1. Fredrik Fors Mechanical Engineering, JLab 09/29/2016
DQW Cavity for the HF-LHC project at CERN, through US-LARP Pressure Test Structural Analysis
Fredrik Fors
Mechanical Engineering, JLab
09/29/2016

2. Summary
Structural analysis of the pressure test rig for Double Quarter Wave (DQW) cavity for the High Luminosity LHC project at CERN
Purpose is to evaluate the stresses induced in the cavity wall during an application of a 1000 Torr vacuum pressure at room temperature.
The stresses in the titanium test cage have also been checked.
The analysis is performed on 3D finite element models using ANSYS Workbench 17.2
A cursory structural check has also been made of the test cage used for BCP treatment

3. Analyzed Geometry
The DQW cavity consists of a 4 mm thick RRR Niobium shell, fitted with tubular flanged ports and tuner attachments.
The CAD geometry used for the FE model was imported directly from Teamcenter. Part No. JL
The niobium cavity is fixed inside the titanium test cage by nitronic rods connected to the tuner attachments, and clamping brackets at the beam tubes.
Due to previous undesirable stress results, additional cross braces and stiffening ribs have been included for this iteration.
Added stiffening ribs
Added cage crossbars

4. FEA Model
The entire cavity and cage structure was included in the FE model. Only minor components not considered to be of structural importance were left out.
The cavity geometry is meshed with 2nd order tetrahedron elements. The nominal mesh size is 4 mm, then subsequently refined to 1.5 mm in the high stress area
For an accurate representation, the stiffener was attached using beam element bolts and a frictionless contact formulation.
Refined mesh
area

5. Material Properties
Material data for the RRR Niobium is same as used in an earlier CERN report1:
Density ρ = 8600 kg/m3
Elastic Modulus E = 100 GPa
Poisson’s Ratio ν = 0.4
Stress limits for the cavity are specified in the previous Crab cavity review by CERN2
S = 50 MPa for primary membrane stress check
SPL = S*1.5 = 75 MPa for bending + membrane stress check
SLF = S*4 = 200 MPa for local failure check against sum of principal stresses
This in approximate correlation with Nb material data used at JLab. Following table is a summary from a JLab Technote3
Properties
Value RT)
Density [kg/m3]
8570
Specific Heat [kJ/kg]
0.268
CTE [m/m/K]
7.1×10-6
Young’s modulus, [GPa]
105
Shear Modulus [GPa] 38
Poison’s Ratio [ - ]
0.38
Yield Stress [MPa] K)
Crab Cavity Stress Analysis v.1, 24/02/2014, Norbert Kuder, EN-MME-DI, CERN
CRAB Cavities Cryomodule Review - Tuner, Kurt Altoon, Rama Calaga, et al.
On Niobium in Construction of Cryogenic Pressure Vessel Systems, 2009, Gary Cheng, Edward Daly, JLab

6. Loads and Boundary Conditions
Test cage fixed at bottom ends of legs
Pressure load of Torr ( kPa) applied to internal surfaces of cavity
Cavity connected to clamping brackets by bonded surface contact

7. FEA Results – Cavity
High equivalent stresses occur in the cavity wall as shown in figure below
Stress maximum in wall σeq,max = MPa (150% of allowable stress)
No significant stresses are seen in the cage and bracket assembly
Stress maximum in cage σeq,max = MPa (42% of yield stress)

8. FEA Results – Cavity
Mesh refined at critical location and stress linearized through wall thickness in accordance with the 2015 ASME Boiler Pressure Vessel Code
Primary membrane Pm = MPa % of allowable
Membrane + Bending Pm + Pb = 69.1 MPa % of allowable
Principal Stresses σ1 + σ2 + σ3 = = MPa 56% of allowable
Membrane+Bending
Membrane

9. Structural Check of BCP Cage
The test cage used for BCP treatment will not be subjected to any vacuum loads and the stresses are expected to be low.
The only loads will be gravity loads from the cavity, brackets and liquid inside the cavity.
A simple check was made of the bolt loads at the curved bracket on the cage, since the will experience an addition moment from the offset.
The resulting forces on the bolts are next to negligible
4” moment arm
Checked
joint