The Science of Forming

Every day human laws are broken—often through ignorance and sometimes by intent. Even if caught, having to pay the consequences can be sporadic, random and rare. In contrast, the laws of nature, often personified as Mother Nature, are really the laws of physics that detail the forces that hold our universe together. Actions not consistent with the laws of nature will result in immediate consequences, usually nature’s corrective actions that are independent of your design intensions. The only way you can violate the laws of nature is with the immediate payment of a penalty. Numerous examples of how laws of nature interfere with metalforming are available.

One key law states: the lowest-energy mode of forming will prevail unless an extra quantity of external energy (the penalty) enters the system. The simplest example is a three-point air bend (Fig. 1A). The goal is to bend sheetmetal to the shape of the punch. Assume in Fig. 1A that this requires seven elements of the sheet to change from a flat blank to the curvature of the punch. Each element must create both elastic and plastic strains to achieve this shape change.

Fig. 1—Schematic A shows complete bend contact with the punch, with seven segments contributing to the bend. Schematic B shows a hinge deformation in only one or two segments, causing kinking with a smaller bend radius.

For higher-strength or thinner sheetmetal, a lower-energy form of deformation over the punch is a localized hinge effect called kinking (Fig. 1B). Kinking can be detected easily by measuring the inner radius of the bend and comparing it to the outer radius of the punch. Two corrective methods prevent kinking, but each requires extra energy (paying the penalty). One is increasing the back tension (F) at the ends of the blank to force conformation of the sheetmetal to the punch contour. Another is applying a stiff rubber pad to the area of the blank that kinks. A strong spring or nitrogen cylinder attached to the pad provides the extra energy to force the blank to remain in contact with the punch.

The above bending example was a tension-compression deformation mode. Preventing buckles in sheetmetal when formed only in the compressive mode is more challenging.

The most common example is the outer portion of circular blank moving radially toward the die radius to form a cylindrical cup. Each element of the blank under the blankholder compresses in the circumferential direction as the circumference decreases in length. However, instead of all the elements in the blank uniformly decreasing in circumferential length and increasing in thickness, the sheetmetal tries to form a series of buckles. That is the deformation mode of least energy. Here the extra energy (penalty) inserted into the forming mode is the increased blank-holder load.

This blankholder problem becomes more difficult to solve when forming higher-strength materials. Weight-reduction schemes usually provide for an increased strength accompanied by a corresponding reduction in blank thickness. Both higher strength and reduced thickness drive the blank toward buckles in the blankholder area. Thus, one needs to use significantly higher blank-holder forces—a double penalty when overcoming the laws of nature.

Now imagine trying to make a part designed like a truncated cone. Depending on the difference in diameter of the punch and the die ring, the

Fig. 2—Schematic shows the theoretical flow around a square draw bead (dashed line) and the actual flow (solid line) determined by videotaping. (Draw-bead assembly not to scale.)

compressive forming without any support through the blank thickness generates a large portion of the wall. Because of the laws of nature, this part often is impossible to make with higher-strength sheetmetal in thinner gauges. Attempts to eliminate the vertical wall buckles by greatly increased blankholder force will result in tearing the top of the truncated cone because of the high stress now concentrated on the punch radius.

A final example of deformation taking the least energy path does not deal with kinking or buckling. Instead, it describes how sheetmetal will flow though a draw bead along the path of least energy. Assume the die designer uses a flat-bottom bead instead of a round bead because the blank has to undergo four bend/unbend cycles instead of only three. That is the engineering analysis of draw beads based on tangent-to-tangent material flow through the beads (dashed line in Fig. 2). Several years ago, researchers videotaped sheetmetal flowing through various bead configurations. The videos showed that the material took the path of least resistance through the bead system (solid line in Fig. 2). The videos forced rethinking the entire concept of how draw beads work and how much restraining force each geometry creates. The videos are at www.a-sp.org, then Publications, Enhanced Forming Limit Diagrams and finally Bead Wrap Videos.

Sometimes we understand the laws of nature and can work with them. Unfortunately, the draw-bead study showed us that too many times we do not have a clue about the laws causing our latest split, cosmetic defect or other forming problem. MF