Practice of Improving Roll Deformation Theory in Strip Rolling Process Based on Boundary Integral Equation Method
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trip rolling process, the strip-shape control technology plays a very important role for improving the product quality. Roll deformation theory is the core part of shape control theories, which includes rolls flattening and rolls bending deformation. The rolls bending can be obtained by the influence function method, which is accurate enough for engineering application. The rolls flattening account for a large proportion of the total deformation of the roll and the roll flattening theory is significant for calculation of pressure between rolls, which is important for optimization of roll geometrical parameters and roll camber design. Finite element method (FEM) can be used to calculate roll deformation accurately, but due to its time-consuming, it is difficult for on-line calculation. Compared to FEM, the analytical model can greatly shorten the calculation and calculation accuracy is acceptable. Foppl formula[1] and semi-infinite body model[2] are the most popular analytical models in the roll flattening calculation. Yu et al.[3] studied the strip edge drop for Sendzimir mill based on analytical models. Xiao et al.[4] simulated the strip rolling process of PC mill coupled with analytical models of rolls deformation and FEM. Foppl formula is derived based on the assumption of half-plane theory and ignores the effect of the force beyond the contact application area and stress along the axial direction, which leads to the low-precision of ZHENGWEN YUAN, Ph.D. Student, HONG XIAO, Professor and Dean, and HONGBIAO XIE, Associate Professor are with the National Engineering Research Council for Equipment and Technology of Cold Strip Rolling and with the College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, P.R. China. Contact e-mail: [email protected] Manuscript submitted December 31, 2012. Article published online November 26, 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A
Foppl formula shown as Figure 1(b). Semi-infinite body model is derived based on Boussinesq solution[5] of the problem that boundary of semi-infinite body is subjected to a single force. In the semi-infinite body model, the effect of shear stress and normal stress along the axial direction is considered. However, it increased the restriction of outside area to the barrel edges shown as Figure 1(c). As the result, the roll flattening calculated by semi-infinite body model has a great deviation from actual situation, especially near the barrel edges as shown in Figure 1. In order to increase the accuracy of the calculation, some improvements have been made in the past years. Berger et al.[6] improved roll flattening predictions by taking the pressure gradients along the roll axis direction and finite roll radii into account. Zhou et al.[7,8] modified the semi-infinite body model by using the flattening result obtained by a three-dimensional FEM. Hacquin et al.[9] proposed a semi-analytical model, which coupled to FEM and analytical model based on Berger’s theory. In order to remove the edge effects of roll barrel, Hacquin et al. added an imaginary dis
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