Engineering Analysis of β=0.9, 650 MHz cavity for safety...As per ASME section II part D AS Near...

In partnership with:

India/DAE

Italy/INFN

UK/STFC

France/CEA/Irfu, CNRS/IN2P3

Engineering Analysis of β=0.9, 650 MHz cavity for safety

Nitin Nigam

PIP-II β=0.90 & 0.92 Jacketed Cavity FDR

1 February 2019

Outline

• Introduction

• Load considered during design

• Load Case Description

• Materials Property for simulation

• Design of Dressed cavity as per Technical Division Technical

Note TD-09-005

• Safety analysis during pressure test

• Conclusion

2/1/2019Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for safety 2

Introduction

• Four of 650 MHz 0.9 Beta Dressed Cavity is going to be used in HB

650 MHz prototype cryomodule.

• It is a 5-cell SRF cavity made of 300 RRR niobium.

• Engineering Analysis of this cavity was performed for safety in

accordance with “Technical Division Technical Note TD-09-005”


Loads and Constraints

1) Pressure Loads

P1= Pressure due to Helium Volume

P2 = Insulating Vacuum

P3 = Beam Vacuum

2) Gravity Load

3) Hydrostatic Pressure on Cavity due to Helium Weight

4) Cool Down to 2 K

5) Tuner Extension of 0.4 mm

P1 P2 P3

Face Fixed Free in Axial Direction


Load Case Description

Where

Pm primary membrane stress

Pl primary local stress

Pb primary ending stress

Q secondary stress


Load

Case

Loads ConditionSimulated Temp. Applicable

Stress

Categories

1

1. Gravity

2. P1= 0.205 MPa

3. P2=P3 = 0

Warm Pressurization 293 K Pm, Pl , Pl + Q

2

1. Gravity

2. P1=0.41 MPa

3. P2=P3 = 0

Cold operation, MAWP

at cold

2 K Pm, Pl , Pl+Q

3

1.Cool down to 2K

2. Tuner extension

Cool down and

tuner extension

2 K Q

4

1. Gravity

2. Cool down to 2 K

3. Tuner extension

4. P1=0.41 MPa

5. P2=P3 = 0

Cool down, maximum

pressure -

2 K Q

5

1.Gravity

2. P1 = 0

3. P2 = P3 = 0.1 MPa

Insulating and beam

vacuum upset, helium

volume evacuated

293 K Pm, Pl , Pl+Q

Materials Property for simulation

• Niobium 300 RRR

• Niobium -Titanium

• Titanium Grade 2

• SS 316

The Temperature dependent material properties used in the analysis have been taken from Fermilab

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


Material Allowable Stress As per

ASME section II part D

2 K 300 K

Nb 171 25

Ti-45Nb 156 156

Gr. 2Ti 319 99

Design of Dressed cavity (as per Technical Division Technical Note TD-09-005)

▪ Design by Rules –Section VIII Division 1

• Design of He vessel done & report is in Teamcenter with Doc. ED0005130

• Design of Bellow done & report is in Teamcenter with Doc. ED0004939

▪ Design by Analysis –Section VIII Division 2

• ASME BPV Code Section VIII Division 2 Part 5 guidelines are followed for

Design by Analysis.

• Design of cavity was performed and presented in here.


Design by Analysis –Section VIII Division 2

The design by analysis requirements were satisfied for following

failure modes.

I. Plastic collapse –

II. Ratcheting -

III. Local failure -

IV. Buckling -

V. Fatigue -


FEM Simulation was performed

for all the five load cases descried

earlier, Out of which, load case 1

was found to be critical, hence it

is discussed in detail and for

other load cases only results have

been presented.

Simulation detail- Load case -1


3D Finite Element Model 3D Meshed Model

SCL drawn in the dressed cavity Loads and boundary condition

1. Gravity

2. P1= 0.205 MPa

3. Tuner stiffness 45 kN/mm

Result Load Case-1


Stress distribution in cavity

Stress distribution in bellow

Max. stress 40.9 MPa

Max. stress 146 MPa

Result Load Case-1


Material SCL Pm (MPa)Welding

efficiency

Allowable stress

(A1) (MPa)

Ratio

Pm /A1

Pm +Pb

(MPa)

Allowable

stress (A2)

MPa

Ratio

(Pm +Pb)/A2

Nb-NbTi 1 0.01 0.6 15 0.001 0.012 22.5 0.001

Nb 2 0.31 0.6 15 0.021 0.8 22.5 0.036

Nb 3 1.5 0.6 15 0.1 1.8 22.5 0.08

Nb 4 13.5 0.6 15 0.9 18.4 22.5 0.818

Nb-NbTi 5 2.9 0.6 15 0.193 8.7 22.5 0.387

Nb 6 7.8 0.6 15 0.52 10.4 22.5 0.462

Nb 7 15.6 0.6 15 1.04 21.5 22.5 0.95

Nb 8 15.8 0.6 15 1.053 33.8 22.5 1.502

Nb 9 15.6 0.6 15 1.04 21.7 22.5 0.964

NbTi-Ti 10 1.9 0.6 59.4 0.032 4 89.1 0.045

Ti 11 2.6 0.6 59.4 0.044 4 89.1 0.045

Ti 12 13.9 0.6 59.4 0.234 32 89.1 0.359

Ti 13 31.7 0.6 59.4 0.534 38.5 89.1 0.432

Ti 14 23 1 99 0.232 108 148.5 0.727

Ti 15 10 0.6 59.4 0.168 11 89.1 0.123

Ti 16 3 0.6 59.4 0.051 5.4 89.1 0.061

NbTi-Ti 17 2.3 0.6 59.4 0.039 11.1 89.1 0.125

Nb-NbTi 18 1.6 0.6 15 0.107 4.3 22.5 0.191

Nb 19 8.2 0.6 15 0.547 14.9 22.5 0.662

Nb 20 2.1 0.6 15 0.14 7.8 22.5 0.347

Nb 21 3.6 0.6 15 0.24 3.7 22.5 0.164

Nb-NbTi 22 0.83 0.6 15 0.055 0.91 22.5 0.040

Table-1

Estimation of allowable stress values for Niobium


38 MPa

38/ 1.5 = 25 MPa

25 X 0.6 = 15 MPa

Yield strength(20% derating included as it is

not a code material as per

Technical Note TD-09-005)

Allowable Stress (AS)

As per ASME section II part D

AS Near weld

(non radiographed)

Y S originally was 46 MPa

Finally from 46 MPa yield strength of the material we have 15 MPa

allowable, it is highly conservative …. So performed non linear stress

analysis as per Limit load analysis of ASME considering elastic perfectly

plastic material property. (Assumed yield stress 38 MPa which already

includes 20% reduction)

Limit Load Analysis


Last converged pressure 0.54 MPa, applying FOS 1.5, which gives 0.36 MAWP MPa this is

75% higher then the applicable MAWP (0.205 MPa) at room temperature

Zoomed view with mesh detail

Stress distribution at the last conversed time step

Bilinear elastic perfectly

plastic mat. Property

Yield stress= 38 MPa

Simulation with fine mesh finer mesh size

Limit Load Non Linear analysis for load case-1 (as per ASME Section VIII Div. 2)

(No hardening)

With this analysis

safety is insured

for load case-1

2/1/2019 Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for safety 14

Result Load Case-2


Material SCLPm

(MPa)

Welding

efficiency

Allowable stress

(A1) (MPa)RatioPm /A1

Pm +Pb

(MPa)

Allowable

stress (A2)

MPa

Ratio(Pm +Pb)/A2

Nb-NbTi 1 2.9 0.6 93.6 0.001 2.9 93.6 0.001

Nb 2 1.6 0.6 102.6 0.008 1.6 102.6 0.012

Nb 3 4.4 0.6 102.6 0.03 4.4 102.6 0.023

Nb 4 16.1 0.6 102.6 0.286 16.1 102.6 0.263

Nb-NbTi 5 3.9 0.6 93.6 0.06 3.9 93.6 0.142

Nb 6 17.4 0.6 102.6 0.155 17.4 102.6 0.135

Nb 7 33.9 0.6 102.6 0.311 33.9 102.6 0.26

Nb 8 31.3 0.6 102.6 0.309 31.3 102.6 0.439

Nb 9 35.2 0.6 102.6 0.308 35.2 102.6 0.286

NbTi-Ti 10 12.5 0.6 191.4 0.019 12.5 191.4 0.029

Ti 11 4.5 0.6 191.4 0.028 4.5 191.4 0.028

Ti 12 1.3 0.6 191.4 0.139 1.3 191.4 0.22

Ti 13 1.4 0.6 191.4 0.322 1.4 191.4 0.263

Ti 14 37.8 1 319 0.146 37.8 319 0.451

Ti 15 51.5 0.6 191.4 0.106 51.5 191.4 0.078

Ti 16 44.2 0.6 191.4 0.03 44.2 191.4 0.051

NbTi-Ti 17 30.9 0.6 191.4 0.023 30.9 191.4 0.077

Nb-NbTi 18 21.4 0.6 93.6 0.036 21.4 93.6 0.067

Nb 19 39.8 0.6 93.6 0.188 39.8 93.6 0.229

Nb 20 9.6 0.6 102.6 0.043 9.6 102.6 0.101

Nb 21 32.3 0.6 102.6 0.072 32.3 102.6 0.049

Nb-NbTi 22 2.9 0.6 93.6 0.017 2.9 93.6 0.013

Table-2

At all SCLs stresses are within the limit

Result Load Case-3


Material SCLPm

(MPa)

Welding

efficiency

Allowable stress

(A1) (MPa)

Ratio

Pm /A1

Pm +Pb

(MPa)

Allowable stress

(A2) MPa

Ratio

(Pm +Pb)/A2

Nb-NbTi 1 15.4 0.6 93.6 0.165 25.1 140.4 0.179

Nb 2 6.3 0.6 102.6 0.061 10.1 153.9 0.066

Nb 3 6.1 0.6 102.6 0.059 15 153.9 0.097

Nb 4 22.9 0.6 102.6 0.223 42.1 153.9 0.274

Nb-NbTi 5 11.4 0.6 93.6 0.122 42.4 140.4 0.302

Nb 6 5.6 0.6 102.6 0.055 7.6 153.9 0.049

Nb 7 12.1 0.6 102.6 0.118 17.3 153.9 0.112

Nb 8 2.4 0.6 102.6 0.023 4.6 153.9 0.03

Nb 9 12.3 0.6 102.6 0.12 17.2 153.9 0.112

NbTi-Ti 10 18.4 0.6 191.4 0.096 22 287.1 0.077

Ti 11 3.2 0.6 191.4 0.017 5.6 287.1 0.02

Ti 12 6.9 0.6 191.4 0.036 47 287.1 0.164

Ti 13 31 0.6 191.4 0.162 50.7 287.1 0.177

Ti 14 24.3 1 319 0.076 240 478.5 0.502

Ti 15 4 0.6 191.4 0.021 5.3 287.1 0.018

Ti 16 9.8 0.6 191.4 0.051 11 287.1 0.038

NbTi-Ti 17 11 0.6 191.4 0.057 26 287.1 0.091

Nb-NbTi 18 15.7 0.6 93.6 0.168 41.5 140.4 0.296

Nb 19 9.1 0.6 93.6 0.097 23 140.4 0.164

Nb 20 2.1 0.6 102.6 0.02 5.3 153.9 0.034

Nb 21 3.9 0.6 102.6 0.038 4 153.9 0.026

Nb-NbTi 22 15.3 0.6 93.6 0.163 25 140.4 0.178


Table-3

Result Load Case-4



efficiency

Allowable stress (A1)

(MPa)

RatioPm /A1

Pm +Pb

(MPa)

Allowable stress (A2)

MPa

Ratio(Pm +Pb)/A2

Nb-NbTi 1 15.4 0.6 93.6 0.165 25.1 140.4 0.179

Nb 2 6 0.6 102.6 0.058 9.2 153.9 0.06Nb 3 6.8 0.6 102.6 0.066 15.7 153.9 0.102Nb 4 10 0.6 102.6 0.097 20.7 153.9 0.135

Nb-NbTi 5 5.6 0.6 93.6 0.06 28 140.4 0.199

Nb 6 15.5 0.6 102.6 0.151 24.6 153.9 0.16Nb 7 19.5 0.6 102.6 0.19 26 153.9 0.169Nb 8 29 0.6 102.6 0.283 70 153.9 0.455Nb 9 19 0.6 102.6 0.185 30 153.9 0.195

NbTi-Ti 10 14.8 0.6 191.4 0.077 21.7 287.1 0.076

Ti 11 4 0.6 191.4 0.021 4.9 287.1 0.017Ti 12 5.7 0.6 191.4 0.03 7.6 287.1 0.026Ti 13 17.4 0.6 191.4 0.091 49.4 287.1 0.172Ti 14 45.5 1 319 0.143 305 478.5 0.64Ti 15 25 0.6 191.4 0.131 26 287.1 0.091Ti 16 5.2 0.6 191.4 0.027 10.5 287.1 0.037

NbTi-Ti 17 10.5 0.6 191.4 0.055 24.6 287.1 0.086

Nb-NbTi 18 17.7 0.6 93.6 0.189 39.5 140.4 0.281

Nb 19 7.2 0.6 93.6 0.077 14.8 140.4 0.105Nb 20 1.6 0.6 102.6 0.016 18.1 153.9 0.118Nb 21 12.5 0.6 102.6 0.122 12.6 153.9 0.082

Nb-NbTi 22 15 0.6 93.6 0.16 25 140.4 0.178

Table-4


Result Load Case-5



efficiencyAllowable stress

(A1) (MPa)RatioPm /A1

Pm +Pb

(MPa)Allowable stress

(A2) MPaRatio

(Pm +Pb)/A2

Nb-NbTi 1 0.45 0.6 15 0.030 1 22.5 0.044

Nb 2 2.3 0.6 15 0.153 3.6 22.5 0.160Nb 3 0.9 0.6 15 0.060 2.6 22.5 0.116Nb 4 8.5 0.6 15 0.567 12.8 22.5 0.569

Nb-NbTi 5 1.3 0.6 15 0.087 7 22.5 0.311

Nb 6 3.8 0.6 15 0.253 5.2 22.5 0.231Nb 7 6.5 0.6 15 0.433 8.4 22.5 0.373Nb 8 7.5 0.6 15 0.500 16.7 22.5 0.742Nb 9 6.2 0.6 15 0.413 9.2 22.5 0.409

NbTi-Ti 10 1.8 0.6 59.4 0.030 4.3 89.1 0.048

Ti 11 1.8 0.6 59.4 0.030 2.1 89.1 0.024Ti 12 4.9 0.6 59.4 0.082 12.7 89.1 0.143Ti 13 10.8 0.6 59.4 0.182 14.7 89.1 0.165Ti 14 13.9 1 99 0.140 40.2 148.5 0.271Ti 15 6.4 0.6 59.4 0.108 5.8 89.1 0.065Ti 16 1.9 0.6 59.4 0.032 5 89.1 0.056

NbTi-Ti 17 2 0.6 59.4 0.034 6.7 89.1 0.075

Nb-NbTi 18 0.79 0.6 15 0.053 2.79 22.5 0.124

Nb 19 4.3 0.6 15 0.287 7.9 22.5 0.351Nb 20 1.3 0.6 15 0.087 3.6 22.5 0.160Nb 21 1.7 0.6 15 0.113 2.3 22.5 0.102

Nb-NbTi 22 0.34 0.6 15 0.023 1.1 22.5 0.049

Table-5


I. Protection against Plastic collapse

• The criterion for protection against plastic collapse is given in Div. 2, 5.2.2.

• The criterion is applied to load cases in which primary (load-controlled)

stresses are produced, i.e. for Load Case 1, Load Case 2, and Load Case 5.

• The following stress limits criteria was satisfied (per 5.2.2.4(e)):

▪ Pm = primary membrane stress ≤ S▪ Pl = primary local membrane stress ≤ 1.5 ∙ S▪ Pl + Pb = primary local membrane + primary bending ≤ 1.5 ∙ S


Note:- For load case-1 criteria is satisfied as per limit load analysis

II. Protection against Local Failure


The criterion for protection against local failure is given in Div. 2, 5.3.2:

𝜎1 + 𝜎2 + 𝜎3 ≤ 4 ∙ 𝑆

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 0.947 0.043 0.568

2 0.288 0.087 0.343

3 0.219 0.240 0.629

4 0.37 0.27 0.86

5 0.233 0.027 0.326

III. Protection against Buckling of Niobium cavity


• linear elastic buckling analysis was performed.

• Proper design factor was applied as per code. 5.4.1.3(c).

• The critical pressure was found to be 30 MPa.

• Considering design factor buckling pressure 1.875 MPa

• Further reduction of 20% as per Technical Division Technical Note TD-

09-005 which gives buckling pressure 1.5 MPa.

• Which is 7 times greater than the required MAWP of 0.205 MPa

external at room temperature.

IV. Protection against fatigue for Niobium cavity

The need for a fatigue analysis can be determined by applying the fatigue

assessment procedures of Div. 2, Part 5, 5.5.2.3, “Fatigue Analysis Screening,

Method A.” In this procedure, a load history is established which determines

the number of cycles of each loading experienced by the Dressed SRF Cavity.


Loading Designation Number of Cycles

Cooldown N∆T E 100

Pressurization N∆FP 200

Tuning N∆tuner 200

For all the components that do not contain a flaw

N∆T E + N∆FP + N∆tuner ≤ 1000

100 + 200 + 200 = 500 ≤ 1000

No further fatigue assessment is necessary for the dressed cavity.

V. Protection against ratcheting for Niobium cavity


As there are no stress reversals in normal operation of the cavity, if

results from Table 1 to Table 5 are satisfied for all the load cases then

this criteria is also satisfied.

Safety assessment during room temperature pressure test

with safety bracket


Stress distribution in dressed cavity

Stress distribution in cavity

Pm= 17.45 MPa ……….40% safe

Pm + Pb = 37.8 MPa …..17% safe

Stresses are within limits except iris weld region

Pm ≤ 0.8Sy=30.4 MPa

Pm + Pb ≤ 1.2*Sy=45.6 MPa

Allowable as per code

Simulation model with loads & BC

Safety assessment during room temperature pressure test

Reference To Cavity Safety Table


Deformation Pattern in dressed cavity

Cavity expands by 185 µ

• Maximum allowable cavity expansion/ compression is 0.3 mm.

• if cavity is unconstrained during pressure test, it will expands by 0.95

mm.

• With safety bracket, cavity will deform by ~= 0.2 mm ….which is

lower then the max. allowable deformation…

Summary

• The design of the cavity, performed according to “Technical

Division Technical Note TD-09-005” .

• Cavity is safe for all the applicable load cases.

• Safety of the cavity is insured during pressure test with safety

bracket.

• Cavity can be dressed to assemble in CM.

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END

Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for safety

2/1/2019Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for

safety

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Back up slides

2/1/2019Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for

safety

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Regarding Limit Load analysis

2/1/2019 Nitin Nigam | Engineering Analysis of β=0.9, 650 MHz cavity for safety 30

Material

Sy

Poison’s

ratio

Allowable

Pm (MPa)

Allowable Pm +

Pb (MPa)

Nb 38 0.39 30.4 45.6

Ti-45Nb 476 0.36 380.8 571.2

Gr. 2Ti 276 0.33 220.8 331.2

Allowable stress values for Pressure test

Applicable Formulae

Engineering Analysis of β=0.9, 650 MHz cavity for safety...As per ASME section II part D AS Near...

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