STRUCTURAL ANALYSIS OF THE VACUUM VESSEL FOR THE LHCb VERTEX LOCATOR (VELO)

National Institute for Nuclear Physics and High Energy Physics Kruislaan 409 1098 SJ Amsterdam The Netherlands NIKHEF Reference no.: MT-VELO 04-1 EDMS no: 432626 OF THE VACUUM VESSEL FOR THE LHCb VERTEX LOCATOR (VELO) M. J. Kraan, J. Buskop, M. Doets, C. Snippe Abstract The structural verification of the LHCb VELO Vacuum vessel is the subject of this document. Purpose of these calculations is to investigate stress and displacements in the stainless steel VELO Vacuum vessel. The Vacuum vessel has to comply with the CODAP Code. Numerical analysis was performed with the IDEAS TM finite element analysis software. January 2004

Table of Contents 1. Introduction...3 2. General description of the vacuum vessel...4 2.1 Design of the vessel...4 2.1 Operational conditions...6 2.3 Material...8 2.4 Classification of the vessel....8 3 Finite element analysis...10 3.1 Vessel...10 3.2 FEA results for the vessel...11 3.2.1 Stress analysis of the vessel...12 3.2.2 Buckling analysis of the vessel...14 3.2.3 Deformations from the stress analysis...14 3.3 End cover...15 3.4 FEA results for the end cover...16 3.4.1 Stress analysis of the end cover...17 3.4.2 Buckling analysis of the end cover...19 3.4.3 Deformations from the stress analysis...19 3.5 Results of the analysis....20 3.5.1 Vessel...22 3.5.2 End cover...22 4 Tests, safety and quality control...23 4.1 Tests...23 4.2 Safety...23 4.3 Quality control...23 5 Compliance with CODAP...24 5.1 Vessel...24 5.2 End cover...24 6 Summary...25 APPENDICES A.. All FEA results. B.. Material Technical Specification of Stainless steel AISI 316L. C.. Equations used for Von Mises and CODAP stress. D.. Calculating loads. E.. Construction Category. F.. Calculating Energy Error Norm G.. All Technical Drawings. 2

1. Introduction LHCb is one of the four particle physics experiments around the LHC accelerator, which is located at CERN. The LHCb VErtex LOcator (VELO), shown in figure 1.1, is one of the sub detectors of the LHCb experiment Fig 1.1: VELO detector. The physics requires the detectors to be located as close as possible to the interaction point. This in terms requires the detector to be placed in a vacuum vessel. The scope of this document is the safety analysis of the vacuum vessel, regarding only the structural integrity of the vessel. The safety requirements are put forward by the Technical Inspection and Safety division (TIS) at CERN. The TIS has requested to use to CODAP (Code De Construction des Appareils a Pression), the French design code for pressure vessels, to verify the safety of the vacuum vessel. The document is structured as follows: Chapter 2 gives a general description of the vessel. Described are the operation condition, the selection of the used material used for the vessel and classification of the vessel for the CODAP. Chapter 3 describes the finite element analysis of the vessel and the end cover. Chapter 4 describes steps to verify and ensure the structural integrity of the vessel. Chapter 5 summarizes the results and steps in a conclusion. Chapter 6 gives a summary of the document. 3

2. General description of the vacuum vessel Described are the vessel in general, its main components, the conditions under which the vessel is operated, the material selected for the vessel and the classification of the vessel in correspondence with the CODAP. 2.1 Design of the vessel The design of the vessel is determined by two main constraints: the requirements from the physics, which is to bring the detector as close as possible to the IP (interaction point) and the vacuum requirements for the operation of the LHC accelerator. To best meet all the requirements there are two separated volumes, see figure 2.1. The main volume (beam vacuum) is part of the LHC accelerator, the second volume (detector vacuum) encloses the detector. This secondary volume is mainly enclosed inside the vessel. The pressure in both volumes should be as the low as possible. The current aim is a pressure 10-9 mbar for the beam vacuum and a pressure better than 10-4 mbar for the detector vacuum. The detector inside the secondary volume can move in- and outwards with respect to the IP to allow injection of the beam. Fig 2.1: schematic vertical crossing of the VELO detector The main difficulty with regards to the structural integrity of the vessel are the openings at both sides. The openings, in which the detector is mounted, encompass almost the full length of the vessel, see figure 2.2. These openings result in a reduction of stiffness of the primary cylindrical shape of the vessel. 4

Second difficulty is that the vessel has openings for the support and movement of the detector. The influence zone of the opening on the side of the vessel is connected to the influence zone of the opening for the support of the detector. this results in stress concentrations. There are additional openings in the vessel for connection of pumps and to allow access for maintenance. Fig 2.2: At both sides of the vessel are openings for installation of a detector half. Several parts are connected to the vessel: Exit Window, end cover, two Detector Hoods and 2 getter pumps, shown in figure 2.3. See appendix G for all technical drawings of the vessel. Within the document only the end cover of the vessel are considered. The exit foil is the responsibility of the CERN vacuum group. The aspects of the two detector hoods will be covered in a different document. Fig 2.3: Several parts are connected to the vessel. In the analysis only the loads of the connecting elements are transferred to the vessel, the stiffness of these elements is disregarded. Using these assumptions, the worst case effects of the elements are regarded in the analysis of the vessel. The end cap cover is regarded in a similar way. 5

2.1 Operational conditions The load of the vessel is determined by the weight of the vessel, the connecting elements, and the vacuum force. The vessel is operated at two temperatures. The operation temperature and pressure are given by the vacuum procedures. The conditions for the analysis of the vessel are given in table 2.1. Operations temperature [0C] pressure [mbar] pumping down 20-25 1.10-9 baking out 150 1.10-9 venting 20-25 1000 operational 20-25 1.10-9 Table 2.1: Different operation conditions of the vacuum vessel. medium neon - The loads for the vessel are show in figure 2.1 and table 2.2. The loads on the vessel are described in detail in appendix D. Fig 2.1: Loads (visualized by arrows) in the FEA model of the vessel. Load Type Weight Detector Hood Weight vessel Cover Weight Getter pump 1000 [N] 1000 [N] 900 [N] Pressure Detector Hood Pressure vessel Cover Pressure Exit Foil Pressure Flange CF 200 Pressure Flange CF 150 Pressure Bellow External Pressure 28441[N] 882[N] 50895[N] 3048 [N] 1720 [N] 567 [N] 0.1 [MPa] Table 2.2: Loads used in the FEA model of the vessel 6

For the end cover the loads are given in figure 2.2 and table 2.3. A detailed description of the loads is given in appendix D. Fig 2.2: Loads (visualized by arrows) in the FEA model of the end cover. load type Weight Turbo + Valve 457 [N] Weight Gravity Valve + Getter 290 [N] Pressure Flange CF 200 3048 [N] Pressure Flange CF 150 1720 [N] Pressure Flange CF 63 229 [N] Moment Turbo + Valve 92 [Nm] Moment Gravity Valve + Getter 87 [Nm] Vacuum Pressure 0.1 [MPa]] Table 2.3: Loads used in the FEA model of the end cover. All the parts of the vessel are connected in such a way that thermal effects have no effect on the load on the vessel and end cover. Also the support of the vessel is designed in such a way that thermal expansion does not induce stresses in the vessel. All loads are applied without any safety factors. The vessel and end cover have been designed based on an operation temperature of 150 o C. These conditions will occur during the bake-out of the vessel. Currently it is assumed that the vessel will be baked-out at most once a year, taking approximately 2 days. Normal operation conditions are room temperature and vacuum. 7

2.3 Material The vessel and the end cover will be made from AISI 316L TYPE X2CrNiMo17-12-2 (1.4404). The material has been selected based on the vacuum requirements and the welding ability of the material. A further description of the material requirements and conditions at delivery are given in appendix B. Embitterment, corrosion effects and creep rupture effects are not considered as they are not relevant for either the vessel or the end cover. A summary of the mechanical properties is given in table 2.4. At 20-25 o C At 150 o C Tensile strength R m [MPa] min. 585 525 Yield strength R p 0.2% [MPa] min. 260 230 Young s modulus E [GPa] min. 200 186 Density ρ [g/cm 3 ] 7.85 Poisons ratio 0.30 Elongation at break A5 [%] min. 35 Brinell hardness HB max. 180 Table 2.4: Properties AISI 316L after solution annealing. 2.4 Classification of the vessel. For the classification of the vessel chapters G6, G7 and GA1 of the CODAP code where taken as a guide line. The classification according to GA1 can be found in appendix E. The main considerations for the classification: To minimize the need for quality control during production, and to minimize the requirements for the final inspection, the maximum safety factors are chosen. To ensure a lowest possible vacuum level the material quality control is relative extensive. The extensive material quality control is also chosen as a compensation for the limited quality control during production. These choices are related to the problem of testing welds. The most critical welds are difficult to test, either by X- ray or ultrasonic testing. As the vessel is designed as a vacuum vessel it is difficult to test the vessel at higher external pressures. Higher external pressures would require another pressure vessel in which to place the VELO vessel. 2.4.1 Classification referring to the CODAP guidelines; The vessel is made of a single material AISI 316 L, the material quality control is relative extensive, corresponding to type 1 (see also appendix B). The maximum values for the design stress and the welding coefficients have been chosen respectively f 3 and 0.7. The vessel is complex due to the large openings at the side and the openings for the support of the detector. The verification of the critical weld at 8

the critical points is difficult. The normal operation conditions, vacuum and at room temperature, are far less severe then the design conditions, vacuum and 150 o C. During normal operation there are no variations in the load conditions, except from the variations in the atmospheric pressure which variance is small compared to the total load. The energy stored in the vessel is low. The content of the vessel is nontoxic. The operational life time of the vessel is less than 15 years. The vessel is operated in a closed area with no access, except for maintenance of the detector. The vessel is remotely operated during normal operation. There is no influence to be expected from the environment. The vessel will not be serviced or tested during its expected life time as the critical points (critical welds) are not accessible. The impact of failure of the vessel depends on the moment of failure. During the bake-out of the vessel, the vessel is accessible for authorized personal. Failure in terms of leakage of the vessel will require a shutdown of the LHC accelerator and the related experiments, to allow replacement of the vessel with a standard beam pipe section or to repair the leak. The shutdown period would be 3 days to 2 weeks. There would be no risk of personal injury. Failure in terms of implosion of the vessel (catastrophic failure) would cause an unacceptable loss of scientific equipment. When a failure occurs, in the presence of persons, would this have severe and possible lethal consequences for personal working within a range of approximately 5 meters to the vessel. It has been considered that the effects of catastrophic failure might require the vessel to be classified differently. However catastrophic failure is highly unlikely. During inspection the vessel will be tested at design conditions (vacuum 150 o C). Given the vessel passes this test it is highly unlikely that the vessel will fail catastrophically at another point in time. The material is not subjected to aging, given the 150 o C is ensured there is no reason the vessel would fail later on. It has been decided that the vessel and end cover are classified as a class C vessel. The loads of the vessel are the weight of the mounted components and the vacuum forces. The design is based on an operation temperature of 150 o C and an external pressure of 0.1 MPa. The vessel and the end cover are made out of AISI 316L. The material acceptance control is relatively extensive. 9

3 Finite element analysis A finite element analysis has been done to model the expected stresses and to verify that these stresses are within the limits defined by the CODAP. The finite element analysis of both the vessel and the end cover where done with the finite element analysis module of Ideas. For both parts a stress- and a buckling analysis where made. Presented are a description of the models, the results and the interpretation of the results. Following the chosen construction class C and welding coefficient z=0.7, defined in previous section 2.4, the stress limits according to CODAP are: Global zones: 525 f = f3 = = = 150 MPa 3.5 3.5 Weld regions: z Rm 0.7 525 fw = = = 105 MPa 3.5 3.5 Peak regions: f = 1.5 f 3 = 1.5 150 = 225 MPa. Peak/Weld regions: p R m f pw = 1.5 f w = 1.5 105 = 157 MPa 3.1 Vessel Half the vessel is modeled, as the vessel is symmetric about YZ, see also figure 3.1. Fig 3.1: The vessel is symmetric about YZ. The boundary conditions for the model are given by the loads on the vessel, the reaction forces from the support of the vessel, and the symmetry constraints. The loads are given in table 3.1 and the boundary conditions are given in table 2.2 (see also figure 2.1 chapter 2). 10

At the flanges no bending moments are introduced, the connecting elements at the flanges are given sufficient stiffness to avoid the transfer of a bending moment at the flanges. Symmetry surface X translation Y translation free Z translation free X rotation free Y rotation Z rotation Table 3.1: Boundary conditions of the vessel support flexible support free free The vessel is modeled using thin shell parabolic quadrilateral and solid parabolic tetrahedron elements. 2D shell elements are used at the relatively thin parts of the vessel. 3D solid elements are used to model the relatively thick parts of the vessel, see figure 3.2. Given that solid elements can underestimate the stresses due to bending, this effect has been verified. No adverse effect due to the use of solid elements was found in the model.. Fig 3.2: FEA model of the vessel. Blue and yellow elements are 2D shells with thickness respectively 2.5 and 6 mm. Green are 3D solid elements. 3.2 FEA results for the vessel Only the most important results are presented in this chapter. Further results of the analysis can be found in appendix A. The results of the stress analysis are presented in terms of von Mises equivalent stress and, by the CODAP code required, Tresca equivalent stress (in the following text named as CODAP stress). See appendix C for the used Von Mises and CODAP equations. A buckling analysis is presented as the stresses in the vessel are mainly compressive. Given the compressive stress, a verification of the stability (buckling) of the vessel is required. In addition the calculated deformations from the stress analysis are presented. 11

3.2.1 Stress analysis of the vessel The general picture of the stresses is given in figure 3.3 and 3.4. Figures 3.5 and 3.6 give a magnified picture of the highest stress peak. The two detailed circles show the regions where the stresses are below (green) or above (red) the acceptable design stress. fig 3.3: CODAP stress; max. = 210 MPa fig 3.4: Von Mises stress; max. = 206 MPa 12

fig 3.5: CODAP stress, stress limited at the Nominal Design Stress. green 150 MPa; red 150 MPa fig 3.6: Von Mises stress, stress limited at the Nominal Design Stress. green 150 MPa; red 150 MPa 13

3.2.2 Buckling analysis of the vessel The buckling analysis calculates a load factor on the original load at which buckling will occur. The figure 3.6 shows the first buckling mode. The calculated buckling (load) factor is 15.8. fig 3.7: first buckling mode vessel = 15.8 3.2.3 Deformations from the stress analysis To complete the picture of the analysis the deformations from the stress analysis are presented in figure 3.8. The maximum displacement = 0.9 mm. fig 3.8: Deformation of the vessel; max. = 0.9 mm 14

3.3 End cover Figure 3.9 shows the exploded view of the end cover with all main components. One flange (CF150) on the spherical head will be used to mount a turbo pump. An other flange (CF200) wil be used to mount a safety gravity valve with his vacuum components. The conflat flange (CF63) in the center of the spherical head forms the connection to the beam pipe of the LHC accelerator. Fig. 3.9: Exploded view of the end cover. The boundary conditions for the model are given by the loads on the end cover and the constraints on the connection flange to the vessel. The loads are given in table 2.3 and the boundary conditions are given in table 2.3 (see also figure 2.2 chapter 2). x translation y translation z translation x rotation free y rotation free z rotation free Table 3.2: Constrains of the end cover, placed at the connection flange to the vessel. Figure 3.10 shows the FEA model built up from 3D solid parabolic tetrahedron - and 2D thin shell parabolic quadrilateral elements. 2D shell elements are used at the relatively thin parts and 3D elements in the relatively thick parts of the end cover. 15

Fig 3.10: FEA model of the end cover. Blue and yellow elements are 2D shells with thickness of respectively 2.5 and 6 mm; green areas are 3D solid elements. 3.4 FEA results for the end cover The results are presented in a similar way as in section 3.2. Only the most important results are presented in this section. Further results of the analysis can be found in appendix A. The results of the stress analysis are presented in terms of von Mises equivalent stress and in the by the code required Tresca equivalent stress (in the following text named as CODAP stress). See appendix C for the used Von Mises and CODAP equations. A buckling analysis is presented as the stresses in the end cover are mainly compressive, requiring a verification of the stability of the end cover against buckling. In addition the calculated deformations from the stress analysis are presented. 16

3.4.1 Stress analysis of the end cover The Von Mises and CODAP results are shown respectively in figures 3.11, 3.12 and figures 3.13, 3.14. The max CODAP stress is 45 MPa. The max Von Mises stress is 83 MPa. fig 3.11: CODAP stress, inside view; max. stress = 45 MPa. fig 3.12: CODAP stress, outside view; max. stress = 45 MPa. 17

fig 3.13: Von Mises stress, outside view; max. stress = 83 MPa fig 3.14: Von Mises stress, inside view; max. stress = 83 MPa 18

3.4.2 Buckling analysis of the end cover The buckling analysis shows at how many times the original load the onset of buckling occurs. Figure 3.15 shows the first buckling mode. The calculated buckling (load) factor is 108. fig 3.15: first buckling mode of the end cover =108. 3.4.3 Deformations from the stress analysis To complete the picture of the analysis the deformations from the stress analysis are presented in figure 3.16.. The maximum displacement = 0.15 mm. fig 3.16: Deformation of the end cover; max = 0.15 mm. 19

3.5 Results of the analysis. The results are compared with the requirements defined by the CODAP. The limitations of the analysis are presented, and the compliance with the code is verified. The main focus is on the vessel as the results of the end cover are far less critical. For the analysis the general calculations from the CODAP have been taken as a guideline (Section C10 CODAP). The code aims to verify possible failure due to: Gross plastic deformation Plastic instability Incremental collapse The stress analysis verifies possible failure due to gross plastic deformations. The buckling analysis is done to verify failure due to instability. Failure due to incremental collapse is not applicable as the vessel is not subjected to dynamic or changing loads. All the loads on the vessel are primary loads. The stresses are, contrary the requirements of the CODAP, not sub-divided in membrane stresses, bending stresses and non-linear stresses. This has been chosen as most of the stresses lay well within the requirements of the CODAP. Even for the local regions, where stresses are higher, this subdivision is not made, since these regions are mainly modeled using 3D solid elements. Stresses are almost impossible to subdivide using 3D solid elements. The code emphasizes the need to verify the analysis for close concentrated local regions. This is mainly applicable for the vessel, and is of lesser concern for the end cover. Fig 3.17; Regions of concern for the vessel. Regions of concern for the vessel are the region where the openings for the detector support are close to the big opening in the sides of the vessel (see A in fig 3.17). Other regions of concern are the three openings on top and two at the bottom of the vessel (C) and in the region where the end flange is connected to the big openings in the side of the vessel (B). The regions at the top (C) require different approach as 20

these regions can not be inspected. The region where the openings for the detector support are close to the big openings at the side of the vessel (A) is also the region where the transitions from solid to shell elements take place. In this region the model is less accurate due to the difficulty of transferring the bending moments from the shells into the solids. To get a best possible connection a layer of shells is put onto the solids, whereby the shells are given a zero thickness. Also the difference in stiffness in that region is unfavorable for the FEA. The stresses could further be negatively influenced when the hoods are mounted to the vessel. This would increase the stiffness of the flange, which in term would lead to higher stresses in this region. The effects of the welds have not been modeled. The welds are full penetrating, preventing a weakening of the structure. The avoidance of weakening the structure is provided by the proper selection of the type of welds and the filler material for the welds. The region where the openings on the side meet the flanges is fully modeled in solid elements. These elements tend to underestimate the stresses. The quality of the FEA is verified using the strain energy error norm, figure 3.18. The strain energy error norm compares the summary of the energy errors per element with the total strain energy of the model. More information on the strain energy error norm can be found in appendix F. The global value for the strain energy error norm in the vessel (8.1 %) and end cover (8.4%) are high (below 7% is recommended by the IDEAS TM software). This is related to the significant stiffness differences in the vessel and end cover. Therefore one can conclude that the FEA gives a representative presentation of the expected stresses in the vessel. The figure 3.18 shows no elements in the critical regions with relative high values for the strain energy error norm. High values would indicate the need of re-meshing of the concerned regions. Fig 3.18: Strain energy error norm of the vessel (8.1%) and end cover (8.4 %). The buckling analysis requires small deformations and linear material response. The analysis assumes the initial shape and stresses in the object are sufficiently taken into account. The deformations in the vessel are small per element (correct mesh size) which ensures that the material behavior remains linear. This was also implicitly assumed in the stress analysis. The tolerances for the fabrication of the vessel ensure that the shape of the vessel will be in accordance with the model. 21

3.5.1 Vessel The general stresses in the vessel are well below the acceptable values. The stresses in the mentioned local regions are more critical. The analysis shows a significant difference between the Von Mises equivalent stress and the CODAP stress for several of this local regions. The stresses (both Von Mises and CODAP) at the detector support openings at the end cover side and in the middle are below 50 MPa (see D in fig 3.17). Increasing the stiffness of the big side opening related to the connection of the hood would only influence the stresses for the middle detector support opening. Though, the acceptable stress levels give sufficient margin against a possible underestimate of the stresses. The stresses at the detector support openings on the exit foil side and the stresses at the flanges on top of the vessel at the exit foil side (see C and A in fig 3.17) are close to acceptable values for non-localized effects. The Von Mises stresses are close to 100 MPa, the CODAP stresses are below 50 MPa in the same region. Taking into account these are localized regions the acceptable stress would be 157 MPa. The stresses are well below the acceptable stresses for localized regions allowing sufficient safety against possible underestimates of the stresses in these regions due to model errors. Some stress peaks in the region between the big side openings and the end flanges (see B in fig 3.17) are above the normally accepted values. These values are however acceptable given the fact that the stresses are compressive, and lay in a transition region of the model where the effects of fillets are not taken into account. The buckling factor is 16, where a factor larger than 3 is required. From the stress analysis point of view, the simulation at the given load (load factor of 1) shows that in the buckling region no plastic deformation occurs. 3.5.2 End cover The model for the end cover is relatively simple. The main difficulty is the stiffness difference at the connection between the connection flange of the vessel and the end cover. See also figure 3.18 for the strain energy error norm. The maximum equivalent stress according to Von Mises is 83 MPa and the maximum equivalent stress according to CODAP is 45 MPa. Both values allow sufficient margin with respect to the acceptable stress of 105 MPa. The calculated buckling factor is 108, much higher than the required factor 3. 22

4 Tests, safety and quality control The test, safety and quality control are the steps taken to ensure a safe operation of the vessel. 4.1 Tests The vessel will be tested at design conditions before installation at CERN. The tests might also encompass ultrasonic testing of a limited number of critical welds. This is to be decided depending on the production quality. A limited number of strain gauges might be used to get an indication about the stresses in the critical regions. The strain gauge tests are not aimed at verifying the modeling of the vessel. The main aim of the tests is prove that catastrophic failure of the vessel is not to be expected. 4.2 Safety The vessel is provided with a burst disc to ensure against overpressure. The burst disc is chosen to open at 1.5 +/- 10% absolute pressure. Inside the vessel is a cooling system using CO 2 at approximately 42 Bar. This cooling system will be separately qualified. The burst disc should protect the vessel against failure of the cooling system. 4.3 Quality control Quality control is mainly aimed at the construction materials. Quality control during manufacturing is aimed to be minimal. Given the choices construction class and tests, the manufacturer needs to make test welds for the different material thicknesses These test welds need to be tested in accordance with the specifications in CODAP. Further quality control will be decided upon, depending on the results of the fabrication and the standard quality control in place at the manufacturer. The vessel is designed in order to minimize the required quality control during manufacturing. This is mainly related to the fact that a number of the critical welds are difficult to verify. The tests of the vessel are at the same time the vacuum tests of the vessel. The quality control is mainly related to the quality control of the delivered material for the fabrication of the vessel. To prevent against pressures in the vessel, the vessel is equipped with a burst disc. The burst disc will open at 1.5 +/- 10% bar absolute pressure at 20 C. 23

5 Compliance with CODAP The compliance with the CODAP is only regarded in terms of the stresses and stability of the vessel and end cover. The stress analysis and the stability analysis where done with the finite element module of Ideas TM. The vessel and end cover are designed based on an operation temperature of 150 o C and an external pressure of 0.1 MPa. Both the vessel and the end cover comply with the requirements for stresses and stability as defined by the CODAP. 5.1 Vessel The general stresses are well below the acceptable values. The general stresses are between 50 MPa and 75 MPa, where 150 MPa is acceptable. Local regions show higher stresses mainly in weld regions. These stress levels lay above the accepted values for general regions. Taking into account the stresses may be 1.5 times the stresses in general regions most of the stresses are with in the accepted limits. The peak stresses which are above 1.5 times limit are acceptable within special provision set within the code. These stresses are in a transition region where the influence of fillets is not modeled. The stresses are compressive. The peak stresses in the model are 210 MPa which is below the yield strength (230 MPa). The buckling factor for the vessel is 16, required is buckling factor of 3. 5.2 End cover The stresses for the end cover lay all well below the accepted values. The highest value of the equivalent stress is 45 MPa, where 150 MPa is acceptable. The buckling factor for the end cover is 108, where a factor of 3 is required. 24

6 Summary Presented is the analysis is the VELO vacuum vessel of the LHCb experiment. The vacuum vessel must comply with the CODAP requirements as enforced by the CERN safety division (TIS). The design condition of the vessel is 150 o C and an external pressure of 0.1 MPa. The vessel will be made of AISI 316 L. The material will be verified upon delivery. The quality of the material will be verified by means of ultrasonic testing. The vessel is qualified as category C vessel. The stresses in the vessel are compliance with the requirements put forth by the CODAP. Also the stability requirements (buckling) lay within the requirements of the CODAP. 25