DESIGN AND STRUCTURAL ANALYSIS OF HIGH SPEED HELICAL GEAR USING ANSYS

ABSTRACT

Marine engines are among heavy-duty machineries, which need to be taken care of in

the best way during prototype development stages. These engines are operated at very

high speeds which induce large stresses and deflections in the gears as well as in other

rotating components. For the safe functioning of the engine, these stresses and deflections

have to be minimized.

In this project, static-structural analysis on a high speed helical gear used in marine

engines, have been performed. The dimensions of the model have been arrived

at by theoretical methods. The stresses generated and the deflections of the tooth

have been analyzed for different materials. Finally the results obtained by

theoretical analysis and Finite Element Analysis are compared to check

the correctness. A conclusion has been arrived on the material which is best suited for

the marine engines based on the results.

TABLE OF CONTENTS

CHAPTER DESCRIPTION Abstract Acknowledgment

1. Introduction 1 1.1 Advantages of Gear Drives 2 1.2 Disadvantages of Gear Drives 2 1.3 General classifications of gears 3 1.3.1 According to position of axes of shafts 3 1.3.2 According to the peripheral velocity of the gears 3 1.3.3 According to the type of gearing 3 1.3.4 According to the position of teeth on gear surface 3 1.3.5 According to the position of axes of the shafts 3

2. Marine engines 7 2.1 Reciprocating Diesel Engines 7 3. Finite Element Methods 9 3.1 Terms commonly used in Finite Element Method 11 3.2 General Description of FEM 14 3.3 Advantages of FEM 17 3.4 Limitation 19 3.5 Basic Approach to FEA Software 21 3.5.1 Pre Processor 21 3.5.1.1 Building of Model 21 3.5.1.2 Creation of Finite Element Model for Meshing 21 3.5.2 Solver 23 3.5.3 Post Processor 24 4. FEA software-ANSYS 25 4.1 Introduction to ANSYS program 25 4.2 Evolution of ANSYS Program 25

4.3 Overview of the Program 26 4.4 Reducing design, manufacturing costs using Ansys 29 4.5 Types of Structural Analysis 31 4.5.1 Structural Static Analysis 32 4.6 Procedure for Ansys Analysis 32 4.6.1 Build the model 32 4.6.2 Obtain the solution 33 4.6.2.1 Pre-processor 34 4.6.2.2 Solution 38 4.6.2.3 Post processor 38 5. Theoretical Design calculations 39 5.1 Calculations for Steel 39 5.1.1 Design of Hole 46 5.2 Calculations for Aluminium Alloy 47 5.2.1 Design of Hole 54 6. Definition of Problem 55 6.1 Element considered for static analysis 55 6.2 Assumptions and Restrictions 56 6.3 Materials Used 57 6.4 Mesh Generation 57 6.5 Boundary conditions 58

7. Experimental Results 59 7.1 Results for Steel 59 7.2 Results for Ceramics 67 8. Discussion of Results 71 8.1 Results for Steel as Material 71 8.2 Results for Ceramics as Material 72 8.3 Results Comparison for Steel 74 8.4 Results Comparison for Ceramics 75 9. Conclusion 77 10. Future Scope of Work 78 11. References 79

CHAPTER 1

INTRODUCTION

Gears are most commonly used for power transmission in all the modern devices.

These toothed wheels are used to change the speed or power between input and output.

They have gained wide range of acceptance in all kinds of applications and have been

used extensively in the high-speed marine engines.

In the present era of sophisticated technology, gear design has evolved to a

high degree of perfection. The design and manufacture of precision cut gears,

made from materials of high strength, have made it possible to produce gears

which are capable of transmitting extremely large loads at extremely high

circumferential speeds with very little noise, vibration and other undesirable

aspects of gear drives.

A gear is a toothed wheel having a special tooth space of profile enabling it to mesh

smoothly with other gears and power transmission takes place from one shaft to other by

means of successive engagement of teeth.

Gears operate in pairs, the smallest of the pair being called “pinion” and the larger

one “gear”. Usually the pinion drives the gear and the system acts as a speed reducer and

torque converter.

1.1 ADVANTAGES OF GEAR DRIVES:

The following are the advantages of the gear drives compared to other drives.

Gear drives are more compact in construction due to relatively small centre

distance.

Gears are used where the constant velocity ratio is desired.

Gears can be operated at higher speeds.

It has higher efficiency.

Reliability in service.

It has wide transmitted power range due to gear shifting facility.

Gear offers lighter loads on the shafts and bearings.

Gear can change the direction of axis of rotation.

1.2 DISADVANTAGES OF GEAR DRIVES:

Not suitable for the shafts which are at longer center distance.

Manufacturing is complex. It needs special tools and equipment.

Require perfect alignment of shafts.

Requires more attention to lubrication.

The error in cutting teeth may cause vibration and noise during operation.

1.3 GENERAL CLASSIFICATION OF GEARS:

Although the types and the modalities of gear design vary widely for mechanical

power transmission, gears are generally categorized into the following types.

1.3.1 ACCORDING TO THE POSITION OF AXES OF THE SHAFTS:

The axes of the two shafts between which the motion is to be transmitted, may be

( a) Parallel, (b) Intersecting, and (c) Non-Intersecting and Non-parallel

1.3.2 ACCORDING TO THE PERIPHERAL VELOCITY OF THE GEARS:

The gears, according to the peripheral velocity of the gears, may be classified as: (a)

Low Velocity, (b) Medium Velocity and (c) High Velocity.

1.3.3 ACCORDING TO TYPE OF GEARING:

The gears, according to the type of gearing may be classified as (a) External Gearing,

(b) Internal Gearing, (c) Rack and Pinion.

1.3.4 ACCORDING TO THE POSITION OF THE TEETH ON THE GEAR

SURFACE:

The teeth on the gear surface may be (a) Straight (b) Inclined (c) Curved.

1.3.5 ACCORDING TO THE POSITION OF AXES OF THE SHAFTS:

Spur Gears: Spur gears are the simplest and most common type of gear. Their general

form is a cylinder or disk. The teeth project radially, and with these "straight-cut gears",

the leading edges of the teeth are aligned parallel to the axis of rotation. These gears can

only mesh correctly if they are fitted to parallel axles. Spur gears on non-parallel shafts

can mesh, but only point contact will be achieved, not line contact across the full width of

the tooth; also the length of the path of contact may be too short. This causes impact

stress and noise. Spur gears make a characteristic whine at high speeds and can not take

as much torque as helical gears because their teeth are receiving impact blows.

Fig: 1.1

Helical Gears: Helical gears offer a refinement over spur gears. The leading edges of

the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is

curved, this angling causes the tooth shape to be a segment of a helix. The angled teeth

engage more gradually than do spur gear teeth. This causes helical gears to run more

smoothly and quietly than spur gears. Helical gears also offer the possibility of using

non-parallel shafts.

With parallel helical gears, each pair of teeth first makes contact at a single point at

one side of the gear wheel; a moving curve of contact then grows gradually across the

tooth face. It may span the entire width of the tooth for a time. Finally, it recedes until the

teeth break contact at a single point on the opposite side of the wheel. Thus force is taken

up and released gradually.

.

Fig: 1.2

Double Helical Gears:

Double helical gears, also known as herringbone gears, overcome the problem of axial

thrust presented by 'single' helical gears by having teeth that set in a 'V' shape. Each gear

in a double helical gear can be thought of as two standards, but mirror image, helical

gears stacked. This cancels out the thrust since each half of the gear thrusts in the

opposite direction. They can be directly interchanged with spur gears without any need

for different bearings.

Bevel Gears:

Bevel gears are essentially conically shaped, although the actual gear does not extend

all the way to the vertex (tip) of the cone that bound it. With two bevel gears in mesh, the

vertices of their two cones lie on a single point, and the shaft axes also intersect at that

point. The angle between the shafts can be anything except zero or 180 degrees. Bevel

gears with equal numbers of teeth and shaft axes at 90 degrees are called miter gears.

Fig: 1.3 Fig: 1.4

Worm Gears:

Worm gear is a special case of a spiral gear in which the larger wheel usually has

hollowed or concave shape such that a portion of the pitch diameter of the other gear is

enveloped on it. The smaller of the two wheels called the worm which also has a large

spiral angle. The shafts may have any angle between them, but normally it is 90 °.The

system can be non-throated, single throated, double throated types.

Hypoid Gears:

These are similar to spiral bevel gears, but have non-intersecting axes i.e. the axes of

pinion is offset relative to the gear axis. However the plane containing the two axes is

usually at right angles to each other.

CHAPTER 2

MARINE ENGINES

2.1 RECIPROCATING DIESEL ENGINES:

The engine used in 99% of modern ships is diesel reciprocating engines. The rotating

crankshaft can power the propeller directly for slow speed engines, via a gearbox for

medium and high speed engines, or via an alternator and electric motor in diesel-electric

vessels.

The reciprocating marine diesel engine first came into use in 1903 when the diesel

electric rivertanker Vandal was put in service by Branobel. Diesel engines soon offered

greater efficiency than the steam turbine, but for many years had an inferior power-to-

space ratio.

Diesel engines today are broadly classified according to

Their operating cycle: two-stroke or four-stroke

Their construction: Crosshead, trunk, or opposed piston

Their speed

o Slow speed: any engine with a maximum operating speed up to 300

revs/minute, although most large 2-stroke slow speed diesel engines

operate below 120 revs/minute. Some very long stroke engines have a

maximum speed of around 80 revs/minute. The largest, most powerful

engines in the world are slow speed, two stroke, and crosshead diesels.

o Medium speed: any engine with a maximum operating speed in the range

300-900 revs/minute. Many modern 4-stroke medium speed diesel engines

have a maximum operating speed of around 500 rpm.

o High speed: any engine with a maximum operating speed above 900

revs/minute.

Most modern larger merchant ships use either slow speed, two stroke, crosshead

engines, or medium speed, four stroke, trunk engines. Some smaller vessels may use high

speed diesel engines.

The size of the different types of engines is an important factor in selecting what will

be installed in a new ship. Slow speed two-stroke engines are much taller, but the area

needed, length and width, is smaller than that needed for four-stroke medium speed diesel

engines. As space higher up in passenger ships and ferries is at a premium, these ships

tend to use multiple medium speed engines resulting in a longer, lower engine room than

that needed for two-stroke diesel engines. Multiple engine installations also give

redundancy in the event of mechanical failure of one or more engines and greater

efficiency over a wider range of operating conditions.

As modern ships' propellers are at their most efficient at the operating speed of most

slow speed diesel engines, ships with these engines do not generally need gearboxes.

Usually such propulsion systems consist of either one or two propeller shafts each with

its own direct drive engine. Ships propelled by medium or high speed diesel engines may

have one or two (sometimes more) propellers, commonly with one or more engines

driving each propeller shaft through a gearbox.

CHAPTER 3

FINITE ELEMENT METHODS

The finite element method is numerical analysis technique for obtaining approximate

solutions to a wide variety of engineering problems. Because of its diversity and

flexibility as an analysis tool, it is receiving much attention in engineering schools and

industries. In more and more engineering situations today, we find that it is necessary to

obtain approximate solutions to problems rather than exact closed form solution.

It is not possible to obtain analytical mathematical solutions for many engineering

problems. An analytical solutions is a mathematical expression that gives the values of

the desired unknown quantity at any location in the body, as consequence it is valid for

infinite number of location in the body. For problems involving complex material

properties and boundary conditions, the engineer resorts to numerical methods that

provides approximate, but acceptable solutions.

The finite element method has become a powerful tool for the numerical solutions of a

wide range of engineering problems. It has developed simultaneously with the increasing

use of the high-speed electronic digital computers and with the growing emphasis on

numerical methods for engineering analysis. This method started as a generalization of

the structural idea to some problems of elastic continuum problem, started in terms of

different equations or as an extrinum problem.

The fundamental areas that have to be learned for working capability of finite element

method include:

MATRIX ALGEBRA.

SOLID MECHANICS.

VARIATION METHODS.

COMPUTER SKILLS.

Matrix techniques are definitely most efficient and systematic way to handle algebra

of finite element method. Basically matrix algebra provides a scheme by which a large

number of equations can be stored and manipulated. Since vast majority of literature on

the finite element method treats problems in structural and continuum mechanics,

including soil and rock mechanics, the knowledge of these fields became necessary. It is

useful to consider the finite element procedure basically as a Variation approach. This

conception has contributed significantly to the convenience of formulating the method

and to its generality.

The term “finite element” distinguishes the technique from the use of infinitesimal

“differential elements” used in calculus, differential equations. The method is also

distinguished from finite difference equations, for which although the steps in to which

space is divided into finite elements are finite in size; there is a little freedom in the

shapes that the discrete steps can take. F.E.A is a way to deal with structures that are

more complex than dealt with analytically using the partial differential equations.

F.E.A deals with complex boundaries better than finite difference equations and gives

answers to the ‘real world’ structural problems. It has been substantially extended scope

during the roughly forty years of its use.

F.E.A makes it possible it evaluate a detail and complex structure, in a computer

during the planning of the structure. The demonstration in the computer about the

adequate strength of the structure and possibility of improving design during planning

can justify the cost of this analysis work. F.E.A has also been known to increase the

rating of the structures that were significantly over design and build many decades ago.

In the absence of finite element analysis (or other numerical analysis), development of

structures must be based on hand calculations only. For complex structures, the

simplifying assumptions are required to make any calculations possible can lead to a

conservative and heavy design. A considerable factor of ignorance can remain as to

whether the structure will be adequate for all design loads. Significant changes in design

involve expensive strain gauging to evaluate strength and deformation.

3.1 TERMS COMMONLY USED IN FINITE ELEMENT METHOD:

DESCRITIZATION: The process of selecting only a certain number of discrete

points in the body can be termed as Descritization.

CONTINUUM: The continuum is the physical body, structure or solid being

analyzed.

NODE: The finite elements, which are interconnected at joints, are called nodes or

nodal points.

ELEMENT: Small geometrical regular figures are called elements.

DISPLACE MODELS: The nodal displacements, rotations and strains necessary to

specify completely deformation of finite element.

DEGREE OF FREEDOM: The nodal displacements, rotations and strains necessary

to specify completely deformation of finite element.

LOCAL COORDINATE SYSTEM: Local coordinate system is one that is defined for

a particular element and not necessary for the entire body or structure.

GLOBAL SYSTEM: The coordinate system for the entire body is called the Global

coordinate system.

NATURAL COORDINATE SYSTEM: Natural coordinate system is a local system,

which permits the specification of point within the element by a set of

dimensionless numbers, whose magnitudes never exceeds unity.

INTERPOLATION FUNCTION: It is a function, which has unit value at one nodal

point and a zero value at all other nodal points.

ASPECT RATIO: The aspect ratio describes the shapes of the element in the

assemblage for two dimensional elements; this parameter is defined as the ratio of

largest dimension of the element to the smallest dimension.

FIELD VARIABLES: The principal unknowns of a problem are called the field

variables.

PROCESS OF FINITE ELEMENT ANALYSIS: [Fig: 3.1]

3.2 GENERAL DESCRIPTION OF FEM:

Physical Problems

Mathematical Model

Governed by Different

Equations, Assumptions

In

Geometry

Kinematics

Material Law

Loading

Boundary

Conditions etc

Change of Physical Problems

Finite Element Solution Choice of Finite Element Mesh Density Solution

Parametric Representation

Loading Boundary

Conditions

Interpolation of Results

Assessment of accuracy of Finite Element Solution of Mathematical Model

Improve Mathematical Model

Define Mesh

Define Analysis

In the finite element method, the actual continuum of body of matter like solid, liquid

or gas is represented as an assemblage of sub divisions called Finite elements. These

elements are considered to be inter connected at specified points known as nodes or nodal

points. These nodes usually lie on the element boundaries where an adjacent element is

considered to be connected. Since the actual variation of the field variables (like

Displacement, stress, temperature, pressure and velocity) inside the continuum are is not

know, we assume that the variation of the field variable inside a finite element can be

approximated by a simple function. These approximating functions (also called

interpolation models) are defined in terms of the values at the nodes. When the field

equations (like equilibrium equations) for the whole continuum are written, the new

unknown will be the nodal values of the field variable. By solving the field equations,

which are generally in the form of the matrix equations, the nodal values of the field

variables will be known. Once these are known, the approximating function defines the

field variable throughout the assemblage of elements.

The solution of a general continuum by the finite element method always follows as

orderly step-by-step process. The step-by-step procedure for static structural problem can

be stated as follows:

Step 1:- DESCRITIZATION OF STRUCTURE (DOMAIN).

The first step in the finite element method is to divide the structure of solution region

in to sub divisions or elements.

Step 2:- SELECTION OF PROPER INTERPOLATION MODEL.

Since the displacement (field variable) solution of a complex structure under any

specified load conditions cannot be predicted exactly, we assume some suitable solution,

within an element to approximate the unknown solution. The assumed solution must be

simple and it should satisfy certain convergence requirements.

Step 3:- DERIVATION OF ELEMENT STIFFNESS MATRICES (CHARACTERISTIC

MATRICES) AND LOAD VECTORS.

From the assumed displacement model the stiffness matrix [K(e)] and the load vector

P(e) of element ‘e’ are to be derived by using either equilibrium conditions or a suitable

Variation principle.

Step 4:- ASSEMBLAGE OF ELEMENT EQUATIONS TO OBTAIN THE EQUILIBRIUM

EQUATIONS.

Since the structure is composed of several finite elements, the individual element

stiffness matrices and load vectors are to be assembled in a suitable manner and the

overall equilibrium equation has to be formulated as

[K]φ = P

Where [K] is called assembled stiffness matrix,

Φ is called the vector of nodal displacement and

P is the vector or nodal force for the complete structure.

Step 5:- SOLUTION OF SYSTEM EQUATION TO FIND NODAL VALUES OF DISPLACEMENT

(FIELD VARIABLE)

The overall equilibrium equations have to be modified to account for the boundary

conditions of the problem. After the incorporation of the boundary conditions, the

equilibrium equations can be expressed as,

[K]φ = P

For linear problems, the vector ‘φ’ can be solved very easily. But for non-linear

problems, the solution has to be obtained in a sequence of steps, each step involving the

modification of the stiffness matrix [K] and ‘φ’ or the load vector P.

Step 6:- COMPUTATION OF ELEMENT STRAINS AND STRESSES.

From the known nodal displacements, if required, the element strains and stresses can

be computed by using the necessary equations of solid or structural mechanics.

In the above steps, the words indicated in brackets implement the general FEM step-by-

step procedure.

3.3 ADVANTAGES OF FEM:

ANALYSIS AND OPTIMIZATION (A&O) OF DISC BRAKE ROTOR

The main objective behind undertaking the project “Analysis and

Optimization of Disc Brake Rotor” is to study and evaluate the performance of

disc brake under severe braking conditions and thereby assisting in disc brake

rotor design and analysis.

ANSYS is a flexible and cost effective tool. ANSYS is used in industries in

order to solve several mechanical problems.

In this project, an Axis-Symmetric disc brake rotor is considered for

analysis. Flange width of 8mm, 10mm and 12mm made of Cast Iron, Aluminum

and Aluminum composite are considered. A Coupled Field Analysis (Transient

Thermal Analysis and Structural Coupled field analysis is performed, a graph is

plotted between the distance and temperature.

An attempt is made to suggest the best combination of material and flange

width for disc brake rotor, which yields a low temperature variation across the

rotor disc and minimum von mises stress possible.

Vishal Reddy Boda

12/17/2008

Chapter 1

INTRODUCTION

A brake is an instrument or equipment that makes use of artificial

frictional resistance to stop the motion of a moving member. While performing

this function, the brakes imbibe potential energy or kinetic energy of the moving

member. The energy that is absorbed by the brakes is dissipated in the form of

heat. The dissipated heat is in turn liberated into the surrounding atmosphere.

Braking Requirements

1. Brakes should be a good anti wear resistant.

2. While braking the driver should have good control over the vehicle i.e. the

vehicle should not skid.

3. Brakes of a vehicle should be strong so that it can stop a vehicle in

minimum time.

4. Brakes should have good anti fade characteristics.

Classification of brakes

1. Hydraulic brakes

2. Electric brakes

3. Mechanical brakes

Radial Brakes

Axial Brakes

Radial Brake. Then force acting on brake drum is in radial direction for

Radial brakes. These brakes are of two types: Internal Brakes and external brakes.

Axial Brakes. The force acting on the brake drum is in axial direction for

axial brakes.

Disc Brake

A disc break is a device, composed of cast iron or ceramic composites that

are connected to the wheel hub or axle and a caliper. In order to stop the wheel

hub, friction views of Disc Brake Rotor are shown in the figure 1(a) and 1(b).

Principle

Disc brake is a very essential brake application device in a vehicle. This part

of the brake helps in the slowing and stopping the motion of the vehicle. The

principle of disc brake is to produce a braking force on the brake pads which in

turn compresses the rotating disc.

Working

The main components of a disc brake are:

1. Rotor

2. Brake Pads

3. Caliper

Rotor. The disc rotor is connected to the wheel and it rotates with respect

to the wheel. When brakes are applied, the brake pads come in contact with the

rotor in order to stop or slow down the vehicle.

(a)

Brake pads. Brake pads are present in the disc which scrapes against the

disc that rotates with the wheel hub and creates high friction.

Caliper. A caliper is a motionless housing which is clipped to the frame of a

vehicle containing a piston. This piston forces the pads onto the rotor in order to

stop or slow down the vehicle.

In order to bring the and dissipated into the surrounding atmosphere.

Applications of Disc brakes

1. Cars

2. Motorcycles

3. Bicycles

Assumptions

1. Brakes are applied on four wheels.

2. Thickness of 0.5mm is considered for all the models.

3. Only ambient cooling is considered for dissipation of heat.

4. This analysis does not determine the life of the disc brake

5. The disc brake model used is of solid type.

6. The thermal conductivity of the material is uniform throughout.

7. The specific heat of the material is constant throughout and does not

change with the temperature.

8. The kinetic energy of the vehicle is lost through disc brakes i.e. there is no

heat loss between the tire and the road side.

Project Statement

This project deals with the analysis and optimization of disc brake rotor

using ANSYS 10.0 software.

Objective

For analysis, the axis symmetric model of disc brake is carried out using

ANSYS 10.0 software.

1. A transient thermal analysis is carried out using direct time

integration technique of 4 seconds.

2. Static structure analysis coupled with thermal solution is carried

out.

3. Different combinations of flange width-8mm, 10mm and 12mm and

materials-Cast iron, Aluminum and Aluminum composites are

considered.

Deliverables

1. Minimum temperature at the contact surface of the disc brake

rotor is observed.

2. Minimum Von Mises stress is observed.

3. A graph is plotted between Distance on X-axis and Temperature on

Y-axis.

4. Obtained results are compared and analyzed to arrive at the best

possible combination.

Chapter 2

LITERATURE REVIEW

Finite Element Method

Introduction

Finite Element Method (FEM) is also called as Finite Element Analysis

(FEA). Finite Element Method is a basic analysis technique for resolving and

substituting complicated problems by simpler ones, obtaining approximate

solutions Finite element method being a flexible tool is used in various industries

to solve several practical engineering problems. In finite element method it is

feasible to generate the relative results.

In the present day, finite element method is one of the most effective and

widely used tools. By doing more computational analysis the approximate

solution can be improved or refined in Finite element method.

The fundamental areas that have to be mastered for finite element

method include:

1. Matrix algebra

2. Solid mechanics

3. Variational methods

4. Computer skills

In Finite element method, the method.

FEM/FEA helps in evaluating complicated structures in a system during the

planning stage. The strength and design of the model can be improved with the

help of computers and FEA which justifies the cost of the analysis. FEA has

prominently increased the design of the structures that were built many years

ago.

General Description of FEM

To acquire a solution for a continuum problem by FEM, the procedure

follows an orderly step by step process. The step- by step procedure is as follows:

Discretization of the Structure. The first step involves dividing the

structure into elements. Therefore suitable finite element should be used to

model the structure.

Selection of a proper interpolation or displacement model. Since the

displacement solution is not known exactly for a complex structure under any

given load, we assume an form.

Derivation of element stiffness matrices and load vector. From the second

step, stiffness matrix [k^ (e)] and load vector P^ (e) of element e is solved from

either equilibrium conditions or variation principle.

Assemblage of element equations to obtain the overall equilibrium

equation.

Since the structure is divided into several finite elements, load vector and

individual element stiffness matrices are arranged in a suitable manner. From

this, the overall equilibrium equation is formulated as

[K]φ = P

~ ~ ~

Where [k] = assembled stiffness matrix

~

φ = vector of nodal displacement

~

P = vector of nodal forces for the complete structure

~

Solution for unknown nodal displacement. The overall equilibrium

equation is modified so that it is suitable for boundary condition of a particular

problem. After the boundary condition is modified, the equilibrium equation is

represented as

→ →

[K] φ = P

Computation of element strains and stresses. Since φ is known, element strain and

stress are computed using necessary equations.

Engineering Applications of Finite Element Method

Initially FEM method was used for only structural mechanics problems but

over the years researchers have successfully applied it to various engineering

problems. It has been validated that this method can be used for other numerical

solution of ordinary and partial differential equations.

The finite element method is applicable to three categories of boundary

value problems:

Equilibrium or Steady State or Time-Independent problems

Eigen value problems

Propagation or transient problems

Various applications of FEM:

1. Civil Engineering Structures

2. Aircraft Structures

3. Heat Conduction

4. Geomechanics

5. Hydraulic and Water Resource Engineering

6. Nuclear engineering

7. Bio-Medical Engineering

8. Mechanical Engineering

9. Electrical Machines and Electromagnetic

Advantages of FEA/FEM

1. Non-linear problems are easily solved.

2. Several types of problems can be solved with easy formulation.

3. Reduces the costs in the development of new products.

4. Improves the quality of the end product.

5. Life of the product is increased.

6. Rapid development of new products

7. High product reliability.

8. Product fabrication process is enhanced.

Disadvantages of FEA/FEM

1. Extreme aspect ratios can cause problems.

2. Not well suited for open region problems.

FEA Software-ANSYS

Introduction to ANSYS

ANSYS stands for Analysis System Product. Dr. John Swanson was the

founder of ANSYS Inc. in the year 1970. ANSYS was founded in order to establish

a technology that facilitates several companies/industries to compute or simulate

analysis issues. The screenshot of ANSYS user interface is shown in Figure 2.

ANSYS is a out equations that regulate the performance of these elements and

solves them resulting in an overall description of how the system works

integrally. The obtained results are displayed in a tabulated or graphical form.

This type of system is used for optimization of systems.

Figure 2 Screenshot of ANSYS User Interface

Analysis Types Available

The different type Linear buckling

Non linear buckling

1. Structural non linearity

2. Static and dynamic kinematics analysis

3. Thermal analysis

4. Electromagnetic field analysis

5. Electric field analysis

6. Fluid flow analysis

Computational fluid dynamics

Pipe flow

7. Coupled- THERMAL ANALYSIS