 Open Access
 Total Downloads : 1440
 Authors : Mr. Abdul Sayeed Aw Shaikh, Prof. P.T.Nitnaware
 Paper ID : IJERTV1IS10089
 Volume & Issue : Volume 01, Issue 10 (December 2012)
 Published (First Online): 28122012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
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

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, GTSTRUDEL, 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.

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 Xaxis. 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)

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.

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

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 .

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.

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.

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.

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

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 Ã— area
= pÃ—DÃ—L
The total resisting force acting on the vessel walls
= h Ã— 2t Ã— L
From above two equations,
h Ã— 2t Ã— L = pÃ—DÃ—L
h
= pÃ—D
2t
Graph 2
The compressive hoop force,
Wh = hÃ— LÃ— 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 Ã—( 3) (2 )
Table 3 Solid Structural Analysis Result
W = 3
3
Equating eq (1) & (2)
(2)
2
No. of Element 
p=700 torr,p=7999.34 pa 

Max Deformation(m) 
Von Mises Stress (Mpa) 

253148 
0.0040077 
12.065 
646331 
0.0040333 
12.882 
756102 
0.004034 
12.92 
=
( )3
3
= 2Ã—2Ã—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

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

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