4-point bending of power cable

A power cable installed in a 4-point bending rig is modelled.

Figure 1. Bflex model of a power cable in a 4-point bending test rig.

Model description

Power cable

There are different options on how to model the power cable. In this model the following approach is applied:

Make a model of one conductor phase to obtain the global properties for that component
Make a model for the complete power cable using input from the step above, including a complex filler geometry
Simplify the geometry of the fillers, and use propreties for the fillers as obtained from the step above

Single conductor phase model

A 2 element long model of the single power phase is built, using thickwall hshear364 elements for all layers, where the helical layers applies the shear2helix option:

#ELCON        ELGR            ELTY       MATNAME      ELID       NOD1 [NOD2 NOD3 NOD4][REPEAT N NELINC NODINC]
Elcon  coppercontact1        hcont464    contmat-1    50001      40002 41001           
                                                      50002      40004 41003
Elcon  coppercontact2        hcont464    contmat-1    51001      41002 42001              
                                                      51002      41004 42003
Elcon  coppercontact3        hcont464    contmat-1    52001      42002 43001              
                                                      52002      42004 43003
Elcon  coppercontact4        hcont464    contmat-1    53001      42002 43001              
                                                      53002      42004 43003
Elcon  insulationcontact1    hcont464    contmat-1    54001      43002 44001              
                                                      54002      43004 44003
Elcon  copperscrcontact      hcont464    contmat-1    55001      44002 45001              
                                                      55002      44004 45003
Elcon  insulationcontact2    hcont464    contmat-1    56001      45002 46001              
                                                      56002      45004 46003

Figure 2. Bflex model of single conductor phase. The layers of copper wires are shown in red - insulation layers in purple - copper sheath in yellow

The model is fixed in degree of freedom 1-3 - direction x,y,z - creating a pinned connection in end 1. In addition, torsion (dof 4) is fixed in this end.
End 2 is fixed in dof 2-3 (y,z), but otherwise free.

Then the following loads are applied in sequence:

displace end 2 in x-direction, dof 1
rotate/twist end 2, dof 4
tilt both ends with an oposite rotation, dof 5 - which will cause the model to bend

# axial
CONSTR PDISP GLOBAL 3 1  1.0 300
# twist
CONSTR PDISP GLOBAL 3 4  1.0 310
# bending (rotation of ends)
CONSTR PDISP GLOBAL 1 5 -0.0005 320
CONSTR PDISP GLOBAL 3 5  0.0005 320

Based on the applied axial strain, twist and curvature and the resulting axial force, torque and bending moment, the axial, torsional and bending stiffness of the model can be obtained by postprocessing with bflex2010post:

nrplot "bflex2010_01" "strain-force"       "Displacement (m)" hist300 "Force (N)"   qx-all 3 3 1.0/0.01     1.0 2
nrplot "bflex2010_01" "twist-torque"       "Twist (rad/m)"    hist310 "Torque (Nm)" mx-all 3 3 1.0/0.01     1.0 2
nrplot "bflex2010_01" "curvature-moment"   "Curvature (1/m)"  hist320 "Moment (Nm)" my-all 3 3 0.0005/0.005 1.0 2

Complex geometry filler

The fillers in a power cable may have a complex geometry. This can be modelled by applying the element type hshear353 for the filler, and specifying the use of crossgeom geometry type, and general type of cross section.

ELPROP pvcfiller      shearhelix    crossgeom general pvcprofile     d        d     1.0

With this option, the user can describe the shape of filler profile using a crossgeom input section, with geometry type general:

CROSSGEOM pvcprofile  general
0	0	S	0.00225		180	0	8	1
0	0	S	0.006		270	0	21	1
0	0	CI	280		310	0.015	28	1
0	0	CI	310		340	0.015	28	1
0	0	CI	340		360	0.035	43	1
0	0	CO	90		70	0.08	99	1
0	0	S	0.003		240	0	11	1
0	0	CI	57		95	0.0615	142	1
0	0	CO	30		0	0.017	31	1
0	0	CO	340		321	0.05	59	1
0	0	CO	219		200	0.05	59	1
0	0	CO	180		150	0.017	31	1
0	0	CI	85		123	0.0615	142	1
0	0	S	0.003		120	0	11	1
0	0	CO	110		90	0.08	99	1
0	0	CI	180		200	0.035	43	1
0	0	CI	200		230	0.015	28	1
0	0	CI	230		260	0.015	28	1
0	0	S	0.006		90	0	21	1
0	0	S	0.002234215	180	0	8	1

The following python script may be used as a starting point to plot the geometry while building it:

Python file for plotting the profile geometry

The resulting model is vizualised in Figure 3.

Figure 3. Bflex model with complex filler geometry.

The visual representation of the filler consists of a thin bar positioned in the area center of the geometry, in addition to the actual outline of the profile. The visual representation tends to become messy. For that reason, as well as for efficiency and for improved contact behaviour, it is recomended to instead use a simplified representation with e.g. a cylindrical shape. The global properties of the profile in terms of axial-, torsional- and bending-stiffness can be obtained from the *.bof file and applied in the simplified model using a linear material model.

In this case, the basis for obtaining the filler properties is the same input file as for the full model explained further below. However, a minimal model in terms of elements and element groups could have been applied for this purpose.

Cable model with simplified filler

The cable is modelled with the structural components as shown in Figure 4. To complete the cable model, internal contact elements between the relevant components must also be included. Further, bondary conditions for the individual components at the end of the cable, i.e. end fitting, and in some cases along the cable length.

Figure 4. Structural components in the cable.

Test rig

The the structural components of the test rig are shown in Figure 5. The principle of constructing the test rig is based on:

Defining a set of nodes that are fixed in all dofs, i.e. fixed points.
Connnect nodes that are free in the relevant dofs of displacment (fixed in the non-relevant directions) to the fixed points by strong springs.
Connect roller contact elements to the nodes that can move in selected dofs.

The method of moving the rollers/frames by initial straining of strong springs have shown to be numerically more stable than direct displacement of the frames.

$E043 rig$

Figure 5. Structural components of the test rig.

The roller contact cont164 must contact a pipe31 element. Hence a pipe is connected to the center node system of the cable to pick up the contat towards the rollers/rig frame.

Boundary conditions and loads

The bondary conditions and load are as follows:

the cable is fixed in axial motion and twist at the mid point
tension is applied in oposite directions at both cable ends
yarn layers and the armour layer are subjected to a certain pre-tension level
The two mid frames are displaced horizontally by applying initial straning (inistr) on the springs connecting to a fixed point
The frames are tilted by applying initial straning (inistr) in rotational dofs on the springs to the fixed point. This is to ensure that the cable contacts only one side of the roller pairs during bending.

This simulation is time consuming and requires small time steps. Running one bend cycle will likely require a couple of days. The timeco section of this file is by default only a short time, but may be extende to cover a full bending cycle.

Relevant files

Go to bflex2010 file - short model for obtaining properties of a single power phase

Go to bflex2010 file - for obtaining properties of the complex fillers

Go to bflex2010 file - for the main simulation

Go to bflex2010post file - post processing the single phase model

User manual for reference

Processing of files from command line

bflex2010 -n bflex2010_01
bflex2010post -n bflex2010post_01
bflex2010 -n bflex2010_02
bflex2010 -n bflex2010_03

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