Demand for three-dimensional (3D) curved sheet metals for the manufacture of the skin structures used
in various industrial fields continues to increase. Three-dimensional curved sheet metals have generally
been manufactured using conventional die forming (CDF) processes, which can ensure forming quality
and productivity. However, they are not economically efficient since they incur the additional production
costs associated with the development and maintenance of the forming tools. For these reasons,
many investigations into alternative flexible forming technologies have been conducted. Flexible forming
technologies requiring only one forming die enable the manufacture of 3D curved components while
simultaneously resolving the limitations of CDF processes. In this paper, a progressive forming process
called “flexibly reconfigurable roll forming” (FRRF), which utilizes adjustable punches and reconfigurable
rollers as forming tools, is discussed, together with its detailed mathematical methodology. Using this
methodology, curved shapes as well as arcs can be created by adopting conic section curves. This method
is superior to existing flexible forming technologies. In this process, the formed shapes are not intuitively
predictable since two-dimensional design lines corresponding to the reconfigurable rollers produce a 3D
curved surface. To alleviate this limitation, a new predictive model for predicting the deformed shapes of
the sheet metal, as derived from the mechanics of plastic deformation considering the law of volume constancy,
is described with detailed techniques using a geometrical relationship. The experimental results
also demonstrate that the predictive model for the FRRF process can be used to successfully ascertain the
deformed shapes of the sheet metal.