1. Focusing Coil Support Tube Stress Analysis under different static load Stephanie Yang, Oxford University MICE collaboration meeting at CERN March 29 – April 1, 2004

2. 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;

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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.

9. - 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:

10. Coarse Vs Fine meshed FE models study the effect of mesh refinement

11. Coarse meshed 2D asymmetrical coil structure FEA model (1) Pressure force applied Z-displacement plot along the end plate AB C Von mises stress along A-B section Z Y Max end plate bowing = 4.5mmMax Von-Mises stress of 736MPa at corner Note: the coil was not modelled here. Force were applied as an equivalent pressure load

12. Pressure force applied Mesh refined coil structure (1) AB C Z-displacement along the end plate 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)

13. 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

14. 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

15. 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

16. The test By applying opposite pressure force on the coil Focus coil displacement test case (2)--pull

17. Conclusion: The gap elements were shown to behave the way it was expected to operate

18. 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.

19. 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

20. 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

21. Focus Coil mesh refined 2D asymmetrical model (2) Average stress: 81.4 MPa 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%

22. Average stress: 90.8 MPa Focus Coil mesh refined 2D model (3) 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%

23. Conclusion: The presence of the Coil helps reduce the end-plate bowing thereby lowering the general stress level by 40 – 50%

24. Effect of the inner coil tube (inner coil tube thickness 5mm) Inner coil tube

25. Focus coil refined 2D model with a 5mm thick inner tube 127MPa

26. Coil structure tube thickness increased from 25mm to 30mm 125MPa

27. 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

28. Cases on the various Young’s modules of the coil

29. Case 1 – Model with no fillet, Magnet Young’s Modulus: 130GPa (1)

30. Case 2 – Model with no fillet, Magnet Young’s Modulus is 0.5GPa (1)

31. 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.

32. Sensitivity of the coil tube corner fillet

33. Case 1 – Model with fillet, magnet E = 130GPa

34. Case 2 – Model with fillet, magnet E = 5GPa

35. Case 3– Model with fillet, magnet E = 0.5GPa

36. Conclusion The 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.

37. 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

38. ADG BEH CFJ ABCDEFGHJ Fz N/m767975127105-478807854810124334-582579796561119992-547429 Fr N/m-288130-344907-220225370163456944444784102550712490891100174 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 1.65mm Epoxy Insulation Conductor 1.1mm Unit cellThe 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

39. Stress and displacement results on Model#1 Note that the coil is not displayed in all result plots.

40. 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:

41. 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:

42. 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:

43. 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^3 E: 5GPa Poisson’s Ratio: 0.4 The same nodal force applied to the coil

44. 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?

45. 30mm 45mm 12mm 25mm The 2-half bobbin model Max stress reduced by ~40%

46. 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

47. 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: 2227947N Old coil

48. The result plots on the new coil with new force profile applied (4 x 4 force output)

49. 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