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MICE collaboration meeting at CERN March 29 – April 1, 2004. Focusing Coil Support Tube Stress Analysis under different static load Stephanie Yang, Oxford University. Outline. Background of the study:- - PowerPoint PPT Presentation
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Focusing Coil Support Tube Stress Analysis under different static load
Stephanie Yang, Oxford University
MICE collaboration meeting at CERNMarch 29 – April 1, 2004
Outline
• Background of the study:-
During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.
During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;
Outline
• Background of the study:-
During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.
During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;
2 half coil tube design
Outline
• Background of the study:-
During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.
During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;Then a two half bobbin design with the coil wound directly onto each of them before bolted up to form a complete coil magnet
Outline
• Background of the study:-
During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.
During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;Then a two half bobbin design with the coil wound directly onto each of them before bolted up to form a complete coil magnet
2-half bobbin design
Outline
• Background of the study:-During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;Then a two half bobbin design with the coil wound directly onto each of them before bolted up to form a complete coil magnet
Finally, a single piece bobbin.
Outline
• Background of the study:-During operation, it is understood that there exists a very significant equal and opposite force between the focus coil pair. This force must be contained and the coil support tube needs to be strong enough to take on this force.During the course of this study, the design concept of the coil support tube has been modified;
First version was a two half tube design with the coil pre-fabricated and “shrink fitted” into the tube. The two half tubes are then welded up to form a single magnet;Then a two half bobbin design with the coil wound directly onto each of them before bolted up to form a complete coil magnet
Finally, a single piece bobbin.
One-piece bobbin design
Background of this study:-
The previous coil design was based on a maximum current of 200 MeV/C which could produce an equal and opposite magnetic force of 1900KN. The coil support tube has to be designed to withstand this force.
With the current increased to 240 MeV/C, the same magnet load would increase by a further 40% to about 260 tones. Consequently there was a need to review the effect of the coil support tube design to see if this could cause any concern.
In this study, we have looked at the different stiffness of the coil itself to the behave of the coil support tube. We argue that the bowing at the support tube end-plate is limited by how much the coil itself can deform at the interfacing surfaces. Therefore, any contribution from the coil, however small, would ultimately have an effect on the support tube behaviour. A value of 5GPa was assumed for the Young’s Modulus of the coil.
Gap elements were used to simulate the behaviour at the space between the coil and the support tube end plate.
- study the effect of mesh refinement- ensure that the gap between the coil and the
support tube is properly accounted for in our FE model
- investigate if the coil can help reduce the bowing at the end plate
- study the effects of the inner tube- Investigate if the thickening of the end plate
helps reduce the inner tube stress- to finally verify the final coil support tube
configuration with respect to the latest magnet force
The aim of this exercise is to:
Coarse meshed 2D asymmetrical coil structure FEA model (1)
Pressure force applied
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
255 265 275 285 295 305 315 325 335 345 355 365 375
distance mm
dis
pla
cem
ent
mm
Z-displacement plot along the end plate
A B
C
0
100
200
300
400
500
600
700
800
345 350 355 360 365 370
mm
MP
a
Von mises stress along A-B section
Z
Y
Max end plate bowing = 4.5mm Max Von-Mises stress of 736MPa at corner
Note: the coil was not modelled here. Force were applied as an equivalent pressure load
Pressure force applied
Mesh refined coil structure (1)
A B
C
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
255 275 295 315 335 355 375
distance mm
dis
pla
cem
ent
mm
Z-displacement along the end plate
Von Mises stress along A-B section
-150
50
250
450
650
850
1050
345 350 355 360 365 370
mm
MP
a
End-plate bowing remains at 4.5 mm – not affected by mesh density
Max corner stress increased to 1159 MPa (c.f. 726MPa on coarse model)
The fine model reduces the average stress along the corner section by as much as 20%, although the peak stress at the corner appeared to be higher in this model – character of an FE model
Conclusion on the selection of mesh refinement
This was done by connecting the coil to the coil support tube end plate with “Gap” elements
Extensive tests were carried out to see if the gap elements behave in the way that we expect them to, i.e. when applying a push load to the coil against a rigidly restrained end plate, it will only take up a prescribed gap, and no further. When a load of reversed direction is applied to the coil, it will result in infinite movement. This demonstrates that the gap elements are not rigidly linking the two structures together.
Ensuring that the gap between the coil and the support tube is properly accounted for in
our FE model
Focus coil displacement test case (1) --push
The same pressure force applied
Suppressed vertical movement (Tz)
0.5mm Z-displacement at coil interface
The gap between coil and structure is 0.5mm
The test
The test By applying opposite pressure force on the coil
Focus coil displacement test case (2)--pull
How the rigidity of the magnet Coil affect the bowing of the Support tube end-plate?
Previous analysis assumed the magnet forces to be applied as an equivalent pressure load. This did not take into account the effect of the coil rigidity. It is expected that the rigidity of coil may help redistribute the magnet force across the end-plate.
In this analysis, the presence of the coil was modelled with an equivalent Young’s Modulus.
Zoom In
1mm
Gap element
used
FEA model (coarse mesh) (1)
Y
Z
Note: max bowing is about 2.5mm at the end-plate
The FE model The FE results
Focus Coil mesh refined 2D model (1)
Note:- End-Plate bowing not affected by mesh refinement
However, stress pattern changed markedly in the
refined model
Focus Coil mesh refined 2D asymmetrical model (2)
-165
-65
35
135
235
335
435
535
320 325 330 335 340 345
distance mm
stre
ss N
/mm
^2
Average stress: 81.4 MPa
0
100
200
300
400
500
600
700
320 325 330 335 340 345
Average stress: 105.9 MPa
Compared with a stress of 179 MPa without coil, a reduction of nearly 50%
Compared with a stress of 172 MPa without coil, a reduction of nearly 40%
0
100
200
300
400
500
345 350 355 360 365 370
Average stress: 90.8 MPa
Focus Coil mesh refined 2D model (3)
-210
-110
-10
90
190
290
390
490
590
690
345 350 355 360 365 370
distance mm
stre
ss N
/mm
^2
Average stress: 131.9 MPa
Compared with a stress of 173 MPa without coil, a reduction of nearly 50%
Compared with a stress of 227 MPa without coil, a reduction of nearly 45%
Conclusion:
The presence of the Coil helps reduce the end-plate bowing thereby lowering the general stress level by 40 – 50%
The Coil contributes significantly to the stress reduction at the support tube – about 40% in average.
The inner tube will experience high stresses even with the inclusion of the coil. This is not unexpected because it provides an anchor to the end plate bowing. We do not see this as a problem as the stresses are well below yield point and it is limited by the deformation of the end plate which in itself is well below the allowable stress
The thickening of the end plate has little effect on the general stresses in the Inner Tube
Conclusion
Conclusion:If a very high Young’s Modules was assumed, then it re-distribute the magnet force in such a way that the end plate bowing is controlled by the deformation of the coil itself.
If the coil uses a deliberately low Young’s Modules, it behaves as though it is not acting as a load re-distributor. Rather, it behaves similar to the case where an equivalent pressure load was applied across the surface of the tube end plate.
This means that the coil support tube is sensitive to the coil stiffness.
ConclusionThe presence of a fillet in the FE model reduces the peak stress significantly.
Since these peak stresses were not real in the first place (they were as a result of numerical instability and singularity in the FE algorithm), we had carried out a series of stress linearization across the relevant sections. The results showed that the linearized stresses remained fairly consistent.
Detail modelling of the Coil
The individual conductor, the surrounding epoxy and insulation layer between each conductor section were modelled.
The geometry:
Sizes of each conductor cell, the thickness of the epoxy and insulation, their material properties etc are outlined in the next diagram.
Coil size: 90mm x 180 mm
Coil support structure thickness: 25mm
ADG
BEH
CFJ
A B C D E F G H J
Fz N/m 767975 127105 -478807 854810 124334 -582579 796561 119992 -547429
Fr N/m -288130 -344907 -220225 370163 456944 444784 1025507 1249089 1100174
Nodal force data is extracted from Jim Rochford (RAL)’ s focusing coil force profile 3x3 output and applied to the 2D FEA model
0.3 mm epoxy layer
1.65
mm
Ep
oxy
Insu
lati
on
Co
nd
uct
or
1.1mm
Unit cell The coil consists of 81 x 109 cells
Coil Material properties:
Conductor:)
Mass density: 6520 kg /m^3
E = 120 GPa
Poisson’s Ratio: 0.3
Epoxy:
Mass density: 1280 kg /m^3
E: 5GPa
Poisson’s Ratio: 0.4
Model#1: the model with the detail coil modelled
ADG
BEH
CFJ
Y
Z
Total Fr: 7150394N
Total Fz: 2227947N
The model that we have just seen is very detailed. It consists of every single conductor cell with its surrounding epoxy and insulation. While it gives very good information on how the coil behaves during the various loading scenarios, it takes up too much computing power to run the model.
Why the need for a simplified coil model:
The model that we have just seen is very detailed. It consists of every single conductor cell with its surrounding epoxy and insulation. While it gives very good information on how the coil behaves during the various loading scenarios, it takes up too much computing power to run the model.
Most of the information from this detail coil model was not strictly needed. All we needed from the coil model was to find out how it re-distribute the forces to the coil support tube.
Why the need for a simplified coil model:
The model that we have just seen is very detailed. It consists of every single conductor cell with its surrounding epoxy and insulation. While it gives very good information on how the coil behaves during the various loading scenarios, it takes up too much computing power to run the model.
Most of the information from this detail coil model was not strictly needed. All we needed from the coil model was to find out how it re-distribute the forces to the coil support tube.
With that in mind, the following exercise was conducted to see if we could simplify the coil modelling. Instead of modelling every single cell of the conductor with its surrounding epoxy and insulation, we simply model the whole coil with a block structure and by applying an equivalent material property to this block structure, it may be sufficient for the purpose of what we try to do.
Why the need for a simplified coil model:
Model #2 – the model with the simplified coil detail modelling
The results on Model#2 are shown below, very similar to that of Model#1
Note that the coil is not displayed in all result plots.
Coil equivalent orthotropic material property for this model are (advised by Mike Green):
Mass density: 6520 Kg/m^3
Er: 50GPa
Ez: 70GPa
Eθ: 90GPa
Poisson Ratio: 0.3
Epoxy: Mass density: 1280 kg /m^3E: 5GPaPoisson’s Ratio: 0.4
The same nodal force applied to the coil
The simplified coil model did very little to affect the stress and displacement results of the coil support tube.
The result indicates that a simplified coil model, with the correct material property, is appropriate for future analysis
Is the simplified Coil model good enough?
Cases on new configuration (coil size 84mm x 210 mm)
with a one piece bobbin
With all the checking and sensitivity study carried out on the various coil geometry, we are now confident that the model that we have developed on this new Coil support configuration can be used to produced a valid final design check
With the new coil configuration, the total force will increase by ~40%.
the total force on old coil configuration was 260 T, while on the new coil is 360 T.
Force profile 4 x 4 output on the new coil from Jim Rochford (RAL) that are used for the new coil FEA model:
New coil Total Fr: 8867667 N
Total Fz: 3521119 N
Total Fr: 7150394N
Total Fz: 2227947NOld coil
The new coil geometry (84 x210 mm) resulted in a near 40% increase in the axial force onto the coil support tube end plates. However the existing 1 piece bobbin design is capable of containing this force without causing any over-stress to the coil support tube.
The absence of any mechanical or welded joint to the one-piece bobbin design ensures that the relative positions of the coil would not be “shifted” or “moved” when this large force occurs.
When the coil rigidity was properly accounted for, it redistribute the force to the coil support tube end-plate. The results show that the very large local peak stress at the crotch corner of the tube, found previously, has largely disappeared.
The maximum stress at the coil support bobbin during the force occurrence is well below its allowable limit.
Summary Conclusion