During the stamping of complex three-dimensional sheet metal parts, the in-plane compressive stresses created often lead to failure by buckling. These are typically suppressed by binding the material at the periphery to provide a tensile bias. In practice, these biases are difficult to determine, and must be addressed with a combination of a priori analysis and die-making skill. Even then, in-process variations Introduction Three-dimensional sheet forming is a highly productive process capable of forming complex shapes at high rates. However, this productivity comes at the expense of lengthy and costly tooling development. A primary element of this tooling is the "blankholder" which provides the in-plane tensile bias necessary to avoid buckling failure of the sheet caused by in-plane compressive strains. Blankholder design is complicated not only by the difficult contours involved, but also by the critical nature of sheet stability in such bi-axial strain conditions. As a result, sheet-forming production is often disrupted by tensile or compressive instabilities (tearing and wrinkling failures) caused by incorrect blankholder forces. Despite careful design and optimization, variations in lubrication, material properties, and blankholder wear can drive a process into an unstable region of operation. This paper treats the problem of sheet stability as a real-time process control problem. The objective is to keep the margins of process stability within acceptable limits even when the abovementioned disturbances occur. The approach taken here is largely empirical, and is based on the concept of trajectory or signature following. In this method, two accessible measures of process performance (punch force and flange draw-in) are monitored during "optimal" forming conditions. In subsequent forming cycles, the process is forced to follow these trajectories, and the blankholder force is modulated to accomplish real-time tracking. The key issues become robustness of the scheme to the expected variations and the ability to apply the method to general processes. In earlier reports on this work Background Research into the stability of sheet metal forming has concentrated on topics such as material properties, circular grid strain analysis, forming limit diagrams, finite element analysis, strain path corrections, and shape analysis. Below is a brief review of studies involving tearing, buckling, and forming limits, concentrating on those of direct relevance to the conical cup geometry. The frequently used forming limit diagram, developed by Goodwin (1968) and Keeler (1969), is a good indicator of the tearing strains in plane strain, loading. For a given material, these diagrams are developed by using a hemispherical punch stretch test and plotting the circumferential and radial strains
