Dynamic Characterization of the

Transportation Tooling for

Cryomodule SSR1

Paolo Neri, Francesco Bucchi

University of Pisa

Department of Civil and Industrial Engineering

Aim

Design of the shock absorbing system for the transportation of cryomodule SSR1:

- Length: 5.5 m

- Diameter: 1.4 m

- Weight: 8-10 t

- Number of cavities: 8

Design plan

Design approach:

- Dynamic characterization of the main sub-assembly

- Assessment of shock absorber capabilities

- Transportation tooling design

- Transportation tooling performance verification

Cryomodule dynamic characterization

FEM modeling

Thin surfaces: shell elements to reduce model size

Material properties and shell thickness derived from CAD

Cryomodule structure

Main parts:

1. Vessel

2. Thermal shield

3. Strong back

4. Cavities

5. Support posts

6. Solenoid

1

2

3

4

6

3

Model structure

Each main part represents a sub-assembly, which is modelled separately.

Sub-assembly are then imported (and copied) to produce the full model

Vessel

3900 kg43489 nodes35521 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Thermal shield

220 kg29386 nodes30977 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Strong back

300 kg31759 nodes39377 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Cavities

Two different geometries, each repeated 4 times:170 kg118882 nodes126509 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

320 kg14565 nodes14534 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Support posts

One geometry, repeated 4 times:40 kg14519 nodes14257 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Solenoid support

Assembly

6200 kg1127769 nodes1190605 elements

All connections guaranteed exploiting node merging and fixed joint connections (no contact elements)

Results

Natural frequencies and detailed mode shapes

e.g. antennaout-of-phase mode, 130 Hz

What is missing?

In order to reduce the number of elements, the bellows connecting the cavities and the two-phase pipe were removed.They were replaced with lamped stiffness (6x6 matrix)

Fixed

Unit displacement

𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

=⋯

⋮ 𝐾 ⋮⋯

𝑈𝑥𝑈𝑦𝑈𝑧ϑ𝑥ϑ𝑦ϑ𝑧

K can be estimated by applying unit displacement/rotation along each direction and computing the corresponding reaction force/moment.

Assessment of shock absorber capabilities

Shock absorber performances

Mechanical filter, cut frequency depending on modal analisys

Springs element for filtering

Mixed approach fem-Adams→ evaluation of springs , model simplification (field vs bellows)

Shock absorber performances

CM vessel imported from FEM using Modal Neutral File (.mnf)

Cavities imported from CAD as rigid bodies

Two-phase pipe modeled in MB environment using beam theory

Bellows modeled as lumped stiffness matrices whose characteristics were derived from FEM

Shock absorber performances

Cryomodule

Inner frame

4 Spherical joints in total

Cryomodule

Cavities

4 Spherical joints per cavity

Model details - Constraints

Shock absorber performancesModel details – Bellows modeling

Cavity ith Cavity jth

Field Element

Solenoid Field Element

𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

=

𝑘11𝑘21𝑘31𝑘41𝑘51𝑘61

𝑘12𝑘22𝑘32𝑘42𝑘52𝑘62

𝑘13𝑘23𝑘33𝑘43𝑘53𝑘63

𝑘14𝑘24𝑘34𝑘44𝑘54𝑘64

𝑘15𝑘25𝑘35𝑘45𝑘55𝑘65

𝑘16𝑘26𝑘36𝑘46𝑘56𝑘66

𝑢𝑥𝑢𝑦𝑢𝑧𝜗𝑥𝜗𝑦𝜗𝑧

Cavity

Shock absorber performancesModel details – Two-phase pipe

𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

=

𝑘11𝑘21𝑘31𝑘41𝑘51𝑘61

𝑘12𝑘22𝑘32𝑘42𝑘52𝑘62

𝑘13𝑘23𝑘33𝑘43𝑘53𝑘63

𝑘14𝑘24𝑘34𝑘44𝑘54𝑘64

𝑘15𝑘25𝑘35𝑘45𝑘55𝑘65

𝑘16𝑘26𝑘36𝑘46𝑘56𝑘66

𝑢𝑥𝑢𝑦𝑢𝑧𝜗𝑥𝜗𝑦𝜗𝑧

Timoshenko beam elements

Field Elements

Shock absorber performancesModel details – Modal Neutral File (mnf)

• FE model has ~800000 dofs

• 50 natural modes were extracted from Ansys (r = 50)

• 46 interface nodes were selected (𝑖 = 276)

Mode Number MB Frequency (Hz) MB no Pipe/Bellows (Hz) Difference (%)

7 9,6 9,5 2%

8 15,2 15,3 1%

9 17,9 17,1 4%

10 21,6 18,8 15%

11 23,1 20,8 11%

12 23,3 22,4 4%

13 26,4 22,8 16%

14 27,1 24,1 13%

15 27,3 24,4 12%

16 27,8 24,8 12%

17 27,9 24,8 12%

18 28,2 25,4 11%

19 28,4 25,7 10%

20 28,4 26,1 9%

21 28,9 26,3 10%

22 30,1 26,5 14%

23 30,9 26,6 16%

24 31,1 26,8 16%

25 31,6 27,4 15%

26 32,9 30,1 9%

27 34,0 30,9 10%

28 34,5 32,3 7%

29 38,0 33,8 13%

30 38,5 34,3 12%

31 40,8 37,9 8%

32 42,2 40,6 4%

33 43,1 42,3 2%

34 43,7 43,0 2%

35 45,2 43,7 3%

36 45,6 43,9 4%

37 46,1 44,3 4%

38 46,8 44,7 5%

39 46,9 45,5 3%

40 47,2 46,3 2%

41 47,7 46,8 2%

42 48,3 49,5 2%

43 49,5 49,5 0%

44 49,5 50,7 2%

45 50,7 52,5 3%

46 52,5 54,9 4%

47 54,9 55,4 1%

48 55,3 57,4 4%

49 56,7 59,2 4%

50 59,5 59,2 0%

Shock absorber performances

Adding pipes and bellows, natural

frequencies are generallydifferent from the onesfound in the previousanalysis. However no low-frequency new

natural modes arise.

STEP 1 - Verification of .mnf import + rigid cavities

Maximum difference5%, ascrivable to the different (FEM-MB)

connection technique between Cavities and their bases, belongingto the rigid cylinder.

The difference isconsiderd negligible

for our purposes.

Mode Number MB Frequency (Hz) FEM Frequency (Hz) Difference (%)

7 9.5 9.5 0%

8 15.3 15.4 1%

9 17.1 17.2 1%

10 18.8 19.1 1%

11 20.8 21.2 2%

12 22.4 22.7 1%

13 22.8 23.1 1%

14 24.1 24.8 3%

15 24.4 25.1 3%

16 24.8 25.4 3%

17 24.8 25.6 3%

18 25.4 25.7 1%

19 25.7 26.9 5%

20 26.1 27.2 4%

21 26.3 27.3 4%

22 26.5 27.4 3%

23 26.6 27.5 3%

24 26.8 27.7 3%

25 27.4 27.7 1%

26 30.1 30.4 1%

27 30.9 31.2 1%

28 32.3 32.4 0%

29 33.8 33.8 0%

30 34.3 34.5 0%

31 37.9 37.8 0%

32 40.6 40.9 1%

33 42.3 42.5 1%

34 43.0 43.1 0%

35 43.7 43.8 0%

36 43.9 44.1 0%

37 44.3 44.5 0%

38 44.7 44.9 0%

39 45.5 45.5 0%

40 46.3 46.3 0%

41 46.8 46.8 0%

42 49.5 49.7 0%

43 49.5 50.0 1%

44 50.7 51.2 1%

45 52.5 52.3 0%

46 54.9 55.3 1%

47 55.4 55.5 0%

48 57.4 57.3 0%

49 59.2 59.1 0%

50 59.2 59.4 0%

STEP 2 – Implementation of piping and bellows

Shock absorber performances

1st natural mode – 9.6 Hz 2nd natural mode – 15.2 Hz

Mode displacements are magnified

Some examples of natural modes

Shock absorber performances

4 vertical springs under the flexible cylinder Rigid body model with same mass/intertia

VerticalFictitious

Springs

𝛿𝑠𝑡~ 25 mm𝑓𝐻𝑒𝑎𝑣𝑒 ~ 3.1Hz

𝑓𝐻𝑒𝑎𝑣𝑒 =1

2𝜋

𝑘𝑡𝑜𝑡𝑚

𝑚~ 9500 kg

Assessment of CM mass + TT

𝑘𝑡𝑜𝑡 ~ 3600 N/mm

First Assessment!

4 springsFirst attempt

𝑘𝑣 ~ 900 N/mm

𝑓𝐻𝑒𝑎𝑣𝑒 =1

2𝜋

𝑔

𝛿𝑠𝑡

First assessment of natural frequency

Transportation tooling design

Transportation frame design

Square tubular beam: 4x4x0.375 inch

Helical isolator

Positions of springs can be adjusted to hold different cryomodules

Inner frame

Outer frame

Commercial components

M32-850-08

Up to 110 mm travel

Commercial components

One spring along each direction

VS

45° angled springs

!!Travel reduction in case of combined vertical/lateral loading!!

Frame dimensions

276 inch

87

inch

(<

90

inch

)

Transportation frame static analysis

Fixed constraint

Cryomodule weight: 8 t

Bushing spring to represent helical isolator

Transportation frame static analysis

Equivalent Von Mises Stress, MPa

Structural SteelYield stress 250 MPa

Transportation frame static analysis

Vertical displacement (magnified plot)

Transportation tooling performance verification

Shock absorber performances

Actual springs configuration

Longitudinal spring

Verticalspring

LateralspringFL Corner

Longitudinal bushing

Verticalbushing

Lateralbushing

𝐹𝑥𝐹𝑦𝐹𝑧

=𝑘𝑥 0 00 𝑘𝑦 00 0 𝑘𝑧

𝑢𝑥𝑢𝑦𝑢𝑧

Charge 2.2

Shock absorber performancesFrequency response

Heave unitary input Roll unitary input

Pitch unitary input

Natural frequencies

𝑓 (Hz)1,903,013,274,064,465,31

Computed considering total CM + inner TT mass of 9500 kg

Charge 2.2

Shock absorber performances

1st NM 2nd NM

Frequency Response – Central Cavity CM – Heave excitation

Absolute magnitude is not realistic. The ratio between static and

considered frequency magnitude has to be considered.𝑦-disp 𝑥-disp

Solid line: with springsDashed line: without springs

Charge 2.2

Shock absorber performancesFrequency Response – Central Cavity CM – Roll excitation

1st NM 2nd NM

𝑥-disp

Absolute magnitude is not realistic. The ratio between static and

considered frequency magnitude has to be considered.

Solid line: with springsDashed line: without springs

Charge 2.2

Shock absorber performancesFrequency Response – Central Cavity CM – Pitch excitation

1st NM 2nd NM

𝑧-disp

Absolute magnitude is not realistic. The ratio between static and

considered frequency magnitude has to be considered.

Solid line: with springsDashed line: without springs

Charge 2.2

Shock absorber performancesSome doubts

• Pitch, Roll and Heave NM haveresonances in the range 2-5 Hz.

• The amplitude of the resonancepeak is determined consideringsprings datasheet

May the TT resonances match the truck loading bed resonances, causing large springs travel?

Stiffer springs would move the TT resonances at higher frequency,

avoiding matching with truck resonances, but should reduce the

filtering effect Charge 2.2

Shock absorber performancesAlternative springs set

Stiff spring set

Soft spring set

49 110

Charge 2.2

Shock absorber performancesFrequency Response – Central Cavity CM – Heave excitation

Which is better?Reference actual road loading bed displacement profile is needed!

1st NM 2nd NM

Soft Springs

Stiff Springs

Charge 2.2

Shock absorber performancesActual loading bed displacement implementation

Outer TT

Inner TT

x, y and z time histories are imposed to three points of the lower TT (corresponding to the vertical spring position for 3 corners).

Highly stiff complaint constraints were used to avoid over-constraing.

Recorded TT displacement during LCLS-II CM transportation

Charge 2.2/2.3

Shock absorber performancesActual loading bed displacement implementation

Charge 2.2/2.3

Shock absorber performancesDisplacement of vertical springs – Gravity + Actual vertical profile

Vertical displacement of a vertical spring

Lat Dis Long Dis

Charge 2.2/2.3

Shock absorber performancesReference bellow forces - Gravity + Actual vertical profile

Charge 2.2/2.3

Shock absorber performancesDisplacement of soft vertical spingsGravity + Actual vertical profile + Severe turning + Emergency braking

Charge 2.2/2.3

Shock absorber performancesDisplacement of soft spings (all springs in every direction)Gravity + Actual vertical profile + Extreme bending and braking

Max Available Travel~ 110 mm

Charge 2.2/2.3

Critical components structural assessment

Plot Vs time/frequency

Bellows Forces/Moments

Kext1

K1K2K3 K1K2 K3K3 K1K2Kext1

K1K2Kv

KpKv Kv Kv

6 different bellows types are identified:

• Kext1, between end cavities and external vessel;• K1, between cavity and solenoid (solenoid rightside in Fig.);• K1, between cavity and solenoid (solenoid leftside in Fig.);• Kv, between solenoid and two phase pipe;• Kp, between different parts of the two phase pipe.

Charge 2.3

Bellows forces and moments

Forces Moments

Soft

Rigid

2 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Forces Moments

Soft

Rigid

4 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Forces Moments

Soft

Rigid

4 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Forces Moments

Soft

Rigid

3 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Forces Moments

Soft

Rigid

14 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Forces Moments

Soft

Rigid

4 bellows

Forces/moments related to the most critical bellow of each type are plotted Charge 2.2

Bellows forces and moments

Exemplification plots refer to the bellow subject to higher forces/moments (bellow 11, type Kp)

Soft

Rigid

Frequency contribution for 𝑓 > 10 Hz are cut by mechanical filter due to

TT springs

The ratio between forces amplitude (soft vs. rigud) is about 5.

Time Domain Frequency Domain

Charge 2.2

Thermal shield – bellows clearence

Time Domain Frequency Domain

1st natural mode contribution, involving

thermal shield, is filtered

Displacement amplitude is reduced by about 5

Maximum displacement for soft config. ~0.3 mm

y

x

c~70 mm

c

Charge 2.2

Bellows assessment

BextB1B2B3 B1B2 B3B3 B1B2Bext B1B2

BvBv Bv Bv

2 × Bext4 × B14 × B23 × B34 × Bv14 × Bp: 2-phase pipe

Bellows assessment

Modal analysis of each bellow: natural frequencies higher then excitation frequencies

B1, 𝑓1 = 835 Hz B2, 𝑓1 = 835 Hz B3, 𝑓1 = 40 Hz

Bp, 𝑓1 = 283 Hz Bv, 𝑓1 = 330 Hz Bext, 𝑓1 = 66 Hz

Charge 2.2

From Ansys model, constant in time

Linear analysis: sum of single analysis, already performed to assess lamped stiffnesses

Bellows assessment

Fixed

Unit displacement𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

=⋯

⋮ 𝐾 ⋮⋯

𝑈𝑥𝑈𝑦𝑈𝑧ϑ𝑥ϑ𝑦ϑ𝑧

σ𝑥𝑥σ𝑦𝑦σ𝑧𝑧τ𝑥𝑦τ𝑦𝑧τ𝑥𝑧

=⋯

⋮ ෩𝐾 ⋮⋯

𝑈𝑥𝑈𝑦𝑈𝑧ϑ𝑥ϑ𝑦ϑ𝑧

෩𝐾 = 6 × 6𝑛 (n is the number of nodes)

σ𝑒𝑞(𝑡)

From Adams model, time dependent

Determining the worst combination is not trivial, analysis along time history

Charge 2.2

Bellows assessment

Example: edge bellow, Bext

Charge 2.2

Bellows assessment

Bext, σeq,max = 22 MPa B1, σeq,max = 60 MPa B2, σeq,max = 62 MPa B3, σeq,max = 2 MPa

Bv, σeq,max = 84 MPa Bp, σeq,max = 35 MPa

Charge 2.2

Bellows assessment

Comparison between helical isolator and rigid connection

Bellow With Isolators:𝝈𝐞𝐪,𝒎𝒂𝒙 MPa

Without Isolators:𝝈𝐞𝐪,𝒎𝒂𝒙 MPa

Ratio

Bext 22 118 5.4

B1 60 296 4.9

B2 62 282 4.5

B3 2 10 5.0

Bv 29 150 4.9

Bp 35 137 3.9

Charge 2.2

Antenna assessment

Antenna stem(two concentric flexible beams)

Antenna tip(lumped mass)

Charge 2.2

Displacement magnitude (<0.01 mm for soft configuration) of the antenna tip is measured on the plane normal to the antenna stem. Without inner beam, the displacement is reduced due to the less

weight.

Antenna assessmentAntenna tip

(lumped mass)

In & Out

Rigid

High frequency natural modes are filtered by TT

Charge 2.2

Sensors positioning

BextB1B2B3 B1B2 B3B3 B1B2Bext B1B2

BvBv Bv Bv

2 × Bext4 × B14 × B23 × B34 × Bv14 × Bp: 2-phase pipe

Sensor positioning: tri-axial piezoelectric accelerometers

3 on the inner frame3 on the outer framen End-coupler flangesn Bextn Bv

Charge 4

Frame details

Possibility to shift main parts for adjustments or for other cryomodules

Outer frame Inner frame

Frame details

HelicalIsolator

Mounting plates

Different helical isolator can be mounted on the frame through different mounting plates

Frame details

Without the end-couplersWith the end-couplers: vertical and lateral isolators must be switched

!

Conclusions

Conclusions

Finite element model for dynamic characterization

Combined FEM – MB for shock absorber system design

Transportation tooling mechanical design

Performance verification through recorded data

Conclusions

What to check before transportation:

Assembled Cryomodule weight

Inner and outer frame weight

Displacement along vertical direction (due to gravity)

Transportation trial from vendor to Fermilab with simulated loading (concrete beams)

FRF measurement between outer frame and inner frame (filtering assessment)

Charge 4

THANK YOU

Paolo Neri, Francesco Bucchi

University of Pisa

Department of Civil and Industrial Engineering

THANK YOU

Paolo Neri, Francesco Bucchi

University of Pisa

Department of Civil and Industrial Engineering