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## COPRA® – the First, Second and Third Software Generation...

### Technical Information

Let’s have a short review of how calculation of theoretical material strain has been developed over the last years.

### 1st COPRA® Generation

Calculation of Strip Edge Stress

During flower design special importance has been attached to the course of the strip edge. The biggest problem was a precise ca lculation of the course of the strip edge and the resulting stress and strain. Many authors have been dealing with this topic. Software programs dealing with calculation of strip edge stress have been mushrooming all over the world.

There were many different approaches for this task. One group determined limit strain values whereas others defined that the strip edge should not be strained beyond a certain value, which, according to Hook´s law would mean the same, anyway.

Stress of the strip edge was calculated on the basis of trigonometric formulas. Some methods considered the stand distance between the individual forming steps or the length of the legs to be. Other (few) approaches were based on the so-called forming length instead of the stand distance. The calculation algorithms, however, remained the same.

Basically, these calculations were based on two different approaches. The first method according to Schulze claimed a straight course of the strip edge. The second according to Pawalkat assumed, that the forming length depends on the roll tool. Here, the roll diameter was decisive and the forming length was the connection line between sheet metal and tool. * Approaches for calculation of strip edge stress*

When the first COPRA® version was released for commercial use in 1987, the method according to Schulze was implemented. Below please find a simple example for a calculation according to this method:

According to Schulze (method of triangle calculation) the theoretical stress of the edge is approx. 0.9% (strain could be deduced according to Hook’s law). With an assumed maximal stress value of 0.35% design would have been doomed to failure.

But what would happen if the most critical point is not the edge but another one of the cross section? Imagine, that we are having an 180 degrees overlap.

For every rollform designer the result is obvious. If above shown U-section fails according to the stress calculation - this one having the 180 degrees crimping will fail as well!

But watch out! The calculated values are far beyond the critical values shown above: just 0.25 % elongation.

**How can this happen?**

The answer is simple. For the software program (1st generation) the strip edge is something different to the real critical edge. In the practical work, critical areas are not always identical with the strip edge. They can be located somewhere else in the cross section.

Tricky forming methods like "down hill forming" would make this result even worse.

This tells us: a strip edge strain calculation program taking into account only strip edges is upmost dangerous!!

By the way: a similar calculation method has been (and is still being) used by a competitive software program "Profil" as the only method to predict strip edge stress since 1987 (as of July 2003).

Due to above mentioned restrictions data M had released already in 1988 another improved COPRA® software program - the 2nd generation....

### 2nd COPRA® Generation

The COPRA® Wire Frame Model

**The basic idea is the following one:**

A 3-dimensional wire frame model is generated, where characteristic points of the cross section´s geometry are defined. These points are followed through all forming steps and joined by straight lines. By this means you are getting a 3-dimensional wire frame model. The target is not only a comfortable visualisation but the possibility to calculate longitudinal elongations of characteristic points over the whole cross section - not only at the strip edge. Even tricky forming methods, e.g. turning the section during the roll forming process as it is occasionally practiced, can be taken into acount.

As if you had modelled the forming process by a rubber band you are now able to determine every wire´s elongation separately. The calculation method used is again the "straight line" statement. The result is shown graphically on the computer monitor. Each elongation range is presented by a different colour.

The wire frame diagram verifies that the critical areas of the U-section with crimping are having approximately the same elongation values than the strip edge of the U-section (about 0.9%).

Even if this software program is able to determine important results depending on certain technological and geometrical parameters, there is a restriction: the "straight line" statement implemented in this 2nd generation software.

Due to the very complex deformation process a more accurate calculation model for roll forming was required. The solution was found in the COPRA® Deformation Technology Module - the 3rd generation!

### 3rd COPRA® Generation

COPRA® RF Deformation Technology Modul

Following you can see the sample U-section once more. This time it is being calculated by COPRA® RF Deformation Technology Module.

This time, parameters like roll diameter, respective position, strip gauge, kind of material, profile shape etc. are taken into account. COPRA® RF DTM uses these values to calculate a theoretical forming surface of the coil. For the first time it is possible to calculate stress values for the top surface and bottom surface of the formed coil separately.

The peaks of longitudinal elongations are locally much higher than before according to practical experience and experiments. In both examples, U-section as well as U-section with crimping, the calculated values are approximately similar. They show the designer that this specific flower pattern has to be modified urgently. That is what the experienced roll former would have expected as well. Modifications can be done easily by using COPRA®´s editing functions.

- The shown examples are demonstrating that a properly working simulation software is able to prevent a designer from mistakes, e.g. developing a set of roll tools which is bound to fail. The designer´s "belly ache" while producing a new set of rolls will be eased due to this elimination of possible sources of errors.
- Cutting off the peaks on the diagram means also smoothing the roll forming process. The result is a uniform distribution of deformation work. The experience from customers who are producing tubes is that this can result in a reduction of power consumption up to 10%. Only this saving enables the user to profit from an investment in roll form design software