C100 Cryomodule Vacuum Vessel Structural Analysis An Addendum to JLAB-TN

Introduction C100 Cryomodule Vacuum Vessel Structural Analysis An Addendum to JLAB-TN-07-081 Gary G. Cheng and Edward F. Daly The C100 cryomodule (CM) vacuum vessel structural analysis per ASME Boiler & Pressure Vessel (BPV) code [1] requirements was summarized in JLAB-TN-07-081 [2]. A few design changes have been made since then: 1) the instrumentation ports are enlarged from 8.0" OD to 12.75" OD, 2) the support brackets are reduced in size, and 3) vessel support tabs have a new look now and are relocated. These changes affect previous structural analysis. Pertinent calculations are revisited. Results are updated in this technical note. I. Stresses in Vacuum Vessel Shell (UG-22 and UG-23) The mechanical loads are defined in JLAB-TN-07-081. The external design pressure for vacuum vessel is reduced to 14.7 psi (1.0 atm) in view of the fact that vacuum vessel is actually under atmospheric pressure all the time. One of the support tabs is relocated so that the two support tabs are not symmetric about the median plane of vacuum vessel, see Fig. 1. The 6 stiffening rings are still geometrically symmetric about the median plane. Note that the support tabs in Fig. 1 are placed at their center line positions. 66.15" 53.22" Ring 1 Transportation support Ring 2 Ring 3 Ring 4 Ring 5 Ring 6 Transportation support 52.67" 58.86" 5.57" 7.29" Median plane Fig. 1 Vacuum vessel supports and stiffening rings layout The finite element model used in previous analysis [2] is modified to reflect the changes and rerun for stresses in vacuum vessel shell and forces and moments in stiffening rings. The support tabs are mounted on 9" wide saddles that are fixed to the ground. In the finite element model, the width of the saddle is now considered. Three load cases are defined as follows (different from previous definitions): 1/13

Case 1: Internal pressure (2.0 atm) and normal load Case 2: External pressure (1.0 atm) and normal load Case 3: External pressure (1.0 atm) and transportation load The case 3 is defined according to past experiences in transporting cryomodules: no liquid helium in all cryogenic circuits, with vacuum jacket inside the vacuum vessel and ultra high vacuum in the cavity. During the transportation, at least two more end supports are used to resist the g-forces from cantilevered end cans. They are illustrated in Fig. 1 with dashed blocks. Stresses developed in vacuum vessel shell are summarized in Table 1 for all three load cases. None of the peak membrane stresses (axial, hoop, and shear) in Table 1 exceeds the 16,700 psi allowable stress for 304 stainless steel (cited from Table 1A of reference [3]), neither does the sum of the membrane stress and bending stress. Von Mises stress plots and transverse bending moment diagrams for the three cases are given in Figs. 2-7 for information. Table 1. A summary of peak stresses in vacuum vessel subjected to various loadings Peak Stresses (psi) Case 1 Case 2 Case 3 Bending stress 424 425 701 Axial stress 1,850 955 1,020 Hoop stress 1,850 940 940 Shear stress 129 129 393 Max. Principal Stress 2,281 1,385 1,339 The minimum thickness of vacuum vessel shell under internal pressure calculation in JLAB- TN-07-081 is still valid. The allowable pressure calculation needs to be amended to include three more segments due to the relocated support tab. Table 2 shows the calculation. The allowable pressures calculated are much higher than design external pressure of 14.7 psi. This indicates that the wall thickness of 0.25" is sufficient. Table 2. Calculation of allowable pressure in vacuum vessel segments Segment 5 Segment 6 Segment 7 Length, L 58.86 7.29 70.65 L/D o 1.84 0.228 2.21 Factor A 0.00051 0.0051 0.00042 Factor B 6,560 12,962 5,578 P a, psi 64.89 135.02 58.10 The required available Moment of Inertia (MOI) for stiffening rings 4, 5, and 6 needs to be evaluated since the support tab is relocated. The calculation is shown in Table 3. The available MOI in each stiffening ring is actually greater than 0.265 in 4. Therefore, the stiffening rings can provide enough MOI. 2/13

Fig. 2 Von Mises stress in vacuum vessel under load case 1 Fig. 3 Transverse bending moment diagram in vacuum vessel under load case 1 3/13

Fig. 4 Von Mises stress in vacuum vessel under load case 2 Fig. 5 Transverse bending moment diagram in vacuum vessel under load case 2 4/13

Fig. 6 Von Mises stress in vacuum vessel under load case 3 Fig. 7 Transverse bending moment diagram in vacuum vessel under load case 3 5/13

Table 3. Calculation of required available MOI in stiffening rings Ring 4 Ring 5 Ring 6 Length, L s (53.22"+58.86")/2=56.04" (7.29"+58.24")/2=32.77" 58.24"/2=29.12" Factor B 2,569 2,405.5 2,360 Factor A 0.00018 0.00017 0.000166 I s, in 4 0.205 0.12 0.106 II. Instrumentation Port Analysis The four instrumentation ports are designed to use NW320 (12.75" OD and 0.188" wall) half nipples instead of NW200 half nipples. The weight of NW320 is 14 lbs, which is 9 lbs heavier than NW200 one. So, the total weight increase is 4 9 = 36 lbs. In JLAB-TN-07-081, vacuum vessel wall thickness determination was based on a model that includes gravity loads from all components. However, the resulted stresses were quite low. Therefore, 36 lbs increase in weight is not considered to raise the stress level significantly. According to BPV code, the wall thickness of the half nipples, weld size, and weld strength shall be examined. The formulations are detailed in JLAB-TN-07-081 and BPV code section VIII, Division 1, UG-37. The analysis results related to instrumentation ports are updated as follows. Table 4 Nozzle wall thickness calculation Nozzle OD 12.75 Actual nozzle wall, t n 0.188 Nozzle inner radius, R n 6.19 Req d nozzle wall, t rn 0.0098 Is t n > t rn? yes From Table 4, the wall thickness of the half nipples is much more than the required wall thickness. Table 5 shows the calculation of required reinforcement area. It is clear that no additional reinforcement is needed for these enlarged instrumentation ports. Table 5 Required reinforcement areas instrumentation port diameter of opening d= 12.75 wall thickness of nozzle t n = 0.188 required nozzle thickness t rn = 0.0098 From Eq. (4), A= 0.32 From Eq. (5a), A 1 = 2.87 From Eq. (5b), A 1 = 0.20 larger A1 from above two = 2.87 6/13

From Eq. (6a), A 2 = 0.2228 From Eq. (6b), A 2 = 0.1676 smaller A2 from above two = 0.1676 From Eq. (7), A 41 = 0.0144 A 1 +A 2 +A 41 = 3.05 A 1 +A 2 +A 41 >A? Full penetration weld is used to attach the instrumentation ports to the vacuum vessel outer wall. The leg size of 0.12" is checked through calculations in Table 6. The safety factor is found to be greater than 12. Yes Table 6 Weld strength verification for instrumentation ports Instrumentation port Weld leg h = 0.12 Weld inner radius, i.e. port tube outer radius, r o = 6.38 Port tube inner radius, r i = 6.19 Throat area A=1.414π h r o 3.40 Unit 2nd moment of area, I u = π r o 2 127.68 MOI, I = 0.707h*I u 10.83 Stainless steel yield strength S y, psi 30,000.00 Internal pressure P i, psi 29.60 Logitudinal force due to pressure F x = P i π r 2 i, lbf 3,559.61 Shear stress due to F x and M z, τ x = F x /A+M z *r/i, psi 1,047.47 Hoop stress due to pressure, τ z = 2 r 2 i P i /(r 2 o -r 2 i ) 959.54 Total shear stress, τ=(τ 2 x +τ 2 y +τ 2 y ) 1/2, psi 1,420.53 Safety factor = 0.577*S y /τ 12.19 III. Support Bracket Analysis In JLAB-TN-07-081, a preliminary design drawing for support bracket was used and dimensions from that drawing are cited in the 2.0" 2.0" 0.188" square 304 stainless steel support bracket weld and self strengths analyses. The support bracket design is finalized afterwards and some dimensions have been changed. Figure 8 shows the current design for support brackets. The analysis procedure for support brackets in JLAB-TN-07-081 is repeated and the results are presented as follows: 7/13

Fig. 8 Support bracket dimensions (updated) Dimensions of the square tube is: b := 2.0 in d := 2.0 in t := 0.188 in L := ( 28.46 9.16) in Self weight of the bracket is estimated as: 8/13

cross-section area: A tube := bd ( b 2 t) ( d 2 t) A tube = 1.363in 2 W tube := 0.289 lbf in 3 A tube L W tube = 7.6lbf Refer to Fig. 7, y-direction force is calculated as: F y := 190 lbf + 34 lbf + W tube F y = 231.6lbf Yield strength of stainless steel is: Sy = 30,000 psi The bending or torsional moments created by F x and F y are: M x := 190 lbf 13.5 in M x = 2,565 lbf in 4.0 ( 28.46 9.16) in M z := 190 lbf 28.46 1.7 + in+ 34lbf ( 28.46 9.16 3.18 4) in+ W tube 2 2 M z = 5,949.8 lbf in Stresses in the weld Weld leg h := 0.25 in Weld throat area A weld := 1.414 h ( b + d) A weld = 1.414in 2 Unit polar 2nd monent of area J u := ( b + d) 6 J u = 10.667in 3 Polar 2nd moment of area J weld := 0.707 h J u J weld = 1.885in 4 d 2 Unit 2nd moment of area I u := ( 3b + d) 6 I u = 5.333in 3 2nd moment of area I weld := 0.707 h I u I weld = 0.943in 4 M z d Shear stress in x-direction: τ x := 2I weld τ x = 6,311.7 psi 2 F y M x b + d 2 Shear stress in y-direction: τ y := + A weld 2J τ y = 2,087.8 psi weld 2 2 Total shear stress τ weld := τ x + τ y τ weld = 6,648 psi 0.577 S y Safety factor: Sf weld := Sf weld = 2.6 τ weld Stresses in support bracket tube 2nd Moment of area: bd 3 ( b 2 t) ( d 2 t) 3 I tube := I tube = 0.754in 4 12 12 Polar 2nd moment of area: 9/13

( ) J tube := bd b 2 + d 2 ( b 2 t) ( d 2 t) ( b 2 t) + ( d 2 t) 12 12 J tube = 1.507in 4 M z d Tensile stress in x-direction: σ x := 2I tube σ x = 7,894.3 psi 2 F y M x b + d 2 Shear stress in yz plane: τ yz := + A tube 2J tube 2 2 Von Mises stress σ tube := σ x + 3 τ yz τ yz = 2,576.4 psi σ tube = 9,068.3 psi S y Safety factor: Sf tube := Sf tube = 3.3 σ tube IV. Stiffening Ring Weld Strength Verification The relocation of one of the support tabs has largely affected the shear force and bending moment distributions in the vacuum vessel. This can be observed from transverse bending moment diagrams presented in section II. The vacuum vessel shell segments are held together by virtually the welds adjacent to the six stiffening rings. It is thus important to re-verify the stiffening ring weld strengths. In JLAB-TN-07-081, stiffening ring weld strength calculations were performed for four load cases. The load case definitions are now revised to be three cases only and the external pressure is reduced to be 1.0 atm. Please also note when transportation loads appear, two additional end supports are added as shown in Fig. 1. The calculation procedure is similar to which was followed in JLAB-TN-07-081. The basic weld properties, such as weld leg size, throat area, unit 2 nd moment of inertia, are the same. Internal forces and moments are extracted from finite element models used in analyses in section I. Since the supports are not symmetric about vacuum vessel median plane any more, welds associated with all six stiffening rings shall be investigated. Tables 7, 8, and 9 presents weld strength calculations according to the three load cases defined earlier. Reviewing the safety factors listed in Tables 7, 8, and 9, it is found that all welds are safe in any load case. For cases 1 and 2, the welds associated with ring 5 have the lowest safety factor. This observation is consistent with the bending moment diagrams. For load case 3, the two additional end supports helped greatly in reducing stresses in welds. In reality, the specified 4.0 g vertical, 2.0 g axial, and 0.5 g horizontal accelerations are really for long-distance shipping by trucks over mountainous routes. The C100 CMs will be assembled at JLab and used in CEBAF tunnel. A typical scene occurs during transferring a CM to CEBAF tunnel is that a staff will walk in front of the trailer with hot coffee in hands. In other words, great caution will be taken while moving the CMs to the tunnel. 10/13

Table 7. Stiffening ring weld strength verification for vacuum vessel under load case 1 Case 1: 2.0 atm internal pressure and normal loads Ring 1 Ring 2 Ring 3 Ring 4 Ring 5 Ring 6 Axial force F x, lbf 23,068.00 9,688.40 9,688.40 9,688.40 23,068.00 23,068.00 Vertical force F y, lbf 806.50 1,124.00 269.76 486.58 1,505.50 750.00 Horizontal force F z, lbf 0.00 0.00 0.00 0.00 0.00 0.00 F yz = (F y 2 +F z 2 ) 1/2, lbf 806.50 1,124.00 269.76 486.58 1,505.50 750.00 Moment M y, lbf-in 0.00 0.00 0.00 0.00 0.00 0.00 Moment M z, lbf-in 14,739 32,663 14,694 10,049 79,445 13,961 M yz =(M y 2 +M z 2 ) 1/2, lbf-in 14,739 32,663 14,694 10,049 79,445 13,961 Shear stress due to F yz, τ 1 =F yz /A, psi 46.11 64.26 15.42 27.82 86.07 42.88 Shear stress due to F x and Myz, τ 2 =F x /A+M yz *r/i, psi 3,004.14 4,288.69 2,234.06 1,702.94 10,402.83 2,915.18 Total shear stress, τ=(τ 2 1 +τ 2 2 ) 1/2, psi 3,004.49 4,289.17 2,234.11 1,703.16 10,403.18 2,915.49 Safety factor = 0.577*S y /τ 5.76 4.04 7.75 10.16 1.66 5.94 11/13

Table 8. Stiffening ring weld strength verification for vacuum vessel under load case 2 Case 2: 1.0 atm external pressure and normal loads Ring 1 Ring 2 Ring 3 Ring 4 Ring 5 Ring 6 Axial force F x, lbf 11,903 5,001.50 5,001.50 5,001.50 11,903 11,903 Vertical force F y, lbf 806.49 1,124.00 269.76 486.58 1,505.50 750.00 Horizontal force F z, lbf 0.00 0.00 0.00 0.00 0.00 0.00 F yz = (F y 2 +F z 2 ) 1/2, lbf 806.49 1,124.00 269.76 486.58 1,505.50 750.00 Moment M y, lbf-in 0.00 0.00 0.00 0.00 0.00 0.00 Moment M z, lbf-in 14,739 32,663 14,694 10,049 79,445 13,961 M yz =(M y 2 +M z 2 ) 1/2, lbf-in 14,739 32,663 14,694 10,049 79,445 13,961 Shear stress due to F yz, τ 1 =F yz /A, psi 46.11 64.26 15.42 27.82 86.07 42.88 Shear stress due to F x and Myz, τ 2 =F x /A+M yz *r/i, psi 2,365.82 4,020.73 1,966.10 1,434.98 9,765 2,276.86 Total shear stress, τ=(τ 2 1 +τ 2 2 ) 1/2, psi 2,366.27 4,021.25 1,966.16 1,435.25 9,765 2,277.26 Safety factor = 0.577*S y /τ 7.32 4.30 8.80 12.06 1.77 7.60 12/13

Table 9. Stiffening ring weld strength verification for vacuum vessel under load case 3 Case 3: 1.0 atm external pressure and transportation loads Ring 1 Ring 2 Ring 3 Ring 4 Ring 5 Ring 6 Axial force F x, lbf 10,290 2,753.1 4,461.0 5,974.3 4,341.7 13,403 Vertical force F y, lbf 3,226.00 4,502.00 1,085.00 1,940.30 1,324.90 3,000.00 Horizontal force F z, lbf 403.24 584.16 157.04 221.13 173.12 375.00 F yz = (F y 2 +F z 2 ) 1/2, lbf 3,251.1 4,539.74 1,096.31 1,952.86 1,336.16 3,023.35 Moment M y, lbf-in 7,369.7 15,906 7,689.00 4,627.80 649.40 6,980.6 Moment M z, lbf-in 58,958 130,730 59,087 39,898 9,328.2 55,845 M yz =(M y 2 +M z 2 ) 1/2, lbf-in 59,417 131,694 59,585 40,165 9,351 56,280 Shear stress due to F yz, τ 1 =F yz /A, psi 185.87 259.54 62.68 111.65 76.39 172.85 Shear stress due to F x and Myz, τ 2 =F x /A+M yz *r/i, psi 7,382.2 15,216 7,068.20 4,934.2 1,317 7,201.46 Total shear stress, τ=(τ 2 1 +τ 2 2 ) 1/2, psi 7,384.54 15,218 7,068.48 4,935.47 1,320 7,203.53 Safety factor = 0.577*S y /τ 2.34 1.14 2.45 3.51 13.12 2.40 V. Summary of Revisions C100 CM vacuum vessel structural analysis is revisited due to design changes. The relocation of one support tab has ruined the symmetry of loading in the vacuum vessel and in general, safety factors in stiffening ring welds are lowered. However, all welds are safe. All other strength verifications that are slightly affected do not raise any concerns. Additional end supports are essential to resist the g-forces generated in transportation of CMs. REFERENCES [1]. 2007 ASME Boiler & Pressure Vessel Code, Section VIII, Division 1, Rules for Construction of Pressure Vessels, The American Society of Mechanical Engineers. [2]. G. Cheng and E. F. Daly, C100 Cryomodule Vacuum Vessel Structural Analysis, JLAB-TN-07-081, Jefferson Lab, Newport News, VA. [3]. 2007 ASME Bolier & Pressure Vessel Code, Section II, Part D, Material Properties (Customary), The American Society of Mechanical Engineers. 13/13