Subject:STRUCTURAL ANALYSIS OF THE DETECTOR HOOD FOR THE LHCb VERTEX LOCATOR (VELO)
Group:Engineering dept. NIKHEF
Date:December 2004
Prepared by:M.J. Kraan
Checked by: J. Buskop; C. Snippe; M. Doets;
Project ID:LHCb NIKHEF Document No:MT-VELO 04-3
Cern Safety Code :Pressure equipment CERN EDMS No:536195
SC Safety Study Report :537184
PDF documentsMain document (14 MB)
Appendices (14 MB)

Abstract:

The structural verification of the LHCb VELO Detector hood is the subject of this document. Purpose of these calculations is to investigate stress and displacements in the aluminium VELO Detector hood, which is a part of the VELO vacuum system. The Detector hood has to comply with the CODAP Code. Numerical analysis was performed with the IDEAS TM finite element analysis software.

Summary:

Presented is the analysis is the VELO detector hood of the LHCb experiment. The detector hood must comply with the CODAP requirements as enforced by the CERN safety division (SC). The design condition of the detector hood is 20 degrees Celcius and an external pressure of 0.1 MPa. The design of the detector hood is determined by two main constrains: housing of 12 vacuum feedthrough flanges and 'closing' the volume of the vacuum vessel for the operation of the LHC accelerator. The detector hood will be made of AlMg4.5Mn. 12 vacuum feedthrough flanges, which are mounted on the detector hood, will be made of AISI 316L. The material will be verified upon delivery. Based on the CODAP guideline, the detector hood is qualified as category C vacuum vessel. The stresses in the detector hood and vacuum feedthrough flange are compliance with the requirements put forth by the CODAP. Also the stability requirements (buckling) lay well within the requirements of the CODAP.

Design of the Detector Hood

The design of the detector hood is determined by two main constraints: housing of 12 vacuum feedthrough flanges and 'closing' the volume of the vacuum vessel for the operation of the LHC accelerator.

Operational conditions

The load of the detector hood is determined by the weight of the detector hood, the connecting elements, and the vacuum force. The detector hood is operated at one temperature. The operation temperature and pressure are given by the vacuum procedures. The conditions for the analysis of the detector hood are given in the following table:

    Operationstemperature [0C] pressure [mbar] medium
    pumping down20-251.10-9-
    venting20-251000Air
    operational20-251.10-9-
    Loads on hood
    Load Type
    Pressure vacuum feedthrough flange (6x)4866 [N]
    Pressure service flange (3x)1227/2 [N]
    Pressure cooling flange (1x)342/2 [N]
    Pressure vacuum connection flange (1x)1767/2 [N]
    External Pressure0.1 [MPa]


Material data:

The Hood will be made from AlMg4.5Mn (5083; 3.3547) according DIN 1725 part 1. Welding material will be s-AlMg4.5Mn (5183). The vacuum feedthrough flange 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. Embrittlement, corrosion effects and creep rupture effects are not considered as they are not relevant for either the detector hood or the vacuum feedthrough flange. The mechanical properties are given in the following table:

    AlMg4.5MnAISI 316L
    Tensile strengthRm [MPa]min.250585
    Yield strengthRp 0.2% [MPa] min. 130 260
    Young's modulusE [GPa] min. 70 200
    Density[g/cm3]. 2.66 7.85
    Poisons ratio..0.30 0.30
    Elongation at breakA5 [%] min. 6 35
    Brinell hardness HB max. 85180

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 where done with the finite element analysis module of Ideas TM. In the analysis a quarter of the vacuum vessel (the weakest top part) is modeled to transfer the displacement of this vessel into the detector hood. For the remaining connecting elements only the vacuum loads are transferred to the detector hood, the stiffnesses of these elements are considered infinite. Using these assumptions, the worst case effects of the elements are regarded in the analysis of the detector hood. The vacuum feedthrough flange is regarded in a similar way.

Half the hood is modeled, as the hood is symmetric about XZ, see the figure below. The boundary conditions for the model are given by the vacuum loads on the hood, 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.

The detector hood is modeled using 3D solid parabolic tetrahedron elements. The vessel is modeled with thin 2D shell parabolic quadrilateral at the relatively thin parts and 3D solid parabolic tetrahedron elements for the other volumes, shown in figure below. 2D null-shell elements, with a thickness of 0 mm are used to connect in a correct way the 2D elements with the 3D solids. Due to the horizontal symmetry plane, gravity is not included in this analysis. Hand calculation shows that, caused by this gravity, a negligible additional stress of 0.83 N/mm2 will be in the weld of the detector hood.

Mesh types:

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

    AlMg4.5MnAISI 316L
  • Global zones:
    		• f g = Rm/3.5 = 72 MPa150MPa
  • Weld regions:
    		• fw = z * Rm/3.5 = 50 MPa105MPa
  • Peak regions:
    		• fp = 1.5 * fg = 108 MPa 225 MPa
  • Peak/Weld regions:
    		• fpw = 1.5 * fw = 75 MPa 157 MPa

Type of Solution:
    Linear Statics
Units:
    Length [mm]; Force [N]; Stress/Pressure [Mpa]
RESULTS HOOD:
    Stress (Von Mises)
    Max 47.2 Mpa
    limit 10 Mpa
    limit 20 Mpa
    limit 30 Mpa
    limit 40 Mpa

    Stress (according CODAP NORM)
    Max 48 Mpa
    limit 10 Mpa
    limit 20 Mpa
    limit 30 Mpa
    limit 40 Mpa

    Deformation; Max 0.53mm

    Buckling modes
    Strain energy error
    Mode 1
    buckling factor=30.6
    Mode 2
    buckling factor=43
    Mode 3
    buckling factor=44.2
    10.4 %
RESULTS FEEDTHROUGH FLANGE:
    Stress (Von Mises)
    Stress (according CODAP NORM)
    Max 62.6 Mpa
    Max 63.5 Mpa

    Deformation
    Max 0.05mm
    Strain energy error
    7.7 %

CONCLUSION:

Detector hood

Four peak regions
in the detector hood		 The results of the analysis of the hood show that all stresses are well within the bounds for global regions (72 MPa). Peak stresses occurs in three weld regions (see number 1,2 and 4 in figure) and in one of the corners of a vacuum feedthrough opening (number 3). These peak stresses (max. = 48 MPa) are still below the bounds for weld regions (50 MPa).

As measure of the quality of the FEA the strain energy error norm is given, for the hood the general value for the model is 10.4% . For normal practice it is recommend that the general value for the strain energy error norm is below 8%. The strain energy error shows that the highest errors are at the connection surface to the vessel. Though these places with relative high strain energy error, stresses are far below the admissible value this is given no further attention. The buckling factor is 30.6 where a factor larger than 3 is required. Also the maximum deformation of 0.53 mm is no problem.

Vacuum feedthrough flange

The results of the analysis of the feedthrough flange show that all stresses are well within the defined limits. Again the strain energy error norm is relatively high, though given the large safety margin between the calculated stresses and the acceptable stresses this is given no further attention. The maximum deformation of 0.05 mm is no problem.