Abstract
Many industries such as shipbuilding require steel bending plates in a wide range of radii, thus bending machines are often designed and produced on a custom basis in shipyards. From a design perspective, however, the bending force and the radius of the bending plate as a function of vertical displacement of the upper roller must be known. In this paper, a hybrid numerical–analytical approach is proposed to investigate the three-roller bending process for two plates of steel used in the naval industry. Firstly, the bending process is modeled using the finite element (FE) method and regression models for the bending force as a function of plate thickness and vertical displacement of the upper roller were constructed. Then, based on the findings from FE analysis, using the bent bar theory, two analytical expressions for the bending force were derived. Using geometric and deformation compatibilities, analytical expressions for the vertical displacement of the upper roller as a function of the curvature of the bending plate were also developed. The FE results suggest that the cross section of the plate is practically a plastic hinge in the tangent area of the upper roller and that the deformation compatibilities must be considered in order to estimate the curvature radius of the bending plate using analytical formulations. These results are of practical importance in designing rolling machines to estimate the setting parameters.
Highlights
Cylindrical and conical steel shells are important components used in various engineering applications such as bilge planking as a part of the naval hull, cylindrical tanks, pressure vessels, etc. [1]
The finite element (FE) results suggest that the cross section of the plate is practically a plastic hinge in the tangent area of the upper roller and that the deformation compatibilities must be considered in order to estimate the curvature radius of the bending plate using analytical formulations
The FE results for the bending force as a function of vertical displacement of the upper roller and the sheet thickness are shown in Figure 15 for S235JR and S275JR steels
Summary
Cylindrical and conical steel shells are important components used in various engineering applications such as bilge planking as a part of the naval hull, cylindrical tanks, pressure vessels, etc. [1]. Pandit and Srinivasan presented an explicit numerical approach for three-point bending of a thin elastoplastic beam undergoing large deflection supported on cylindrical rollers with a radius comparable to the deflection [15] Using both analytical and finite element approaches, Zemin et al studied the three-roll bending of a large workpiece using a model based on one dimension beam theory to determine the inner radius displacement and the Abaqus FE model for optimizing the process parameters [16]. Regression models for the bending force as a function of plate thickness and vertical displacement of the upper roller are derived for two types of structural steel commonly used in the shipbuilding industry. The inner radius of the bending plateTwhaesrafoduiunsdoftocubreva2t1u8r.e6o±f t4h.e8bmenmd,in1g58p.l4at±e (2i..e9.,mthme ,raadnidus1o1f7t.6he±ne1u.5trmalmlayfeorr) 3c0anmm, 4b0emdemte,ramnidne5d0 mbamsedveornticthael dgiesopmlaectermic ecnotm, rpeastpibeiclittiyveolfy.the three-roller bending system, shown in Figure 10, as follows: 3. Analytical Modeling of the Three-Roller Bending Process
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