Bend it like an expert: sheet-metal flat patterns made easy - From the trenches: practical solutions to real-world problems - using AutoCAD

CADalyst, Dec, 2003 by Andy Wendt

Few CAD users seem to know how to create a sheet-metal flat pattern with proper bend allowance. Except for those that use 3D CAD software that automatically creates sheet-metal flat patterns, most companies have their engineering departments create a dimensioned drawing of formed sheet-metal parts and leave the flat-pattern calculations to the shop.

The manufacturing trend for sheet-metal parts, especially for prototypes and small production runs, is to use computer-controlled laser or water-jet cutting machines. These precision machines cut with outstanding accuracy, and they can import CAD geometry for a cutting pattern.

I formulated a method to produce accurate sheet-metal flat patterns using AutoCAD to perform the calculations while constructing geometry. This method is ideal for small production runs of accurately cut and formed parts without a custom-made die. However, it works for any sheet-metal flat pattern, even if total precision isn't needed.

One machinist at a shop I contacted was skeptical. He had received flat patterns from customers before but was never able to use them. After reviewing my geometry and finding nothing wrong with it, he used my flat pattern. He later informed me that the part formed perfectly. Without my flat pattern, he would have formed the part in two pieces that would then be joined with 99 of welding. My pattern required a total of 100 of welding.

With this method, you construct an end view of the formed part in AutoCAD. Then the inside radius of each bend is offset to define the neutral axis of the bend. To begin with, let's review how to calculate an offset value.

FIGURE OUT THE MATH

The Machinery's Handbook lists the following formulas to calculate sheet-metal bending allowance, where L 5 length of straight material required to form the bend, T 5 thickness of sheet metal, and R = inside radius of bend:

L 5 (0.55 3 T) 1 (1.57 3 R)

for 908 bend in soft brass/copper.

L 5 (0.64 3 T) 1 (1.57 3 R)

for 908 bend in half-hard brass, copper, soft steel, aluminum.

L 5 (0.71 3 T) 1 (1.57 3 R)

for 908 bend in hard copper, bronze, cold-rolled steel, spring steel.

You may recognize 1.57 as 0.5 of p. This isn't a coincidence. As you'll remember from your first geometry class, the formula for finding the circumference of a circle is C 5 2p 3 R, where C 5 circumference and R 5 radius.

Because a 90[degrees] bend forms an arc equal in length to 0.25 of the circumference of a circle, C/4 5 (2p 3 R)/4, and 0.25C = 0.5p 3 R. Each formula includes 1.57 3 R to find the length of a 908 arc. The portion of the formula that varies with metal type and hardness compensates for changes in the metal during bending. Remember that metal near the outside radius is stretched when bending, while metal near the inside radius is compressed. Softer metals tend to stretch more easily, which explains the different factors in the formulas for different metals.

Using the proper formula returns the length of a straight section of sheet metal equal to the arc length. Observe that the arc defined by the inside radius of the formed part is less than the straight length, while the arc defined by the outside radius is greater than the straight length. A plane through the thickness of a flat piece of sheet metal where no stretching and compressing occurs while bending is known as its neutral plane.

Because a plane is defined as a flat surface, and the neutral plane is not flat after bending, the location of the neutral plane in a curved part is referred to as the neutral axis. The arc length through the neutral axis after bending and the flat length of the sheet metal before bending are equal. The differences between the outside radius and flat length and the inside radius and flat length are not equal. This means that the neutral axis is not in the center of the material. It's closer to the inside radius--the softer the material, the nearer its neutral axis is to the inside radius.

The formulas are simple to use, but what if you need to calculate a bend allowance for a bend other than 908? For a 458 bend, you use the appropriate formula and divide the result by two. For a 2358 bend, multiply the result by 1.5. Luckily, we have calculators.

If you define the neutral axis relative to the inside radius of the bend, you can create AutoCAD geometry and have AutoCAD find the proper bend allowance calculations.

First, let's examine the second formula, as it applies to more commonly used general-purpose materials:

L 5 (0.64 3 T) 1 (0.5p 3 R)

using 10 for the sheet-metal thickness and 10 for the inside radius, so L 5 (0.64 3 1) + (0.5p 3 1).

Performing the multiplication of both thickness and inside radius by 1 leaves: L 5 0.64 1 0.5p, and then L 5 2.21.

It takes a straight section 2.210 long to form a 10 inside radius bend in 10-thick sheet metal.

Remember that the straight length and arc length through the neutral axis are equal. Use the formula:

A 5 0.5p 3 R

where A 5 length of arc through neutral axis (and straight length) and R 5 radius of arc through neutral axis.