especially for the shorter one, and the Foppl formula [13] is employed for solving this frequently
Summary
The flattening between work roll and strip and the flattening between rolls are important components of the important influence on controlling of the strip crown and flatness [1,2,3,4,5,6,7,8,9,10]. Jiang et al [19, 20] chosen the semi-infinite body as the roll flattening model and proposed a roll deformation model in cold thin strip rolling with roll edge contact. Tension to the elastic theory [33], the stress component of the roll cross section along the directions of the X axis and Y axis in the rectangular coordinate system can be expressed as: of the classical formulae by comparison of the results from different methods and modified the semi-infinite body model based on FEM. Xiao and Yuan et al [23,24,25,26,27] analyzed the error of semi-infinite body model in roll calculation and proposed an analytical model in flat rolling by boundary integral equation method.
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