Modeling And FEA Based Analysis Of Vacuum Chamber For Buckling Failure

Modeling And FEA Based Analysis Of Vacuum Chamber For Buckling Failure

Modeling and FEA Based Analysis of Vacuum Chamber for Buckling Failure

1st Author: Mr. Abdul Sayeed AW Shaikh. 2nd Author: Prof. P.T.Nitnaware, 1st Author: Student M.E Design, D.Y.Patil college of Engineering Akurdi, Pune 2nd Author: Professor D.Y.Patil college of Engineering Akurdi, Pune

Abstract

This paper shows the solid structural analysis of vacuum chamber. The analysis is done for electron microscopy applications, for scanning electron microscope it require vacuum atmosphere for viewing of the specimen. The specimen is to be viewed in vacuum. The vacuum level required for that is in the range of 700 torr, which is less than atmospheric pressure lead to compressive forces on the chamber The vacuum chamber is modeled in Catia and Simulation is done in Ansys. Also theoretical calculation is done for safety of vacuum chamber from buckling failure.

Keywords- FEA, Electron Microscope, Buckling Propagation

Introduction

An Electron Microscope uses particle beam of electrons to illuminate the specimen and produce a magnified image. Scanning electron microscope (SEM) and Transmission electron microscope (TEM) are types of its applications. Both these applications requires an vacuum atmosphere to operate. Also the level of vacuum requirement is same for both the applications. The electron gun without vacuum will experience constant interference from air particles in the atmosphere. The distraction would lead to block the path of electron beam and also they would be knocked out of the air and onto the specimen which ultimately distort the surface of the specimen. The vacuum level required for that is in the range of 690 to 720 torr, which is less than that of atmospheric pressure which lead to compressive forces on chamber which causes buckling.

Figure 1

1. Finite Element Analysis The finite element analysis is a numerical technique. In this method all the complexities of the problems, like varying shape, boundary conditions and loads are maintained as they are but the solutions obtained are approximate.. The fast improvements in computer hardware technology and slashing of cost of computers have boosted this method. The different types of packages which are used for analysis such as STAAD- PRO, GT-STRUDEL, NASTRAN, NISA and ANSYS. Using these packages one can analyse several complex structures. It is used for solving different engineering problems like stress analysis , heat transfer, fluid flow etc. A finite element analysis has been done to the model for the expected stresses for 700 torr.

   1. Modelling

      The vacuum chamber comprises of cylindrical vessel with hemi spherical elliptical cover on one side and base plate on other side. The vessel and end cover is modeled in Catia part body workbench separately and fixed together in Catia assembly workbench. The assembly model is then save in stp format so it can be imported to Ansys workbench. The model is split by YZ plane as it is symmetric about it, and giving translation constrain in X-axis. A face to face contact is defined between cover flange and vessel flange.

      Table 1 General dimensions of vacuum chamber

      Description	Value (mm)
      Vessel Inner Diameter
      Vessel Thickness
      Length of Cylindrical Portion
      Cover inner diameter
      Cover Thickness
      Cover Height
      Base Plate Thickness
      Vessel Flange Thickness
      Cover Flange Thickness

      Table 2 Dimension of Flanges

      Valves	Value (mm)	Thickness (mm)	Flange Thickness (mm)

   2. Meshing

      Meshing is the method of dividing the model into the number of element to obtain the good accuracy in the analysis. As the number of element increases the accuracy of analysis increases. A 15 mm 10 node tetrahedron element is used for meshing.

   3. Material Properties

      Material: Structural Steel

      Youngs Mod. of Elasticity, E = 2e11 pa Poissons ratio, = 0.3

      Density, = 7850 kg / m3 Compressive yield strength = 205e6 pa

   4. Boundary Conditions

      The simulation is done for internal pressure 700 torr which is less than of atmospheric pressure 760 torr that leads to compressive pressure on chamber. One atmospheric pressure equals to 760 torr (mm of Hg). (700 -760) torr = -60 torr = -7999.342 pa

      Thus 7999.342 pa pressures is applied on vacuum chamber walls. Due to negative sign, the direction of pressure is inwards. The faces of valve flanges and side base plate are fixed .

   5. Structural Analysis

      A static structural analysis determines the displacements, stresses, strains, and forces in structures or components caused by loads that do not induce significant inertia and damping effects. Steady loading and response conditions are assumed; that is, the loads and the structure's response are assumed to vary slowly with respect to time.

   6. Solver

      253148 tetrahedron elements are used for meshing which are connected at 759444 nodes. As there is three degree of freedom in solid structural analysis. So no of equations to be solved for displacement are 759444. Deformation is defined as the displacement in body dimensions due to application of force. The max deformation calculated from analysis is 0.0004033 m in the base plate of the vessel.

   7. Results

Deformation and Von Mises Stress at different regions has been calculated using post processor. VON Mises Criterion also known as the maximum distortion energy criterion, octahedral, is often used to estimate the yield of ductile materials. The Von Mises criterion states that failure occurs when the energy of distortion reaches the same energy for yield/failure in uniaxial compression/tension. Max Von Mises stress calculated from the analysis is 12.065 Mpa on the vessel between valve and base plate as shown in fig which is very less than compressive yield strength 205 Mpa. So it is safe from this criterion.

1. Reinfinement of Meshing To get accurate value of deformation and stress, the element size is changed from 15 mm to 10 mm and 9 mm resulting increase in elements from 253148 to 646331 and 756102 respectively. It is clear from the graph that as no of elements has been increased, high precision value is obtained. The max deformation has increased to 0.0004033 m from 0.00040033 m as no of elements increased to 756102 from 253148. Max Von Mises stress is converged at 12.92 Mpa for 756102 elements

   Graph 1

2. Theoretical Calculations

0.00404

0.00402

0.004

0.00398

200000 400000 600000

Buckling is a failure mode characterized by a sudden failure of a structura member subjected to high compressive stress. Cylindrical vacuum vessels subject to external pressure are subject to compressive hoop stresses. Consider a length L of the vessel

The total force acting = Intensity of pressure × area

= p×D×L

The total resisting force acting on the vessel walls

= h × 2t × L

From above two equations,

h × 2t × L = p×D×L

h

= p×D

2t

Graph 2

The compressive hoop force,

Wh = h× L× t

Wh =

2 (1)

13 Buckling will occur when compressive hoop force will

12

12 equal to buckle force, W

11

200000 400000 600000

2 EI

2

W =

(L )2 =

42

( )

2 =

42 ×( 3) (2 )

Table 3 Solid Structural Analysis Result

W = 3

3

Equating eq (1) & (2)

(2)

2

=

( )3

3

= 2×2×1011

3

( 7 )3

1056

= 38836.59 pa

We have applied approximately p = 7999.342 pa for 700 torr (10 to 15) % of max buckling pressure as per requirement, the impact will be very small. So it is safe from buckling failure.

Conclusion

• The Vacuum chamber is safe from buckling failure as applied p is very small in comparison to max theoretical buckling pressure.

• Compressive yield strength of structural steel is greater than Von Mises stress is calculated by solid structural analysis so it is safe from this criterion.

• A linear graph comes out for max deformation and max Von Mises stress with internal pressure so for different value of internal pressure theoretically they can be calculated.

References

1. WANG Wenlong, CAI Guobiao, ZHOU Jianping Large-Scale Vacuum Vessel Design and Finite Element Analysis Chinese Journal of Aeronautics 25(2012) 189-197.

2. M. J. Kraan, Buskop, M. Doets, C. Snippe on Structral analysis of the vacuum vessel for Lhcb Vertax locator.

3. J.N.Reddy , An introduction to the Finite Element Method 3rd edn. McGraw-Hill, New Delhi, 2009.

4. K. Ioki, P. Barabaschi, V. Barabash, S. Chiocchio,W. Daenner,F. Elio, et al., Design improvements and R&D achievements for vacuum vessel and in-vessel components towards ITER construction, Nucl. Fusion 43, 268273.