Machinery's Handbook, 31st Edition
Bending Sheet Metal 1421 Allowances for Bending Sheet Metal: In bending steel, brass, bronze, or other metals, the problem is to find the length of straight stock required for each bend; these lengths are added to the straight section lengths to obtain the total length of material before bending. If L = length (inch or mm) of straight stock required before bending; T = thickness (inch or mm); and R = inside radius of bend (inch or mm): For 90 ° bends in soft brass and soft copper see Table 10 or: (32) For 90 ° bends in half-hard copper and brass, soft steel, and aluminum see Table 11 or: (33) For 90 ° bends in bronze, hard copper, cold-rolled steel, and spring steel see Table 12 or: (34) Example, Showing Application of Formulas 32–34: Find the length before bending of the part illustrated by Fig. 13. Soft steel is to be used. . 055 . 157 L T R # # = + h ^ ^ h . 064 . 157 L T R # # = + h ^ ^ h . 071 . 157 L T R # # = + h ^ ^ h
R ” 5 8
” 1 8
R ” 3 8
60°
3
” 1 2
Fig. 13. For bend at left-hand end (180-degree bend): . . . . For bend at right-hand end (60-degree bend): . . . .
. L 064 0125 157 0375 90 180 1338 # # # = + = ^ h ^ h 6 @
. L 064 0125 157 0625 90 60 0707 # # # = + = ^ h ^ h 6 @ Total length before bending = 3.5 + 1.338 + 0.707 = 5.545 inches Angle of Bend Other Than 90 Degrees: For angles other than 90 degrees, find length L , using tables or formulas, and multiply L by angle of bend, in degrees, divided by 90 to find length of stock before bending. In using this rule, note that angle of bend is the angle through which the material has actually been bent; hence, it is not always the angle as given on a drawing. To illustrate, in Fig. 14, the angle on the drawing is 60 degrees, but the angle of bend A is 120 degrees (180 − 60 = 120); in Fig. 15, the angle of bend A is 60 degrees; in Fig. 16, angle A is 90 − 30 = 60 degrees. Formulas (32), (33), and (34) apply to parts bent with simple tools or on the bench, where limits of ± 1 ∕ 64 inch are specified. If a part has two or more bends of the same radius, it is, of course, only necessary to obtain the length required for one of the bends and then multiply by the number of bends, to obtain the total allowance for the bent sections.
120°
A
30°
A
60°
Fig. 14. Fig. 16. Springback: Every plastic deformation is followed by elastic recovery. As a consequence of this phenomenon, which occurs when a flat-rolled metal or alloy is cold-worked, upon release of the forming force, the material has a tendency to partially return to its original shape. This effect is called springback and is influenced not only by the tensile and yield strengths, but also by the thickness, bend radius, and bend angle. To estimate springback, an approximate formula in terms of the bend radius before springback R i and bend radius after springback R f is as follows (35) Fig. 15. 4 3 1 i 3 = − + c ^ c ^ h m h m
R R
ET R YS i
ET R YS i
f
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