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In the previous articles, we established a strong link between the complexity of the layup surface of CFRP components, their design requirements, and the effects on the prepreg tapes that are placed onto them. We talked about angular and positional deviations, steering, and how the topology of the surfaces relates to them. The more complex (= curved) the surface is, the harder it is to maintain straight tapes as they need to be bent to follow the curvature of the surface. In this article, we built an example 3D geometry that is curved in multiple directions. We then created two geometries using CATIA: an intersection with a plane and a geodesic curve that follows the curvature of the surface. Now we will compare their differences to understand what the use-case for both methods is.

*Figure 1: This is the reference part used in this example. The profile has a primary direction across the black curve in the center, but the cross-sections vary. It is therefore curved along the primary direction and perpendicular to it and qualifies as a complex surface for CFRP manufacturing.*

*Figure 2: In this video, the red plane is intersected with the brown surface geometry. We will use the resulting intersection to explain how a planar intersection with a complex surface differs from a geodesic curve on this surface. You can see that the white and the red curve intersect in the center. The white curve however starts to deviate towards the top and bottom side (roughly speaking the ±y direction, see the compass in the top right), since it is following the surface curvature and the surface is curved along either direction. *

First, let’s use the red curve (planar intersection) as the centerline of a tape. Where does that lead?

*Figure 3: The brown surface geometry is intersected with the red plane. Following the resulting red curve, a tape is generated. Especially on the radii on either side, you can see that the tape is bent a lot to follow the curve. These bends often lead to reduced adhesiveness to the surface since the tape is compressed on one side and stretched on the other.*

Now, let’s see how a tape behaves when its centerline is geodesic:

*Figure 4: Following the white curve, you can see that the tape follows the curve without being bent along the underlying surface. For single tapes, geodesic curves are often the optimal solution concerning adhesiveness and strength. *

I want to make a very important point here: The geodesic line shown in the 2nd video is technically the best solution for a curvature-free line on a surface. However, there is an important distinction between prepreg stripes and lines – lines don’t have a width. If we use a geodesic line as the guide curve (centerline) of a stripe, the very center of the stripe is not steered at all and therefore not exposed to the negative effects of steering. Yet all other areas of a stripe are, since they do not follow the optimal, steering-less path on the surface. Because a tape has a fixed width, the tape’s outer edges are parallel to the central, geodesic curve and it is not guaranteed that they are geodesics themselves. It is almost impossible for them to be geodesic unless the base surface is flat. If we look back at the part that we are working with it is clear why: every point of the surface differs from the next by its curvature. This means that working with a single, broad stripe may be difficult if the surface is too small and curved. **Think about wrapping a golf ball with gift wrap paper and scotch tape. **

**Now you might be asking yourself “If using the geodesic strategy is best, why would I ever use the straight/planar one?”. **

There are a variety of reasons. First of all, it always depends on the surrounding conditions:

- The end-effector used and the number of tapes per course,
- the angle of each ply,
- the complexity of the underlying surface and
- the specific design requirements.

**Generally, the more tapes per course, the more difficult it is to maintain the benefits of a geodesic strategy. **

Let’s assume the following scenario:

The end-effector can place 16 tapes at the same time. The guide curve of the course is geodesic. All centerlines of the tapes are now parallel to the guide curve of the course since the end-effector can only place tows in parallel by design. This means all individual centerlines of the tapes are parallel to the geodesic curve and are not, by definition, geodesic curves. Let’s also assume that the surface is curved in such a way that the underlying curvature of the first and the last tape of this course differs quite a lot, as in the geometry shown in the first figure. This means that all the tapes that are placed in parallel are steered, twisted, and strained in different areas and directions. This time, **think about wrapping multiple scotch tape stripes in parallel around a bowl. **

To summarize: there is a difference in the surface adhesion and tension between the different tapes in a course! This difference might be relatively low if the curvature and the number of tapes per course are low, but it depends on the setup. The more complex the surface is, the harder it is to place many tows at once that undergo the same loads and strains. Uneven distribution of these leads to a reduced quality of the laminate and the final component.

There is a delicate balance to strike between using geodesic and parallel courses. Placing courses parallel to each other produces constant and therefore simpler gaps but leads to angular deviations and steering, which reduce the total stability. Courses that are only based on geodesic curves introduce complex (“triangular”) gaps that are hard to control but are almost free of angle and steering problems. Using tools to analyze the gaps, angle deviation, and steering during laminate programming can be used to create a well-balanced laminate. The CAESA® Composites TapeStation offers a wide range of tools that can be used to create such a laminate. We will showcase these features in upcoming articles.

In this article, we explained the basics of curvature-based path planning for CFRP stripes. This is our last article in 2021. If you followed this series from the beginning, by now you should have a good grasp of the basics of the technology, its applications, and many of the complex steps to consider when programming a CFRP laminate. In 2022 we will shift our content towards talking about additive manufacturing and printing CFRP components.

Until then, stay safe and stay tuned.

SWMS Systemtechnik Ingenieurgesellschaft mbH is a consulting and technology company in the field of software conception and development and virtual product development.

If you have any __questions__ , feel free to contact us at any time by mail (info@swms.de) or during business hours by telephone in Oldenburg at +49 (0) 441 960 21 0.

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