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E. Todesco, June 2020
Unit 11Mechanical structures
Ezio TodescoMSC Group, TE Department
European Organization for Nuclear Research (CERN)
This is a brand new unit, with all caveats associated
Thanks to S. Farinon, S. Izquierdo Bermudez, P. Ferracin for contributions
Thanks to L. Bottura and G. de Rijk for proposing and supporting this initiative
All the units will use International System (meter, kilo, second, ampere) unless specified
First revision, slides 23 and 26 corrected, plus reference on axial loading added
E. Todesco, June 2020
Part 1 – From beam dynamics to magnet specificationsUnit 1: The energy and specifications for cell dipole and quadrupole
Unit 2: The luminosity and specifications for insertion region magnets
Appendix A: Beam optics from stable motion to chaos
Part 2 – Principles of electromagnetsUnit 3: Multipolar expansion of magnetic field
Unit 4: How to generate pure multipole field
Part 3 – Basics of superconductivityUnit 5: Elements of superconductivity
Appendix B: Maxwell and scales in atomic physics
Unit 6: Instability and margins
PLAN OF THE LECTURES
Unit 11 - 2
E. Todesco, June 2020
Part 4 – Magnet designUnit 7: Strand, cable and insulation
Unit 8: Short sample field/gradient of sector coils and sensitivity to parameters
Unit 9: Grading the current density and iron effect
Unit 10: Forces
Unit 11: Structures
Unit 12: Protection
Appendix C: A parade of magnet designs
Appendix D: A digression on costs, and two case studies, from Terminator to FCC
PLAN OF THE LECTURES
Unit 11 - 3
E. Todesco, June 2020
Structures based on collars
Structures based on iron yoke
Structures based on Al shell
Structures based on stress management
Structures for axial support
CONTENTS
Unit 11 - 4
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
Tevatron dipole used for the first time the collar concept (A. Tollestrup et al.)
A rigid structure, provided by stainless steel “collars”, to give the required preload
Collars are assembled under a press and locked through keys
Can be either external keys or pins in holes
Collars guarantee a rigid structure and a well defined cavity(and good field quality)
Unit 11 - 5
Twin collars with pins for the LHC dipole(D. Perini, P. Fessia, et al.)
Collars for the D2 in HL-LHC(S. Farinon et al.)
keys
pins
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
Collaring model of 11 T dipole
Unit 11 - 6
11 T collaring simulation (E. Gautheron, S. Izquierdo Bermudez)
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
The collar drawback: one needs to prestress much more to get a given prestress at 1.9 K/4.2 K – for two different reasons
The collaring requires a higher compression to insert pins in the holes or keys
The thermal contraction of stainless steel is low with respect to the coil, so a non negligible loss of prestress is present in the transition room temperature 1.9 / 4.2 K
The prestress loss is systematically underestimated, in all models
For the LHC dipoles, 120 MPa during collaring, 70 MPa at room temperature after press release, 25 MPa at 1.9 K (internal pins)
For the HL-LHC nested corrector, 140 MPa during collaring, 120 MPa at room temperature after press release, 40/60 MPa at 1.9 K (external keys)
Unit 11 - 7
PreassemblyPo
le o
r m
idp
lan
est
ress
Pins/key insertion
Press release
Cool-down
1.9 KRoom temperature
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
Dimensioning the collar thicknessCollar thickness determines the cost (material) and the distance between coil and iron (decrease of current density)
Even though the problem is intrinsically two-dimensional, one can try to slice it in two main aspects
Thickness needed to give the required prestress (white arrow)
Thickness needed to avoid a large deformation in
the horizontal plane due to radial forces (black arrow)
Difficult to find this in the literature
How large should be the collar to give the prestress?First: having a rigid structure, not deforming the collars
Thumb rule: since SS has ten times larger modulus than the coil, having collar width as the coil width guarantees very small deformation i.e. the coil takes 90% of the deformation
Second: having the collars far from yield
This prevents to go to very very thin collars, otherwise you reach the yield point – or you need an additional support (support of the iron)
Unit 11 - 8
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
The system can be approximated with two springs in equilibrium
In the coil (compression) in the structure (tension)
Equilibrium condition is on the forces/unit length
Two requirementsThe stress in the structure well below yield point
The deformation of the structure much smaller than the coil deformation
Unit 11 - 9
sc= E
cec
ss= E
ses
Fc=ws
c=wE
cec F
s=w
sss=w
sEses
ss<< E
s,y
es<<e
c
FsFc
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
The Tevatron case is a case with collar thickness smaller than the coil width
ws=10 mm thick collars versus w=16 mm thick coil
But prestress is low: sc=360*4.3*38/2000=30 MPa
That becomes sc=33 MPa with the refined estimate – this is what we need as coil stress
Stress in the structure: 50 MPa, well below yield point
Coil versus structure deformation: ten times larger
Unit 11 - 10
Fs=w
sss=w
sEses
Fc=ws
c=wE
cec
wsss= F
s=w
csc
ss=wcsc
ws
=16´33
10= 50MPa
ec
es
=wsEs
wEc
=10
16
210
15= 9
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
The LHC dipoles case is a special case with oversized collar thickness40 mm thick stainless steel collars versus 30 mm thick coil
Initially the design was for Al collars
Change was done in a late phase of prototyping, and redesigning the iron was not an option
So the thickness was set for the softer material
This thickness also allowed to keep a double collaring, with saving on the manufacturing time – otherwise one should have had separate collars (as Mfisc)
Unit 11 - 11
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
The LHC dipoles casew=31 mm
wc=40 mm (but a good fraction is removed for the pin hole, so I would take 20 mm)
sc=55 MPa
Stress in the structure
Collar deformation is small
With Al collars, a ratio 1:3 in the deformation taken by the structure:coil
Unit 11 - 12
ss=wcsc
ws
=31´55
20= 80MPa
ec
es
=wsEs
wEc
=20
31
210
15= 9
ec
es
=wsEs
wEc
=20
31
70
15= 3
E. Todesco, June 2020
STRUCTURE BASED ON COLLARS
HERA dipole used Al collars for the first time: why?Larger thermal contraction, less prestress loss
Lower cost
Collar thickness similar to the coil width (20 mm) is adequate to have a rigid structure and being far from yield point
Aperture radius: 37.5 mm
Current density: 290 A/mm2
Field: 4.7 T
Midplane stress: 28 MPa
Stress in the structure
Collar deformation is non negligibleIron gives additional support
Unit 11 - 13
Al collars for HERA main dipoles(R. Wolf, et al.)
ss=wcsc
ws
=20´ 28
20= 28MPa
ec
es
=wsEs
wEc
=20
20
70
28= 2.5
E. Todesco, June 2020
Structures based on collars
Structures based on iron yoke
Structures based on Al shell
Structures based on stress management
Structures for axial support
CONTENTS
Unit 11 - 14
E. Todesco, June 2020
STRUCTURE BASED ON COLLARING AND IRON SUPPORT
The iron can contribute to the collar structureExample of MFISC magnet, a Nb-Ti double aperture dipole with separate stainless steel collars (25 mm thick) and line-to-line fit between iron and collars
The advantage is that one has a larger rigidity, and one can use thinner collars, increasing the iron contribution (see Unit 9)
The drawback is that one adds another interface
Unit 11 - 15
Mfisc structure: collars and line-to-line fit(G. Spigo, D. Leroy, D. Perini, et al. IEEE TAM 32 (1996) 2097)
10.5 Trecord
E. Todesco, June 2020
STRUCTURE BASED ON COLLARING WITH IRON
The iron can make the whole work of the collarsIn this case we use thin spacers and the keys are applied to the iron
Can be in stainless steel or (RHIC case) plastic spacers
The advantage is that the iron is closer and can reduce the current and enhance the field (see Unit 9)
The drawback is that one has to align one more components
The coils inside the spacers
The pre-collared pack inside the yoke
Examples: D1 in HL LHC, MQXA in LHC, RHIC dipole
Unit 11 - 16
RHIC dipole(E. Willen, P. Wanderer, et many al. NIM A 499 (2003))
E. Todesco, June 2020
STRUCTURE BASED ON COLLARING WITH IRON
The iron can make the whole work of the collarsIn this case we use thin spacers and the keys are applied to the iron
Can be in stainless steel or (RHIC case) plastic spacers
The advantage is that the iron is closer and can reduce the current and enhance the field (see Unit 9)
The drawback is that one has to align one more components
The coils inside the pre-collars
The pre-collared pack inside the yoke
Examples: D1 in HL LHC, MQXA in LHC, RHIC dipole
Unit 11 - 17
Iron collars for MQXA in LHC(T .Nakamoto, T .Ogitsu, et al.)
E. Todesco, June 2020
STRUCTURE BASED ON COLLARING WITH IRON
The iron can make the whole work of the collarsIn this case we use thin spacers and the keys are applied to the iron
Can be in stainless steel or (RHIC case) plastic spacers
The advantage is that the iron is closer and can reduce the current and enhance the field (see Unit 9)
The drawback is that one has to align one more components
The coils inside the precollars
The precollared pack inside the yoke
Examples: D1 in HL LHC, MQXA in LHC, RHIC dipole
Unit 11 - 18
Iron collars for D1 in HL-LHC(T .Nakamoto, M. Sugano, et al.)
E. Todesco, June 2020
Structure based on steel collars
Structure based on iron yoke
Structure based on Al shell
Structures based on stress management
Structures for axial support
CONTENTS
Unit 11 - 19
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
In this structure, an Al shell gives the azinuthal prestress on the coil
Low prestress is given at room temperature through bladders that create clearance for the keys (no need of collaring press)
During cool-down, the Al shrinks and the prestress is increased to reach the target
The structure is open gap
First proposed by S. Caspi
and engineered in LBNL
Review paper for MQXF in
IEEE TAS 26 by P. Ferracin, G. Ambrosio 4000207
Unit 11 - 20
MQXF cross-section(P. Ferracin, G. Ambrosio , et al.)
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
Advantages:
Better control of stress
Maximum stress is reached at 1.9 K, when it is needed
No heavy tooling
DisadvantagesContrary to collars, you do not impose position but you impose stress – so field quality could be more problematic (but FQ is found to be good)
Unit 11 - 21
Po
le o
r m
idp
lan
est
ress
key insertionBladder removal
Cool-down
1.9 KRoom temperature
Po
le o
r m
idp
lan
est
ress
Pins/key insertion
Press release
Cool-down
1.9 KRoom temperature
Stress during assembly and cool-down, collars Stress during assembly and cool-down, AL shell
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
LHC Accelerator R&D program (LARP) launched in 2000-2010 the TQ program to compare Al shell and the collar structure
The magnets used the same design of coil
Both designs reached required performance, with the Al shell guaranteeing a better reproducibility of the results on the several models
LARP opted for Al shell for the next step, HQ quadrupole (120 mm aperture)
Unit 11 - 22See review papers by S. Gourlay, P. Wanderer, G.L. Sabbi on IEEE TAS in 2000-2010
TQC TQS
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
Prestress increase during cool-downAl has a thermal shrinkage of 4.2×10-3
The preload increase during cool down
depends on the ratio between
the shell radius and the aperture radius
Example of MQXFShell diameter 630 mm
Increase of 60 MPa during cool-down
Unit 11 - 23
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
Thickness of the shellThe shell thickness should be large enough to keep internal stresses well below yield limit and to have a much rigid structure than the coil arc
These are the same equations shown for the collars (one dimensional approximation)
c stand for coil, s for shell
Condition for yield – for Al yield is 550 MPa, 300 is a safe value for peak stresses, so 150 MPa for average is reasonable
Deformation of the structure – it is not a strong requirement, i.e. we can have structures with 1/3 deformation
orUnit 11 - 24
sc= E
cec
ss= E
ses
Fc=ws
c=wE
cec
Fs=w
sss=w
sEses
ss<< E
s,y
es<< e
ces<e
c
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
Example of MQXFShell thickness ws=29 mm
Coil thickness w=36 mm
Midplane compression sc=110 MPa
Shell internal stresses(150 MPa average, 300 MPa peak found with ANSYS)
Comparison of coil and shell deformation1/3 of the deformation is taken by the shell (dilatation), 2/3 by the coil (compression)
Unit 11 - 25
ss=wcsc
ws
=36´110
29=136MPa
ec
es
=wsEs
wEc
=29
36
70
30=1.9
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
The design for FCC of a 16 T magnet from INFNWith a coil with 60 mm width, and two apertures, and a azimuthal stress of the order of MPa, a very large Al shell thickness is required to avoid that it enters the plastic regime
I would judge as 100 mm necessary, design of INFN has 50 mm – to be further discussed
Unit 11 - 26
E. Todesco, June 2020
STRUCTURE BASED ON THE AL CLAMP
The MDPCT1 dipole recently built in FNAL makes use another concept based on prestress increase due to Al but with a closed gap
Iron yoke vertical split, I-shaped Al clamps give prestress increase during cool down
The gap is closed after cool-down, so the structure is not open as in Al shell and B&k– this is easing alignment but requiring a very careful control of the gap closing
Assembly needs a press, 50-70 MPa at room temperature, 100-130 MPa after cool-down
Unit 11 - 27(See papers in IEEE TAS by A. Zolbin, I. Novitski et al., between 2015 and 2020)
E. Todesco, June 2020
SCISSOR LAMINATIONS
This structure was proposed for the LHC correctors, also relies on the shrinking due of an external ring of Al to give prestress
See works from A. Ijspeert, M. Allit M. Karppinen, for instance A. Ijspeert et al., IEEE TAS 12 (2002) 90
Unit 11 - 28
E. Todesco, June 2020
Structure based on steel collars
Structure based on iron yoke
Structure based on Al shell
Structures based on stress management
Structures for axial support
CONTENTS
Unit 11 - 29
E. Todesco, June 2020
STRESS MANAGEMENT
The equation for stress shows that to go above 15-20 T fields for a sector coil accelerator dipole of 25 mm aperture radius one has to start decreasing the current density
The community has proposed exploring an alternative way: stress management
Stress management: having a mechanical structure that intercepts the stress accumulation
As in a building, the weight of the furniture of each floor
does not accumulate on the family living at ground floor,
but is taken by the walls
See works from P. Mcintyre, IEEE TAS between 1995 and today
Unit 11 - 30
E. Todesco, June 2020
STRESS MANAGEMENT
The case of radial stress seems even more challenging, since it is proportional just to the magnetic pressure so even a less effective magnet (lower current density) has the same stress
In this case stress management has to be with an horizontal frame taking the horizontal forces
The main problem (still open today) of stress management structures is the following
How to give preload to each part ?
The second feature is that the structure gives a dilution of the current density, i.e. a less effective design
But this is a price we are ready to pay
Unit 11 - 31
E. Todesco, June 2020
STRESS MANAGEMENT
The idea for a block dipoleObviously, some efficiency is lost to make room for the supporting structure
Main difficulty is to have both stress interception and preload
Several years of research, concept not yet proved
P. Mcintyre, IEEE TAS between 1995 and today
Unit 11 - 32
E. Todesco, June 2020
STRESS MANAGEMENT
Stress management has been proposed for a sector coilThrough wedges and cylinders – but how to give prestress ?
Unit 11 - 33
I. Novitski, A. Zlobin, FNAL-CONF-17-340 (2017)
E. Todesco, June 2020
STRESS MANAGEMENT
The canted cos theta is the extreme case of stress management
Each turn is individually supported
The stress is managed also radially since there is a segmentation in several layers, each one supported
No mechanism to provide azimuthal prestress
Unit 11 - 34
A 16 T dipole based on CCT design, S. Caspi, et al. IEEE TAS 27 (2017) 4001505
E. Todesco, June 2020
STRESS MANAGEMENT
Perhaps the real extreme case of stress management is a double collar
This is the design of the nested corrector for HL LHC, a magnet with 2.1 T in each direction
Large dilution of the current density, but here you can give azimuthal prestress
Unit 11 - 35
A double collar nested corrector for HL LHCF. Toral, P. Fessia, J. C. Perez, J. Garcia Matos et al. IEEE TAS 2016-2020
E. Todesco, June 2020
CONTENTS
Structure based on steel collars
Structure based on iron yoke
Structure based on Al shell
Structures based on stress management
Structures for axial support
Unit 11 - 36
E. Todesco, June 2020
AXIAL STRUCTURE: TIE RODS VS STOPPERS
Longitudinal rods can be used to have a preload to compensate the axial forces
Typically they are made of very stiff material (SS) to avoid occupying a large fraction of the magnet cross-section
Bullets and end plates are used to give some axial loading at room temperature
The load aims at compensating only a fraction of the total force since friction keeps good part of it
Nevertheless, some axial precompression is beneficial
Examples: all Nb3Sn LARP magnets (HQ, TQ), and in HL-LHC: MQXF and D2 magnets
An alternative structure is to have no preload, but stoppers to prevent from longitudinal dilatation due to forces during powering
The stoppers are welded on the stainless steel shell that is used for He containment
This is the solution adopted for the LHC dipoles and for the HL-LHC 11 T dipole
Unit 11 - 37
E. Todesco, June 2020
AXIAL STRUCTURE
Example of longitudinal rods
See slides from S. Izquierdo Bermudez for a detailed talk on axial support
Unit 11 - 38
FrescaIIMQXF
E. Todesco, June 2020
CONCLUSIONS
There are several ways of designing a support structureThe solution for a given magnet is not unique
Structures based on collars are the workhorse of Nb-Ti magnets
Guarantees adequate support to avoid deformation and allows giving azimuthal prestress
A partial support of the iron yoke has been used in several cases
This allows reducing the collar thickness, and having more contribution to the field, and reduction of collar deformation
A total support of the yoke is also an optionVery thin spacers allow to place the iron much closer to the coil, reducing the current density, and therefore stress
It a very rigid structure due to the large thickness of the iron
Unit 11 - 39
E. Todesco, June 2020
CONCLUSIONS
Al shell structure guarantees that the peak prestress is reached in operational conditions
Introduced in LNBL, used in several Nb3Sn magnets where the degradation threat at 150 MPa is present
It showed to be suitable to a very precise control of prestress
It has been scaled from 1-m-long to 3.4 m long magnets with LARP, and to 7.15 m long magnet in HL LHC MQXFB at CERN
The open gap gives a large simplification, and the drawback of alignment does not show: field quality proves to be very good
The concept has been recently extended in FNAL to a 14 T dipole magnet based on Al clamps
Al shell was used in HL-LHC correctors, with a scissor laminations concept
Unit 11 - 40
E. Todesco, June 2020
CONCLUSIONS
As shown in Unit 10, above a certain field (for radial stress) and a certain combination of aperture, field and current density (for azimuthal stress) the 150 MPa limit is reached
The only alternative in this case is to dilute the coil with a structure to partially intercept the stress (stress management)
Proposed for blocks, extended to sector coils, has its extreme version in the canted cos theta design
The main open point of these structure is how to give azimuthal prestress
Unit 11 - 41
E. Todesco, June 2020
STRUCTURE BASED ON BLADDER AND KEYS
Four examples of configurations
Unit 11 - 42
Aperture (mm)
Coil width (mm)
Shell thickness
(mm)
Shell outer radius (mm)
TQ 90 20 20 250
HQ 120 30 25 285
MQXF 150 36 29 307
FrescaII 100 80 65 515