JLAB-TN-09-029 C100 Cryomodule Vacuum Vessel Structural Analysis-Addendum II to JLAB-TN-07-081
C100 Cryomodule Vacuum Vessel Structural Analysis
- Addendum II to JLAB-TN-07-081
Gary G. Cheng, Edward F. Daly, and Mark Wiseman
Introduction
The C100 cryomodule (CM) vacuum vessel structural analysis per ASME Boiler & Pressure Vessel code (BPVC) [1] requirements was addressed in JLAB-TN-07-081 [2] and JLAB-TN-09-007 [3]. This technical note (TN) is to amend the previous two TNs in a few aspects:
(1) More comprehensive ASME pressure vessel code analyses are conducted in consideration of the complicated loading condition for vacuum vessel,
(2) Since the C100 CM design is finalized, the weights of components to be supported by the vacuum vessel are found to be more than the previously estimated. Most calculations are affected.
(3) The manufacturer suggested some design changes that affect weld details. They are addressed in this TN.
In the summary of this TN, a chronological list of editions in all three TNs on vacuum vessel structural analysis is given to facilitate tracking of changes. This TN is primarily aimed to implement the procedure of ASME BPVC analysis per Section VIII, Division 1 rules (S8D1), with reference to pertinent Division 2 rules/definitions. A short discussion of scenarios to apply either Division 1 or 2 rules in analyzing pressure vessel is presented in Appendix 1.
I. Allowable Stresses and Required Wall Thicknesses (UG-22, UG-23, and UG-28)
The estimated weights used in JLAB-TN-07-081 and JLAB-TN-09-007 are based on SNS CM. The weights for C100 CM components are updated as follows:
Part name / volumes, in3 / weightSingle Nb cavity / 172.6 / 53.51 / lbs
8 Nb cavities / 1,380.8 / 428 / lbs
Inner mag shield (all 8 modules) / 219.2 / 69 / lbs
Outer mag shield / 1,424.9 / 450 / lbs
Thermal shield / 2,556.3 / 826 / lbs
SS parts (spaceframe, HV, headers, tuners, rods & brackets, etc.) / 13,209.0 / 3,817 / lbs
Spaceframe & associated components / 5,591 / lbs
Supply End Can / 3,913.6 / 1,131 / lbs
Return End Can / 3,653.3 / 1,056 / lbs
Other loads include:
Weight of single waveguide assembly: 190 lbf
Internal design pressure: 29.4 psi (2.0 atm)
External design pressure: 14.7 psi (1.0 atm)
Transportation loads are not considered in most part of this TN due to two reasons: 1) the C100 cryomodules will be assembled at JLAB and transported with great caution to CEBAF tunnel, and 2) the cryomodule transportation fixture has abundant supports that have been proven being very safe in the past. Please refer to JLAB-TN-09-007 for the revised locations of support brackets.
I.1 Tensile and Compressive Allowable Stresses
ASME BPVC S8D1, UG-23 (a) states that for tensile allowable stress, Section II tables [4] are to be used. For 304 stainless steel, the allowable tensile stress at room temperature is found to be 20,000 psi.
UG-23(b) describes the steps to calculate the compressive allowable stress, the Factor B, according to vessel geometrical dimensions. During normal operation, the vacuum vessel is under external atmospheric pressure, hence, in compression. The allowable compressive stress is determined as follows (thickness is chosen per UG-16(b)):
At room temperature, 304 stainless steel’s young’s modulus per Section II, Part D, Subpart 3, Table HA-1 is E = 2.8×107 psi.
Ro= / 16.0 / inchest= / 0.0625 / inches
Factor A= / 0.000488
Do interpolation in Table HA-1 for Factor B= / 6,770 / psi
The Factor B is the allowable compressive stress to use.
I.2 Minimum Wall Thickness per UG-22 and UG-23 Requirements
UG-23(c) requires that the determination of vessel wall thickness shall consider all loads and the “maximum general primary membrane stress” and “combined maximum primary membrane stress plus primary bending stress” need to be checked respectively. S8D1 does not clearly define how the primary membrane and bending stresses are evaluated and combined. In the history, ASME formed a Task Group on Primary Stress [5] to study how to extract such stresses from finite element analysis (FEA) [5-6]. In 2007 ASME BPVC S8D2, these stresses are clearly defined. Thus, definitions and evaluation procedures in Section VIII Division 2 (S8D2) Parts 4 & 5 are applied. The 1-D finite element model that was used in JLAB-TN-07-081 and JLAB-09-007 is revised to include the lateral loads due to waveguides and the stress results are post-processed to generate the stresses (Pm for primary membrane stress and Pb for primary bending stress) per BPVC definitions. Note that this FEA is based on elastic material model and therefore the stress linearization procedure per S8D2 Annex 5A is applied (see Appendix 2).
In the 2004 ASME BPVC, maximum shear failure theory is enforced by calculating the stress intensity = 1st principal stress – 3rd principal stress. The 2007 BPVC tends to apply the distortion energy failure theory that requires the calculation of von Mises stress. From the 1-D FEA, nodal stress components are calculated. The three principal stresses are obtained by solving a cubic equation in this form:
σ3-I1σ2+I2σ-I3=0 (1)
The I1, I2, I3 are stress invariants evaluated from stress components and the roots to this equation can be derived from Cardano’s formula, see Appendix 2. The three roots are sorted to obtain the 1st , 2nd, and 3rd principal stresses: s1, s2, and s3. Stress intensity is equal to s1- s3. The von Mises stress is:
σeq=σ1-σ22+σ1-σ22+σ1-σ222 (2)
The finite element model was run for both internal pressure and external pressure cases with normal loads. Transverse shear force, bending moment, and stress plots are attached in Appendix 3 for information. The purpose of these FEA is to determine the required vacuum vessel shell thickness per UG-23(c). It is noted that UG-16(b) states that in general, the minimum wall thickness for shells and heads shall be no less than 0.0625". So there is no need to investigate thicknesses that are lower than 0.0625". The 0.0625" thickness would be a good initial guess of the required wall thickness. In other words, if the vessel with 0.0625" thickness proves to be safe per UG-23(c) conditions, then the required minimum shell thickness is 0.0625".
The primary membrane stresses, Pm, and the combined primary membrane stress and primary bending stress, Pm + Pb, for the case of t = 0.0625" are given in Table 1. The Pm’s are much lower than tensile allowable stress of 20,000 psi and compressive allowable stress of 6,770 psi. The Pm+Pb’s are not much different from Pm’s and they are lower than 1.5 times of the tensile or compressive allowable stresses. Therefore, combining the requirements in UG-16(b) and UG-23(c), the required minimum shell thickness is tr = 0.0625".
Table 1 Summary of stresses in vacuum vessel with shell thickness = 0.0625"
Cases / t = 0.0625"1st principal / 2nd principal / 3rd principal / stress intensity / von Mises
Pin = 2 atm, top of shell, Pm / 7,485 / 5,750 / -29 / 7,955 / 6,908
Pin = 2 atm, top of shell, Pm+Pb / 7,485 / 5,754 / -29 / 7,955 / 6,907
Pin = 2 atm, bottom of shell, Pm / 7,485 / 3,364 / -29 / 8,186 / 7,218
Pin = 2 atm, bottom of shell, Pm+Pb / 7,485 / 3,363 / -29 / 8,186 / 7,219
Pext = 1 atm, top of shell, Pm / 1,036 / -1,561 / -3,760 / 4,795 / 4,153
Pext = 1 atm, top of shell, Pm+Pb / 1,037 / -1,561 / -3,760 / 4,796 / 4,154
Pext = 1 atm, bottom of shell, Pm / 620 / -3,748 / -3,924 / 4,382 / 3,887
Pext = 1 atm, bottom of shell, Pm+Pb / 620 / -3,748 / -3,928 / 4,381 / 3,889
The actual design thickness for vacuum vessel shell is t = 0.25". For information, the Pm’s and Pm+Pb’s are evaluated for vessel with real design thickness and stress results are presented in Table 2. Clearly, all these stresses are quite small compared to the tensile and compressive allowable stresses mentioned above. This also indicates that a detailed 3-D model stress analysis is not so necessary. The difference between Pm and Pb+Pm is very small for the reason explained in Appendix 2.
Table 2 Summary of stresses in vacuum vessel with shell thickness = 0.25"
Cases / t = 0.25"1st principal / 2nd principal / 3rd principal / stress intensity / von Mises
Pin = 2 atm, top of shell, Pm / 1,838 / 1,487 / -29 / 1,996 / 1,734
Pin = 2 atm, top of shell, Pm+Pb / 1,838 / 1,491 / -29 / 1,996 / 1,736
Pin = 2 atm, bottom of shell, Pm / 1,838 / 823 / -29 / 2,093 / 1,840
Pin = 2 atm, bottom of shell, Pm+Pb / 1,838 / 823 / -29 / 2,094 / 1,841
Pext = 1 atm, top of shell, Pm / 335 / -397 / -934 / 1,269 / 1,100
Pext = 1 atm, top of shell, Pm+Pb / 336 / -397 / -934 / 1,270 / 1,101
Pext = 1 atm, bottom of shell, Pm / 166 / -933 / -1,050 / 1,102 / 1,005
Pext = 1 atm, bottom of shell, Pm+Pb / 166 / -933 / -1,055 / 1,101 / 1,007
I.3 Thickness of Shells under External Pressure (UG-28)
ASME BPVC UG-28 gives detailed steps to determine the required minimum thickness for cylindrical shells under external pressure. UG-28 (c) (1) has an 8-step procedure that applies to cylindrical shell with Do/t >10. In the case of vacuum vessel shell, the Do/t = 128 for design OD and thickness. Since this is a procedure to determine minimum required thickness, which is believed to be more likely less than design thickness of 0.25", options of Do/t will be greater than 128. The UG-28 (c) (1) procedure is thus applied.
Table 3 Allowable external pressure for vacuum vessel with minimum required thickness
Segment 1 / Segment 2 / Segment 3 / Segment 4 / Segment 5 / Segment 6 / Segment 7Length, L / 65.08 / 5.57 / 66.15 / 53.22 / 58.86 / 7.29 / 70.65
L/Do / 2.0338 / 0.1741 / 2.0672 / 1.6631 / 1.8394 / 0.2278 / 2.2078
Factor A / 0.0001769 / 0.0023136 / 0.0001740 / 0.0002184 / 0.0001965 / 0.0017461 / 0.0001624
Factor B / 2800.48 / 11899.08 / 2755.91 / 3405.13 / 3089.41 / 11103.89 / 2582.44
Pa, psi / 15.99 / 67.92 / 15.73 / 19.44 / 17.64 / 63.38 / 14.74
Safe? / Yes / Yes / Yes / Yes / Yes / Yes / Yes
The entire vacuum vessel shell length is divided into 7 segments due to reinforcing rings and ground supports [3]. Per Step 8 of UG-28 (c) (1), the major verification is the maximum allowable external pressure, Pa, which shall be greater than 1 atm (14.7 psi) on all segments of the vacuum vessel shell. The wall thickness is adjusted iteratively to meet this requirement. Table 3 shows the results of Pa at the determined required wall thickness of tr = 0.137". In Table 4, the allowable external pressures for vessel with design thickness of t = 0.25" are shown for information.
Table 4 Allowable external pressure for vacuum vessel with design thickness
Segment 1 / Segment 2 / Segment 3 / Segment 4 / Segment 5 / Segment 6 / Segment 7Length, L / 65.08 / 5.57 / 66.15 / 53.22 / 58.86 / 7.29 / 70.65
L/Do / 2.0338 / 0.1741 / 2.0672 / 1.6631 / 1.8394 / 0.2278 / 2.2078
Factor A / 0.0004345 / 0.0058817 / 0.0004270 / 0.0005377 / 0.0004833 / 0.0044221 / 0.0003983
Factor B / 6180.92 / 13817.91 / 6095.83 / 7255.65 / 6718.00 / 13430.38 / 5759.90
Pa, psi / 35.28 / 78.88 / 34.80 / 41.42 / 38.35 / 76.67 / 32.88
Safe? / Yes / Yes / Yes / Yes / Yes / Yes / Yes
The conclusion from this study is that to meet UG-28 requirements on allowable external pressure, the minimum required shell thickness is 0.137". The design thickness of 0.25" is found to be sufficient. The required wall thickness is useful in subsequent reinforcement area code calculation per UG-37.
II. Reinforcement Area at Welds for Openings (UG-36, UG-37, UG-40, UG-41, UW-15, and UW-16)
II.1 Reinforcement Areas for Vessel under Internal Pressure
There are welds at waveguide ports, instrumentation ports, accesses port, and tuner ports. The steps for determining whether reinforcement areas are needed for these welded openings are detailed in UG-37. A prelude to the reinforcement area calculation is the determination of required nozzle wall thickness, i.e. trn. The rules governing nozzle wall thickness are in UG-16(b) and UG-45. For nozzles subjected to internal pressure, if no other mechanical loads but pressure load exist, UG-45(a) can be conveniently carried out by use of formulas given in UG-27 for cylindrical nozzles. Please note that waveguides ports carry waveguides [2]. The nozzles are seamless so that the weld joint efficiency is 1.0. Table 5 shows the detailed calculations for trn’s:
Table 5 Determining trn for nozzles under internal pressure
center waveguide port / side waveguide port / Instrument-ation port / access port / tuner port
ID of nozzle / 14.40 / 11.21 / 12.37 / 5.834 / 4.12
Inner radius of nozzle / 7.2 / 5.61 / 6.19 / 2.91 / 2.06
Vertical force, Fy, lbf / 380 / 190 / 0 / 0 / 0
Distance from C.G. to interface, in / 13 / 13
Bending moment, Mz, lbf-in / 4940 / 2470 / 0 / 0 / 0
Nozzle thickness by UG-45(a) / 0.011 / 0.008 / 0.009 / 0.004 / 0.003
Nozzle thickness by UG-45(b)(1), UG-16(b) / 0.0625 / 0.0625 / 0.0625 / 0.0625 / 0.0625
Nozzle thickness by UG-45(b)(4) / 0.375 / 0.375 / 0.375 / 0.28 / 0.258
Nozzle thickness by UG-45(b) / 0.0625 / 0.0625 / 0.0625 / 0.0625 / 0.0625
Required nozzle wall thickness, trn / 0.0625 / 0.0625 / 0.0625 / 0.0625 / 0.0625
OD of nozzle with required wall thickness / 14.53 / 11.34 / 12.75 / 6 / 4.5
Maximum shear stress, psi / 1,715.5 / 1,340.4 / 500.7 / 538.8 / 181.8
Allowable shear stress by UG-45(c) / 14,000 / 14,000 / 14,000 / 14,000 / 14,000
Is UG-45(c) satisfied? / Yes / Yes / Yes / Yes / Yes
The actual nozzle wall thicknesses are found to be thicker than required as stated in Table 6.
Table 6 Comparison of actual nozzle wall thicknesses with required minimum thicknesses