unit 11 mechanical structures - cern

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


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


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


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


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



Collaring model of 11 T dipole

Unit 11 - 6

11 T collaring simulation (E. Gautheron, S. Izquierdo Bermudez)



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



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



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



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



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



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



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


Structures based on collars

Structures based on iron yoke

Structures based on Al shell



CONTENTS

Unit 11 - 14


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


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))







The coils inside the pre-collars

The pre-collared pack inside the yoke


Unit 11 - 17

Iron collars for MQXA in LHC(T .Nakamoto, T .Ogitsu, et al.)







The coils inside the precollars

The precollared pack inside the yoke


Unit 11 - 18

Iron collars for D1 in HL-LHC(T .Nakamoto, M. Sugano, et al.)


Structure based on steel collars

Structure based on iron yoke

Structure based on Al shell



CONTENTS

Unit 11 - 19


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.)



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


Po

le o

r m

idp

lan

est

ress

Pins/key insertion

Press release

Cool-down


Stress during assembly and cool-down, collars Stress during assembly and cool-down, AL shell



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



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



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



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



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


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)


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







CONTENTS

Unit 11 - 29


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


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


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


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)


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


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


CONTENTS






Unit 11 - 36


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


AXIAL STRUCTURE

Example of longitudinal rods

See slides from S. Izquierdo Bermudez for a detailed talk on axial support

Unit 11 - 38

FrescaIIMQXF


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


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


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



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

unit 11 mechanical structures - cern

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