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Line theory: Clashing |
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Line theory: Clashing |
OrcaFlex provides two different ways of modelling contact between lines: the line contact model and the line clashing model. The clashing model is described below. For a summary of the differences, advantages and disadvantages of the two models see line contact versus line clashing.
To include clash modelling between two lines, you must enable clash checking and set contact stiffness to a non-zero value, for both lines. You can also specify a contact damping value.
The facility to suppress clash modelling has been included because the clashing algorithm is time consuming. It is therefore best to suppress clash modelling on all sections that will never clash with other lines, or if you are not interested in the effects of clashing.
For the purposes of calculating clash force, OrcaFlex assumes constant spring stiffness and damping values and neglects friction. The calculation effectively pushes lines apart if they try to pass through one another, and it permits lines to separate again after contact. Multiple contact points along the line length are allowed for.
| Note: | Line clashing is not modelled during statics. |
OrcaFlex checks for clashing between any two line segments for which clash checking is enabled and contact stiffness is non-zero for both segments. The two segments do not need to belong to different lines - a line can clash with itself.
The clash check between segment $S_1$ (on line $L_1$) and segment $S_2$ (on line $L_2$) is done as follows. Let the radii of the two segments be $r_1$ and $r_2$ (as defined by the line type outer contact diameter). First OrcaFlex calculates the shortest separation distance, $d$, between the centrelines of the two segments. If $d\geq(r_1+r_2)$ then the segments are not in contact and no contact force is applied.
If $d\lt(r_1+r_2)$, then the segments are in contact. In this case OrcaFlex applies equal and opposite clash contact forces to the two segments to push them apart, as follows. Let $\vec{p}_1$ and $\vec{p}_2$ be the two points of closest proximity – i.e. $\vec{p}_1$ is on the centreline of segment $S_1$ and $\vec{p}_2$ is on the centreline of segment $S_2$, and these are the two points that are minimum distance $d$ apart. Also, let $\vec{u}$ be the unit vector in the direction from $\vec{p}_1$ towards $\vec{p}_2$. Then the magnitude of the clash contact force applied is given by \begin{equation} f_\mathrm{C} = f_\textrm{Cstiff} + f_\textrm{Cdamp} \end{equation} where the stiffness and damping terms on the right are documented below. A force of this magnitude $f_\mathrm{C}$ is applied to segment $S_1$, at $\vec{p}_1$, in direction $-\vec{u}$. And the equal and opposite force is applied to segment $S_2$, at $\vec{p}_2$, in direction $+\vec{u}$.
The stiffness term is given by \begin{equation} f_\textrm{Cstiff} = k\ \{d - (r_1+r_2)\} \end{equation} where $k$ is the combined contact stiffness of the segments, given by \begin{equation} k = \begin{cases} 0 & \text{if $k_1{=}0$ or $k_2{=}0$} \\ \cfrac{1}{(1/k_1+1/k_2)} & \text{otherwise} \end{cases} \end{equation} with $k_1$ and $k_2$ the clash stiffness values of the two segments.
The damping term is based on the rate of penetration, $v$, which is the $\vec{u}$-direction component of the velocity of $\vec{p}_1$ relative to $\vec{p}_2$. If $v{\leq}0$, then the two segments are moving apart (or relatively stationary) and no damping force is applied. If $v{\gt}0$, then the penetration is increasing and the damping term is given by \begin{equation} f_\textrm{Cdamp} = c\ v \end{equation} where c is the combined contact damping value of the two segments, given by \begin{equation} c = \begin{cases} 0 & \text{if $c_1{=}0$ or $c_2{=}0$} \\ \cfrac{1}{(1/c_1+1/c_2)} & \text{otherwise} \end{cases} \end{equation} where $c_1$ and $c_2$ are the clash damping values of the two segments.
In general, clashing will take place between one segment of one line and one segment of another (the probability of a clash occurring exactly at a node is very small unless you take special measures to make it happen). OrcaFlex determines the force as just described, and reports the force as a segment variable – i.e. when you ask for the clash force at a particular arc length along the line, the force reported is the clash force for the segment which contains the specified point.
If multiple clashes occur simultaneously on the same segment then the clash force reported is the magnitude of the vector sum of the clash forces involved.
In OrcaFlex all forces act at the nodes, so the clash force (described above as being applied to a segment) has to be divided between the two nodes at the ends of the segment. The force is divided in such a way that the moments of the two forces about the contact point are equal and opposite.
Contact between lines can be a violent impact at high relative velocity, or a gentle drift of one line against another, or anything in between. We need to view the results in different ways for different sorts of contact. The following notes give some general guidance based on our experience, but in difficult cases it is essential that users develop their own understanding of the underlying physics, and confirm it by sensitivity analysis.
OrcaFlex provides three measures of the severity of a clash event:
Various OrcaFlex results may be used for analysing clashing:
Where one line drifts quite slowly against another as a result of weight or drag forces, then the contact is essentially quasi-static. The clash force at the point of contact is the best measure of what is happening, and will be insensitive to segmentation and contact stiffness.
The case of violent impact at high speed is much more complicated. Contact forces arrest the relative movement of the lines over a very short time interval. Momentum is transferred from the faster moving to the slower moving line. Kinetic energy at the moment of impact is converted partly to local strain energy at the point of contact, and partly to axial and bending strain energy elsewhere in the lines.
If the discretisation of the lines is sufficiently fine, the contact stiffness value is correct, and contact damping is small, then OrcaFlex models the impact accurately, and all the reported results (force, impulse, energy) are correct. In practice, however, contact stiffness is rarely known with any precision, and it may not be practicable to discretise the line sufficiently to represent the deformation of the line axially, or particularly in bending, following a violent impact. (Deformation of the colliding cross sections is represented by the contact stiffness.) Under these circumstances, we need a measure of clash severity which is both meaningful for engineering purposes, and insensitive to discretisation and contact stiffness. Of the three measures available:
Clash events are often intermittent and short lived. Consequently, simulations of clash events can be sensitive to the choice of time step.
For explicit integration this is usually not an issue because use of the explicit solver typically necessitates the use of short time steps. However, when implicit integration is used, you should take extra caution when interpreting clashing results because of the longer time steps allowed by the implicit solver. We recommend that you carry out sensitivity studies to show that the time step in use is sufficiently short.