Modelling spool pieces

Spool pieces, rigid jumpers, and similar items with the characteristic of being curved in their unstressed state can be represented in OrcaFlex by a pre-bent line. The pre-bend data describe the path that the line takes through space in 3D.

Setting pre-bend data

The bent shape must be separated into sections that correspond to line sections in OrcaFlex. Each OrcaFlex line section can represent either a straight length or a constant curvature bend in a single plane of bending, so the more complex the bend the greater the number of sections required.

The node at the start of each section provides the reference axes for the pre-bend of that line section. Views of the unstressed line shape and node axes are provided by the view pre-bend shape button.

The figure below shows a line that begins with a straight length, and then has a bend of constant curvature about the local $x$ axis.

At least two line sections will be needed in OrcaFlex to represent this shape, one for the straight length and another for the bend. You can have more sections if desired, for example to vary the segmentation along the bent shape. For each bent section, you must provide OrcaFlex with the curvature and the bending axis, by defining either the curvature components or the bend angle, radius and direction.

For the above figure, the bend axis coincides with the $x$ axis so its direction $\theta$ is $0\degree$. The bend angle $\alpha$ is $90\degree$. The definition can then be completed by entering either section length $l$ or bend radius $r$; the other quantity is automatically updated.

To specify the same shape by entering curvature directly, the components, $c_x$, $c_y$ would be \begin{equation} \left(c_x, c_y \right) = \left( \frac{\alpha}{l}, 0 \right) \end{equation} where

$l$, the section length, is the length of straight line which is consumed by forming the required bend.

$\alpha$ is the bend angle shown on the figure, measured in radians.

A more complex example is shown in the next figure below. This shape still has a single constant curvature, but this time the bend axis is between the reference $x$ and $y$ axes.

If pre-bend is specified by bend angle, then the bending can be defined just as for our first figure, with the exception that the bend axis direction $\theta$ is now (approximately) $30\degree$.

The same bend specified by curvature would then have components \begin{equation} \left(c_x, c_y \right) = \left( \frac{\alpha\cos\theta}{l}, \frac{\alpha\sin\theta}{l} \right) \end{equation}