Examples of deflected shapes

a b c a A O 1r M p P P B a B a A a O 1r P B B a A a B a O 1r P B a A a B Figure 6.26 Bending line construction for a sheet bent by a horizontal line force for a a rigid, perfectly plastic sheet, b a strain-hardening sheet, and c a sheet having a linear stress–strain relation. curvature of the sheet will be proportional to the height above the line of application of the force. In Figure 6.27, a sheet is bent between two smooth, parallel plates. This is similar to the operation of hemming where the edge of a sheet is bent over itself or another sheet. If we assume that the force is applied at the tangent point and is normal to the plates, then the construction is shown in the diagram. The curvature will vary from zero at the tangent point to a maximum at the nose. In the manufacture of articles such as hose clips, a strip may be bent over a form roll as shown in Figure 6.28. The curvature of the strip should match that of the form roll at the tangent point, i.e. 1ρ B = 1R. If the force to bend the strip is applied by a small roller at A and at the instant shown the strip is horizontal, then the angle of the normal at Bending of sheet 103 MP P P R A B a b O a b 1r Figure 6.27 Bending a strip between two parallel, frictionless dies. B A P a B R Q g a B Figure 6.28 Process for curving a strip over a form roll of radius R. A is zero and at B is α B . For a given moment curvature characteristic, the distance, g, at which the roller should be located to satisfy the above conditions can be found.

6.9 Bending a sheet in a vee-die

A common process for bending a sheet in a press is shown in the Introduction in Figure I. 3b and in more detail in Figure 6.29. If the angle of the die face is α in Figure 6.29a and there is some friction between the sheet and the die, the force on the sheet will be at an angle ψ to the normal, where the coefficient of friction is μ = tan ψ. The force on the punch is P = 2 cos α − ψ 6.51 104 Mechanics of Sheet Metal Forming F R A t P P a y a−y a B B B MP 1r O r A P F1 B Punch Die Resultant of F 1 and P H 1 Moment arm of B Moment arm of B′ B′ R a b Figure 6.29 Bending a strip in a vee-die with a punch of nose radius R. a At the start of the process. b When the punch has nearly reached the bottom of its stroke. Bending of sheet 105