Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering ConferenceShanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical Study on Shrinkage Control Method in Sail Plate Forming by Line HeatingHan Zhang, Yao Zhao, Zhen Shuai Wei
School of Naval Architecture & Ocean Engineering, Huazhong University of Science and Technology
Wuhan, Hubei, China

processing parameters is established. Then find the realization methodof variable strain along the heating line and the strain variation rule.
Finally, the shrinkage is correlated with the strain value to select thecorresponding processing parameters.

ABSTRACT
For modern shipbuilding, line heating is widely employed as aneffective method to form complex double-curvature plates, and theshrinkage control method is the key to form the target plate. Taking sailplate forming as an example, heating simulation is realized by thermal
elastic-plastic FEM, path planning of sail plate is completed according
to the heating line layout of shipyard. Finally, variable shrinkage
distribution is realized by loading of different length heating lines
which are controlled by the in-plane strain, so as to realize the constantcurvature bending deformation of the steel plate under the given
shrinkage condition.

THERMAL-ELASTIC-PLASTIC FEM ANALYSIS
Strain Distribution Characteristics
The numerical calculation model of the steel plate is shown in Fig. 1.
The dimensions of the steel plate are: L(Length)=2 m, B(Breadth)=1 m,h(thickness)=0.02 m. The center diameter of the circular coil is 0.1 m,
heating through the upper surface, and the lower surface is globallycooled by water. The maximum heating temperature of the uppersurface is lower than 850 ℃, and the heating temperature of the lower
surface is lower than 300 ℃. The calculation method adopts thermal
elastic-plastic finite element calculation. The validity of this calculation
method has been verified in my related paper (Zhang H, 2021), and thematerial properties refer to relevant papers (Hu CC, 2020). The element
size of the finite element model is 0.01m×0.01m, and the height
direction is divided into five layers of integration points, with a total of
20,000 rectangular elements and 20,301 nodes. The heat source model
adopts the Gaussian heat source model, and the water cooling model isrealized by changing the heat transfer coefficient of the lower surfaceof the steel plate (Vega A, 2011).

KEY WORDS: Sail Plate Forming; Induction Coil Heating;
Shrinkage

INTRODUCTION
In the shipyard, the processing of ship plate depends on thecombination of cold processing and hot processing. The typical doublecurvature plates include sail plates and saddle plates, and the forming
process of sail plates is mainly discussed in this paper. In recent years,
the application of induction coil heating in ship plate forming has been
widely studied. Hu CC (2017) of Huazhong University of Science andTechnology proposed the cold and heat integration automatic line
forming machine. First, the main curvature cylindrical plate is formedby concave and convex rollers, and then the target shape plate isformed by hot processing according to the in-plane and out-of-planestrain.
During the hot forming process of the sail plate from the cylindricalplate, the main deformation characteristics are reflected in theshrinkage and the bending degree. The fibers of the slats show different
shrinkage at different positions, the maximum shrinkage occurs at theedge of the plate, and the smaller the shrinkage occurs at the center ofthe plate. In the actual heating line layout, the heating line is usuallyarranged at the edge of the plate without passing through the center ofthe plate. The closer the heating line is to the edge, the greater the heat
input is, so the shrinkage of the fiber at the edge is larger (UEDA Y,1994).
In sail plate forming process, how to control the shrinkage of the edge
area with parameters collocation is an urgent problem that needs to besolved. It is complex to directly establish the relation of shrinkage ofslats and processing parameters, so the strain value is seen as
intermediate parameter, the relationship between the strain and theFig. 1 Line heating model
The deformation of the steel plate can be reflected by the distribution of
in-plane and out-of-plane strains. The in-plane strain  m reflects theshrinkage of the slat fibers, and the out-of-plane strain  b reflects thebending degree of the steel plate. Under the heating condition of thisheat source, the width of the plastic strain zone is about 0.15m. The
section strain sec− strain is defined as the average strain value in the2910