Machinery's Handbook, 31st Edition
1422 Bending Sheet Metal where R i = bend radius before springback, inch (mm); R f = bend radius after springback, inch (mm); YS = yield strength of the material, lb/in 2 (MPa); E = modulus of elasticity of the material lb/in 2 (MPa); and, T = material thickness, inch (mm). Other Bending Allowance Formulas: When bending sheet steel or brass, add from 1 ∕ 3 to 1 ∕ 2 the thickness of the stock, for each bend, to the sum of the inside dimensions of the finished piece, to get the length of the straight blank. The harder the material the greater the allow ance ( 1 ∕ 3 of the thickness is added for soft stock and 1 ∕ 2 of the thickness for hard material). The data given in Table 13 refer to the bending of sheet metal for counters, bank fittings, and general office fixtures, for which purpose it is not essential to have the sections of the bends within very close limits. Absolutely accurate data for this work cannot be deduced as the hardness and other mechanical properties vary considerably. The values given in the table apply to sheet steel, aluminum, brass and bronze. Experience has demonstrated that for semi-square corners, such as those formed in a V-die, the amount to be deducted from the sum of the outside bend dimensions, shown in Fig. 17 as the sum of the letters from a to e , is as follows: X = 1.67 BG , where X = the amount to be deducted; B = the number of bends; and G = the decimal equivalent of the gage thickness of the stock. The values of X for different gages and numbers of bends are given in the table. b a
c
d
e
Fig. 17. Table 13. Allowances for Square Bends in Sheet Metal
Amount to be deducted from the sum of the outside bend dimensions, (in.)
1 Bend
2 Bends
3 Bends
4 Bends
5 Bends
6 Bends
7 Bends
Square Bends
Gage
18 0.0500 0.083 0.166 0.250 0.333 0.416 0.500 0.583 16 0.0625 0.104 0.208 0.312 0.416 0.520 0.625 0.729 14 0.0781 0.130 0.260 0.390 0.520 0.651 0.781 0.911 13 0.0937 0.156 0.312 0.468 0.625 0.781 0.937 1.093 12 0.1093 0.182 0.364 0.546 0.729 0.911 1.093 1.276 11 0.1250 0.208 0.416 0.625 0.833 1.041 1.250 1.458 10 0.1406 0.234 0.468 0.703 0.937 1.171 1.406 1.643 18 0.0500 0.066 0.133 0.200 0.266 0.333 0.400 0.466 16 0.0625 0.083 0.166 0.250 0.333 0.416 0.500 0.583 14 0.0781 0.104 0.208 0.312 0.416 0.521 0.625 0.729 13 0.0937 0.125 0.250 0.375 0.500 0.625 0.750 0.875 12 0.1093 0.145 0.291 0.437 0.583 0.729 0.875 1.020 11 0.1250 0.166 0.333 0.500 0.666 0.833 1.000 1.166 10 0.1406 0.187 0.375 0.562 0.750 0.937 1.125 1.312
Formed in a Press by a V-die
Rolled or Drawn in a Draw-bench
Approximate values for sheet steel, aluminum, brass, and bronze. The lower part of the table applies to square bends that are either drawn through a block of steel made to the required shape, or are drawn through rollers in a drawbench. The pres sure applied not only gives a much sharper corner, but it also elongates the material more than in the V-die process. In this example, the deduction is X = 1.33 BG . Example: The following further illustrates this type of calculation. A strip having two bends is to have outside dimensions of 2, 1 1 ∕ 2 and 2 inches, and is made of stock 0.125 inch thick. The sum of the outside dimensions is thus 5 1 ∕ 2 inches, and from Table 13 the amount to be deducted is found to be 0.416; hence, the blank will be 5.5 − 0.416 = 5.084 inches long. Bending Force: The bending force is a function of the strength of the material, the length of the workpiece, and the die opening. A good approximation of the required force F is (36) F W LT UTS 2 = ^ h
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