Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity › event › 22161 › contributions ›...

In partnership with: India/DAEItaly/INFNUK/STFCFrance/CEA/Irfu, CNRS/IN2P3

Sundeep GhoshSudeshna SethVECC, India

Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity

Design and analysis approach by VECC

RF design of bare LB650 β=0.61 SRF cavity is taken from INFN.

Optimization of stiffener ring position of dressed cavity is carried out firstbased on LFD, dF/dP, cavity stiffness and tuning sensitivity criteria asper FRS.

Safety analyses of dressed cavity are performed under several loadcases to check its structural integrity.

Mechanical modes of vibration of dressed cavity are also found out.

2 Oct 29, 2019 Sundeep Ghosh| Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity

3

Methodology to find out Lorentz Force Detuning Coefficient (LFD)

Parametric modelling of dressed cavity with several stiffener ring radius, tuner

stiffness and cavity wall thickness

High frequency electro-magnetic analysis of original RF volume

Structural analysis of dressed cavity under Lorentz pressure (Prad)

High frequency electro-magneticanalysis of deformed RF volume

Electric field (E)

Modal frequency (F1)

Magnetic field (H)

Modal frequency (F2)

𝐿𝐿𝐿𝐿𝐿𝐿 = ⁄(F1 − F2) Eacc2

Prad =14 μ0 H2 − ϵo E2

Sundeep Ghosh| Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity Oct 29, 2019

Code used: ANSYS Multi-Physics

4

Methodology to find out Helium Pressure Sensitivity (dF/dP)


Code used: ANSYS Multi-Physics

Parametric modelling of dressed cavity with several stiffener ring radius, tuner

stiffness and cavity wall thickness

High frequency electro-magnetic analysis of original RF volume

Structural analysis with applied P on dressed cavity

High frequency electro-magneticanalysis of deformed RF volume

Modal frequency (F1) at P=0

Modal frequency (F2) after applying P

𝑑𝑑𝐿𝐿/𝑑𝑑𝑑𝑑 = ⁄(F1 − F2) 𝑑𝑑

Helium pressure (P)

Stiffener ring radius (mm)

(midcell-endcell)

Tuner stiffness (kN/mm)

LFD [Hz/(MV/m)^2]

dF/dP(Hz/mbar)

70-90 10 -3.92 31.0370-90 25 -2.27 27.3370-90 40 -1.79 26.2770-90 50 -1.62 25.8770-90 60 -1.50 25.6370-90 68 -1.43 25.4770-90 80 -1.35 25.2770-90 100 -1.26 25.0780-90 40 -1.88 25.4785-90 40 -1.94 22.990-90 40 -1.99 17.57

100-100 40 -2.2 4.4

LFD Vs Tuner Stiffness for Stiffener ring radius 70mm/90mm

dF/dP Vs Tuner Stiffness for Stiffener ring radius 70mm/90mm

5

Results of LFD & dF/dP with 4.2 mm cavity wall thickness


• Cavity deformation simulated in ANSYS with1mm displacement at one end of LB650 cavity.

• Electromagnetic simulation carried out in ANSYSfor undeformed and deformed cavity to find outfrequency shift.

• Undeformed and deformed RF volumes wereexported to CST Microwave studio from ANSYSfor cross-validation of results.

Tuning Sensitivity Calculation in ANSYS and CST

Note: The figure is an old one with double stiffener ring configuration. It is shown here for demonstration purpose only.

6

Methodology to find out tuning sensitivity


Bare cavity stiffness = Reaction Force/Applied Displacement X

Y

Z

1 mm displacement

Fixed

AUG 16 201615:32:20 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 USUM (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatDMX =.001 SMN =.261E-07 SMX =.001

1

MN

MX

X

Y

Z

ZV =1 DIST=.614085 XF =.119472 YF =.558259 Z-BUFFER

.261E-07

.111E-03

.222E-03

.333E-03

.444E-03

.556E-03

.667E-03

.778E-03

.889E-03

.001

CAVITY STIFFNESS WITH SR1 = 70 mm & SR2 = 90 mm

Contour plot of total displacement (m)

Un-deformed edge

7

Methodology to find bare cavity stiffness

Note: Similar method used to find out dressed cavity stiffness


Lorentz Force Detuning Coefficient

LFD = -2.2 Hz/(MV/m)^2

Helium pressure sensitivity df/dP = 4.4 Hz/mbar

Dressed cavity stiffnesskc = 3.1 kN/mm

Tuning sensitivitykt = 254.4 kHz/mm

Bare cavity stiffnesskb = 2.1 kN/mm

8

Summary of results of INFN’s EM design

Results shown below considering the following parameters

Single stiffener ring at 100 mm radius

Cavity wall thickness = 4.2 mm

Stiffener ring thickness = 4.0 mm

Tuner stiffness = 40 kN/mm


• After several discussions, it was decided to proceed with 90 mm radius and 3.75mm cavity wall thickness (after processing) since VECC has already procured 4mm Nb sheets.

• LFD,df/dP , cavity stiffness and tuning sensitivity with 90 mm radius and 3.75mm cavity wall thickness have not been calculated again. It is inferred from theresults of 4.2 mm cavity wall thickness.

• Our prior experience with VECC EM design shows reduction in cavity wallthickness from 4.2 mm to 3.75 mm results in increase in LFD by 5% anddecrease in dF/dP by 10%.

• Considering this variation, LFD and df/dp of INFN EM with 3.75 mm cavity wallthickness and 90 mm stiffener ring radius, LFD will be less than 2.1 Hz/(MV/m)^2and df/dP will be less than 19.3 Hz/mbar.

• Decrease in cavity wall thickness (from 4.2 mm to 3.75 mm) and stiffener ringradius (from 100 mm to 90 mm), will decrease cavity stiffness and increasetuning sensitivity. Hence values of these two parameter will be less than 5kN/mand greater than 180kHz/mm respectively. Thus they satisfy FRS/TRS criteria.

9

Operational parameters of INFN’s EM design based LB 650 model with 3.75 mm wall thickness and 90 mm stiffener ring radius


Safety analysis of dressed cavity• Identification of several operational and accidental loading

conditions of dressed cavity• Elastic stress analysis to check structural integrity of cavity

under the load cases• Limit load analysis to find out plastic collapse pressure of

cavity• Buckling analysis of bare cavity• Critical buckling pressure of Helium Vessel • Check for local failure• Fatigue assessment

10 Oct 29, 2019 Sundeep Ghosh| Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity

Thickness of cavity wall taken as 3.75 mm assuming 0.25 mm removal of 4 mm thick material by processing

Thickness of stiffener rings taken taken as 4 mm.

Single stiffener ring at 90 mm radius.

Dimensions of helium vessel taken similar to that HB650 except the length.

Half-symmetry used.

Actual tuner not modelled.

Simplified model for tuner used to simulate 40 kN/mm tuner stiffness.

11

CAD model and boundary conditions


F

F

M

y

FFMM

x

From Free Body Diagram, Reaction moment, 𝑀𝑀 = 𝐿𝐿𝐿𝐿2 Bending moment at any section in link#1, 𝑀𝑀1 = 𝑀𝑀(i.e. constant) Bending moment at any section in link#2, 𝑀𝑀2 = 𝐹𝐹𝑦𝑦2

2

Total strain energy, 𝑈𝑈 = 𝐹𝐹2𝐿𝐿12𝐸𝐸𝐸𝐸1

+ ∫0𝐿𝐿1 𝑀𝑀1

2

2𝐸𝐸𝐸𝐸1𝑑𝑑𝑑𝑑 + ∫0

𝐿𝐿2 𝑀𝑀22

2𝐸𝐸𝐸𝐸2𝑑𝑑𝑑𝑑

F

L2

L1

Link# 1

Link# 2

Applying Castigliano’s Theorem, deflection in x-direction at point P,

δ = 𝜕𝜕𝜕𝜕𝜕𝜕𝐹𝐹

= 𝐿𝐿 𝐿𝐿1𝐸𝐸𝐸𝐸1

+ 𝐿𝐿1𝐿𝐿22

𝐸𝐸𝐸𝐸1+ 𝐿𝐿23

3𝐸𝐸𝐸𝐸2

Stiffness, 𝐾𝐾 = 𝑃𝑃𝛿𝛿

= 1𝐿𝐿1𝐸𝐸𝐴𝐴1

+𝐿𝐿1𝐿𝐿2

2

𝐸𝐸𝐼𝐼1+

𝐿𝐿23

3𝐸𝐸𝐼𝐼2

Analytical model: A simplified model consisting of 2 links is chosen to provide a stiffness of 20 kN/mm. 2 such

models in parallel connection will effectively give 40 kN/mm of stiffness.

E = Hypothetical Young’s Modulus of link material

𝐿𝐿1, 𝐿𝐿2 = Length of link#1 & 2 respectively

𝐼𝐼1, 𝐼𝐼2 = Moment of Inertia of link#1 & 2 respectively

𝐴𝐴1 = Cross-section area of link#1

Taking,

E = 4.2*10^14 Pa (hypothetical) gives K = 20 kN/mm for one pair

2 such pairs in parallel will provide 40kN/mm stiffness

P

12

Simplified model for tuner


13

Material

Elastic

Modulus

[GPa]

Poisson’s

RatioYield Strength [MPa]

Ultimate Strength

[MPa]

Integrated Thermal

Contraction

293 K to

2 K [Δl/l]293 K 2 K 293 K 2 K

Nb 105 0.39 38 317 115 600 0.001455 Ti-45Nb 62 0.36 476 476 545 545 0.0019

Ti Gr. 2 107 0.33 276 834 345 1117 0.0015

Material Allowable stress as per

ASME Sec II Part D

293 K 2 KNb 25 171

55 Ti-45Nb 156 156Ti Gr. 2 99 319

Material properties taken from Fermilab specifications :5500.000-ES-371110 titled as “ Material Properties for Engineering Analyses of SRF cavities.”

Material properties


14

Finite element model

Cavity Main Coupler End Field probe end

Helium vesselBellows 20-noded mesh element

with 3 DOF/node

Total no. of elements = 9,35,290 Total no. of nodes = 44,18,001


• Gravity

• Helium pressure on outer surface of cavity and inner surface of helium vessel (P2 = 0.205 MPa)

Condition Simulated: Warm Pressurization

Applicable Temperature of allowable stress limits = 300 K

P2

15

Load case-1


Loads

16

Results: Load case-1

Contour plot of total deformation

Max deformation ~ 0.5 mm


17


Contour plot of Von-Mises stress in cavity

Localized high stress due to high (hypothetical) Young’s Modulus of simplified tuner

Max stress~24 MPa excluding localized high stress



Stress classification lines

SCL Material

Allowable stress of un-

welded material (MPa)

Weld joint efficiency

Allowable Pm(MPa) (S)

Simulated Pm (MPa)

Ratio (Simulated/Allowable)

A Nb-Nb 25 0.7 17.5 7.92 0.45

B Nb-55Ti45Nb 25 0.6 15 9.84 0.66

E 55Ti45Nb -Ti 79 0.6 47.4 1.30 0.03

F Ti-Ti 79 0.6 47.4 3.83 0.08

G Ti-Ti 79 0.6 47.4 46.23 0.97

H Ti-Ti 79 0.6 47.4 17.20 0.36

I Ti-Ti 79 0.45 35.55 4.20 0.12

J Nb-Nb 25 0.6 15 5.95 0.40

L Nb-Nb 25 0.6 15 5.24 0.35M Nb-Nb 25 0.7 17.5 6.29 0.36

N Nb-55Ti45Nb 25 0.6 15 3.62 0.24

Q 55Ti45Nb - Ti 79 0.6 47.4 4.19 0.09

R Ti - Ti 79 0.6 47.4 3.68 0.08

Membrane Stress (Pm) Results

As per ASME Sec VIII Div 2,Pm ≤ S

Pm: Primary Membrane StressS: Allowable Stress

Safe design




Local Membrane Stress (Pl) Results on stiffener ring connections

SCL Material




Allowable Pl(MPa) (1.5S)

Simulated Pl (MPa)


C Nb-55Ti45Nb 25 0.6 22.5 1.70 0.08

D Nb-Nb 25 0.6 22.5 12.57 0.56K Nb-Nb 25 0.6 22.5 12.61 0.56O Nb-Nb 25 0.6 22.5 12.18 0.54

P Nb-55Ti45Nb 25 0.6 22.5 1.58 0.07

As per ASME Sec VIII Div 2,Pl ≤ 1.5S

Pl: Local Membrane StressS: Allowable Stress

Safe design

Connections of stiffener rings to cavity are regions of gross structural discontinuities. It produces secondary local stress even though the applied load is primary in nature. Hence local membrane stress limit is used.

Justification of using 1.5S limit




Membrane + Bending (Pm + Pb) Stress Results

As per ASME Sec VIII Div 2,Pm + Pb ≤ 1.5S

Pm: Primary Membrane StressPb: Primary Bending StressS: Allowable Stress

Safe design

SCL Material




Allowable Pm + Pb(MPa) (1.5S)

Simulated Pm + Pb(MPa)


A Nb-Nb 25 0.7 26.25 8.35 0.32

B Nb-55Ti45Nb 25 0.6 22.5 16.96 0.75

E 55Ti45Nb -Ti 79 0.6 71.1 6.12 0.09

F Ti-Ti 79 0.6 71.1 13.21 0.19G Ti-Ti 79 0.6 71.1 49.78 0.70H Ti-Ti 79 0.6 71.1 33.33 0.47

I Ti-Ti 79 0.45 53.325 7.33 0.14

J Nb-Nb 25 0.6 22.5 12.88 0.57L Nb-Nb 25 0.6 22.5 10.01 0.45M Nb-Nb 25 0.7 26.25 7.49 0.29

N Nb-55Ti45Nb 25 0.6 22.5 3.71 0.16

Q 55Ti45Nb -Ti 79 0.6 71.1 12.21 0.17

R Ti - Ti 79 0.6 71.1 4.31 0.06




Membrane + Bending (Pm + Pb) Results on stiffener ring connections

As per ASME Sec VIII Div 2,Pm + Pb + Q ≤ 3.0 S Safe design

Connections of stiffener rings to cavity are regions of gross structural discontinuities. It produces secondary local stress even though the applied load is primary in nature.

Justification of using 3S limit

SCL Material



Weld joint

efficiency

Allowable Pm+ Pb (Primary +Secondary

stress) (MPa) (3S)

Simulated Pm + Pb

(MPa)


C Nb-55Ti45Nb 25 0.6 45 4.50 0.10

D Nb-Nb 25 0.6 45 23.25 0.52K Nb-Nb 25 0.6 45 24.27 0.54O Nb-Nb 25 0.6 45 22.73 0.51

P Nb-55Ti45Nb 25 0.6 45 5.30 0.12

Pm: Primary Membrane StressPb: Primary Bending StressQ: Secondary stressS: Allowable Stress

Note:ANSYS does not differentiate between primary and secondary loads and it clubs the membrane and bending stress components of both primary and secondary loads together as ‘Pm + Pb’


22


Stress classification plot at junction of stiffener ring with half-cells

Stre

ss in

tens

ity

Typical stress classification plot shown above

MEM+BEND plot clubs both primary and secondary stress together

Values encircled in green are used in Tables (shown in earlier slides) for comparison

Note


Gravity Liquid helium pressure on outer surface

of cavity and inner surface of helium vessel (P2 = 0.41 MPa)

Hydrostatic pressure of Liquid Helium Head

Condition Simulated: Cold operation, full liquid helium head and maximum pressure of LHe


P2

23

Load case-2


Loads

Hydrostatic pressure of liquid helium at 2 K

24





25


Contour plot of Von-Mises stress in cavity Max stress ~ 60 MPa excluding localized high stress

Allowable strength of Nb at 2K = 137 MPa

Safe design





As per ASME Sec VIII Div 2,Pm ≤ S

Pm: Primary Membrane StressS: Allowable Stress

Safe design

SCL Material




Allowable Pm (MPa)

(S)

Simulated Pm (MPa)


A Nb-Nb 137 0.7 95.9 16.10 0.17

B Nb-55Ti45Nb 125 0.6 75 21.74

0.29

E 55Ti45Nb -Ti 125 0.6 75 5.020.07

F Ti-Ti 255 0.6 153 14.42 0.09G Ti-Ti 255 0.6 153 107.38 0.70H Ti-Ti 255 0.6 153 33.72 0.22I Ti-Ti 255 0.45 114.75 7.36 0.06J Nb-Nb 137 0.6 82.2 11.91 0.14L Nb-Nb 137 0.6 82.2 10.52 0.13M Nb-Nb 137 0.7 95.9 13.58 0.14

N Nb-55Ti45Nb 125 0.6 75 4.43

0.06

Q 55Ti45Nb -Ti 125 0.6 75 7.37

0.10R Ti - Ti 255 0.6 153 7.06 0.05






Pl: Local Membrane StressS: Allowable Stress

Safe design



SCL Material




Allowable Pl (MPa) (1.5S)

Simulated Pl (MPa)


C Nb-55Ti45Nb 125 0.6 112.5 4.70 0.04

D Nb-Nb 137 0.6 123.3 25.02 0.20K Nb-Nb 137 0.6 123.3 24.72 0.20O Nb-Nb 125 0.6 112.5 24.17 0.21

P Nb-55Ti45Nb 125 0.6 112.5 5.45 0.05





As per ASME Sec VIII Div 2,Pm + Pb ≤ 1.5S

Pm: Primary Membrane StressPb: Primary Bending StressS: Allowable Stress

Safe design

SCL Material







A Nb-Nb 137 0.7 143.85 17.01 0.12

B Nb-55Ti45Nb 125 0.6 112.5 36.30 0.32

E 55Ti45Nb -Ti 125 0.6 112.5 11.19 0.10

F Ti-Ti 255 0.6 229.5 29.52 0.13

G Ti-Ti 255 0.6 229.5 136.18 0.59

H Ti-Ti 255 0.6 229.5 66.16 0.29

I Ti-Ti 255 0.45 172.125 13.53 0.08

J Nb-Nb 137 0.6 123.3 25.99 0.21

L Nb-Nb 137 0.6 112.5 11.19 0.09

M Nb-Nb 137 0.7 143.85 14.10 0.10

N Nb-55Ti45Nb 125 0.6 112.5 6.34 0.06

Q 55Ti45Nb -Ti 125 0.6 112.5 22.91 0.20

R Ti - Ti 255 0.6 229.5 15.40 0.07





As per ASME Sec VIII Div 2,Pm + Pb + Q ≤ 3.0 S Safe design

Connections of stiffener rings to cavity are regions of gross structural discontinuities. It produces secondary local stress even though the applied load is primary in nature.

Justification of using 3S limit

Pm: Primary Membrane StressPb: Primary Bending StressQ: Secondary stressS: Allowable Stress

Note:ANSYS does not differentiate between primary and secondary loads and it clubs the membrane and bending stress components of both primary and secondary loads together as ‘Pm + Pb’

SCL Material

Allowable stress of

un-welded material (MPa)


Allowable Pm + Pb(Primary

+Secondary stress) (MPa) (3S)



C Nb-55Ti45Nb 125 0.6 225 5.55 0.02

D Nb-Nb 137 0.6 246.6 45.98 0.19

K Nb-Nb 137 0.6 246.6 47.72 0.19

O Nb-Nb 125 0.6 225 40.48 0.18

P Nb-55Ti45Nb 125 0.6 225 7.61 0.03


Gravity Cool down to 2 K Cavity compression using tuner

by 2 mm

Condition Simulated: Cool down & cavity compression


30

Load case-3


LoadsCavity compressed by 2 mm

31





32




Safe design





Pm + Pb + Q ≤ 3S Safe design

SCL Material

Allowable stress of

un-welded material (MPa)


Allowable Pm + Pb (Primary +Secondary

stress) (MPa) (3S)

Simulated Pm + Pb

(MPa)


A Nb-Nb 137 0.7 287.7 59.55 0.21

B Nb-55Ti45Nb 125 0.6 225 163.20 0.73

C Nb-55Ti45Nb 125 0.6 225 61.91 0.28D Nb-Nb 137 0.6 246.6 51.86 0.21

E 55Ti45Nb -Ti 125 0.6 225 24.60 0.11F Ti-Ti 255 0.6 459 36.62 0.08G Ti-Ti 255 0.6 459 31.49 0.07H Ti-Ti 255 0.6 459 21.62 0.05I Ti-Ti 255 0.45 344.25 32.66 0.09J Nb-Nb 137 0.6 246.6 2.69 0.01L Nb-Nb 137 0.6 246.6 11.52 0.05K Nb-Nb 137 0.6 246.6 3.90 0.02M Nb-Nb 137 0.7 287.7 6.59 0.02

N Nb-55Ti45Nb 125 0.6 225 6.76 0.03O Nb-Nb 125 0.6 225 15.17 0.07

P Nb-55Ti45Nb 125 0.6 225 11.15 0.05

Q 55Ti45Nb - Ti 125 0.6 225 2.49 0.01R Ti - Ti 255 0.6 459 10.78 0.02


Gravity Liquid helium pressure on outer surface

of cavity & inner surface of helium vessel (P2 = 0.41 MPa)

Hydrostatic pressure of Liquid Helium Head

Cool down to 2 K Cavity compression by 2 mm

Condition Simulated: Cold operation with tuner extension, full liquid helium head and maximum pressure of LHe


P2

34

Load case-4


Loads

Hydrostatic pressure of liquid helium at 2 K

Cavity compressed by 2 mm

35





36




Safe design

Oct 29, 2019 Sundeep Ghosh| Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity




Pm + Pb + Q ≤ 3S Safe design

SCL Material


welded material

(MPa)


Allowable Pm + Pb (Primary +Secondary

stress) (MPa) (3S)

Simulated Pm + Pb

(MPa)

Ratio (Simulated/Al

lowable)

A Nb-Nb 137 0.7 287.7 63.70 0.22

B Nb-55Ti45Nb 125 0.6 225 169.35 0.75

C Nb-55Ti45Nb 125 0.6 225 67.64 0.30

D Nb-Nb 137 0.6 246.6 82.92 0.34

E 55Ti45Nb -Ti 125 0.6 225 27.72 0.12

F Ti-Ti 255 0.6 459 42.33 0.09

G Ti-Ti 255 0.6 459 111.99 0.24

H Ti-Ti 255 0.6 459 47.86 0.10

I Ti-Ti 255 0.45 344.25 34.73 0.10

J Nb-Nb 137 0.6 246.6 28.32 0.11

L Nb-Nb 137 0.6 246.6 36.97 0.15

K Nb-Nb 137 0.6 246.6 22.17 0.09

M Nb-Nb 137 0.7 287.7 14.65 0.05

N Nb-55Ti45Nb 125 0.6 225 6.85 0.03

O Nb-Nb 125 0.6 225 30.74 0.14

P Nb-55Ti45Nb 125 0.6 225 6.69 0.03

Q 55Ti45Nb - Ti 125 0.6 225 23.77 0.11

R Ti - Ti 255 0.6 459 17.00 0.04


Gravity Air pressure on the inner surface of

cavity and outer surface of helium vessel (P1 = P3 = 0.1 MPa)

Condition Simulated: Insulating and beam vacuum upset, helium volume evacuated


P1

38

Load case-5


Loads

P3

39





40




Safe design




SCL Material




Allowable Pm(MPa) (S)

Simulated Pm (MPa)


A Nb-Nb 25 0.7 17.5 4.86 0.28

B Nb-55Ti45Nb 25 0.6 15 3.20 0.21

E 55Ti45Nb -Ti 79 0.6 47.4 1.16 0.02

F Ti-Ti 79 0.6 47.4 1.83 0.04

G Ti-Ti 79 0.6 47.4 25.52 0.54

H Ti-Ti 79 0.6 47.4 7.78 0.16

I Ti-Ti 79 0.45 35.55 2.22 0.06

J Nb-Nb 25 0.6 15 2.91 0.19

L Nb-Nb 25 0.6 15 2.62 0.17

M Nb-Nb 25 0.7 17.5 3.88 0.22

N Nb-55Ti45Nb 25 0.6 15 0.52 0.03

Q 55Ti45Nb - Ti 79 0.6 47.4 1.51 0.03

R Ti - Ti 79 0.6 47.4 1.32 0.03


Pm ≤ S Safe design





SCL Material




Allowable Pl(MPa) (1.5S)

Simulated Pl (MPa)


C Nb-55Ti45Nb 25 0.6 22.5 1.31 0.06

D Nb-Nb 25 0.6 22.5 7.27 0.32

K Nb-Nb 25 0.6 22.5 5.76 0.26

O Nb-Nb 25 0.6 22.5 6.87 0.31

P Nb-55Ti45Nb 25 0.6 22.5 1.42 0.06


Safe design







Pm + Pb ≤ 1.5S Safe design

SCL Material







A Nb-Nb 25 0.7 26.25 5.77 0.22

B Nb-55Ti45Nb 25 0.6 22.5 10.55 0.47

E 55Ti45Nb -Ti 79 0.6 71.1 2.96 0.04

F Ti-Ti 79 0.6 71.1 6.31 0.09

G Ti-Ti 79 0.6 71.1 32.78 0.46

H Ti-Ti 79 0.6 71.1 15.66 0.22

I Ti-Ti 79 0.45 53.325 4.17 0.08

J Nb-Nb 25 0.6 22.5 6.45 0.29

L Nb-Nb 25 0.6 22.5 5.06 0.22

M Nb-Nb 25 0.7 26.25 5.12 0.20

N Nb-55Ti45Nb 25 0.6 22.5 2.26 0.10

Q 55Ti45Nb -Ti 79 0.6 71.1 5.75 0.08

R Ti - Ti 79 0.6 71.1 1.99 0.03





Pm + Pb + Q ≤ 3.0 S Safe design

SCL Material

Allowable stress of

un-welded material

(MPa)

Weld joint

efficiency

Allowable Pm+ Pb (Primary +Secondary

stress) (MPa) (3S)

Simulated Pm + Pb

(MPa)

Ratio (Simulated/Allow

able)

C Nb-55Ti45Nb 25 0.6 45 4.38 0.10

D Nb-Nb 25 0.6 45 12.26 0.27

K Nb-Nb 25 0.6 45 11.21 0.25

O Nb-Nb 25 0.6 45 12.82 0.28

P Nb-55Ti45Nb 25 0.6 45 4.34 0.10


45

Limit load analysis

• Objective is to find out plastic collapse pressure of cavity under the most critical load case (LC-1)

• Assumed elastic-perfectly plastic material properties of Nb (YS=38 Mpa)

• Other material properties taken as linear elastic.• Boundary conditions are similar to previous load

cases.• External pressure on cavity gradually increased

from 0 to 0.75 MPa over load steps.• Gravity load also considered.

Von-Mises stress distribution at last converged solution

Findings Solution failed to continue once it went

beyond 0.5 MPa. Yielding started near junction of

stiffener rings with the half-cells and end spools.

Solution continued until full section yielding took place.

Taking FOS=1.5 and an additional 20% reduction as per TD-09-005, critical collapse pressure comes as 0.266 MPa (> MAWP of 0.205 at 300 K)


46

First buckling mode shape

Buckling analysis of bare Niobium cavity

Loads and boundary conditions

Linear elastic buckling analysis of bare cavity is carried out as per ASME Sec VIII Div 2 “Design by Analysis” guidelines.

External pressure applied on cavity.

Both the flanges at the ends are kept fixed.

Critical pressure at which the bare cavity is found to buckle first is 12.3 MPa.

Design factor of 16 is taken following Code guidelines.

Considering this design factor, the buckling pressure comes out to be 0.77 MPa, which is 3 times higher than the MAWP of 0.205 MPa at room temperature.

Cavity is safe from buckling failure


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Buckling analysis of Helium Vessel

Critical buckling pressure of helium vessel is found out separately as per ASME Sec VIII Div 1 “Design by Rule” guidelines.

Key dimensions: Length of helium vessel shell, L = 722mm Outside diameter, Do = 450 mm Thickness, t = 3 mm (minimum)

Using code procedures; L/Do=1.6 Do/t = 150 E = 107 GPa Factor A=0.00045 (using ASME Section II, Part D, Subpart 3, Figure G) Allowable External Working Pressure (P) = (2/3) * Factor A * E*(t / D0)

This gives, P ~ 0.21 MPa > external working pressure of 0.1013 MPa

Helium vessel is safe from buckling failure


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Protection against fatigue failure

Fatigue failure of dressed cavity is evaluated based on ASME Sec VII Div. 2 Part 5 guidelines.

All types of cyclic operating loads have been considered and their estimated numbers are as follows:

Pressurization (NΔF) = 200 Cool Down (NΔT) = 100 Tuning (NΔTuner) = 200

As per Code, for an integral construction with no attachments or nozzles in the knuckle regions of the heads, applicable criteria for fatigue assessment is NΔFP + NΔPO + NΔTE + NΔTα ≤ 1000

Niobium cavity is an integral construction and there are no attachments or nozzles.

For dressed cavity assembly, Sum of all cycles = 200 +100 + 200 = 500, which is less than 1000.

Therefore, criteria NΔFP + NΔPO + NΔTE + NΔTα ≤ 1000 is satisfied and no fatigue assessment is necessary for the dressed cavity assembly.


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Protection against local failure

The criterion for protection against local failure is given in ASME Sec VIII Div. 2:𝜎𝜎1+𝜎𝜎2+𝜎𝜎3≤4∙𝑆𝑆

Material Allowable stress as per ASME

Sec II Part D (S)293 K 2 K

Nb 25 171

55 Ti-45Nb 156 156

Ti Gr. 2 99 319

Load Case Sum of principal Stresses / Allowable stress for Nb

Sum of principal Stresses / Allowable stress for Nb-Ti

Sum of principal Stresses / Allowable stress for Ti

1 (@300K) 0.36 0.03 0.52

2 (@2K) 0.10 0.07 0.84

3 (@2K) 0.31 0.28 0.86

4 (@2K) 0.33 0.30 0.88

5 (@300K) 0.35 0.01 0.20

Design is safe from local failure


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Modal analysis

Mechanical modal analysis carried out in ANSYS Workbench.

Boundary conditions similar to static structural analysis are used.

1st transverse mode ~ 49 Hz 2nd transverse mode ~ 54 Hz

1st longitudinal mode ~ 78 Hz 3rd transverse mode ~ 103 Hz


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Transport loading “3g”

• Static structural analysis carried out with 3g acceleration inertial load in X, Y and Z directions.

• Cavity assembly constrained on helium vessel lugs.• Maximum deformation comes ~ 0.41 mm.• Maximum Von-Mises stress in cavity is found to be ~ 20 MPa

excluding sharp corners and points of singularities.

Total deformation under 3g transport loading

Oct 29, 2019 Sundeep Ghosh| Mechanical design of LB650 (β=0.61) 3.75mm SRF Cavity

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Conclusion• EM design of LB650 (β=0.61) SRF cavity has been taken from INFN.• Single stiffener ring at 90 mm radius is chosen as the optimized position for LB650 cavity based

on LFD, dF/dP and other operational parameters given in FRS.• Tuner stiffness is taken same as that of HB650 cavity which is 40 kN/mm.• Cavity wall thickness after processing is chosen as 3.75 mm for all mechanical analyses since

VECC has already procured 4 mm thick Nb sheets.• Structural integrity of the dressed cavity has been analyzed under all possible load cases

covering all normal and anticipated loading conditions. • ASME Sec VIII Div 2 “Design by Analysis” rule has been applied to check linearized stress

results (Membrane and Bending) with the allowable limits at several critical locations, mainly weld joints, of the dressed cavity.

• All the linearized stress results for all load cases are found within allowable limits even with conservative material property of Nb.

• Limit load analysis with the most critical load case (LC-1) ensures 30% margin of safety above MAWP at room temperature (0.205 MPa).

• Protection against ratcheting is ensured by checking stress limits within 3S for deformation controlled load cases (LC-3 and 4).

• Buckling analysis of bare Nb cavity shows 3 times higher critical buckling pressure than MAWPat room temperature.

• ASME Sec VIII Div 1 “Design by Rule” calculations ensures safety of Helium Vessel from buckling failure.

• Safety check of dressed cavity has been done against local failure and fatigue failure (cyclic loading) as per Code and it is done to be okay.

• Mechanical modal analysis is carried out and it shows 3 modes below 100 Hz frequency.


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Thank you!


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