To control the deformation of plate in the steel forming process with heating, the electro-magnetic induction process has been used as the substitute of the flame heating process. However, only few studies have been carried out to analyze the deformation of a workpiece in the induction heating process by using a mathematical model. This is mainly due to the difficulty of modeling the heat flux from the inductor traveling on the conductive plate during the induction process. In this study, the heat flux distribution over a steel plate during the induction process is firstly analyzed by a numerical method under the assumption that the process is in a quasi-stationary state around the inductor and also with the consideration that the heat flux itself greatly depends on the temperature of the workpiece. With the heat flux analyzed, heat flow and thermo-mechanical analyses on the plate are then performed with a commercial FEM program for 34 combinations of heating parameters. The deformations from the analyses and the input heating parameters are then synthesized with a statistical method to produce simplified formulas, which can easily provide the relation between the heating parameters and the deformations. The results obtained from the formulas are in good agreement with results of experiments.

Derivation of simplified formulas to predict deformations of plate in steel forming process with induction heating

At most shipyards, flame bending has been widely used to fabricate curved shells. Since residual deformation of flame bending is produced by thermo-elastic-plastic strains, it is difficult to accurately achieve the desired shape. Therefore, mechanical bending processes such as multi-press forming and multi-point press forming have become attractive because such processes can accurately control the desired shape. Springback is one of the major problems associated with mechanical bending. When the pressing tools are removed after the loading stage, the workpiece springs back due to the elastic recovery and the shape deviation needs to be compensated. The tools of the press forming process therefore need to be changed in order for the produced surface to reach the desired shape accurately after springback. Generally, forming tools are designed and constructed to operate through an iterative process in which the die and the pistons are adjusted to compensate for springback after a pressing operation. Such adjustments require significant time and effort. Therefore, the present study investigates not only how to simulate springback deformation, but also the degree of adjustment required to the stroke of pistons in multi-press forming. Finite Element Analysis (FEA) of thick metal forming and an iterative displacement adjustment algorithm are integrated for practical application. Shape deviations between the design surface and the deformed plate are minimized to reach the desired shape.

Springback adjustment for multi-point forming of thick plates in shipbuilding

In engineering, the bending deformations of thin-walled tubes mostly are under three-point loading. However, for the dual rectangle thin-walled tube (DRTWT), the theoretical prediction of the three-point bending collapse is still an unsolved problem. In this paper, the three-point bending collapse of the DRTWT is innovatively investigated using theoretical prediction and experimental verification. The global energy equilibrium theory is applied to derive the bending characteristic of the DRTWT. It is assumed that all the bending energy is absorbed and distributed along the hinge lines and in the toroidal surfaces during the bending collapse. The analytical results show good agreement with the experimental results. Finally, a simplified bumper structure of automobile is created by using beam elements and spring elements with the derived bending characteristics, which can effectively replace the detailed finite element model (FEM) to accelerate the crashworthiness design of automotive structure at the conceptual design stage.

Bending collapse of dual rectangle thin-walled tubes for conceptual design

The steel-forming process in shipyards is considered an important stage with respect to productivity and precision of curved plates. The induction heating process has been of interest to steel formation because the power and its distribution are easier to control and reproduce. Besides, induction heating equipment can be easily integrated with a robotic system for automation. The heating process usually utilizes line heating or triangle heating methods to form hull plates. Even though a number of studies on the line heating method have been performed, there have been few studies on the triangle heating method. In this study, using a simplified elasto-plastic model and laminated plate theory, an analytic means of predicting the bending deformation in triangle heating of steel plates is derived. For the purpose of this, the induction heating process is modeled in advance, with numerical heat flux and heat flow analyses to determine the plastic region. The plastic region is considered as an inclusion that has eigenstrains in the laminated plate. The analytic solution is applied to predict deformations to verify its exactness. The results of the analytic solution are quite good compared with those of the triangle heating experiment, revealing the effectiveness of the analytic solution.

Analysis of Bending Deformation in Triangle Heating of Steel Plates with Induction Heating Process Using Laminated Plate Theory

Triangle heating technique using a gas flame is used to deform steel plate in ship construction. However, in the flame heating process, the heat source is often difficult to control and parts cannot be deformed efficiently. In this study, a numerical model is developed to study the triangle heating technique with the more controllable heat source of high-frequency induction heating and to analyze the deformation of steel plate in the heating process. To simplify the many complex trajectories of the triangle heating technique, a rotational path of inductor is suggested and then a 2-dimensional circular heat input model is proposed. The heat flow and transverse shrinkage in steel plate during triangle heating with the induction heat are analyzed. The results of the analyses are compared with those of experiments to show the good agreement. The heat source and thermo-mechanical analysis models proposed in this study were effective and efficient for simulating the triangle heating technique in the forming of steel plate in shipbuilding.

Analysis of triangle heating technique using high frequency induction heating in forming process of steel plate

In this study, we developed an analysis method of plate forming by induction heating and verified the effectiveness of the present method through a series of experiments. The phenomena of induction heating is a 3-D transient problem coupled with electromagnetic, heat transfer, and elastoplastic large-deformation analyses. To solve the problem, we suggest a proper model and an integrated system. Using the present analysis model, we can estimate the plate deformation in heating without experiments and simulate the plate bending process of induction heating. A series of induction heating experiments was carried out with various heating conditions such as plate thickness, heat speed, and input power. We measured the transient thermal distribution and final configuration of the plates, and acquired useful data to identify the characteristics of the high-frequency induction heating and for comparison with the analysis results.

Prediction of Plate Bending by High-Frequency Induction Heating

The inherent strain method is known to be very effective in predicting the plate deformation by line heating. Traditionally the inherent strain regions have been determined from the temperature distribution and the phase transformation regions(Ac3) of welding experiments. Since the phenomena of line heating are similar to those of welding, the experimental results under the same welding conditions have been applied directly to line heating analysis. The results cannot, however, reflect the effect of heating pattern and plate thickness. Besides, water-cooling in the actual heating process can alter the steel`s phase to martensite and shear plastic deformation occurs during the transformation. In this study, the experimental measurement of temperature distribution was substituted with a transient heat transfer analysis using FEM so that we could obtain the temperature distribution according to heat flux models of the heating pass. In order to consider plastic strains occurring additionally under phase transformation, inherent strain regions were assumed to be limited to the eutectoid temperature(Ac1). Using the regions, plate deformations could be predicted to validate our method and the results were in good agreement with the experimental ones

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Determination of Inherent Strain Regions to Estimate Plate Deformation by Line Heating

Line heating is a method widely used in forming ship hull surface. From the viewpoint of mechanics it is large deformation thermal elasto-plastic problem of arbitrary shaped plate. Many researches have been carried out to resolve this problem. Especially, Jang et al.[1] proposed a simplified thermal elasto-plastic analysis method to predict effectively the deformation of plate due to line heating. In this paper, we improved the method of Jang et al.[1] by considering tension yielding in temperature decreasing stage and verified with experimental results. FEA program using MITC4 degenerated shell element was made to deal with elastic large deformation problem. The newly proposed method can be used in the simulation and control of forming hull surface for higher productivity with simplicity and efficiency.

Realtime Simulation of Deformation due to Line Heating for Automatic Hull Forming System

As the ship hull is a compound-curved structure, plate bending process is indispensible. The process includes press bending process for forming major 1st curvature and heating process for forming the rest curvature. Especially the heating process that is above 50 percents of entire bending work is carried out exclusively by skillful workers. Many researches have been made to automate the heating process but most of these are about line heating process and researches for triangle heating process are rare. This study is a fundamental study to develop a efficient analysis method for triangle heating and focused on clarifying the deformation characteristics of plate by triangle heating. In this paper, we carried out heating experiments and analysed the deformation characteristics of plate to explain the deformation characteristics of plates rationally by showing the phase transformed high temperature region. Also we investigated the heating effect on the hull material properties by mechanical tests.

An Experimental Study of Characteristics of Plate Deformation by Heating Process

The inherent strain method is known to be very efficient in predicting the deformation of steel plate by line heating. However, in the actual line heating process in shipyard, the rapid quenching changes the phase of steel. In this study, In order to consider additional effects under phase transformation, inherent strain regions were assumed to expand. Also, when calculating inherent strain, material properties of steel in heating and cooling are applied differently considering phase transformation. In this process, a new method which can reflect thermal volume expansion of martensite is suggested.8y the suggested method, it was possible to predict the plate deformations by line heating more precisely.Ā᐀會Ā᐀ﶖ⨀ᡰ쾴ഀĀ저會Ā저㡆ﶖ⨀쾴Ā᐀會Ā᐀遆ﶖ⨀碋쾴Ā᐀會Ā᐀ﶖ⨀⁭쾴瀀ꀏ會Ā䁇ﶖ⨀끰쾴Ā᐀會Ā᐀顇ﶖ⨀䡱쾴Ā㰀會Ā㰀ﶖ⨀쾴Ā㈀會Ā㈀䡈ﶖ⨀硲쾴Ā᐀會Ā᐀ꁈﶖ⨀쾴Ā᐀會Ā᐀ﶖ⨀ꡳ쾴Ā저會Ā저偉ﶖ⨀偮쾴Ā저會Ā저ꡉﶖ⨀쾴Ā저會Ā저Jﶖ⨀聯쾴Ā저會Ā저塊ﶖ⨀ႌ쾴؀Ā؀會Ā؀끊ﶖ⨀衬쾴䤀Ā切會Ā切ࡋﶖ⨀롭쾴Ā搀

Chang-Doo Jang

Papers

Prediction of Plate Bending by High-Frequency Induction Heating

Determination of Inherent Strain Regions to Estimate Plate Deformation by Line Heating

Realtime Simulation of Deformation due to Line Heating for Automatic Hull Forming System

An Experimental Study of Characteristics of Plate Deformation by Heating Process

Developed Inherent Strain Method Considering Phase Transformation of Mild Steel in Line Heating