Subject:STRUCTURAL ANALYSIS OF THE VACUUM VESSEL FOR THE LHCb VERTEX LOCATOR (VELO)
Group:Engineering dept. NIKHEF
Date:january 2004
Prepared by:M.J. Kraan
Checked by: J. Buskop; M. Doets; C. Snippe
Project ID:LHCb NIKHEF Document No:MT-VELO 04-01
Cern Safety Code :Pressure equipment CERN EDMS No:432626
TIS Safety Study Report :SSR 434220 / Version2 Material specification:AISI 316 L
FEA documents Main document (8 MB) Appendices (12 MB)
Welding documents Welding Test Certificates
Welding and Welder Qualifications
Material documents Stainless Steel Properties
Aluminium Properties
Control documents THERMO Quality Control Plan

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.

Design of the vessel

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. These openings result in a reduction of stiffness of the primary cylindrical shape of the vessel. Several parts are connected to the vessel: Exit Window, end cover, two Detector Hoods and 2 getter pumps. 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. 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.

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 the following table:

    Operationstemperature [0C] pressure [mbar] medium
    pumping down20-251.10-9-
    baking out1501.10-9-
    venting20-251000neon
    operational20-251.10-9-

    VESSEL
    Load Type
    Weight Detector Hood1000 [N]
    Weight vessel Cover1000 [N]
    Weight Getter pump900 [N]
    Pressure Detector Hood28441[N]
    Pressure vessel Cover882[N]
    Pressure Exit Foil50895[N]
    Pressure Flange CF 2003048 [N]
    Pressure Flange CF 1501720 [N]
    Pressure Bellow567 [N]
    External Pressure0.1 [MPa]
    END COVER
    Load Type
    Weight Turbo + Valve457 [N]
    Weight Gravity Valve + Getter290 [N]
    Pressure Flange CF 2003048 [N]
    Pressure Flange CF 1501720 [N]
    Pressure Flange CF 63229 [N]
    Moment Turbo + Valve92 [Nm]
    Moment Gravity Valve + Getter87 [Nm]
    External Pressure0.1 [MPa]



Material data:

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.

    At 20-25 oCAt 150 oC
    Tensile strengthRm [MPa]min.585525
    Yield strengthRp 0.2% [MPa] min. 260 230
    Young's modulusE [GPa] min. 200 186
    Density[g/cm3]. 7.85 .
    Poisons ratio..0.30.
    Elongation at breakA5 [%] min. 35 .
    Brinell hardness HB max. 180.

FEA:

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.
Half the vessel is modeled, as the vessel is symmetric about YZ, see the figure at the right. 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 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.

    Finite Element Mesh
    Vessel
    End Cover

    Mesh types:

      3D Solid parabolic tetrahedron
      2D Thin Shell parabolic quadrilateral
    Safety Factor:
      Following the chosen construction class C and welding coefficient z=0.7, the stress limits according to CODAP are:

    • Global zones:
      		• fg = Rm/3.5 = 525/3.5 = 150 MPa
    • Weld regions:
      		• fw = z * Rm/3.5 = 0.7 * 525 / 3.5 = 105 MPa
    • Peak regions:
      		• fp = 1.5 * fg = 1.5 * 150 = 225 MPa
    • Peak/Weld regions:
      		• fpw = 1.5 * fw = 1.5 * 105 = 157 MPa

    Type of Solution:
      Linear Statics
    Units:
      Length [mm]; Force [N]; Stress/Pressure [Mpa]
RESULTS VESSEL:
    Stress (Von Mises)
    Displacement
    limit 25MPa
    limit 50MPa
    limit 75MPa
    limit 100MPa
    limit 125MPa
    limit 150MPa
    limit 150MPa (detail)
    same detail

    Stress (according CODAP NORM)
    limit 25Mpa
    limit 50Mpa
    limit 75Mpa
    limit 100Mpa
    limit 125Mpa
    limit 150Mpa

    Buckling modes
    Strain energy error
    Mode 1
    buckling factor=16
    Mode 2
    buckling factor=19.5
    Mode 1
    buckling factor=24.5
    8.1 %

RESULTS END COVER:
    Stress (Von Mises)
    Stress (according CODAP NORM)
    Displacement

    Buckling modes
    Strain energy error
    Mode 1
    buckling factor=108
    Mode 2
    buckling factor=109
    Mode 1
    buckling factor=113
    8.4 %

CONCLUSION:

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.
    Regions of concern for the vessel
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). 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) 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) 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.

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. 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.