JEC COMPOSITES MAGAZINE - Issue #114 - July 2017 - 52

TECHNOLOGY software
pores between the yarns and other parameters. This paper presents an overview of the possibilities offered by such parametric
algorithms [6] for the representation of tubular braids at the filament level.
Methodology
Braided structures for composites are usually produced from carbon or glass fibre rovings, which consist of a large number of filaments. Such rovings have a very flat cross section, so that yarns
with a circular cross section are not suitable (Figure 1a). From
another point of view, using circular cross sections for all rovings
allows a very efficient computation of the distances between the
rovings at the contact areas and significantly simplifies the algorithms. For this reason, such a model is used as a first step in the
modelling process - as a basis for the creation of the braid topology (Figure 1b). In this case, the roving diameter equals its thickness. After defining the mandrel diameter, the number of yarns
and the braiding angle, the algorithm calculates the coordinates of
the rovings at the contact points, based on the principle explained
in [6], and generates the roving axes.
These axes are used for the placement of the filaments in each
roving. For the distribution of the filaments, the user has to define their configuration within the roving. As the rovings for composites usually have very flat sections, the definition of the cross
section based on several parallel layers is suitable here (Figure
2). Let's consider one cross section of a roving with the xy local
coordinate system (Figure 2) oriented so that y is parallel to the
normal vector to the curvature of the current point and x to the
binormal vector. In this cross section coordinate system, each layer can be defined using its own local coordinate system so that
the vertical position, y, and the horizontal position, x, can be
specified. This way, the user has the freedom to move the individual layers horizontally and vertically until he gets the desired
fibre packing density. As an additional parameter, the distance between the filaments, , can be defined for each layer too.

are used. There is no limitation on the number of filaments, so the
user can decide himself, depending on the available computational resources, if he would like to model the roving with 10, 100 or
10,000 filaments. To quickly check the appearance of the braided
structure, the following equation can be used:
(1)
This equation allows the visualisation of the braid very close to
reality, based on a minimum number of visualisation bodies. The
layer definition principle, as explained in Figure 2, can be used, for
instance, to create more precise geometries for FEM calculations.
Figure 3 shows braids created this way for the four industrially
available floating lengths: 1, 2, 3 and 4. The term "floating length"
is not common for classical braiders, but a similar word has been
used traditionally in Germany for more than 100 years [7] and
is explained in English language in reference [8]. Compared to
commonly used terms such as "regular", "plain", "diamond", etc.
braids, it has the advantage of providing a direct connection between the configuration of the braiding machine and the structure of the braid [8]:
(2)

Results
The centre defined for each filament in this way is then swept
along the main axis created during the first step and all its coordinates are calculated. Figure 1c shows a tubular braid with 48
carriers, a floating length of two, where ten filaments per roving

where NS is the number of slots on one horn gear, RL is the repeat
of the carrier arrangement and FL is the floating length. All the
variants in Figure 3 can be generated changing one value (floating length) and computing again in a few seconds. They look very
similar to the unexperienced braider, but different machines are
needed for their production in normal cases. In the TexMind
Braider software [9], these algorithms calculate the machine configuration and make a plot of it. Figure 4.a presents a view of the
machine for the case simulated in Figure 3c, where the floating
length is 3. In this case, a braiding machine with horn gears with
six slots is required. Such a machine requires more space, but the
braid structure has less undulations and, especially for carbon and
glass fibres, it is assumed that it can lead to better behaviour during loading.
As shown in Figure 3, the same algorithms can also be used to
model the inlay yarns within triaxial braids. All the algorithms
are implemented in the C++ language-based program TexMind
Braider with a suitable graphical user interface and 3D visualis-

Fig. 2. Definition of a complex roving configuration using multiple parallel
filament layers

Fig. 3: Simulated braids with 48 carriers, different floating lengths and 0°
yarns (inlay) in some cases: a) braid with a floating length of 1, b) braid with a
floating length of 2, the right part of the braid has inlay yarns, c) braid with a
floating length of 3, d) braid with a floating length of 4

jec composites magazine / N°114 July 2017

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #114 - July 2017