Busbar flat pattern and bend allowance

Why the flat pattern matters

A busbar starts as a flat blank and becomes a formed part. If the blank is cut too short, the legs finish under length and the holes no longer line up. If it is cut too long, the part will not fit the space and the excess has to be removed after forming, which is expensive and can damage the finish.

The flat pattern is the length of the neutral axis when the bar is unbent. Material on the outside of a bend stretches and material on the inside compresses. Somewhere between them is a surface that keeps its length, and that surface is what the blank length has to match. The K factor tells you where that surface sits as a fraction of the thickness.

The bend allowance and bend deduction

The bend allowance is the arc length of the neutral axis through the bend. In degrees, it is the bend angle multiplied by pi divided by 180, multiplied by the sum of the inside radius and the K factor times the thickness. For a 90 degree bend, the angle term is pi divided by 2, which is about 1.5708.

The bend deduction is the difference between the sum of the two outside legs and the developed length. For a bend measured to the virtual sharp, it is twice the setback minus the bend allowance. The setback is the outside radius, which is the inside radius plus the thickness, multiplied by the tangent of half the bend angle. For 90 degrees, the tangent of 45 degrees is 1, so the setback is simply the inside radius plus the thickness.

Use one convention consistently. If the drawing dimensions the legs to the virtual sharp, subtract the bend deduction. If it dimensions to the tangent points, add the bend allowance. Mixing the two is the most common reason a blank comes out wrong.

Choosing a K factor

The K factor depends on the material, the temper, the radius to thickness ratio and the tooling. A tight bend moves the neutral axis towards the inside; a generous bend moves it towards the middle. A soft material flows more than a hard one, so the K factor is usually lower for soft copper than for hard copper.

The table below gives illustrative starting values. They are not a substitute for a trial bend. If the part is critical, bend a sample of the production material, measure the formed legs and back-calculate the K factor that matches the result.

A worked 90 degree example

Take a 100 x 10 mm half hard copper bar with a 90 degree bend, an inside radius of 10 mm and legs of 150 mm and 200 mm measured to the virtual sharp. Use a K factor of 0.42. The neutral radius is 10 mm plus 0.42 times 10 mm, which is 14.2 mm.

The bend allowance is 1.5708 times 14.2 mm, which is 22.31 mm. The setback is 10 mm plus 10 mm, or 20 mm, so the bend deduction is twice 20 mm minus 22.31 mm, which is 17.69 mm. The blank length is 150 mm plus 200 mm minus 17.69 mm, which is 332.31 mm.

Check the result against the tangent method. The leg from the end to the tangent is 150 mm minus 20 mm, or 130 mm, and the other is 200 mm minus 20 mm, or 180 mm. Add the two tangent lengths and the bend allowance: 130 plus 180 plus 22.31 gives 332.31 mm. The two methods agree because the same geometry was used.

The example is illustrative. A real part may need a different K factor, a springback correction and a trim allowance. The value of the calculation is that it makes those assumptions visible, so a change in radius or temper can be reworked quickly.

Flat patterns with more than one bend

For a part with several bends, calculate each bend separately and combine the results along the developed centre line. Work from one datum end and add the straight segments between the bend tangent points. Do not add the outside leg dimensions and subtract one average deduction; each bend has its own radius, angle and K factor.

The bend order matters when bends are close together. A second bend can pull material from the first, especially if the web between them is short. If the tool cannot clear the first bend, the part may need a different order or a different tool. The flat pattern is still the same, but the formed result may not be.

For a part with bends in two directions, keep a simple sketch of the developed line and label each segment. Trying to hold the whole part in your head is how a leg gets counted twice. A table of segments, lengths and deductions is easier to check than a single total.

1. 01

   Measure the legs

   Use the drawing convention, either to the virtual sharp or to the tangent points.

2. 02

   Set the radius and thickness

   Use the finished inside radius and the nominal thickness, not the outside radius.

3. 03

   Choose the K factor

   Start from the material and temper, then confirm with a trial bend.

4. 04

   Calculate each bend

   Work out the bend allowance and the bend deduction for every bend.

5. 05

   Add the segments

   Combine the straight lengths and the allowances along one developed line.

6. 06

   Check against a sample

   Form a trial part and measure the legs and the overall length.

Springback changes the finished length

The flat pattern calculation assumes the bar takes the tool radius. In practice it springs back, so the finished radius is larger and the angle is more open. A larger finished radius means a longer arc and a slightly different developed length. For a tight tolerance, the blank may need a small allowance or the tool may need an overbend.

Springback is larger for hard temper, for a large radius to thickness ratio and for a bar with a high yield strength. It is smaller for a soft bar and a tight bend. If the part has a critical overall length, measure the first formed part and adjust the blank rather than relying on the calculated value alone.

The same applies to a twist or an offset. The developed length is only part of the story; the formed geometry has to be checked as well. A blank that is correct in length can still produce a part that is out of angle or out of plane.

Checking the blank before cutting

Before a blank is cut, check the calculation against a simple sketch and a trial bend. The sketch should show the developed line, each bend, the radius and the angle. The trial should use the production material, because a different temper can move the K factor enough to matter on a long part.

Record the K factor, the radius, the thickness and the resulting blank length with the drawing. If the supplier changes the tool or the material, the record shows what has to be rechecked. The Qumek busbar drawing generator can hold the finished dimensions, but the flat pattern still has to be calculated for the process that will form the part.

• Use the finished inside radius, not the tool radius.
• Use the nominal thickness and state the tolerance.
• Keep one convention for leg measurement.
• Calculate each bend separately.
• Trial bend the production material.
• Record the K factor and the blank length with the drawing.