Grand unifying theory of press brake bending: Part IV

For the past few months I’ve detailed a new way of predicting the inside bend radius. Instead of the traditional terms such as radius and profound-radius bends, we’re using some new terminology. I’m calling this the “Grand Unifying Theory” of radius, bend deduction, and die selection, and ultimately it may help you make your bend calculations more accurate than ever.

For this final installment, I’ll review the definitions and bring you through the entire process, from calculating springback to incorporating the bend function calculations. Note that all measurement values—including material thickness, radius, punch nose diameter, and die width—are in inches unless otherwise specified.

The Terms

Types of Bends

Sharp bend: Specified inside bend radius that is generally 63 percent or less of the material thickness of 60-KSI cold-rolled steel. (For more on this, see “How an air bend turns sharp” on www.thefab ricator.com.)

Perfect bend: Specified inside bend radius that’s between 63 percent and 125 percent of the material thickness.

Radius bend: Specified inside bend radius that’s greater than 125 percent of the material thickness.

Bending Methods

Air forming: Three-point bending in which the material contacts the punch nose and the radius of the die shoulders during the forming cycle. The floated inside radius forms as a percentage of the die width.

Bottoming: Forced bends, usually at 90 degrees, with angular clearance between the punch and die; the punch descends until the material wraps around the punch nose, after which the ram continues to apply pressure, forcing material against the die face to the desired bend angle. This produces a radius that’s slightly larger than the punch nose, which is why a springback factor still needs to be taken into account. Bottoming occurs at about 20 percent of the material thickness, as measured from the bottom of the V die.

Coining: Occurs when the tool geometry is stamped into the material at less than the material thickness. It is rarely performed.

Wiping: Occurs in aircraft tooling during the forming of complementary angles greater than 90 degrees.

Angles

Bend angle: Angle after springback.

Bent-to angle: Angle the press brake overbends to overcome springback.

Included bend angle: Angle of bend as measured between the two legs.

Complementary bend angle: 180 degrees minus the included bend angle.

Sf: Springback factor.

Tooling

Punch: Usually the upper tool, the punch pushes the workpiece into lower die space.

V die: Angles from 85 to 90 degrees included.

For accurate bend calculations, relieved die widths must be measured by the A dimension.

Acute V die: 30 to 85 degrees included.

Relieved V die: Section of the die faces removed, which allows the punch to overbend for springback without crashing into the die.

Aircraft die: Channel dies in which the depth is 120 percent of the width

Channel die: 180-degree dies that do not maintain the width-to-depth relationships of aircraft dies.

Forming Variables

Mt: Material thickness

Dp: Depth of penetration, the distance the punch tip enters the die space

Ir: Inside bend radius

Rp: Radius of punch tip (Note: Ir and Rp sometimes can be interchangeable)

BA: Bend allowance

BD: Bend deduction

OSSB: Outside setback

The Steps

1. Calculate the springback and estimate the bent-to angle.

This is for air forming. Note that Rp and Mt values are in millimeters. Also note that the results are approximations at best. There are far too many variables to predict springback with total accuracy.

2. Select method: Air forming, air forming with backup, bottoming, wiping (aircraft).

3. Select tooling style and calculate optimal die width.

Air forming with V die and acute V die

Channel die (not aircraft tooling)

Aircraft die

For bend angles less than 90 degrees complementary:

For bend angles greater than 90 degrees complementary:

Note: Aircraft tooling does not allow for sharp or “creased” inside bend radii; therefore, it would be highly uncommon to find tooling used in a sharp bend relationship.

Air forming with relieved V die

Bottoming

The formulas here give you the perfect die width, but that value rarely will match available standard die widths, so you need to choose the closest die width available.

4. Determine the tonnage requirements.

5. Determine where the bend turns sharp.

Minimum force per foot necessary to pierce the material surface, based on 1-to-1 material-thickness-to-inside-bend relationship.

Piercing tonnage should be greater than forming tonnage. The radius on the nose of the tool should be no less than the calculated “sharp” value of the bend.

6. Determine the springback factor.

7. Determine the actual radius

Bottoming

Air forming a sharp bend calculated as a parabola

In the online calculator at http://www.had2know.com/academics/parabola-segment-arc-length-

area.html, “Height” equals outside bend radius and “Width” equals the die width. Or, you can perform the following equation:

Use this “Length of Arc” value, along with the die width (“Width of Arc”), at www.handymath.com’s “Complete Circular Arc Calculator.” The result needed is the “Height of Arc” value. The height of arc from the calculator will serve as our initial value for the outside radius. To obtain our final inside radius: