Bend Deduction Calculator

Each bend elongates - it’s often called growth or stretch, though elongate is the technically accurate term. Because of this, you must deduct certain amounts of that value from the flat blank size so that when the material bends, it elongates to the dimension required by the print. The elongation occurs because the bend’s neutral axis shifts toward the inside radius.

Each bend consists of a bend angle and inside bend radius. If two bends on a part have the same bend angle and inside radius, both will have the same bend deduction. If another bend on the part has a different angle/inside radius combination, it will require its own bend deduction calculation.

Although modern bend deduction charts are relatively accurate, older charts have serious variances. More than 100 bend deduction charts have been published over the decades, and not one of them agrees entirely with another. Say you’re putting a 0.063-in. radius in 0.060-in-thick cold-rolled steel. One chart may give a bend deduction of 0.106, another 0.136 - that’s a difference of 0.030 in. This might not be a big deal if you’re working with loose tolerances and have a limited number of bends. But in a part with multiple bends, that 0.030-in. variance will stack up, eventually making it impossible to form a part to print.

True, customers may not care about the inside radius. The part print may specify a specific radius, but as long as the part matches up and works as intended, they’re probably not about to get out their radius gauges to measure each bend. But if you determine the precise bend deduction needed for a particular radius, you effectively make manufacturing easier and reduce the number of inherent mistakes. Hence, your throughput goes up and you are much more productive.

To start, you need to know what happens to sheet metal when it bends. During each bend, the material’s neutral axis - where the material neither compresses nor expands - shifts inward toward the inside radius. The bend allowance is the length of the bend as measured on the material’s neutral axis.

Here is where geometry and trigonometry come into play. Bend allowance = [(0.017453 × Inside bend radius) + (0.0078 × Material thickness)] × Complementary Bend angle. You can insert the value of the inside bend radius as determined by the 20 percent rule. For the bend angle, you use the complementary angle (see Figure 1). (This formula incorporates the K factor and other mathematical functions that will be covered in future articles in this series.)

Next, you need to know the bend’s outside setback, which is the distance from the apex, where the two planes of the bend intersect on the inside surfaces, to the tangent point of the bend, where flat metal transitions to curved metal. Here’s the formula, easily workable with any scientific calculator: Outside setback = [tangent (degree of bend angle / 2)] × (Material thickness + Inside bend radius).

At this point you know the outside setback and the bend allowance. You’re now ready to calculate bend deduction: again, the amount of material deducted from the flat blank to account for material elongation during each bend (see Figures 2 and 3).

Here’s the formula: Bend deduction = (2 × Outside setback) - Bend allowance. With the bend deduction in hand, you can determine the appropriate flat blank size, and program the press brake so that the backgauge fingers accommodate for material elongation during each bend.