RFD Mechanical Design Giovanni Casula Fermilab HLLHC AUP

RFD Mechanical Design Giovanni Casula - Fermilab HL-LHC AUP RFD cavity Preliminary Design Review – June 20 th, 21 st; 2018

Outline § Bare RFD mechanical design § Bare RFD strength assessment § § Protection against Plastic Collapse Protection against Local Failure Protection against Collapse from Buckling Ratcheting Assessment § Multiphysics Analyses § Pressure Sensitivity § Lorentz Force Detuning § Tunability § Bare cavity drawings DF-4 § RFD fabrication procedure § Helium Vessel preliminary design Develop preliminary fabrication and assembly procedures DF-3 Present helium vessel preliminary design HL-LHC AUP RFD PDR - June 2018 2

Mechanical Design § Stiffeners, Racetrack and Ribs are features that improve RFD performances § 3 standard CF flange sizes for 6 UHV connections: H-HOM § DN 100 for Beam pipes and H-HOM § DN 63 for FPC Tuner connection § DN 35 for P-Up and V-HOM Racetrack Materials V-HOM Shell, Ribs, Stiffeners and Racetrack UHP Niobium CF Flanges AISI 316 LN SS Vessel interfaces and Tuner connections Stiffener Nb 55 Ti Rib Pick Up Antenna 3 HL-LHC AUP RFD PDR - June 2018

Methods to Verify Functional Requirements FUNCTIONAL REQUIREMENT [1] ASSESSMENT Strength assessment according to international standards Multiphysics analyses [1] Functional Requirement Specification, US-Hi. Lumi-doc-294 4 HL-LHC AUP RFD PDR - June 2018

Strength Assessment for RFD – International Standards CERN assessment for operations in LHC FNAL Assessment for operations in American labs ASSESSMENT TYPE EUROPEAN STANDARD EN 13445 AMERICAN STANDARD ASME BPVC PLASTIC COLLAPSE • • • LOCAL FAILURE Elastic - perf. plastic model Loads design factor 1. 2 Material design factor 1. 5 Tresca’s yield condition Small displacement theory – Limit Load Analysis Method: • • • Elastic - perf. plastic model Loads design factor 1. 5 Small displacement theory • • Elastic Analysis Compare sum of three lin. principal stress with 4 x. Allowable limit BUCKLING • • • Non-linear buckling Elastic - perf. plastic model Loads design factor 1. 2 + safety factor 1. 5 • • Elastic Analysis Conservative design factor RATCHETING • • • Elastic - perf. plastic model Material design factor 1. 5 20 loading cycles considered Large Deflection OFF • • • Elastic - perf. plastic model 5 loading cycles Large Deflection ON • COMMENTS Not required for EN Large difference in number of cycles to be studied HL-LHC AUP RFD PDR - June 2018 5

Protection Against Plastic Collapse Limit Load Analysis Method § Material model: elastic-perfectly plastic § Yield strength in the model = 52 MPa; 0. 8 FNAL multiplier applied to 65 MPa – value in the material spec. [2] § Small displacement theory → Large Deflection : OFF § Loads multiplied by design factor = 1. 5 § If convergence is achieved in the analysis, the component is stable under the applied loads [2] CERN material spec. N. 3300 - EDMS 1095252, US-Hi. Lumi-doc-1010 HL-LHC AUP RFD PDR - June 2018 6

Protection Against Plastic Collapse Results at P = 2. 7 bar (1. 8 bar x 1. 5) Equivalent Stress Eq. Total Strain § Convergence achieved; cavity is stable under the considered Loads § Mesh independence study performed on eq. total strain HL-LHC AUP RFD PDR - June 2018 7

Protection Against Local Failure Elastic Analysis – Triaxial Stress Limit § The algebraic sum of the three linearized primary principal stresses shall be used for checking : ( σ1 + σ2 + σ3 ) ≤ 4 S Where S = 0. 8 x 43. 3 = 34. 64 MPa § 0. 8 Fermilab multiplier applied to the allowable limit (⅔ Sy) recommended by the code HL-LHC AUP RFD PDR - June 2018 8

Protection Against Local Failure Elastic Analysis – Triaxial Stress Limit – Results Calculation done in the three zones with highest stress values Region A has the highest sum of linearized principal stresses ( σ1 + σ2 + σ3 ) = 83. 4 MPa ≤ 4 S = 138. 6 MPa → OK HL-LHC AUP RFD PDR - June 2018 9

Protection Against Collapse from Buckling Elastic Stress Analysis without geometric nonlin. With the most conservative design factor given by the standard (16. 13) the first buckling mode multiplier is 1. 53 Therefore the cavity is safe against buckling HL-LHC AUP RFD PDR - June 2018 10

Ratcheting Assessment Elastic-Plastic Stress Analysis § Material model: elastic-perfectly plastic § Yield strength = 52 MPa as in Protection against plastic collapse Consider non-linear geometry→ Large Deflection : ON Minimum of three repetitions of the cycle → 5 loadings considered HL-LHC AUP RFD PDR - June 2018 11

Ratcheting Assessment Elastic-Plastic Stress Analysis The ratcheting criteria are satisfied if any one of the following conditions is met: § (a) zero plastic strains in the component § (b) there is an elastic core (…) of the component § (c) there is not a permanent change in the overall dimensions of the component. This can be demonstrated by developing a plot of relevant component dimensions versus time 4 deformation probes defined to check the changes in the RFD dimensions: most displaced points for the 2 tuner areas and for the 2 poles X displ. Y displ. HL-LHC AUP RFD PDR - June 2018 12

Ratcheting Assessment Elastic-Plastic Stress Analysis - Results Displacements vs time 4, 00 E-01 3, 00 E-01 2, 00 E-01 1, 00 E-01 0, 00 E+00 0, 20, 40, 7 1 1, 21, 41, 7 2 2, 22, 42, 7 3 3, 23, 43, 7 4 4, 24, 44, 7 5 5, 25, 45, 7 6 6, 26, 46, 7 7 7, 27, 47, 7 8 8, 28, 48, 7 9 -1, 00 E-01 -2, 00 E-01 -3, 00 E-01 -4, 00 E-01 Y displ tuner 1 [mm] Y displ tuner 2 [mm] X displ pole 1 [mm] X displ pole 2 [mm] Displacements for relevant component dimensions vs Time ↓ no change in dimensions ↓ Ratcheting criteria are satisfied HL-LHC AUP RFD PDR - June 2018 13

ASME strength assessment All the required analyses showed satisfactory results: § Protection against plastic collapse § Protection against local failure § Protection against collapse from buckling § Ratcheting assessment The safety requirement @ 1. 8 bar is satisfied HL-LHC AUP RFD PDR - June 2018 14

Multiphysics Analyses Pressure sensitivity § Boundary conditions: § 1 bar applied to the cavity walls § All cavity ports are fixed § Tuner equivalent stiffness is modeled with a single spring that connects the 2 tuning areas, k=6. 8 k. N/mm Pressure Sensitivity (with tuner 6. 8 k. N/mm) d. F/d. P [Hz/mbar] required |d. F/d. P| [Hz/mbar] -142 <150 HL-LHC AUP RFD PDR - June 2018 15

Multiphysics Analyses Lorentz Force Detuning § Boundary conditions: § Lorentz pressure applied to the cavity walls § All cavity ports are fixed § Tuner equivalent stiffness is modeled with a single spring that connects the 2 tuning areas, k=6. 8 k. N/mm Lorentz Force Detuning (with tuner 6. 8 k. N/mm) ΔF@3. 4 MV [k. Hz] -4. 68 LFD @ 3. 4 MV LFD requirement [Hz/MV^2 ] [Hz/MV^2] -405 <865 HL-LHC AUP RFD PDR - June 2018 16

Multiphysics Analyses Tunability Studies 300 K – Max eq stress 70 MPa Force per side: 1800 N Displ. per side: 0. 26 mm Frequency shift: 277 k. Hz 2 K – Max eq stress 330 MPa Force per side: 8400 N Displ. per side: 1. 2 mm Frequency shift: 1300 k. Hz Boundary conditions Calculated tunability (total) 6. 5 N/k. Hz Max frequency shift estimate @ 2 K 1. 3 MHz FRS assumption about tuner capability is 200 k. Hz, the cavity allows a much higher value HL-LHC AUP RFD PDR - June 2018 17

Bare RFD Drawings HL-LHC AUP RFD PDR - June 2018 18

Bare RFD Drawings (2) HL-LHC AUP RFD PDR - June 2018 19

Braze Joints Drawings – Manufactured at ANL HL-LHC AUP RFD PDR - June 2018 20

Preliminary fabrication procedure for Bare RFD Machining EBW Forming DF-4 Manufacturing Processes Machining EBW Forming Courtesy of CERN Machining EBW HL-LHC AUP RFD PDR - June 2018 21

Preliminary assembly procedure for Dressed RFD Helium Tank: § bolted approach to minimize frequency shift due to weld shrinkage § subsequent TIG welding to assure leak tightness § material: Titanium § connected to the bare RFD through Nb-Ti flanges DF-3 DF-4 HL-LHC AUP RFD PDR - June 2018 22

Conclusions For the presented mechanical design: § Complete strength assessment was performed according to international standards, safety requirements are met § Pressure sensitivity is 142 Hz/mbar, below 150 Hz/mbar threshold § Lorentz Force Detuning coefficient is 405 Hz/MV^2, within 865 Hz/MV^2 requirement § Preliminary design of Helium Vessel is complete § RFD dressed cavity design is about 50% complete. HL-LHC AUP RFD PDR - June 2018 23