January 9, 2007
Energy input at one location in a part during forming is redistributed throughout the part as the forming process advances. The result must be an adequate force transmitted back to the location of target strains and displacements.
Editor's Note: This is the sixth in a series of seven articles that identify and define the need for a new processing theory for the net shape processes (of which draw forming is one) and that explain the general content and configuration that new theory must have.
The first five articles in this series discussed how draw forming (a net shape process) differs from the non-net shape processes (such as machining, assembly, and welding) in the areas of the level II processing functions, metrics, connectivity, geometry, and remoteness.
This article looks at the significance of redistribution of energy and the transformations of the material in space during the forming process.
Sheet metal being pulled across a die radius and simultaneously stretched (see Figure 1) demonstrates the phenomenon of redistribution. The figure shows the three stages of forming:
In a typical stamped part, this process occurs in many places during forming.
The figure also identifies three elements (A, B, and C) within the sheet metal being formed. Each of these elements is a specific volume of material that remains in its location within the sheet but experiences a shape transformation. All other elements in the part are affected equally to A or C, or somewhere between what happens at A and B or between what happens at B and C.
Each element in the sheet metal experiences a changing energy input during the forming process because it's moving. The energy input on the element at one location is redistributed in space as the process advances from one stage to the next, and then different energies are imparted into the same element at its new location.
The net result of all these effects must be an adequate force transmitted back to the location of target strains and displacements.
As the forming process proceeds through each stage, pulling force increases. The pulling force is transferred through the sheet metal from element to element as though the elements were links of a chain. Each element experiences the same force.
However, as the elements rub against the die, a frictional restraining force develops, so the force passed on to the next element is somewhat reduced. Also, elements must bend to conform to the arc shape as they enter the arc of the die, and they must unbend as they leave the arc of the die.
Sometimes additional energy is required to achieve bending or unbending. When that happens, the element will pass along less force than it received. The total force transmitted back to the target conditions must be whatever is required to cause the target strains to happen, so the friction and bending losses must be added to determine the required pulling force.
Element A (red) never touches the die, so the only force it undergoes is the pulling force. (Actually, the forces normal to the plane of Figure 1 also must be considered, but they are ignored here to develop the concept.) If the example is a narrow strip, element A will be strained as though it were in a tensile test before fracture. Element A will thin and stretch as it passes through the forming stages, achieving a maximum thinning and stretching at stage 3. Since element A never touches the die, it transfers all of the pulling force to the next element.
Element B (green) immediately slides into the die radius, but under low pulling force, so it is bent to the shape of the radius while under some tension. Bending under tension causes more stretching than what the pulling force alone would have caused. Element B continues to slide across the die radius, experiencing both friction and stress through its thickness.
The pulling force causes the element to press against the die, which causes the stress through the thickness of the sheet metal. The pulling force increases as the element slides, and because of the increasing pulling force and the increasing stress through the thickness, the element continues to stretch.
Then as the element leaves the die and is again in free space (stage 2), the stress through its thickness disappears, but it straightens (unbends) under the tension of the pulling force, and that straightening (unbending) under tension causes an additional stretching.
The end result is that element B actually is strained more than element A, even though both now experience the same pulling force. The pulling force continues to increase as the process advances to stage 3, but element B is thinner than element A and therefore will experience more straining than element A as both advance to stage 3.
Element C (blue) experiences less pulling force than either elements A or B because friction and bending have reduced the pulling force. As element C slides along the flat die between stages 1 and 2, it is stretched like it would be in a tensile test (provided it is a narrow strip), but it is strained less than either element A or B.
Element C is neither bent nor unbent, and it has no stress imposed through the thickness because the die is flat. Because the pulling force on element C is less than on element A, element C experiences less straining at stage 2 than does element A. Element B is strained the most at stage 2.
As the process continues through to stage 3, element C experiences the same things as did element B between stages 1 and 2. However, element C experiences greater straining both from bending and the stress through its thickness since the pulling force is greater than what it was for element B.
The result is that element C, which has just moved off the die into free space, will have the most stretching and thinning of all the elements in the sheet metal, even though at that instant it has applied to it the same pulling force as elements A and B.
A new element, D, will have moved up to the beginning of the die radius. It will not have entered the die radius at stage 3—the end of the forming process—but before the die starts to open. That new element D will be strained as though it were in a tensile test (if the strip is narrow) but less than element A since the force on it is less. The resulting strains are diagramed qualitatively in Figure 2.
The effects of the redistributions must be taken into account when calculating the energy-affecting elements of the draw die.
The impact of redistribution on die design activity is quite different than on the creation of the chip being peeled off the workpiece in the non-net shape process of lathe turning. Whatever is happening inside the chip in the lathe turning example is only a function of the material being shaped, the cutting tool material, and the cutting tool geometry. The final shape of the workpiece has no effect whatsoever and is not considered when determining the shape of the cutting tool.
In draw forming, however, like the analogous situations in the other net shape processes, the impact of the final part shape on the redistributions and the effects of those redistributions on the forming process must be part of the calculations determining the design of the energy-affecting elements of the die.
Also significant is that the redistributions usually are different at various locations throughout the part, and addenda and the impact of each location must be calculated and accommodated.
The significance of the redistribution is one of several reasons that draw forming (along with the other net shape processes) must have its own die design and draw forming process theory. Practices and procedures borrowed from the non-net shape processes are not adequate and are not directly transferable.