A Method for Three-Dimensional Deformation Predictions in the Rolling of Steel Strips
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FLATNESS control theory is one of the key theories used in strip rolling production. The plastic deformation model of the strips and the elastic deformation model of the rolls are two essential components of the flatness control theory. One of the earliest elastic deformation models that are still widely used today was proposed in the 1930s by Trinks and Hitchcock.[1] Since the 1950s, with the increase of attention to the shape quality of the plates and strips, many related theories and models have been put forward. The elastic deformation calculation methods of the roll system can be divided into three categories: analytical methods, influence function method, and numerical methods. In the 1950s, Saxl[2] investigated the work roll deflection in four-high mills based on the assumption that the work rolls can be regarded as cantilevers fixed in the center. In the 1960s, Stone et al.[3] began to use the Winkler foundation model in the roll deformation investigations. The numerical methods for calculating roll deformation mainly refer to the finite element method and the boundary element method. A new numerical method similar to the influence function method, called the contact element method, was put forward by Yu et al.[4] to predict the strip profile in the rolling with 20-high Sendzimir mills. In recent years, a new analytical
SHAN NIU is with the School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan 250101, China. Contact e-mail: [email protected] Manuscript submitted December 20, 2018.
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flattening model was developed by Xiao et al.[5] based on the boundary integral equation method. The roll deformation calculation based on the influence function method was first proposed by Shohet and Townsend [6] in the 1960s. Through the continuous improvements of many scholars since then, it has become a widely used method today. The three-dimensional (3-D) deformation calculation methods of the rolled piece basically include the classical calculation methods of metal plastic deformation, i.e., mainly include the finite difference method,[7] finite element method,[8] and boundary element method.[9] Among them, the finite element method is widely used in offline simulations. In addition, the strip element method has been proposed exclusively for calculating deformations during the rolling process by Liu et al.[10] Although many integrative models of metal and roll system deformation have been developed, the accuracy of the roll deformation calculation based on the traditional influence function method still needs to be improved.[11] In addition, as using other analytical methods, it is difficult to calculate the influences of some roll structure details on the rolling process, which on occasion might have to be investigated. The time-consuming problem of finite element simulations of the rolling process has not been solved thoroughly at present, to the knowledge of the author, particularly for the cold rolling of comparatively thin and wide strips with cluster mills.
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