July 26, 2001
Quite often I am asked, "Where can I get a bend deduction chart that works, one with valid numbers?" That's a good question.
In reviewing a couple dozen bend deduction charts from a variety of sources, I couldn't find any that agreed with another, with the exception of a single number here and there. For the most part, they varied widely. Figure 1 shows data from five of those charts selected at random.
The total error, or amount of difference between the top and the bottom entries, was 0.039 in. for the 1/32-in. radius and 0.030 in. for the 1/16-in. radius. Assuming that you have a generous tolerance over one bend, the error in bend deduction can be spread out, and a good part still can be produced. However, if tight tolerancing or if multiple bends are involved, the difference between the top and bottom values can make a good part a bad one quickly. For example, a part with three bends could have as much error as 0.117 in. (2.97 mm).
This leads to the question, Which chart is correct? The answer is, All of them! They all are correct for the environment in which they were created. In other words, each chart creator must have said something like, "This is the value of a 1/32-in. (0.81mm) bend radius by virtue of the punch tip's radii." Using this criteria, the creator approximated the punch radius rather than measured the inside radius. Some charts actually measured the resulting inside radius and found the correct bend deduction. Either way, the charts worked for each of them but may not have worked when applied to another shop's set of circumstances.
In the past, it wasn't as important to know precisely what the resulting inside radius was. Everything was coined or bottom-bent, which meant that resulting in the punch tip's radius always was achieved. Bends that were coined or bottom-bent almost always were made with a sharp punch tip. A sharp bend is one whose radius is less than 63 percent of the material thickness and is a requirement of coining and usually a feature of bottom bending. This fact alone made the older charts reasonably accurate.
Today air forming is the standard and the inside radius is no longer achieved by the punch tips radius. Instead, the inside radius is achieved as a percentage of the V-die opening.
Bend deductions (BD), the amount of change in the material between the flat and the formed material, are developed from mathematical formulas. These calculations are, as they always have been, based on the measurable inside radius and the associated geometry of the bend.
The inside radius is measured with radius gauges. Radius gauges come in common forms of measurement: fractional, decimal, and metric gauges are available through a number of manufacturers. Figure 2 shows an inside radius being measured. When a radius gauge rests squarely in the center of the bend, there should be no rocking motion, which occurs when the radius predicted is larger than the actual inside bend radius. You should not be able to see light underneath the gauge, which happens when the actual bend radius is smaller than the predicted inside radius.
Regardless of the forming method—air forming, bottom bending, or coining—or the tools used, the inside radius establishes the basis for the bend deduction. Once the inside radius is established, the following formulas can be used to calculate the true BD/(K-factor):
You also should note the two major camps of formulas.
In Camp No. 1 are bend deductions, bend allowances, and outside setbacks. These are mathematically the same as the formulas in Camp No. 2: K factors (BD), X factors (OSSB), and bend allowances (BA). The K and X factors were developed at Lockheed Corp. in the 1950s. One item of note: The K factor found in the "Machinists Handbook" (Industrial Press Inc., New York) it is the equivalent of the bend allowance and serves the same function.
The numerical value of the inside radius must not be calculated with an inside radius value of 63 percent or less of the material thickness. This is because the natural minimum inside radius that can be made in the material is no less than that. Coining and bottom bending reproduce the punch radius (because of the tonnages involved) and therefore the true punch radius value can be used in the calculations.
A sharp bend in air forming creates only a small ditch in the center of the bend, and the actual and measurable radii still are floated out as a percentage of the V die, a percentage that also changes by material type. Figure 3 shows this principle in action.
If the air-formed part has to be bent as a sharp bend, it is necessary to calculate the BD using the value from 63 percent of material thickness value. Simply multiply the material thickness by 0.63 instead of the actual punch radius.
Based on this example—in which the minimum radius is 0.046—if 1/32 in. (.032) were used in the calculations, the bend deductions then, obviously, would be incorrect.
Depending on the material type, the inside radius based on the V die opening is calculated with the following percentages:
The tensile strength of the material type should allow you to make educated guesses about the relative percentages for other materials.
You can predict the inside radius simply by multiplying the V-die opening (width) by the standard percentage rating listed for that material type and then use it in the calculations.
Charts are OK if you can create your own or find one that fits your operation's methods and tooling. However, it is much more accurate to calculate the BD based on the actual achieved inside radius rather than guessing, especially when you are air forming.