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Jtasr.com Case Study
J. Technological Advances and Scientific Res./eISSN- 2454-1788, pISSN- 2395-5600/ Vol. 2/ Issue 01/ Jan-Mar. 2016 Page 27
DESIGN AND ANALYSIS OF MODERN MISSILE CANISTER TESTING CHAMBER A. Reddeiah1, S. Srinivasa Prasad2 1Post Graduate Student, Department of Mechanical, Nova College of Engineering and Technology. 2Professor, Department of Mechanical, Nova College of Engineering and Technology.
ABSTRACT
Missiles are self-propelled, precision guided and also well-constructed machines. Because of their size and weight handling or
transporting them is very difficult and risky. Most of the missiles are damaged due to carelessness and poor handling practices. To
reduce the damage of missiles they are shipped, stored and handled with special equipment called canisters. These canisters are also
used to launch, transport and store the missiles. During the launch and transport of the missiles, these canisters are subjected to
external pressures and vibrations respectively. So, it is very important that these canisters are tested for the above said loads. These
canisters are tested using canister testing chambers. The canister is placed inside the canister testing chamber and it is pressurized
with water or air. The internal and external pressure testing of the canister is done by closing the canister both ends by dummy
dished ends. Because of this reason, Canister testing Chamber is one of the most critical components in Defense Organization. The
canister testing chamber design proposed is an externally ring stiffened structural shell with dogged lids that open for canister launch
during testing. The canister testing chamber is approximately 1.8 meters outside diameter and 12 meters long and weighs
approximately 14. 5 tonnes. In the present work the. [1] designing of Canister testing chamber is done and its model is prepared by
using Unigraphics software. The testing is performed on the chamber by using ANSYS package for the natural free vibrations during
transportation and also testing is done with specified pressure to withstand.[2]
KEYWORDS
Approved Canisters, Launch, Transport, Store, Unigraphics and ANSYS.
HOW TO CITE THIS ARTICLE: Reddeiah A, Prasad SS. Design and analysis of modern missile canister testing chamber. J.
Technological Advances and Scientific Res. 2016;2(1):27-44, DOI: 10.14260/jtasr/2016/4
INTRODUCTION
The canister testing chamber design proposed is an externally
ring stiffened structural shell with dogged lids that open for
canister launch during testing.[3] The canister testing chamber
is approximately 1.8 meters outside diameter and 12 meters
long and weighs approximately 14.5 tonnes. During launching
of the missile, the canister is subjected to internal pressure of
1.176MPa. The canister is carried horizontally inside the
testing chamber and supported by trunnion and latch at 3
points. [4]One end of the test setup will have dished end welded
integrally to the cylinder. The other end shall be a hinged door
with proper sealing. One of the sides dished end is provided
with screw rod to press the dummy dish end for leak proof
joint, which shall withstand the internal pressure during
testing. The screw is actuated by a hand wheel provided
through nut. The nut is fixed in a welded housing on the dished
end. The screw front portion will have good surface finish with
proper sealing arrangement to withstand 1.176MPa pressure
without any leak. This screw is used to press the dummy dish
end against the canister. Between both the mating faces
rubber/gasket will be provided to avoid any leak of water
during pressure testing.
Financial or Other, Competing Interest: None. Submission 22-01-2016, Peer Review 27-01-2016, Acceptance 29-01-2016, Published 05-02-2016. Corresponding Author: A. Reddeiah, C/o. V. V. Rao, D. No. 57-14-23, New Postal Colony, Patamata, Vijayawada-520010. E-mail: [email protected] DOI: 10.14260/jtasr/2016/4
The chamber shell will have two supports externally for
fixing the same on foundation. Inside the chamber a track is
welded. A trolley is provided on which the canister is mounted
to move the same into the chamber. The chamber will have
inlet, outlet and air removal ports with suitable ball valves.
Two no’s of pressure indicators, one analog and one digital will
be provided. A storage tank and pumping system is also
provided for pressurization of the chamber.
As per the purpose of design, the canister testing chamber
assembly is classified into 3 subsystems
Canister Testing Chamber design
Dogged lids design
Support legs design
In the present study, structural analysis of a canister
testing chamber used for canister testing will be performed.
The most important factors that are concentrated are stress
distribution and deflections.
1.1 COMPONENTS USED IN CANISTER TESTING
CHAMBER
1. Canister Testing Chamber shells
2. Canister dished ends
3. Support legs
4. Bolts
5. Pressure gauges
1.1.1 Chamber Shells/Pressure Vessels [5]A pressure vessel is a closed container designed to hold
gases or liquids at a pressure substantially different from the
ambient pressure. A pressure vessel is defined as a vessel in
which the pressure is obtained from an indirect source or by
the application of heat from an indirect source or a direct
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J. Technological Advances and Scientific Res./eISSN- 2454-1788, pISSN- 2395-5600/ Vol. 2/ Issue 01/ Jan-Mar. 2016 Page 28
source. The vessel proper terminates at: (a) the first
circumferential joint for welded end connections; (b) the face
of the first flange in bolted flange connections; or (c) the first
threaded joint in threaded connections.” Pressure vessels
include but are not limited to compressed gas storage tanks
(i.e. air, oxygen, nitrogen tanks, etc.), anhydrous ammonia
tanks, [6]hydropneumatic tanks, autoclaves, hot water storage
tanks, chemical reactors and refrigerant vessels, designed for
a pressure greater than 15 psi and a volume greater than 5
cubic feet in volume or one and one-half cubic feet in volume
with a pressure greater than 600 psi.
Pressure vessels can theoretically be almost any shape,
but shapes made of sections of spheres, cylinders and cones
are usually employed. A common design is a cylinder with end
caps called heads. Head shapes are frequently either
hemispherical or dished (Torispherical). More complicated
shapes have historically been much harder to analyze for safe
operation and are usually far more difficult to construct.
Theoretically, a spherical pressure vessel has
approximately twice the strength of a cylindrical pressure
vessel.[1] However, a spherical shape is difficult to manufacture
and therefore more expensive, so most pressure vessels are
cylindrical with 2:1 semi-elliptical heads or end caps on each
end. Smaller pressure vessels are assembled from a pipe and
two covers. A disadvantage of these vessels is that greater
breadths are more expensive, so that for example the most
economic shape of a 1,000 liters (35 cu. ft.), 250 bars
(3,600 psi) pressure vessel might be a breadth of 914.4
millimetres (36 in) and a width of 1,701.8 millimetres (67 in)
including the 2:1 semi-elliptical domed end caps.
Fig. 1.1.1: Canister Testing Chamber
1.2 MATERIALS OF CANISTER TESTING CHAMBER
1.2.1 Types of Steel and Uses
Steel is basically an alloy of iron and carbon with a small
percentage of other metals such as nickel, chromium,
aluminium, cobalt, molybdenum, tungsten, etc. Steel is a hard
ductile and malleable solid and is probably the most solid
material after plastic and iron.
If we draw a comparison between iron and steel, we find
steel in many ways even better than iron. Steel may not be as
strong as iron is, but it is far more resistant and does not
corrode and gets rusted like iron does. And that is the reason
it is used in the making of drills and tools and power saws. The
hardness and rigidity of high speed steel depends on the metal
used in the making of the alloy and its percentage of
composition in it. Basically, this steel is used in the making of
tools that cut other metals.
Carbon Steels, which can include High Carbon Steel and
High Alloy Steel, are the softest and usually the cheapest of the
seven types we offer. Many woodworking tools are made from
this material. Many craftsmen like Carbon Steel, because the
tools are soft enough to sharpen with a file. Virtually any
woodworking tool can be found in a carbon steel
version. Some woodworking tools are only available in Carbon
Steel or Carbide Tipped, because it is too difficult to make them
from anything else or they would be too expensive. If you are
cutting softwood or just a few holes in hardwoods or plastics,
Carbon Steel is your answer. If you have a lot of holes to cut in
a hard material, you may want to choose a better grade of
steel. The tools we manufacture from Carbon Steel are heat
treated to 620c hardness and cannot be sharpened with a file. A
stone type of grinding wheel is required to resharpen them.
1.2.2 Types of Carbon Steels
High-Carbon Steel
Carbon steel is simply composed of iron and carbon with a
more percentage of carbon in it than the iron. It is probably the
most commonly used type of steel. The presence of excess
carbon makes this type of steel softer than the other types of
steel, which contain some percentage of other elements as
well.
Carbon steel is mostly used in the making of wood cutting
tools, because they can be sharpened easily. However, it
cannot be used in the making of tools used for the cutting of
hard substances, because it is not hard enough for that
purpose. It is also used in the making of axes, swords, scissors
and other cutting tools.
Mild Steel
The mild carbon steel just like the high carbon steel is simply
composed of iron and carbon, but it has a very low content of
carbon in it. This steel is used in the making of vehicle frames,
panels, boxes, cases and sheet metal for roofs. It is now also
used as a replacement for wrought iron in the making railroad
rails.
Medium Carbon Steel
The medium carbon steels have a normal content of carbon,
that means that they are not as hard as the high carbon and
neither are they as strong as the mild carbon steel. They are
used in the making of tool frames and springs.
Stainless Steel is not normally used to manufacture
tools. However, we have found that heat-treating Stainless
Steel produces tools that not only have longer lasting cutting
edges than Carbon Steel, but also have a spring steel quality
that keeps the tools from breaking in tough
applications. Stainless Steel generally costs only a little more
than Carbon Steel. Our Stainless Steel is heat treated to 450c
hardness and can be sharpened with a file or a stone type of
grinding wheel.
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High Speed Steel, sometimes abbreviated to HSS, comes
in various different grades generally used in the metalworking
industry to make drills, end mills, turning tools and other tools
designed specifically to cut metal. In woods and plastics, all
grades of HSS far outlast the cheaper Carbon Steel or Stainless
Steel. The various grades of HSS we use are identified by M1,
M2, M7 and M50, M1 being the most expensive grade. Very few
woodworking tools are made from HSS. It is too expensive to
use for large tools, very tough to machine and can be subject to
breakage with rough treatment in handheld equipment. M1 is
the hardest and also the most brittle of the bunch. You cannot
have your cake and eat it too! We use M1, M2 and M7 for
applications when better tool life is required and breakage is
not a problem. M50 is used when breakage could be an
issue. Tools made of High Speed Steel will always have HS or
HSS stamped or etched on them. Do not be fooled by
imitations. We recommend HSS for most applications because
the tools are reasonably priced, last a long time in woods and
plastics and have more sizes and lengths available than any
other type of material. However, if you are cutting thousands
of holes in hard materials, you need some type of Carbide
Tooling. Sharpening HSS tools requires a grinding wheel made
of stone or one that is Borazon plated.
Cobalt Steel is very similar to High Speed Steel. Its
identifier is M40CO or M42. Most drills made of Cobalt have a
brownish gold tint and are marked with their identifier. Cobalt
is a step up from HSS and offers better tool life than HSS. Since
Cobalt is harder and therefore more brittle than HSS, Cobalt
drills usually have a more rugged construction with less room
for chips to escape in the flute area. Although they work great
cutting materials like stainless steel and cast iron, they do not
work well in wood or plastics because they do not clear chips
well. In an application in which a good grade of HSS Drill cut
2000 holes before becoming dull, a Cobalt Drill might cut 2200
holes before dulling. Sharpening Cobalt Steel tools requires a
grinding wheel made of stone or one that is Borazon plated.
Carbide Tipped is the material of choice for tools used in
high production applications. The Carbide is super hard,
resharpenable and replaceable. Carbide can cut faster at
higher spindle speeds, because it is impervious to the heat
produced by those speeds. Since Carbide is extremely hard, it
is also extremely brittle. This is especially true in the case of
woodworking tools. The slightest contact with another metal
object could cause the Carbide to chip. Although some grades
of Carbide are designed to work well in metals and cement, the
type found on woodworking tools in not. The Carbide Tips are
usually brazed to the cutting edges of tools made of softer
materials like Carbon Steel. Sharpening Carbide Tipped tools
requires Diamond plated grinding wheels.
Among these material IS: 2062 steel has been selected for
canister manufacturing.
IS: Properties 2062 grade Plates may supply steel plate,
coils, sheet and strip of various material and sizes, details are
listed in Table 1.1:
IS: 2062 - Specification of Steel for General Structural Purposes CHEMICAL COMPOSITION
Grade C% Max. Mn% Max. S% Max. P% Max. Si% Max. C.E.% Max.
A 0.23 1.50 0.050 0.050 0.40 0.42 B 0.22 1.50 0.045 0.045 0.40 0.41 C 0.20 1.50 0.040 0.040 0.40 0.39
MECHANICAL PROPORTIES
Grade UTS (MPa) Min. Y.S. (MPa) Min. El.% Min. 5.65
Sqrt (So) Bend Test
A 410 250 240 230 23 3T B 410 250 240 230 23 2T & 3T * C 410 250 240 230 23 2T
* 2T - <= 25mm * 3T - > 25mm
Table 1.2.2: Chemical Composition and Mechanical Properties of Steel (Indian Standard)
Canister Dished Ends
Dishes are generally used to close the ends of canister
chamber.
Generally, they are two types:
1. Fixed type dishes,
2. Clamped type dishes.
Fixed Type Dishes
In this type, dishes welded to canister chamber for providing
to prevent leakage of pressure.
Clamped Type
In this type, dishes are used to open or close the canister
chamber through clamps and it acts as a Door to loading and
unloading of missile. Clamped type dishes are fastened by
using bolts, bolts also play a major role in designing of canister
chamber. For this application M12, M22&M36 bolts are
analysed. Properties of these bolts are shown below.
Definition of Bolt
Bolts are defined as headed fasteners having external threads
that meet an exacting, uniform bolt thread specification (such
as M, MJ, UN, UNR and UNJ), such that they can accept a no
tapered nut.
Preferred Diameters
Preferred nominal diameters for bolts and threaded rod are as
listed below. The fourth series listed below should be limited
to unusual requirements when none of the preceding series
can be used. Reference individual standards prior to
specification. Sizes M5 to M45 are commonly used in
construction.
First choice:
M2 2.5 3 4 5 6 8 10 12 16 20 24 30 36 42
Second choice: M3.5 14 18 22 27 33 39 45
Third choice: M15 17 25 40
Avoid: M7 9 11 26 28 32 35 38
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II. DESIGN CALCULATIONS OF CANISTER TESTING
CHAMBER
2.1 Design Formulas [7]The design formulas used in the method are based on the
principal stress theory. The principal stress theory of failure
states that failure occurs when one of the three principal
stresses reaches the yield strength of the material.[8] Assuming
that the radial stress is negligible, the other two principal
stresses can be determined by simple formulas based on
engineering mechanics. The Code recognizes that the shell
thickness may be such that the radial stress may not be
negligible and adjustments have been made in the appropriate
formulas. As shown below various formulas used to calculate
the wall thickness for numerous canister testing chamber
geometries.
2.1.1 Shell Design Calculations for external pressure [9]Formulas for calculation of cylindrical shell Thickness
t1 = 𝑃𝑅𝑖
(𝑆𝐸−0.6𝑃)
Where
t1 = Minimum required thickness (mm)
P = Operating pressure (MPa)
Ri = Shell Inside radius (mm)
S = Allowable stress (MPa)
E = Weld joint efficiency factor
Inputs
Operating pressure (P) = 1.176798 MPa
Shell Inside radius (Ri) = 950 mm
Allowable stress (S) = 250 MPa
Weld joint efficiency factor (E) = 0.6
Minimum required thickness (mm)t1 = 1.17 X 950.
250 X0.6-0.6X1.17
Minimum required thickness t1 = 7.0935mm
As per BIS Standard nominal thickness considered
(t1) =16mm
Milling tolerance (m)=0.06xt =0.96mm
Modification in weld portion (w) =1.5+if (t<12)0 .6 else 0 .8
(Considering Only One side welding with no backup plate)
w = 2.3mm
Bending Tolerance (b) = 0.002t
(Considered at 0.2% of the Nominal Thickness) b
= 0.032mm
Final Thickness of canister Testing chamber
= t1+m+w+b+CA
t1= 11.382mm
As per BIS Final Standard Thickness t1 = 16mm
2.1.2 Dished End-1 Design Calculations
Formulas for calculation of Dished End Thickness
t2= 𝑃𝑅𝑖
(𝑆𝐸−0.6𝑃)
Where
t2 = Minimum required thickness (mm)
P = Operating pressure (MPa)
Ri = Shell Inside radius (mm)
S = Allowable stress (MPa)
E = Weld joint efficiency factor
Inputs
Operating pressure (P) = 1.176798 MPa
Shell Inside radius (Ri) = 950 mm
Allowable stress (S) = 250 MPa
Weld joint efficiency factor (E) = 0.6
Minimum required thickness (mm) t2 =1.17 X 950.
250 X0.6-0.6X1.17
Minimum required thickness t2 = 7.4452 mm
Standard nominal thickness considered (t2) = 16mm
Milling tolerance (m)= 0.6 xt = 0.96mm
Modification in weld portion (w)= 1.5+if (t<12)0 .6 else 0 .8
(Considering Only One side welding with no backup plate)
w= 2.3mm
Bending Tolerance (b) = 0.002t
(Considered at 0.2% of the Nominal Thickness) b = 0.032mm
Final Thickness (t2) = t2+m+w+b+CA
t2 = 11.732mm
Final Standard Thickness with Margin t2 = 16mm
2.1.3 Dished End-2 Design Calculations
Formulas for calculation of Dished End Thickness
t3 = 𝑃𝑅𝑖𝑊
(2𝑆𝐸−0.2𝑃)
Where
t3 = Minimum required thickness (mm)
P = Operating pressure (MPa)
Ri = Shell Inside radius (mm)
S = Allowable stress (MPa)
E = Weld joint efficiency factor
Inputs
Operating pressure (P) =1.176798 MPa
Shell Inside radius(Ri) =950mm
Allowable stress (S) =250 MPa
Weld joint efficiency factor (E) = 1
Dished end factor (W) =0.25 ∗ (3 + √𝑅𝑖
0.1𝑅𝑖)
W= 0.833
Minimum required thickness (mm)
=1.17 X 950 X0.833.
2X250 X1-0.2X1.176798
= 1.852 mm
Minimum required thickness = 1.852 mm
Standard nominal thickness considered (t3) =16 mm
Milling tolerance (m) = 0.6xt = 0.96 mm
Modification in weld portion(w) = 1.5+if(t<12)0 .6
else 0 .8
(Considering Only One side welding with no backup plate)
w = 2.3mm
Bending Tolerance (b) = 0.002t
(Considered at 0.2% of the Nominal Thickness)
b= 0.032 mm
Final Thickness (t3) = t1+m+w+b+CA
t3 = 6.144 mm
Final Standard Thickness with Margin t3 =16 mm
2.1.4. Shell Design Calculations for internal pressure
Cylindrical shell Thickness
t4 = 𝑃𝑅𝑖
(𝑆𝐸−0.6𝑃)
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Where
t4 = Minimum required thickness (mm)
P = Operating pressure (MPa)
Ri = Shell Inside radius (mm)
S = Allowable stress (MPa)
E = Weld joint efficiency factor
Inputs:
Operating pressure (P) = 45 MPa
Shell Inside radius (Ri) = 335 mm
Allowable stress (S) = 250 MPa
Weld joint efficiency factor (E) = 1
Minimum required thickness (mm) =45 X 335. = 1.28cm
250X1 -0.6X45
Minimum required thickness =12.8 mm
Standard nominal thickness considered (t) = 20 mm
Milling tolerance (m) = 0.06xt = 1.2 mm
Modification in weld portion (w)
=1.5+if (t<12)0 .6 else 0 .8
(Considering Only One side welding with no backup plate)
w = 2.3 mm
Bending Tolerance (b) = 0.002t
(Considered at 0.2% of the Nominal Thickness)
b = 0.04 mm
Final Thickness(t4) =t+m+w+b+CA
t4 = 20 mm
Margin= 2.6
Final Standard Thickness with Margin= 20mm
III. MODELLING OF CANISTER TESTING CHAMBER
3.1 MODEL OF A CANISTER TESTING CHAMBER [10]Canister Testing Chamber has been designed and optimized
for vibration control and internal pressures. Canister Testing
Chamber is a structural frame used to test the canister used to
store and launch the missiles. The function of the Canister
Testing Chamber is to house the canister and test it for the
internal pressure; 3D modelling software (UNIGRAPHICS NX)
was used for designing and analysis software (ANSYS) was
used for structural analysis.
The methodology followed in my project is as follows:
Perform the Design calculations of the Canister Testing
Chamber.
Perform internal pressure analysis and documents the
deflections and stresses.
Perform Modal analysis to find natural frequencies on the
original model of the Canister Testing Chamber.
Optimize the original model (Iterative method) to shift the
natural frequencies above the operating frequency of
Canister Testing Chamber by changing design stiffness.
Perform internal pressure analysis on the optimized model
and documents the deflections and stresses.
Perform Power Spectral Density analysis (PSD) on the
optimized model to find the effect of all the frequencies
present below the operating frequency range of Canister
Testing Chamber in X, Y and Z direction.
The steps involved while developing the 3D model of a
canister testing chamber:
Fig 3.1: 3D model of the chamber shell
Fig 3.2: 3D model of the shell head plate 1
Fig 3.3: 3D model of the shell head plate 2
Fig 3.4: 3D model of the spacer
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Fig 3.5: 3D model of the bottom supports
Fig 3.6: 3D model of a canister testing chamber assembly
Fig 3.7: Wire Frame 3D model of a canister testing chamber assembly
Fig 3.8: Wire Frame 3D model of a canister testing chamber assembly
IV. STATIC AND DYNAMIC ANALYSIS OF CANISTER
TESTING CHAMBER [11]The finite element is a mathematical method for solving
ordinary and partial differential equations. Because it is a
numerical method, it has the ability to solve complex problems
that can be represented in differential equation form. As these
types of equations occur naturally in virtually all fields of the
physical sciences, the applications of the finite element
method are limitless as regards the solution of practical design
problems.
The [12]finite element method has become a powerful tool
for the numerical solution of a wide range of engineering
problems. It has developed simultaneously with the increasing
use of high-speed electronic digital computers and with the
growing emphasis on numerical methods for engineering
analysis.
4.1 Material Properties of the canister testing chamber: [13] The material used for the construction of canister testing
chamber is IS :2062 grade steel. The mechanical properties are
mentioned below:
Young’s Modulus (Ex) =200GPa
Poisson’s Ratio = 0.3
Density = 7880Tons/mm3
Yield Strength = 250 MPa
4.2 Element Type Used: [14]Shell 63 has both bending and
membrane capabilities. Both in-plane and normal loads are
permitted. The element has six degrees of freedom at each
node: translations in the nodal x, y and z directions and
rotations about the nodal x, y and z axes. Stress stiffening and
large deflection capabilities are included. A consistent tangent
stiffness matrix option is available for use in large deflection
(Finite rotation) analyses.
4.3 Shell 63 Input Data: The [15]geometry, node locations and
the coordinate system for this element are shown in Figure
“SHELL63 Geometry.”
For certain non-homogeneous or sandwich shell
applications, the following real constants are provided: RMI is
the ratio of the bending moment of inertia to be used to that
calculated from the input thicknesses. RMI defaults to 1.0.
CTOP and CBOT are the distances from the middle surface to
the extreme fibers to be used for stress evaluations. Both CTOP
and CBOT are positive, assuming that the middle surface is
between the fibers used for stress evaluation. If not input,
stresses are based on the input thicknesses. ADMSUA is the
added mass per unit area.
Fig 4.1: shows the 3D model of the canister testing chamber used for analysis
Fig 4.2: shows the FE model of the canister testing chamber used for analysis
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a. Meshing Details: The canister testing chamber is meshed
using shell 63 element type. It is a quad 4 node element.
Thickness is given as the real constant. The thickness of the
chamber is given as 20mm. Total number of elements created
is 10223 and the number of nodes created are 11527. The
mesh model of the canister testing chamber is shown below.
Fig.4.3: Shows the Boundary conditions and loading applied on canister testing chamber
4.4 Static Pressure Analysis: Static analysis is carried out on
the canister testing chamber to check the structure behaviour
due to an internal pressure of 1.176 MPa. The boundary
conditions used for the internal pressure analysis is shown
below.
Boundary conditions used for Static Analysis
1. Legs are constrained in all degrees of freedom
2. Dog lids are connected using mesh connectivity.
3. Internal pressure of 1.176 MPa is applied.
RESULTS OF THE STATIC PRESSURE ANALYSIS
Total Deflection (Usum): Maximum Deflection of
4.28mm is observed on the canister testing chamber.
Fig.4.4: Total deflection observed on the testing chamber
Fig 4.5: Total deflection observed on the testing chamber in isometric view
VonMises: Maximum VonMises stress of 194 Mpa
observed on the Testing Chamber
Fig 4.6: Von Mises stress on the Testing Chamber
Fig 4.7: 1st principal stress on the Testing Chamber From the above analysis, it can be observed that the
maximum deflection is 4.5mm and the maximum Von Mises
stress is 195MPa. The yield strength of the material is 250
MPa. From the above analysis it can be concluded that the
canister testing chamber is safe for the internal pressure of
1.176MPa.
4.5 Dynamic Analysis (Modal Analysis)
Modal analysis is used to determine the natural frequencies
and mode shapes of a structure. They are also required if we
want to do a spectrum analysis or a mode superposition
harmonic or transient analysis. You can choose from several
mode-extraction methods: Block Lanczos, subspace, PCG
Lanczos, reduced, unsymmetric, damped and QR damped. The
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damped and QR damped methods allow you to include
damping in the structure.
Modal analysis was carried out to determine the natural
frequencies and mode shapes of a structure in the frequency
range of 0-150Hz. Block Lanczos mode-extraction methods is
used to extract the frequencies and mode shapes. The total
mass of the testing chamber considered for analysis is 14
tonnes.
From the above results it can be observed that there
exists 1 critical frequency in X, Y and Z directions. The critical
frequencies are 135Hz in X-Direction, 36Hz in Y-Direction and
15Hz in Z-Direction. These frequencies are critical because the
mass participation is very high in these frequencies. The mass
participations of critical frequencies are given below.
Fig 4.8: changes made on the chamber shell of the original
canister testing chamber
4.6. Static Pressure analysis on the model
Static analysis is carried out on the modified canister testing
chamber to check the structure behaviour due to an internal
pressure of 1.176MPa. The boundary conditions used for the
internal pressure analysis is shown below.
Boundary conditions used for static analysis
1. Legs are constrained in all degrees of freedom.
2. Dog lids are connect using mesh connectivity.
3. Internal pressure of 1.176MPa is applied.
Fig. 4.9: Shows the Boundary conditions and loading
applied on canister testing chamber
4.7 Results of the Static pressure analysis
Total Deflection (Usum): Maximum Deflection of 2.5mm is
observed on the canister testing chamber.
Fig. 4.10: Total deflection observed on the testing chamber with legs
Fig. 4.11: Total deflection observed on the testing
chamber without legs
Fig. 4.12: Von Mises Stress on the testing chamber with legs
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Fig. 4.13: Von Mises Stress on the testing chamber
with legs on the other side
From the above analysis it can be observed that the
maximum deflection is 2.5mm and the maximum Von Mises
stress is 160 MPa. The yield strength of the material is 250
MPa. From the above analysis it can be concluded that the
canister testing chamber is safe for the internal pressure of
1.176 MPa.
4.8 Modal Analysis of canister testing chamber
Modal analysis was carried out on the model to determine the
natural frequencies and mode shapes of a structure in the
frequency range of 0 - 150 Hz. Block Lanczos mode extraction
methods are used to extract the frequencies and mode shapes.
Eigen values and their mass participations in all the three
directions in the range 0 - 150 Hz are listed in the Table.4.1
MODE FREQUENCY PARTICIPATION FACTOR EFFECTIVE MASS
X-Dir Y-Dir Z-Dir X-Dir Y-Dir Z-Dir
1 17.8606 3.45E-04 4.18E-03 0.32955 1.19E-07 1.75E-05 1.8606 2 42.2239 -0.16714 0.2523 -8.05E-03 2.79E-02 6.36564 6.48E-05
3 53.9966 -0.72492 -4.41E-02 -5.61E-03 0.525509 1.95E-03 3.14E-05
4 57.1675 1.11E-02 -1.99E-02 -1.49E-02 1.24E-04 3.97E-04 2.23E-04 5 76.1107 -6.99E-03 -5.32E-03 0.46948 4.88E-05 2.83E-05 0.220415 6 80.0037 -0.34698 0.11109 2.52E-03 0.120397 0.127893 6.33E-06 7 86.5923 4.78E-02 5.83E-02 1.19E-02 2.29E-03 3.40E-03 1.42E-04 8 94.9678 -8.87E-02 -5.32E-02 -0.15723 7.86E-03 2.84E-03 2.47E-02 9 100.604 0.20752 0.17032 -1.83E-02 0.43649 2.90E-02 3.36E-04
10 109.301 -9.04E-02 -3.37E-03 -0.217 8.17E-03 1.13E-05 4.71E-02 11 121.362 0.25427 0.55581 1.89E-02 6.47E-02 0.308923 3.56E-04 12 122.574 0.18667 0.21288 -2.89E-02 3.48E-02 4.53E-02 8.36E-04 13 126.745 0.14014 0.133033 -5.71E-03 1.96E-02 0.16871 3.26E-05
14 131.632 0.11056 0.11103 1.48E-03 1.11712 1.23E-02 2.18E-06
15 133.84 -0.1771 -1.40E-02 -3.32E-03 0.31051 1.96E-04 1.10E-05 16 140.051 -0.11106 -1.74E-02 0.13495 1.23E-02 3.03E-04 1.82E-02 17 145.375 -0.59621 -0.16892 -1.86E-02 0.35547 2.85E-02 3.45E-04 18 148.219 1.7956 4.96E-02 8.32E-04 3.22406 2.46E-03 6.93E-07
Table 4.8: Modal Analysis Values
4.9 Mode Shapes of the Canister Testing Chamber
Fig. 4.14: 1st and 2nd Mode shapes @17.8 and 42.2Hz
respectively
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Fig. 4.15: 3rd and 4th Mode shapes @53 and
57Hz respectively
Fig. 4.16: 5th and 6th Mode shapes @76 and 80Hz
respectively
Fig. 4.17: 7th and 8th Mode shapes @86 and 94Hz
respectively
Fig. 4.18: 9th and 10th Mode shapes @100 and 109Hz
respectively
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Fig 4.19: 11th and 12th Mode shapes @ 121 and 122 Hz
respectively
Fig. 4.20: 13th and 14th Mode shapes @ 126 and 131 Hz
respectively
Fig 4.21: 15th and 16th Mode shapes @ 133 and 140 Hz
respectively
Fig. 4.22: 17th and 18th Mode shapes @ 145 and 149 Hz
respectively
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From the above analysis results, it is observed that the
critical modes present in the original model are shifted out of
the frequency zone of 0-150Hz due to the changes implement.
Random vibration analysis is performed on the modified
canister testing chamber to check the structure behaviour due
to random loading.
4.9 Power Spectrum Density (PSD) Analysis
A Random Vibration Analysis is a form of Spectrum
Analysis
The spectrum is a graph of spectral value versus
frequency that captures the intensity and frequency
content of time-history loads.
Random vibration analysis is probabilistic in nature,
because both input and output quantities represent only
the probability that they take on certain values. Random
Vibration Analysis uses Power spectral density to
quantify the loading.
A PSD spectrum is a statistical measure of the response
of a structure to random dynamic loading conditions. It
is a graph of the PSD value versus frequency, where the
PSD may be a displacement PSD, velocity PSD,
acceleration PSD or force PSD. Mathematically, the area
under a PSD versus-frequency curve is equal to the
variance.
PSD analysis along X-direction
PSD analysis is carried out on modified model of canister
testing chamber with base excitation in X direction from 0-
150Hz to observe the structure behavior due to random
vibrations.
Boundary Conditions:
Functional vibration levels – PSD:
Random g2/Hz
8 0.003 10 0.02
135 0.02 150 0.001
Table. 4.9.1 shows the spectral values
Vs frequency for PSD analysis
Fig.5.23: Boundary conditions used for PSD in X-dir for
testing chamber
Results-Total Deflection:
The maximum 1 sigma deflection observed is 0.47 mm.
The maximum 3 sigma deflection observed is 1.41 mm.
This implies that only 0.3% of the time the Canister
Testing Chamber deflection reaches 1.41mm.
Fig. 4.24: Total deflection of testing chamber
for PSD in X-dir
Fig. 4.25: Total deflection of legs and chamber shell of testing chamber for PSD in X-dir
Results-Von Mises Stress:
The maximum 1 sigma Stress observed is 48 MPa.
The maximum 3 sigma Stress observed is 144 MPa.
This implies that only 0.3% of the time the Canister
Testing Chamber stress reaches 144 MPa.
Fig. 4.26: VonMises Stress of testing chamber for PSD in X-
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Fig.4.27: Von Mises Stress of legs of testing chamber for
PSD in X-Dir
Fig.4.28: PSD-X Response on Legs of chamber in Linear
and Logarithmic Scale
Fig. 4.29: PSD-X Response on shell of chamber in Linear and Logarithmic Scale
Fig. 4.30: PSD-X Response on Dogged lids of chamber in
Linear and Logarithmic Scale
From the above graphs it is seen that,
Maximum PSD response on the legs is 1.1g2/Hz at a
frequency of 126Hz
Maximum PSD response on the shell is 16g2/Hz at a
frequency of 100.6Hz
Maximum PSD response on the dogged lids is 8.5g2/Hz
at a frequency of 100.6Hz
The Yield strength of the material Steel (IS:2062 grade)
is 250 N/mm2. From the above analysis the maximum 3 sigma
stress observed is 144 N/mm2. From the above results and it
can be concluded the Modified Canister Testing Chamber
assembly is safe for the random vibrations in X-direction.
PSD analysis along Y-direction
PSD analysis is carried out on modified model of canister
testing chamber with base excitation in Y direction from 0-
150Hz to observe the structure behavior due to random
vibrations.
Boundary Conditions
Functional vibration levels – PSD:
Random g2/Hz
8 0.003 10 0.02
135 0.02 150 0.001
Table 4.9.2: Shows the spectral values Vs frequency for PSD analysis
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Boundary Conditions
Fig. 4.31: Boundary conditions used for PSD
in Y-dir testing chamber
Results- Total Deflection:
The maximum 1 sigma deflection observed is 1.58mm.
The maximum 3 sigma deflection observed is 4.74mm.
This implies that only 0.3% of the time the Canister Testing
Chamber deflection reaches 4.74mm.
Fig. 4.32: Total deflection of testing chamber
for PSD in Y-dir
Fig. 4.33: Total deflection of legs and chamber shell
of testing chamber for PSD in Y-dir
Results-Von Mises Stress:
The maximum 1 sigma Stress observed is 29.4MPa.
The maximum 3 sigma Stress observed is 88.2MPa.
This implies that only 0.3% of the time the Canister
Testing Chamber stress reaches 88.2MPa.
Fig. 4.34: Von Mises Stress of testing
chamber for PSD in Y-Dir
Fig. 4.35: Von Mises Stress of legs of
testing chamber for PSD in Y-Dir
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Fig. 4.36: PSD-Y Response on Legs of testing
chamber in Linear and Logarithmic Scale
Fig. 4.37: PSD-Y Response on shell of testing chamber in Linear and Logarithmic Scale
Fig. 4.38: PSD-Y Response on Dogged lids of testing
chamber in Linear and Logarithmic
From the above graphs it is seen that
Maximum PSD response on the legs is 0.33g2/Hz at a
frequency of 42Hz.
Maximum PSD response on the shell is 19g2/Hz at a
frequency of 42Hz.
Maximum PSD response on the dogged lids is 7.5g2/Hz
at a frequency of 80Hz.
The Yield strength of the material Steel (IS:2062 grade)
is 250 N/mm2. From the above analysis the maximum 3 sigma
stress observed is 88.2 N/mm2. From the above results and it
can be concluded the Modified Canister Testing Chamber
assembly is safe for the random vibrations in Y-direction.
PSD analysis along Z-direction
PSD analysis is carried out on modified model of canister
testing chamber with base excitation in Z direction from 0-
150Hz to observe the structure behavior due to random
vibrations.
Boundary Conditions:
Functional vibration levels – PSD:
Boundary Conditions
Random g2/Hz
8 0.003 10 0.02
135 0.02 150 0.001
Table 4.9.3: Shows the spectral values Vs frequency for PSD analysis (Z)
Fig. 4.39: Boundary conditions used
for PSD in Z-dir for testing chamber
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Results- Total Deflection
The maximum 1 sigma deflection observed is 5.07mm.
The maximum 3 sigma deflection observed is 15.21mm.
This implies that only 0.3% of the time the Canister Testing
Chamber deflection reaches 15.2mm.
Fig. 4.40: Total deflection of testing
chamber for PSD in Z-dir
Fig. 4.41:Total deflection of legs and chamber shell of
testing chamber for PSD in Z-directions
Results-Von Mises Stress
The maximum 1 sigma Stress observed is 53.3MPa.
The maximum 3 sigma Stress observed is 159.9MPa.
This implies that only 0.3% of the time the Canister
Testing Chamber stress reaches 159.9MPa.
Fig. 4.42: Von Mises Stress of testing chamber for PSD in Z-Dir
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Fig. 4.43: Von Mises Stress of legs of testing
chamber for PSD in Z-Dir
Fig.4.44: PSD-Z Response on Legs of testing chamber in Linear and Logarithmic Scale
Fig.4.45: PSD-Z Response on shell of testing chamber in Linear and Logarithmic Scale
Fig. 4.46: PSD-Z Response on Dogged lids of testing
chamber in Linear and Logarithmic
From the above graphs it is seen that,
Maximum PSD response on the legs is 0.0032g2/Hz at a
frequency of 109Hz.
Maximum PSD response on the shell is 75g2/Hz at a
frequency of 17.8Hz.
Maximum PSD response on the dogged lids is 21g2/Hz at a
frequency of 17.8Hz.
The Yield strength of the material Steel (IS:2062 grade)
is 250 N/mm2. From the above analysis the maximum 3 sigma
stress observed is 159.9 N/mm2. From the above results and it
can be concluded the Missile Modified Canister Testing
Chamber assembly is safe for the random vibrations in Z-
direction.
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V RESULTS AND DISCUSSIONS
Canister Testing Chamber was studied for 3 different cases for
original model:
Pressure Analysis
Modal Analysis
Power Spectrum Density analysis
The following observations were made from the modal
analysis of the original model: [16]From the modal analysis on the original model it is
observed that there exist 3 critical natural frequencies in the
operation frequency range of 0-150Hz. It is necessary to shift
these natural frequencies above the operating range of 0-
150Hz to protect the Canister Testing Chamber assembly
structure from vibrations.
From the above analysis, it is concluded that the [17]Canister Testing Chamber requires some changes. These
changes are implemented in the model and Pressure Analysis,
Modal Analysis, Power Spectrum Density analysis were
carried out to check the frequencies and temperature.
The following observations are made on the Canister
Testing Chamber. It is observed that the critical natural
frequencies in the operation frequency range of 0-150Hz were
shifted to above 150Hz due to the changes implemented.
VI CONCLUSIONS AND FUTURE SCOPE OF WORK
In this work Canister Testing Chamber has been designed and
optimized for vibration control and internal pressures. For
validating the theoretical values Power Spectrum Density
analysis has been carried out using ANSYS software.
From the above analysis, it is concluded that that the
critical natural frequencies in the operation frequency range
of 0-150Hz were shifted to above 150Hz due to the changes
implemented as shown in the report. Therefore, it is concluded
that the Canister Testing Chamber is safe under the given
operating conditions.
FUTURE SCOPE OF WORK
During transportation Canister Testing Chamber is subjected
to shock loads. Shock analysis has to be carried out to check
the structure behaviour in X, Y and Z directions. Canister
Testing Chamber has to be shock resistant and resilient to
vibration as these are one of its factors of failure.
Transient analysis would be the main analysis where the
shock loading can be simulated onto the Canister Testing
Chamber. The transient simulation has to be divided into two
separate load steps:
1. Initial condition - 1g load at 1e-5 sec
2. Shock pulse - 20g load at 18e-3 sec
A full transient dynamic analysis can be used as
calculation for obtaining the more accurate values when
compared to those obtained by the Reduced or Modal
Superposition methods. However, this calculation method
would be very expensive, meaning it would take a lot more
time and computational resource.
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