we have to select the various material of lathe and remove it and use different material apart from it in order to get better property of lathe bed and reduce the cost.

1. 1
CHAPTER - 1
INTRODUCTION TO LATHE MACHINE
A lathe machine is used for the shaping and machining of various work pieces. There
are many different types depending on the material you are working on.
In manufacturing, it is important to produce work pieces according
to specifications. This is where the lathe machine comes in handy. A lathe machine is
used for the machining and working of hard materials. Conventionally, the lathe
machine is designed for the machining of metals, but as new materials emerged, there
are lathe machines that are used for these materials as well. The main function of the
lathe is to remove material from a work piece through the use of cutting tools. The
lathe shapes a material by holding and rotating the material as a cutting tool is
advanced into it. There are a lot of shapes and forms that can be produced by the lathe
machine. More importantly, these shapes come in various sizes and specifications.
Generally, the lathe is composed of the bed, headstock, tailstock, and the carriage.
The bed allows the carriage and the tailstock to be in parallel with the axis of
the spindle. Moreover, the bed also serves as the base of the lathe and is connected to
the headstock. The headstock basically is where the main spindle, the change gears,
and the speed change mechanism are mounted on. On the other hand, the tailstock is
directly mounted on the spindle axis, and serves as the tool holder. The tailstock is
mounted opposite the headstock. Finally, the carriage is where the tool bit or the drill
bit is placed and holds it in position as it moves perpendicularly or longitudinally. The
direction of the movement of the cutting tool is actually controlled by the operator.
There are three general types of lathe machines which are engine lathes, turret lathes,
and special purpose lathes. Each of these lathes has specific applications and
distinctive characteristics.

2. 2
1.1 MAIN PARTS OF THE LATHE MACHINE
Fig.1 Main parts of the lathe machine
The bed of Lathe acts as the base on which the different fixed and operations
parts of the Lathe are mounted. Lathe beds are usually made as single piece casting of
semi-steel (i.e., toughened cast iron), with the addition of small quantity of steel scrap
to the cast iron during melting; the material ‘cast iron’ facilitating an easy sliding
action. In case of extremely large machines, the bed may be in two or more pieces,
bolted together to from the desired length. Lathe Bed are heavy rigid structure which
is having high damping capacity for the vibrations generated by machines during
machining. The rigid structure will helps to avoid deflections. The guides and ways
which are present on the top of the bed will act as rails and supports other parts like
tail stock. The bed will be designed in such a way that easily bolted to the floor of the
machine shop.
1.1.1 Head stock:
The head stock is the part of the lathe which serves as a housing for the driving
pulleys and back gears, provides bearing for the machine spindle and keeps the latter
in alignment with the bed. It is a fixed part which will present on the left side of the
lathe bed. Head stock will consists of a hollow spindle and drives unit like main
spindle, feed reverse lever, live center cone pulley etc., The tapered bar with pointed
or projected end is going to grip the work piece between two centers of lathe bed.
1.1.2 Tail stock:
It is also sometimes called the LOOSE HEAD- STOCK or PUPPET HEAD. It
is mounted on the bed of the lathe such that it is capable of sliding along the latter
maintaining its alignment with the head stock. On common types of medium size or
small size lathes it is moved along the bed by hand, whereas in heavier types of lathes

3. 3
it is moved by means of a hand wheel through a pinion which meshes with the rack
provided on the front of the lathe bed. The main function of the Tail stock is to provide
bearing and support to the job which is being worked between centers. To enable this,
the tail stock is made to possess a number of parts which collectively help in its
successful function.
1.1.3 Carriage:
The lathe carriage serves the purpose of supporting, guiding and feeding the
tool against the job during the operation of the lathe. The carriage will present between
head stock and tail stock which will slides on the bed ways of the lathe bed. The
carriage will give feed to the tool and it holds the tool, for taper turning the feed is
cross feed, for turning it is longitudinal feed.
The carriage consists of the following parts.
1. saddle
2. cross-slide
3. compound Rest
4. Tool post
5. Apron
1.1.3.1 Saddle:
It is the part of the carriage which slides along the bed way and support the Cross-
slide, compound rest and Tool post.
1.1.3.2 Cross-slide:
The cross-slide function is to provide cutting action to the tool and the action of
cutting tool will be perpendicular to center line of lathe. It can either be operated by
hand, by means of the cross-feed screw, or may be given power feed through the
Apron Mechanism.
1.1.3.3 Compound Rest:
The compound Rest will be placed over the cross slide and it consists of a
graduated circular base which is having swivelling nature.
1.1.3.4 Tool post:
It is the top most part of the carriage and is used for holding the tool or tool holder
in position.
1.1.3.5 Apron:
Apron houses the feed mechanism, clutch mechanism split half nut, gears, leavers,
the apron wheel can be rotated by hand for longitudinal motion of the carriage.
1.1.4 Legs:
They are the supports which carry the entire load of the machine over them. The
prevailing practice is to use cast legs. Both the legs are firmly secured to the floor by
means of foundation blots in order to prevent vibrations in the machine. One of these

4. 4
legs, usually the one on the left hand side of the operator, serves as a housing for the
electric motor and countershaft etc., both these legs should be of robust construction.
1.2 TYPES OF LATHE MACHINES
1.2.1 Engine lathes:
These are probably the most popular among the lathe machines. In fact, no
machine shop is seen without this type of lathe. The good thing about engine lathes is
that it can be used in various materials, aside from metal. Moreover, the set-up of these
machines is so simple that they are easier to use. Its main components include the
bed, headstock, and tailstock. These engine lathes can be adjusted to variable speeds
for the accommodation of a wide scope of work. In addition, these lathes come in
various sizes.
1.2.2 Turret Lathes:
These types of lathes are used for machining single work pieces sequentially.
This means that several operations are needed to be performed on a single work piece.
With the turret lathes, sequential operations can be done on the work piece,
eliminating errors in work alignment. With this set-up, machining is done more
efficiently. Correspondingly, time is saved because there is no need to remove and
transfer the work piece to another machine anymore.
1.2.3 Special Purpose Lathes:
As the name implies, these lathes are used for special purposes such as heavy-
duty production of identical parts. In addition, these lathes also perform specific
functions that cannot be performed by the standard lathes. Some examples of special
purpose lathes include the bench-type jewellers’ lathes, automatic lathes,
crankshaft lathes, duplicating lathes, multi spindle lathes, brake drum lathes, and
production lathes among others.

5. 5
CHAPTER – 2
LITERATURE SURVEY
2.1. DESIGN AND STRUCTURAL ANALYSIS OF CNC VERTICALMILLING
MACHINE BED
B. Malleswara Swami1, K.Sunil Ratna Kumar2
Address for Correspondence
1 PG Student, 2Assistant Professor
Department of Mechanical Engineering, SIR C.R.R. College of Engineering(Affiliated
to Andhra University) Eluru-534007, West Godavari Dist, A.P
ABSTRACT:
In this paper, a machine bed (Manufacturer: M/s Lokesh Machine Tools Ltd) is
selected for the complete analysis for both static and dynamic loads. Then
investigation is carried out to reduce the weight of the machine bed without
deteriorating its structural rigidity and the accuracy of the machine tool by adding ribs
at the suitable locations. In this work, the 3D CAD model for the base line and the
optimized design has been created by using commercial 3D modeling software
CATIA. The 3D FE model has been generated using HYPERMESH. The analyses
were carried out using ANSYS and Design Optimization is done with the help of
Optistruct. The results were shown with the help of graphs to analyze the effect of
Weight reduction on the structural integrity of the machine bed before and after the
weight reduction and conclusions were drawn about the optimized design.
CONCLUSION:
The following points are concluded on a milling machine bed
• From the above results, the weight optimization of milling machine bed
structure has been decrease by 16.1 Kg from 1056.31Kg to 1040.2 Kg (approximately
1.5%), hence the manufacturing cost also has been reduced.
• From the above results, the G15 was selected as the best material due to low
stresses and high natural frequencies, when it is compared with other materials.
• The von-mises stress for G15 was increased from 26.1305 to 33.2082 N/mm2
in structural analysis. (Approximately 21.31%).
• The natural frequency is also incresed.200 Hz to 215 Hz (approximately
6.9%).
• The Effect of Von-mesis stress for G15 was increased and it is in permissible
safe limit.
• Structural ribs with hollow offers a method to improve the conventional
design of machine structure. Based on structural modifications, ribs parameters and
distributions can be further optimized.

6. 6
2.2. Designof Milling Machine Frame and Lathe Bed by Using MATLAB
N. Lenin Rakesh, V. Palanisamy and G. Ravikanth
Department of Mechanical Engineering,
Bharath Institute of Science and Technology P.O. Box: 600073 Chennai, India
ABSTRACT:
This project deals with the design and analysis of lathe bed and milling
machine frame by using MATLAB programming. Initially the design and analysis are
done analytically and later verified by MATLAB programming using the required
parameters.
CONCLUSION:
The complete design procedure of both the Lathe bed and Milling machine
frame has been studied carefully and the program has been written using the
MATLAB programming software. The manual calculation of each design has been
verified using MATLAB results. The manual results and the MATLAB results are
given below.
Lathe Bed:
Manual Result for stress : 0.0026 N/mm .
MATLAB Result for stress : 0.0029 N/mm .
Milling Machine Frame
Manual Result for Deflection : 748mm.
MATLAB Result for Deflection : 750mm.
2.3. Static and Dynamic Analysis of Base of Vertical Machining Center
Nikunj Aadeshra, Prof. R. L. Patel
1 PG Student, Mechanical Engg.Deptt, C.U.Shah University, Wadhwan city,
Gujarat.
2 Asst. Professor, Mechanical Engg.Deptt, C.U.Shah University, Wadhwan city.
ABSTRACT:
In industry the machine tool aims for high precision and repeatability while it
is in operation. Generally machine tool contain several Structural components like
base, saddle, headstock ,column of the machine tool play a vital role in helping to
achieve consistent performance. Vertical machining center base selected for present
study because base is the main structural part of the machine tool. It is a force bearing
component of machine tool so it must contain high structural stiffness and good
damping characteristics during machining operations. Otherwise it will affect accuracy
and performance of that machine tool. So that to overcome this type of issue it is must
need to analyze the structure. It is very difficult to analyse the structure analytically
and the accurate results for stress, deflection etc. are the limitation of this method in
Machine tool. So FEA is the best way to analyze the structural part of the machine
tool. Static analysis is useful for estimating stresses, strains and deflections,
whereasdynamic analysis deals with the prediction of natural frequencies and

7. 7
corresponding mode shapes, which will in turn, prevent the catastrophic failure of the
machine tool.
CONCLUSION:
From the literature review, we can conclude that analysis of the machine tool
structure for the various purpose by the analytical method is the more time consuming
and very complex method also it doesn’t gives the precise way for the analysis
because of its complexity but by using the FEA software we can get batter result with
the more precision and more accurately than analytic method and also in this FEA ,
Static and Dynamic analysis of machine tool structures plays an important role on the
efficiency and job accuracy of the machine tool. Static analysis is useful for estimating
stresses, strains and deflections, and also improving structural stiffness where as
dynamic analysis deals with the prediction of natural frequencies and corresponding
mode shapes, which will in turn; prevent the catastrophic failure of the machine tool
structures.
2.4. DESIGN AND ANALYSIS OF A MACHINE TOOLSTRUCTURE BASED
ON STRUCTURAL BIONICS
Sujeet Ganesh Kore1*, M I Sakri2 and L N Karadi3
*Corresponding Author: Sujeet Ganesh Kore,sujeetkore@gmail.com
ABSTRACT:
A structural bionic design process is systematically presented for lightweight
mechanical structures. By mimicking biological excellent structural principles, the
structure of lathe bed or the stiffening ribs of a lathe bed were redesigned for better
load-bearing efficiency. In this paper, a machine bed (Manufacturer: Indira Machine
Tools Ltd.) is selected for the complete analysis for static loads. Then investigation is
carried out to reduce the weight of the machine bed, reduce the stress induced in the
lathe bed and to reduce the displacement. In this work, the 3D CAD model for the
existing bed model and the optimized bed model has been created by using
commercial 3D modeling software SOLID EDGE V20. The analyses were carried out
using ANSYS 13. The results were discussed.
CONCLUSION:
From the above results, the weight optimization of lathe machine bed has been
achieved (Approximately 15%) for all the three material, hence the manufacturing cost
also has been reduced.
• The von-mises stress for Optimized model 2 and Optimized model 3 has been
reduced. (Approximately 19%).The Natural frequency is also Improved (i.e.,
increased) for Optimized models.
• From the above results, Optimized model 2 selected as the best model due to low
stresses, low weight, less displacements and high natural frequencies, when it is
compared with original model.

8. 8
2.5. Modeling and Analysis of CNC Milling Machine Bed with Composite
Material
Venkata Ajay Kumar. G1 V. Venkatesh2
1,2Assistant Professor
1Department of Mechanical Engineering
1,2Annamacharya Institute of Technology & Sciences, Rajampeta.
ABSTRACT:
Structural materials used in a machine tool have a decisive role in determining
the productivity and accuracy of the part manufactured in it. The conventional
structural materials used in precision machine tools such as cast iron and steel at high
operating speeds develop positional errors due to the vibrations transferred into the
structure. Faster cutting speeds can be acquired only by structure which has high
stiffness and good damping characteristics. Clearly the life of a machine is inversely
proportional to the levels of vibration that the machine is subjected. The further
process is carried out to undergo the deformation, natural frequency and displacement
using Static analysis, Modal analysis and Harmonic analysis respectively. Since the
bed in machine tool plays a critical role in ensuring the precision and accuracy in
components. It is one of the most important tool structures which tend to absorb the
vibrations resulting from the cutting operation. To analyze the bed for possible
material changes that could increase stiffness, reduce weight, improve damping
characteristics and isolate natural frequency from the operating range. This was the
main motivation behind the idea to go in for a composite model involving High
Modulus Carbon Fiber Reinforced Polymer Composite Material (HM CFRP). Though
carbon has good strength and stiffness properties but it lacks in damping requirements.
On the other hand polymer, though it lacks in strength but it has good damping
characteristics and it is used to hold the carbon fibers. This makes it ideal to combine
these materials in a proper manner. In this work, a machine bed is selected for the
analysis static loads. Then investigation is carried out to reduce the weight of the
machine bed without deteriorating its structural rigidity. The 3D CAD model of the
bed has been created by using commercial 3D modeling software and analyses were
carried out using ANSYS.
CONCLUSION:
Based on the configuration principles, the existing bed material was replaced by
HM CFRP material shows improve in the static characteristics. Simulations results
show that the static characteristics of the machine bed have been improved. Generally
Composite materials also offer high specific strength and high specific modulus with
less weight in machine tool industries. This composite materials offers high accuracy
and precession of the component manufactured in such machine tools made of
composite materials. By considering all the results, the induced deformation and strain
in HM CFRP machine bed is less than conventional cast iron machine beds because
specific strength and specific rigidity of HMCFRP machine bed is more than cast iron.
The work suggests that HM CFRP material is best suited for CNC milling machine
bed.

9. 9
CHAPTER– 3
INTRODUCTION TO FEM
3.1. FEM - HISTORICAL BACKGROUND:
The ideas of FEM (Finite Element Method) was evolved gradually from the
significant contributions of many people from different fields of engineering (applied
mathematics, and physics).The basic idea of FEM originated from advances in aircraft
structural analysis. Mathematician named Courant proposed the theoretical basis of
FEM in early 1940
1941: Hrenikoff found out that the elastic behavior of a physically continuous plate
would be similar, under certain loading conditions, to framework of physically
separate one dimensional rods and beams, connected together as discrete points. The
problem then handles for trusses and frameworks with similar computational methods.
1943: Courant put the first efforts to use piecewise continuous function defined over
triangular domains. He used an assemblage of triangular elements and principle of
minimum potential energy to study the St.Venant torsion problem
1946: Schoenberg gave birth to the theory of splines, recommending the use of
piecewise polynomials for approximation and interpolation.
1956: In 1956 the actual solution of plane stress problems by means of triangular
elements whose properties were determined from the equations of elasticity theory was
first given by Turner, Clough, Martin and Topp. These investigators were the first to
introduce direct stiffness method for determining finite elements properties.
1957:Linear functions were defined over triangular elements with Reitz procedure
developed by Synge.
1959: In 1959 Greenstadt brought out a new approach by involving a new term called
“CELLS”. He imagined the solution domain is divided into set of contiguous sub
domains in the form of “Cells”. In his approach he represents an “unknown function”
by the series of functions, which is associated with each cell. His theory consists of
irregular shaped cell meshes and it contains many of essential and fundamental ideas
that serve as the mathematical basis for the FEM (Finite Element Method).
In middle year’s scientist were involved in development of software to analysis
frameworks, and to solve the 3-D problems using tetrahedral elements. Turner in 1956
modeled the add-shaped wings panels of high speed aircraft as an assemblage of
smaller panels of simple triangular shape. This was a breakthrough as it made it
possible to model two- or- three dimensional pieces. In earlier days FEA (Finite
Element Analysis) was limited to expensive mainframe computers generally owned by
aeronautics, automotive, defense and nuclear industries. With rapid growth in
technology Finite Element Analysis has been developed to an incredible precision.

10. 10
3.2. Finite Element Methods (FEM):
The Finite Element Method (FEM) is a numerical analysis technique used
by the engineers, scientists, and mathematicians to obtain solutions to the
differential equations that describe, or approximately describe a wide variety of
physical and non-physical problems. Physical problems range in diversity from
solid, fluid and soil mechanics, to electromagnetism or dynamics.
3.2.1. Applications of FEM:
The finite element methods are mostly used in the field of structural
mechanics. It is also used for solving problems on “Heat Transfer”, “Fluid
Dynamics”, “Deformation and stress analysis of automobile and aircraft”, “electric
and magnetic fields”.
FEM is also applied on the following fields
Civil engineering: Analysis of trusses, frames, folded plates, shell, roofs, bridges,
and pre-stressed concrete structure, shear walls.
 Aircraft structures: Analysis of aircraft wings, fin, rockets, spacecraft and
missile structures.
 Mechanical Design: Stress analysis of pressure vessel, piston, composite
materials, linkages and gears.
 Heat Conduction: Temperature distribution in solids and fluids.
 Hydraulics and water resources engineering: Analysis of potential flows, free
surface flows, and hydraulic structural and dams.
 Electrical machines and electromagnetic: Analysis of synchronous and
induction machines, eddy current and the core losses in electric machine.
 The following software packages are commonly used for finite element
analysis
1) Nastran
2) ANSYS and
3) Abaqus
3.2.2. Advantages and Disadvantages of FEA:
Advantages:
 Complex irregular models can be solved.
 Any general load condition can be handled without difficulty
 Boundary conditions can be handled easily.
 Size of the element can varied to get accurate results
 Finite element analysis are easy and involves less cost
 Finite Element Analysis can save huge amount of design time.
 Finite Element Analysis can handle non-linear behaviour existing with
large deformation and non-linear materials.
Disadvantages:
 Finite element analysis is a time consuming process, it requires longer time
for solving.
 FEA provides approximate solution.
 Huge computing facility is required for solving complex problems.
 Finite Element analysis of any problem requires better understanding of
Mathematics, especially matrix, algebra, differentiation and integration.

11. 11
 The result of FEM is closer when it has maximum number of
smallelements.
3.3. METHODS OF ENGINEERING ANALYSIS
There are basically three methods for analyzing engineering problems. They
are:
1) Experimental methods
2) Analytical methods
3) Numerical methods.
3.3.1. Experimental methods:
In this method, the actual product itself is tested as a prototype, to know the
strength of the product. The prototype is subjected to continuous forces till it
breaks. By this way, the strength of the product will be analyzed. Since this
process requires large amount of material wastage, this method is followed only if
in cases where other analyzing methods cannot be used.
3.3.2. Analytical methods:
Analytical solution is a classical approach that is taught normally in
engineering courses. Only simple and regular shaped problems such as, cantilever,
shafts, plates, cylinders, simple supported beams etc can be analyzed by this
method. Real life problems are quite complex and complicated that it cannot be
solved using analytical approach.
3.3.3. Numerical methods:
Numerical solutions are the mathematical representation of an actual problem.
Any problem can be represented by three basic elements “spring”, “mass” and
“damper”. All real life complicated problems can be solvedusing numerical
methods. But this method involves lots of assumptions. Hence the result of
numerical method solution will be approximate.
Four major methods considered as numerical solution method are:
3.3.3.1 Finite Element Method -- FEM
3.3.3.2 Boundary Element Method -- BEM
3.3.3.3 Finite Volume Method -- FVM
3.3.3.4 Finite Difference Method -- FDM
3.3.3.1 Finite Element Method (FEM):
The finite element method is a numerical analysis technique used by engineers,
scientists, and mathematicians to obtain solutions to the differential equations that
describe, or approximately describe a wide variety of physical (and non-physical)
problems. Physical problems range in diversity from solid, fluid and soil mechanics, to
electromagnetism or dynamic
3.3.3.2 Boundary Element Method (BEM):
The boundary element method (BEM) is a numerical computational method of
solving linear partial differential equations which have been formulated as integral
equations (i.e. in boundary integral form). It can be applied in many areas of

12. 12
engineering and science including fluid mechanics, acoustics, electromagnetic,
and fracture mechanics. (In electromagnetic, the more traditional term "method of
moments" is often, though not always, synonymous with "boundary element method".
3.3.3.3 Finite Volume Method (FVM):
The finite-volume method is a method for representing and evaluating partial
differential equations in the form of algebraic equations]. Similar to the finite
difference method or finite element method, values are calculated at discrete places on
a meshed geometry. "Finite volume" refers to the small volume surrounding each node
point on a mesh. In the finite volume method, volume integrals in a partial differential
equation that contain a divergence term are converted to surface integrals, using
the divergence theorem. These terms are then evaluated as fluxes at the surfaces of
each finite volume. Because the flux entering a given volume is identical to that
leaving the adjacent volume, these methods are conservative. Another advantage of the
finite volume method is that it is easily formulated to allow for unstructured meshes.
The method is used in many computational fluid dynamics packages.
3.3.3.4 Finite Difference Method (FDM):
This is widely applicable Discretization method for the solution of ordinary and
partial differential equations. In this approach all derivatives are replaced by
approximations that involve solution values only, so in general the differential
equations is reduced to a system of non-linear equations or linear algebraic equations.
3.4 IMPORTANT STEPS IN FEM ANALYSIS
3.4.1 Discretisation of the structure:
The first step in the finite element analysis is to divide the continuous complex
structure into discrete entities called finite elements. Smaller the element size, more
accurate the results but larger the computation time. Coarser the elements, lesser
computational time, and lesser accuracy of results. Therefore element size has to be
judiciously chosen based on the application. Fig shows the various elements used for
finite element analysis.

13. 13
Fig.2 Various elements used in FEM
3.4.2. Selection of the shape functions:
This step involves choosing a displacement shape function within each element.
The function is defined within the element using nodal values of the elements.
“Linear, quadratic and cubic polynomials” are frequently used functions because they
are simple to work with finite element formulation. Higher the degree of shape
function, more accurate is the result. Shape functions are used to find the displacement
between the several nodes within the element. Shape functions are denoted in the form
of co-ordinates system. Once the shape function is defined, the linear displacement at
any location with-in the element can be specified.
1-Dimensional shape functions
N1(x) =
X2−X
l
: N2(x)=
𝑋−𝑋1
𝑙
where l=X2-X1
X= N1X1+N2X2
Where N1 and N2 - Shape functions defined by coordinates
X -Coordinates of the point within the element
X1 , X2 - Nodal coordinates
3.4.3. Stiffness matrix and load vector:
This is be done by using either equilibrium conditions or a suitable variation
principle such as minimum potential energy principle. Formation of element
stiffness matrix and global stiffness matrix is an important step in finite element
analysis of any component. The global stiffness matrix will include the shape
function derivative matrix, material property and nodal displacements. Global
stiffness matrix generation involves numerical integration, which is done using
Gauss-Quadrature method.

14. 14
Gauss-Quadrature method:
In numerical analysis, a Quadrature rule is an approximation of the definite
integral of a function, usually stated as a weighted sum of function values at
specified points within the domain of integration. (See numerical integration for
more on quadrature rules.) An n-point Gaussian quadrature rule, named after Carl
Friedrich Gauss, is a quadrature rule constructed to yield an exact result
for polynomials of degree 2n − 1 or less by a suitable choice of the points xi and
weights wi for i = 1,...,n. The domain of integration for such a rule is
conventionally taken as [−1, 1], so the rule is stated as
3.4.4 Formation of the load vector:
Similarly the global load vector is formulated from the element load vector.
The assembly is done through the nodes, which are common to adjacent element.
At the nodes, the continuity of the displacement function and possibly their derivatives
(strain-displacement relations) are established. The Global finite element equation for
the complete structure can be written in the matrix form
[K]{Nodal displacement}= {F}
K = Global stiffness matrix
F = Nodal force vector
3.4.5. Incorporation of boundary conditions:
After forming global finite element equation, the boundary condition is
imposed in that equation. In some approaches, the size of the stiffness matrix may be
reduce or condense in its final form. Two types of boundary condition are commonly
used in finite element analysis. They are :
Essential boundary condition
Essential boundary condition is geometric boundary conditions which are
imposed on the primary variable like displacement.
Natural boundary condition
Natural boundary conditions are which imposed on the secondary variable
like forces and tractions.
3.4.6. Solution of simultaneous equations:

15. 15
In this step the above developed equations are solved to get nodal
displacements commonly by Gauss elimination method or Cholesky’s Factorization
method. Gauss-Seidel or Jacobi iteration method is also followed in some cases.
After this step, the nodal solution (nodal displacements) will be determined.
3.4.7. Calculation of element strains and stress:
From the calculated nodal displacements, the element strains and stress can
be computed by using the necessary equations of solid or structural mechanics. The
displacement within the element is obtained using the shape functions of the
respective elements.
Stress (𝛔) =
𝐥𝐨𝐚𝐝
𝐚𝐫𝐞𝐚
=
𝐅
𝐀
Strain (e) =
𝐝𝐢𝐬𝐩𝐥𝐚𝐜𝐦𝐞𝐧𝐭
𝐥𝐞𝐧𝐠𝐭𝐡
=
𝛅
𝐥
𝛔 = 𝐄𝐞
Where F=load, A= Area, E= Young’s Modulus,δ = dispalcement
L=length
e =
𝐝𝐮
𝐝𝐱
=
𝐮 𝟏−𝐮 𝟐
𝐥
3.4.8. Interpretation of the results obtained:
The final goal of FEA is to interpret and analyze the results obtained for use in
the design and production process. Determination of location in the structure where
large deformation and large stress occur is generally important and essential in
making design and analysis decisions. Post processing of the analysis results is a
key step in success of finite element analysis.

16. 16
CHAPTER - 4
INTRODUCTIONTO CAD
Computer-aided design (CAD), also known as computer-aided design and drafting
(CADD), is the use of computer technology for the process of design and design-
documentation. Computer Aided Drafting describes the process of drafting with a
computer. CADD software, or environments, provides the user with input-tools for
the purpose of streamlining design processes; drafting, documentation, and
manufacturing processes. CADD output is often in the form of electronic files for print
or machining operations. The development of CADD-based software is in direct
correlation with the processes it seeks to economize; industry-based software
(construction, manufacturing, etc.) typically uses vector-based (linear) environments
whereas graphic-based software utilizes raster-based (pixilated) environments.
CADD environments often involve more than just shapes. As in the manual
drafting of technical and engineering drawings, the output of CAD must convey
information, such as materials, processes, dimensions, and tolerances, according to
application-specific conventions. CAD may be used to design curves and figures in
two-dimensional (2D) space; or curves, surfaces, and solids in three-dimensional (3D)
objects.
CAD is an important industrial art extensively used in many applications,
including automotive, shipbuilding, and aerospace industries, industrial and
architectural design, prosthetics, and many more. CAD is also widely used to produce
computer animation for special effects in movies, advertising and technical manuals.
The modern ubiquity and power of computers means that even perfume bottles and
shampoo dispensers are designed using techniques unheard of by engineers of the
1960s. Because of its enormous economic importance, CAD has been a major driving
force for research in computational geometry, computer graphics (both hardware and
software), and discrete differential geometry.
Current computer-aided design software packages range from 2D vector-based
drafting systems to 3D solid and surface modelers. Modern CAD packages can also
frequently allow rotations in three dimensions, allowing viewing of a designed object
from any desired angle, even from the inside looking out. Some CAD software is
capable of dynamic mathematic modeling, in which case it may be marketed as CADD
— computer-aided design and drafting.
CAD is used in the design of tools and machinery and in the drafting and
design of all types of buildings, from small residential types (houses) to the largest
commercial and industrial structures (hospitals and factories). CAD is mainly used for
detailed engineering of 3D models and/or 2D drawings of physical components, but it
is also used throughout the engineering process from conceptual design and layout of
products, through strength and dynamic analysis of assemblies to definition of
manufacturing methods of components. It can also be used to design objects.

17. 17
There are several good reasons for using a CAD system to supportthe
engineering design function:
 To increase the productivity
 To improve the quality of the design
 To uniform design standards
 To create a manufacturing data base

18. 18
4.1 INTRODUCTION TO CREO:
Creo is the industry’s standard 3D mechanical design suit. It is the world’s
leading CAD/CAM /CAE software, gives a broad range of integrated solutions to
cover all aspects of product design and manufacturing. Much of its success can be
attributed to its technology which spurs its customer’s to more quickly and
consistently innovate a new robust, parametric, feature based model, because the Creo
technology is unmatched in this field, in all processes, in all countries, in all kind of
companies along the supply chains. Creo is also the perfect solution for the
manufacturing enterprise, with associative applications, robust responsiveness and
web connectivity that make it the ideal flexible engineering solution to accelerate
innovations. Creo provides easy to use solution tailored to the needs of small, medium
sized enterprises as well as large industrial corporations in all industries, consumer
goods, fabrications and assembly, electrical and electronics goods, automotive,
aerospace etc.
4.1.1 Advantages of Creo:
1. It is much faster and more accurate. Once a design is completed. 2D and 3D
views are readily obtainable.
2. The ability to incorporate changes in the design process is possible.
3. It provides a very accurate representation of model specifying all other
dimensions hidden geometry etc.
4. It provides a greater flexibility for change. For example if we like to change
the dimensions of our model, all the related dimensions in design assembly,
manufacturing etc. will automatically change.
5. It provides clear 3D models, which are easy to visualize and understand.
6. Creo provides easy assembly of the individual parts or models created it also
decreases the time required for the assembly to a large extent.

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CHAPTER - 5
STATIC AND MODEL ANALYSIS OF LATHE BED
5.1 PROBLEM STATEMENT:
Fig: 5.3shows the extra duty lathe machine manufactured by M/s Honest
lathe, this lathe bed is selected for the complete analysis for both static and natural
frequencies. Then investigation is carried out to reduce the weight of the machine
bed without deteriorating its structural rigidity and the accuracy of the machine tool
by reducing the material where lathe bed under goes less stress and deformation
region. In this work, the 3D CAD model for the base model and the optimized
design has been created by using commercial 3D modelling software Creo. The 3D
FE model has been generated using ANSYS APDL. The analyses were carried out
using ANSYS APDL. The results were shown in tabular form to analyze the effect
of weight reduction on the structural integrity of the machine bed before and after
the weight reduction and conclusions were drawn about the optimized design.
5.2. IMPORTANCE OF DOING STATIC AND MODAL ANALYSIS:
The proper design of machine-tool structures requires a thorough knowledge of
their forms designs and properties of the material, the dynamics of the particular
machining process and nature of the forces involved. Recently, researches have
been conducted in the field of improvement of structural design of machine tools by
improving stiffness and lightening weight which is especially urgent for the
structural parts, such as bed, column, and work table, beam and so on. The
arrangement of stiffening - ribs in machine tool structures is a key factor for
structural stiffness and material consumption. So the lightening design of
stiffening-ribs is significant for machining performance and energy saving. It is
generally accepted that the precision of machine tools is determined by their static,
dynamic and thermal characteristics.
Especially, the dynamic characteristics play an important role in high speed,
precision machine tool structures, because vibration during the machining process
results in chatter marks on the machined surface and thus creates a noisy environment.
High static stiffness against bending and torsion, good dynamic characteristics as
reflected by high natural frequency and high damping ratio, ease in production, good
long term dimensional stability, reasonably low coefficient of expansion, low cost and
low material requirements are the basic properties of machine tool structures that
engineers look for designing and fabricating. However, from user’s point of view,
machine tool vibration is an important factor because it adversely affects the quality of
the machined surface. To improve both the static and dynamic performances, the
machine tool structures should have high static stiffness and damping. Using either
higher modulus material or more material in the structure, the static stiffness of a
machine tool may be increased.
But, it is difficult to increases the dynamic stiffness of a machine tool with these
methods and increase in the static stiffness cannot increase it damping property.

20. 20
Material distribution plays on the important role in the structural strength and using
material in required place can increase static stiffness with less mass.
Higher cutting speeds can be facilitated only by structures which have high
stiffness and good damping characteristics. The deformation of machine tool
structures under cutting forces and structural loads are responsible for the poor quality
of products and which in turn is also aggravated by the noise and vibration produced.
In many a situation, it is the level of deformation and vibration that determines the
upper limit on the ability of the machine to produce components with high precision.
All these above said deleterious effects greatly necessitate constant innovations and
continuous research to keep them under check. Increasing structural stiffness could
help in avoiding such problems. To increase the static stiffness and damping, different
form designs can be used.
5.3. INTRODUCTION TO NATURAL FREQUENCY:
Bridges, aircraft wings, machine tools, and all other physical structures have natural
frequencies. A natural frequency is the frequency at which the structure would
oscillate if it were disturbed from its rest position and then allowed to vibrate freely.
All structures have at least one natural frequency. Nearly every structure has multiple
natural frequencies. Resonance occurs when the applied force or base excitation
frequency coincides with a structural natural frequency. During resonant vibration, the
response displacement may increase until the structure experiences buckling, yielding,
fatigue, or some other failure mechanism. The failure of the Cypress Viaduct in the
1989 Loma Prieta Earthquake is example of failure due to resonant excitation.
Resonant vibration caused 50 of the 124 spans of the Viaduct to collapse. The
reinforced concrete frames of those spans were mounted on weak soil. As a result, the
natural frequency of those spans coincided with the frequency of the earthquake
ground motion. The Viaduct structure thus amplified the ground motion. The spans
suffered increasing vertical motion. Cracks formed in the support frames. Finally, the
upper roadway collapsed, slamming down on the lower road.
Dynamic Analysis Engineers performing dynamic analysis must
1. Determine the natural frequencies of the structure.
2. Characterize potential excitation functions.
3. Calculate the response of the structure to the maximum expected excitation.
4. Determine whether the expected response violates any failure criteria.
This report is concerned with the first step. 2 The natural frequencies can be
calculated via analytical methods during the design stage. The frequencies may also be
measured after the structure, or a prototype, is built. Each natural frequency has a
corresponding damping ratio. Damping values are empirical values that must be
obtained by measurement. Frequency Response Function Overview There are many
tools available for performing vibration analysis and testing. The frequency response
function is a particular tool. A frequency response function (FRF) is a transfer
function, expressed in the frequency domain. Frequency response functions are
complex functions, with real and imaginary components. They may also be
represented in terms of magnitude and phase. A frequency response function can be

21. 21
formed from either measured data or analytical functions. A frequency response
function expresses the structural response to an applied force as a function of
frequency. The response may be given in terms of displacement, velocity, or
acceleration. Furthermore, the response parameter may appear in the numerator or
denominator of the transfer function. Frequency Response Function Model Consider a
linear system as represented by the diagram in below Figure.
Fig.3 Function Model
F(w ) is the input force as a function of the angular frequency w . H(w ) is the
transfer function. X(w ) is the displacement response function. Each function is a
complex function, which may also be represented in terms of magnitude and phase.
Each function is thus a spectral function. There are numerous types of spectral
functions. For simplicity, consider each to be a Fourier transform. H(w ) Transfer
function F(w ) Input Force Displacement Response X(w ) 3 The relationship in Figure
1 can be represented by the following equations X(w ) = H(w )×F(w ) (1) ( ) ( ) (w ) w
w = F X H (2) Similar transfer functions can be developed for the velocity and
acceleration responses.
5.4. Solid modelling of Lathe Machine bed:
There are various software packages for carrying out CAD modeling. Some of
the software packages commonly used in industry includes Solid Works, Creo, Catia,
and UniGraphics. Each of the packages has unique advantages and CAD modeling
packages are selected based on the application. Solid model of the lath bed
Fig.4 Solid model of lathe bed

22. 22
Fig.5 Solid model of lathe bed (Sectional View)
Table1 Overall dimensions of lathe bed
5.5. DIFFERENT IMPORT FORMATS:
Following are the few standard formats used for exporting the model to
ANSYS
IGES (Initial Graphics Exchange Specification):
It was originally used only for the exchange of 2D and 3D wire frame models
(ANSI). It is still widely used and supported CAE. Recently IGES extensions include
information about 3D surfaces. This standard is being replaced by STEP
SAT:
The SAT file is a text file format for native ACIS models. Spatial technologies
has made this file format public and declared it an ‘open’ standard
PARA:
Para solid Transmit files contain the geometry, topology, and attached data for
solid models created with the Para solid modeling system from Shape Data Limited.
Para solid is a stand-alone solid modeling kernel and programming library as well as
the modeling engine for the Uni graphics CAD/Cam system of Electronic Data
Systems (EDC)
STL:
Rapid prototyping is the technology in which 3D CAD model is converted into
physical also known as abbreviation of Standard Triangulation Language
Length 1420 mm
Width 174.5 mm
Height 215.7 mm

23. 23
5.6. HOW TO IMPORT INTO ANSYS
ANSYS is not a modeling software. CAD modeling is done by special
software like Pro/E, CATIA, Uni-Graphics and Solid works, and then it is imported to
ANSYS software. While importing CAD model, ANSYS provides two options. They
are
5.6.1. Direct Interface to CAD Software:
Ansys has direct interface with some CAD software like Pro/E, CATIA and
UniGraphics. Special attention need to be given while ANSYS and third party CAD
software is installed, so as to use exchange CAD connection functionality. Then CAD
model can be opened directly.
5.6.2. Using standard format:
This is the most popular method by which we can import any CAD model.
The CAD model is converted and saved in the standard format, and then this
standard format can be easily imported in ANSYS. The most popular word in
industry is NEUTRAL FILE FORMAT. Many external CAD packages will export
a file in this or a similar format. ANSYS provides a number of Neutral File
options and specialized tools for ensuring a correct and valid model import.
5.7. STRUCTURAL ANALYSIS OF LATHE BED:
Structural analysis is carried out in ANSYS (Finite Element package).Finite
Element Analysis is divided into three sub steps:
1) Pre-Processor
2) Solver
3) General Post-Processor
5.7.1. Pre-Processor
Solid model is imported to ANSYS in IGES format. CAD model is prepared
in MKS units. Since the analysis is to be done in SI unit system.
5.7.2. Element type
Element Solid 285 has been chosen for discretizing the domain. SOLID
285 elements are a higher order 3-D, 4-node element. SOLID 285 have quadratic
displacement behavior and are well suited to model irregular meshes. The element
is defined by 4 nodes having three degrees of freedom at each node, translations in
the nodal x, y, and z directions. This element does not have rotational DOF
(Degree of Freedom)
5.7.3. Material Properties:
Cast iron is one of the oldest ferrous metals used in construction and outdoor
ornament. It is primarily composed of iron (Fe)carbon (C) and silicon (Si), but may
also contain traces of sulphur (S), manganese (Mn) and phosphorus (P). It has a
relatively high carbon content of 2% to 5%. It is hard, brittle, nonmalleable (i.e. it
cannot be bent, stretched or hammered into shape) and more fusible than steel. Its
structure is crystalline and relatively brittle and weak in tension. Cast-iron
members fracture under excessive tensile loading with little prior distortion. Cast
iron is, however, very good in compression. The composition of cast iron and the
method of manufacture are critical in determining its characteristics.

24. 24
The most common traditional form is grey cast iron. Common or grey cast
iron is easily cast but it cannot be forged or worked mechanically either hot or cold.
In grey cast iron the carbon content is in the form of flakes distributed throughout
the metal. In white cast iron the carbon content is combined chemically as carbide
of iron. White cast iron has superior tensile strength and malleability. It is also
known as 'malleable' or 'spheroidal graphite' iron.
Cast iron is used in a wide variety of structural and decorative applications,
because it is relatively inexpensive, durable and easily cast into a variety of shapes.
Most of the typical uses include:
o historic markers and plaques
o hardware: hinges, latches
o columns, balusters
o stairs
o structural connectors in buildings and monuments
o decorative features
o fences
o tools and utensils
o ordnance
o stoves and fire backs
o Piping
The basic cast iron material in all of these applications may appear to be the
same, or very similar, however, the component size, composition, use, condition,
relationship to adjacent materials, exposure and other factors may dictate that
different treatments be used to correct similar problems. Any material in question
should be evaluated as a part of a larger system and treatment plans should be based
upon consideration of all relevant factors.
Cast iron is extremely strong and durable when used appropriately and protected
from adverse exposure. It is much stronger in compression than in tension,
therefore it is commonly found in columns, but not in structural beams. It is,
however, highly susceptible to corrosion (rusting) when exposed to moisture and,
has several typical problems which usually can be identified by visual inspection.
The following sections will identify and discuss the most common problems
encountered with cast iron. For general guidance on inspecting for cast iron
failures.
Lathe bed is fabricated with Gray cast iron(ASTM Grade 40). Therefore the below
mentioned material attributes are defined for the element.
Property Value
Young’s Modulus 140e9 N/m2
Poisson’s Ratio 0.3
Density 7200 kg/m3
Table 2 Mechanical properties of Gray cast iron
5.7.4 Meshing:
Meshing of solid model is done by the Element chosen, element edge length have
been adjusted to 0.02 m in order to obtain a regular uniform mesh. Automatic sizing
creates elements of wide range of dimensions. Therefore manual sizing is done.

25. 25
5.7.5. Boundary conditions:
A condition that is required to satisfied at all or parts of the boundary of the boundary
of a region in which a set of different conditions is to be solved.
5.8 LATHE MACHINE
Fig.6 Heavy Duty Lathe machine
MAKE SOUTH BEND LATHE CO.
MODEL NO. SB 1007
OVERALL DIMENSIONS (LXBXH) 1550X724X559)MM
MASS 246 KG
5.8.1 DIMENSIONS OF LATHE BED
Fig.7 Base model

26. 26
OVERALL DIMENSIONS (LXBXH) 1100X174.5X215.7
MASS 90 KG
MATERIAL GRAY CAST IRON
1. The base of the lathe machine bed is fixed to the floor. Therefore base of lathe bed is
constrained in all directions (UX=UY=UZ=0).
2. Gravitational force is applied, to add stress distribution and deformation due to self -
weight.
Below figure shows the boundary conditions applied on the FE model
Fig.8 Fixed boundary conditions and gravitational acceleration applied on lathe bed
5.9 Force Applied On Lathe Bed:
To design a lathe bed, initially we have to analyse, the stresses and deformations
inducing in lathe bed due to cutting forces generated by cutting tool and work piece
interaction. The design of lathe bed is preceded by analysis of forces that are acting on
the system due to tool work piece interaction. In current analysis we considered the
maximum torque which is supplied by electric motor of lathe machine.
Cutting forces will be transferred to lathe bed at carriage region. So we applied
force at carriage region (while in machining process, carriage slides over lathe bed. We
simplified analysis by fixing its location. we considered its location near to the head
stock because in most manufacturing cases we don't slide carriage beyond middle
portion lathe bed) as shown in fig :5.5. The following forces are applied on lathe bed.

27. 27
1. Maximum torque which can be generated by prime mover is converted into force and
applied on carriage region. as shown in calculation.
2. Weight Of Head Stock - 246 – 105.8 = 140.2 kg / 1375 N (Carriage and tailstock
weights are not subtracted due to unavailability of individual weights. It does not affect
FEA results because we are not reducing loads and as compared to lathe bed weight
these weight are very less in magnitude)
3. Self weight of the lathe bed due to gravitational force
4. Maximum Weight Between Centre - 36.2 kg / 355 N. This force is divided into 2
equal parts (i.e., 177.5 N). This force is applied on headstock and tailstock. All forces
applied on lathe bed are shown in fig. 5.5.
Spindle bore (Diameter) 34.5 mm (r=17.25 mm)
Spindle speed range 55 - 2200 rpm (N)
Electric motor 2 Hp or 1.5kW (P)
Table.3 Technical specifications of lathe machine
𝐏 =
𝟐 𝐗 𝛑 𝐗 𝐍 𝐗 𝐓
𝟔𝟎
1500 =
𝟐 𝐗 𝛑 𝐗 𝟓𝟓 𝐗 𝐓
𝟔𝟎
T = 260.33 N-m
T = F X r
260.33 = F X 0.01725
F = 15092 N
This force applied at region of carriage for simulating actual locations from where
cutting forces transferred to lathe bed. since number of nodes are 700 at this region,
hence force is divided into 700 parts (21.6 N). The forces applied as shown in below
figure: 5.5.

28. 28
Fig.9 Force applied on lathe bed
5.9.1 Solution
Next step in the analysis is the solution phase. A 3D static steady state structural
analysis is carried out on the lathe bed.
5.9.2 Deformation of the solid model:
Fig: 5.6. shows the deformed shape of the lathe bed.In lathe bed,maximum
deformation occurring at carriage region. This deformation is in downward side
and induced stress is compressive stress as shown in Fig: 5.7. It is due to the force
is applied in downward direction (-Y). Induced deformations and stresses are
gradually decreasing towards tailstock, due to structural stiffness, damping
capacity of lathe bed. From these stress and deformation results, it is
recommended to remove material at middle and tailstock regions of lathe bed. In
modified lathe bed material is removed, with adding ribs to maintain structural
stiffness evenly.
After modification, Structural analysis and modal analysis is carried out on
lathe bed. Results of modified model is shown in Fig: 5.17. to Fig :5.26. Results of
both initial model and modified model are compared in Table : 5.4 and Table: 5.5.
After analyzing modified model results, compressive stress is reduced by 2.3 MPa.
Because design is changed at high stress region by adding material. From modal
analysis, it is observed that natural frequency range variation is within 10%. This
variation is expected because design of lathe bed is changed. Weight of lathe bed
is decreased by 7.82 kg (Equal to 7.4% of lathe bed weight before modification).
From these comparative study, we can conclude that modified model is best in
terms of weight, stresses and damping capacity.

29. 29
5.10 STATIC AND MODAL ANALYSIS RESULTS BEFORE WEIGHT
OPTIMIZATION
Fig.10 Deformation of lathe bed before weight optimization
Fig.11 Stress Distribution of lathe bed in Y direction before modification

30. 30
Fig.12 Von-mises stress Distribution of lathe bed before modification
Fig.13 Natural Frequency mode – 1 Deformation

31. 31
Fig.14 Natural Frequency mode – 2 Deformation
Fig.15 Natural Frequency mode – 3 Deformation

32. 32
Fig.16 Natural Frequency mode – 4 Deformation
Fig.17 Natural Frequency mode – 5Deformation

33. 33
Fig.18 Natural Frequency mode – 6 Deformation
Table.4 Mass of lathe bed before modification

34. 34
5.11 STATIC AND MODAL ANALYSIS RESULTS AFTERWEIGHT
OPTIMIZATION:
Fig.19 Solid model of modified lathe bed
Fig.20 Deformation of lathe bed after modification

35. 35
Fig.21 Von-mises stress Distribution of lathe bed after modification
Fig.22 Natural Frequency mode – 1 Deformation

36. 36
Fig.23 Natural Frequency mode – 2 Deformation
Fig.24 Natural Frequency mode – 3 Deformation

37. 37
Fig.25 Natural Frequency mode – 4 Deformation
Fig.26 Natural Frequency mode – 5 Deformation

38. 38
Fig.27 Natural Frequency mode – 6 Deformation
Table.5 Mass of lathe bed after modification

39. 39
Fig.28 Stress Distribution of lathe bed in Y direction after modification

40. 40
5.12 RESULTS
5.12.1 Static Analysis:
LATHE BED
(BEFORE WEIGHT
OPTIMIZATION)
LATHE BED (AFTER
WEIGHT
OPTIMIZATION)
STRESS IN Y
DIRECTION(MPa)
13.4 (Compressive
stress)
2.23 (Tensile stress)
10.8 (Compressive stress)
2.38 (Tensile Stress)
VON-MISES STRESS
(MPA)
15.9 13.6
DISPLACEMENT(mm) 0.0286 0.0302
MASS (kg) 105.816 97.992
Table.6 Structural analysis results comparison

41. 41
5.12.2 Modal Analysis:
LATHE BED
(BEFORE
OPTIMIZATION)
LATHE BED
(AFTER
OPTIMIZATION)
% CHANGE
Mode 1 Frequency (Hz) 211.24 230.40 8.3
Displacement (mm) 204.898 238.068
Mode 2 Frequency (Hz) 474.16 507.81 6.6
Displacement (mm) 204.41 247.97
Mode 3 Frequency (Hz) 595.13 572.46 3.8
Displacement (mm) 322.561 336.216
Mode 4 Frequency (Hz) 634.89 649.25 2.2
Displacement (mm) 226.61 225.292
Mode 5 Frequency (Hz) 794.16 838.73 5.3
Displacement (mm) 218.397 346.006
Mode 6 Frequency (Hz) 1031.8 938.13 9
Displacement (mm) 334.217 431.994
Table.7 Modal analysis resultscomparison

42. 42
CONCLUSION
In this project, we have prepared Lathe bed CAD model of M/s South Bend Lathe
Co.
The weight of the lathe bed before modification is 105.816 Kg, after modifying
the design weight of the bed has reduced to 97.992 kg. This weight reduction is equal
to 7.4% base model weight.
We identified concentrated stress and low stress zones in lathe bed by
conducting structural analysis. We achieved linear stress distribution at concentrated
stress zones after lathe bed design modification.
We conformed that modified Lathe bed CAD model is not deviating with base
Lathe bed CAD model in terms of vibrational damping capacity by conducting modal
analysis for 6 modes (Natural Frequencies). There is no much variation in modal
analysis results.
Through these structural and modal analysis results, we can conclude that
modified model is best in terms of weight, stresses and damping capacity.

43. 43
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