lava final report

ANALYSIS OF GAS TURBINE ROTOR DISC

CHAPTER 1 INTRODUCTION

The gas turbine is a rotating internal combustion engine, which takes air from the

atmosphere and compresses it to a higher pressure in an axial compressor (compressor

section) and the compressed air flow into combustion chamber where fuel is admitted and

ignited with the help of a sparkplug the products of combustion are used as a working

fluid for developing power in the turbine section of the gas turbine.

Generally heavy-duty alloy gas turbine is a bolted construction made up of forged

compressor and turbine wheels, distance pieces (junction between compressor and

turbine), spacers (between some of the turbine wheel) and stub shafts.

For efficient functioning of gas turbine proper design of rotor is essential. The

most critical components in the rotor are the turbine wheels (discs) because of combined

conditions of elevated temperatures and requirements for strength and toughness. Further,

unlike the aircraft gas turbine, these wheels (discs) are of very large diameter and section

thickness.

Gas turbine discs are mainly subjected to centrifugal stresses with high

temperature gradients. In the present work the net effects of superposed thermal and

structural stresses, and the effect of pre-stressing on stress distribution in the disc is

investigated with the help of a finite element software ANSYS.

Department of Mechanical engineering (CAD/CAM)


TYPES OF GAS TURBINES

1.1 JET ENGINES

Diagram of a gas turbine jet engine

Air breathing jet engines are gas turbines optimized to produce thrust from the

exhaust gases, or from ducted fans connected to the gas turbines. Jet engines that produce

thrust primarily from the direct impulse of exhaust gases are often called turbojets,

whereas those that generate most of their thrust from the action of a ducted fan are often

called turbofans or (rarely) fan-jets.

Gas turbines are also used in many liquid propellant rockets, the gas turbines are

used to power a turbo pump to permit the use of lightweight, low pressure tanks, which

saves considerable dry mass.

1.2 AERODERIVATIVE GAS TURBINES

Diagram of a high-pressure turbine blade


http://en.wikipedia.org/wiki/Jet_engine

http://en.wikipedia.org/wiki/Turbine_blade

http://en.wikipedia.org/wiki/Turbopump

http://en.wikipedia.org/wiki/Turbofan

http://en.wikipedia.org/wiki/Turbojet

http://en.wikipedia.org/wiki/Ducted_fan


http://en.wikipedia.org/wiki/File:Jet_engine.svg

http://en.wikipedia.org/wiki/File:GaTurbineBlade.svg


Aeroderivatives are also used in electrical power generation due to their ability to

be shut down, and handle load changes more quickly than industrial machines. They are

also used in the marine industry to reduce weight. The General Electric LM2500, General

Electric LM6000, Rolls-Royce RB211 and Rolls-Royce Avon are common models of this

type of machine.

1.3 AMATEUR GAS TURBINES

Increasing numbers of gas turbines are being used or even constructed by

amateurs. In its most straightforward form, these are commercial turbines acquired

through military surplus or scrapyard sales, then operated for display as part of the hobby

of engine collecting. In its most extreme form, amateurs have even rebuilt engines

beyond professional repair and then used them to compete for the Record. The simplest

form of self-constructed gas turbine employs an automotive turbocharger as the core

component. A combustion chamber is fabricated and plumbed between the compressor

and turbine sections.

More sophisticated turbojets are also built, where their thrust and light weight are

sufficient to power large model aircraft. The Schreckling design constructs the entire

engine from raw materials, including the fabrication of a centrifugal compressor wheel

from plywood, epoxy and wrapped carbon fibre strands.

Like many technology based hobbies, they tend to give rise to manufacturing

businesses over time. Several small companies now manufacture small turbines and parts

for the amateur. Most turbojet-powered model aircraft are now using these commercial

and semi-commercial microturbines, rather than a Schreckling-like home-build.

1.3.1 Auxiliary power units

APUs is small gas turbines designed for auxiliary power of larger machines, such

as those inside an aircraft. They supply compressed air for aircraft ventilation (with an

appropriate compressor design), start-up power for larger jet engines, and electrical and

hydraulic power.



http://en.wikipedia.org/wiki/Aircraft

http://en.wikipedia.org/wiki/Auxiliary_power_unit

http://en.wikipedia.org/wiki/Kurt_Schreckling

http://en.wikipedia.org/wiki/Turbocharger

http://en.wikipedia.org/wiki/Rolls-Royce_Avon

http://en.wikipedia.org/wiki/Rolls-Royce_RB211

http://en.wikipedia.org/wiki/General_Electric_LM6000




1.3.2 Industrial gas turbines for power generation

GE H series power generation gas turbine: in combined cycle configuration, this

480-megawatt unit has a rated thermal efficiency of 60%. Industrial gas turbines differ

from aeroderivative in that the frames, bearings, and blading are of heavier construction.

Industrial gas turbines range in size from truck-mounted mobile plants to enormous,

complex systems They can be particularly efficient—up to 60%—when waste heat from

the gas turbine is recovered by a heat recovery steam generator to power a conventional

steam turbine in a combined cycle configuration. They can also be run in

a cogeneration configuration: the exhaust is used for space or water heating, or drives

an absorption chiller for cooling or refrigeration. Such engines require a dedicated

enclosure, both to protect the engine from the elements and the operators from the noise.

The construction process for gas turbines can take as little as several weeks to a

few months, compared to years for plants. Their other main advantage is the ability to be

turned on and off within minutes, supplying power during peak demand. Since single

cycle (gas turbine only) power plants are less efficient than combined cycle plants, they

are usually used as peaking power plants, which operate anywhere from several hours per

day to a few dozen hours per year, depending on the electricity demand and the

generating capacity of the region. In areas with a shortage of base load and load

following power plant capacity or low fuel costs, a gas turbine power plant may regularly


http://en.wikipedia.org/wiki/Load_following_power_plant

http://en.wikipedia.org/wiki/Load_following_power_plant

http://en.wikipedia.org/wiki/Peaking_power_plant

http://en.wikipedia.org/wiki/Gas-absorption_refrigerator

http://en.wikipedia.org/wiki/Cogeneration

http://en.wikipedia.org/wiki/Combined_cycle

http://en.wikipedia.org/wiki/Thermodynamic_efficiency

http://en.wikipedia.org/wiki/Megawatt

http://en.wikipedia.org/wiki/Combined_cycle

http://en.wikipedia.org/wiki/File:GE_H_series_Gas_Turbine.jpg


operate during most hours of the day. A large single cycle gas turbine typically produces

100 to 400 megawatts of power and has 35–40% thermal efficiency.

1.3.3 Compressed air energy storage

One modern development seeks to improve efficiency in another way, by

separating the compressor and the turbine with a compressed air store. In a conventional

turbine, up to half the generated power is used driving the compressor. In a compressed

air energy storage configuration, power, perhaps from a wind farm or bought on the open

market at a time of low demand and low price, is used to drive the compressor, and the

compressed air released to operate the turbine when required.

1.3 .4 Turbo shaft engines

Turbo shaft engines are often used to drive compression trains (for example in gas

pumping stations or natural gas liquefaction plants) and are used to power almost all

modern helicopters. The first shaft bears the compressor and the high speed turbine (often

referred to as "Gas Generator" or "Ng"), while the second shaft bears the low speed

turbine (or "Power Turbine" or "Nf" - the 'f' stands for 'free wheeling turbine' on

helicopters specifically due to the fact that the gas generator turbine spins separately from

the power turbine). This arrangement is used to increase speed and power output

flexibility.

1.4 RADIAL GAS TURBINES

In 1963, Jan Mowill initiated the development at Kongsberg

Våpenfabrikk in Norway. Various successors have made good progress in the refinement

of this mechanism. Owing to a configuration that keeps heat away from certain bearings

the durability of the machine is improved while the radial turbine is well matched in

speed requirement.

1.5 SCALE JET ENGINE

Scale jet engines are scaled down versions of this early full scale engine. Also

known as miniature gas turbines or micro-jets. With this in mind the pioneer of modern

Micro-Jets, Kurt Schreckling, produced one of the world's first Micro-Turbines, the


http://en.wikipedia.org/wiki/Kurt_Schreckling

http://en.wikipedia.org/wiki/Norway

http://en.wikipedia.org/wiki/Kongsberg_V%C3%A5penfabrikk

http://en.wikipedia.org/wiki/Kongsberg_V%C3%A5penfabrikk

http://en.wikipedia.org/w/index.php?title=Jan_Mowill&action=edit&redlink=1

http://en.wikipedia.org/wiki/Turboshaft

http://en.wikipedia.org/wiki/Thermodynamic_efficiency


FD3/67. This engine can produce up to 22 Newton’s of thrust, and can be built by most

mechanically minded people with basic engineering tools, such as a metal lathe.

1.5.1 Microturbines

Also known as:

Turbo alternators

MicroTurbine

Turbogenerator

Microturbines are becoming widespread for distributed power and combined heat

and power applications. They are one of the most promising technologies for

powering hybrid electric vehicles. They range from hand held units producing less than

a kilowatt, to commercial sized systems that produce tens or hundreds of kilowatts. Basic

principles of microturbine are based on micro combustion.

Part of their success is due to advances in electronics, which allows unattended

operation and interfacing with the commercial power grid. Electronic power switching

technology eliminates the need for the generator to be synchronized with the power grid.

This allows the generator to be integrated with the turbine shaft, and to double as the

starter motor.

Microturbine systems have many advantages over reciprocating

engine generators, such as higher power-to-weight ratio, low emissions and few, or just

one, moving part. Advantages are that microturbines may be designed with foil

bearings and air-cooling operating without lubricating oil, coolants or other hazardous

materials. Microturbines also have a further advantage of having the majority of the

waste heat contained in the relatively high temperature exhaust making it simpler to

capture, whereas the waste heat of reciprocating engines is split between its exhaust and

cooling system.

However, reciprocating engine generators are quicker to respond to changes in

output power requirement and are usually slightly more efficient, although the efficiency


http://en.wikipedia.org/wiki/Coolant

http://en.wikipedia.org/wiki/Foil_bearing

http://en.wikipedia.org/wiki/Foil_bearing

http://en.wikipedia.org/wiki/Power-to-weight_ratio

http://en.wikipedia.org/wiki/Reciprocating_engine

http://en.wikipedia.org/wiki/Reciprocating_engine

http://en.wikipedia.org/wiki/Micro_combustion

http://en.wikipedia.org/wiki/Kilowatt

http://en.wikipedia.org/wiki/Hybrid_electric_vehicle



http://en.wikipedia.org/wiki/Distributed_generation

http://en.wikipedia.org/wiki/Metal_lathe

http://en.wikipedia.org/wiki/Newton_(unit)


of microturbines is increasing. Microturbines also lose more efficiency at low power

levels than reciprocating engines.

When used in extended range electric vehicles the static efficiency drawback is

irrelevant, since the gas turbine can be run at or near maximum power, driving an

alternator to produce electricity either for the wheel motors, or for the batteries, as

appropriate to speed and battery state. The batteries act as a "buffer" (energy storage) in

delivering the required amount of power to the wheel motors, rendering throttle response

of the GT completely irrelevant. There is, moreover, no need for a significant or variable-

speed gearbox; turning an alternator at comparatively high speeds allows for a smaller

and lighter alternator than would otherwise be the case. The superior power-to-weight

ratio of the gas turbine and its fixed speed gearbox, allows for a much lighter prime

mover than those in such hybrids as the Toyota Prius (which utilised a 1.8 litre petrol

engine) or the Chevrolet Volt (which utilises a 1.4 litre petrol engine). This in turn allows

a heavier weight of batteries to be carried. The weight can be made up of more batteries,

which allows for a longer electric-only range. Alternatively, the vehicle can use heavier

types of batteries such as lead acid batteries (which are cheaper to buy) or safer types of

batteries such as Lithium-Iron-Phosphate.

When gas turbines are used in extended-range electric vehicles, like those planned

by Land-Rover/Range-Rover in conjunction with Bladon, or by Jaguar also in partnership

with Bladon, the very poor throttling response (their high moment of rotational inertia)

does not matter, because the gas turbine, which may be spinning at 100,000 rpm, is not

directly, mechanically connected to the wheels. It was this poor throttling response that

so bedevilled the 1960 Rover gas turbine-powered prototype motor car, which did not

have the advantage of an intermediate electric drive train.

Gas turbines accept most commercial fuels, such as gasoline, natural

gas, propane, diesel, and kerosene as well as renewable fuels such

as E85, biodiesel and biogas. However, when running on kerosene or diesel, they will

typically be unable to start without the assistance of a more volatile product, such as

propane gas.


http://en.wikipedia.org/wiki/Biogas

http://en.wikipedia.org/wiki/Biodiesel

http://en.wikipedia.org/wiki/E85

http://en.wikipedia.org/wiki/Renewable_fuels

http://en.wikipedia.org/wiki/Kerosene

http://en.wikipedia.org/wiki/Diesel_fuel

http://en.wikipedia.org/wiki/Propane

http://en.wikipedia.org/wiki/Natural_gas

http://en.wikipedia.org/wiki/Natural_gas

http://en.wikipedia.org/wiki/Gasoline

http://en.wikipedia.org/wiki/Lithium_iron_phosphate_battery


Microturbine designs usually consist of a single stage radial compressor, a single

stage radial turbine and a recuperator. Recuperators are difficult to design and

manufacture because they operate under high pressure and temperature differentials.

Exhaust heat can be used for water heating, space heating, drying processes or absorption

chillers, which create cold for air conditioning from heat energy instead of electric

energy.

Typical microturbine efficiencies are 25 to 35%. When in a combined heat and

power cogeneration system, efficiencies of greater than 80% are commonly achieved.

MIT started its millimeter size turbine engine project in the middle of the 1990s when

Professor of Aeronautics and Astronautics Alan H. Epstein considered the possibility of

creating a personal turbine which will be able to meet all the demands of a modern

person's electrical needs, just as a large turbine can meet the electricity demands of a

small city.

Problems have occurred with heat dissipation and high-speed bearing in these

new microturbines. Moreover, their expected efficiency is a very low 5-6%. According to

Professor Epstein, current commercial Li-ion rechargeable batteries deliver about 120-

150 W·h/kg. MIT's millimeter size turbine will deliver 500-700 W·h/kg in the near term,

rising to 1200-1500 W∙h/kg in the longer term.

1.6 Literature review

Although the name of the finite element method is given recently, the concept has

been used several centuries back. For, example ancient mathematics found the

circumstances of circle by approximated it as a polygon. In terms of the present day

notation each side of the polygon can be called a “finite element”. By considering the

approximating polygon inscribed or circumscribed, one can obtain a lower bound or an

upper bound for the true circumference. Further, as the number of the sides of the

polygon is increased, the approximate values converge to the true value. These

characteristics will hold true in any general finite element application. In recent times R.

Courant first suggested an approach similar to the finite element method, involving the


http://en.wikipedia.org/wiki/MIT


http://en.wikipedia.org/wiki/Absorption_chiller

http://en.wikipedia.org/wiki/Absorption_chiller

http://en.wikipedia.org/wiki/Recuperator

http://en.wikipedia.org/wiki/Radial_turbine

http://en.wikipedia.org/wiki/Radial_compressor


use of piece wise continuous functions defined over triangular regions, in 1943 in the

literature of applied mathematics.

M.J. Tumer, R.W, today has presented the finite element method as known in

1956 by M.J. Tumer, R.W.Clough, H.C. Martin and L.J. Troop. This paper presents the

application of simple finite elements (pin-jointed bar and triangular plate with in plane

loads) for the analysis of aircraft structure and is considered as one of the key

contributions in the development of the finite element method. The digital computer

provides a rapid means of performing the many calculations involved in the finite

element analysis and made the method practically viable. Along with the development of

high-speed digital computers, the application of the finite element method progressed at

very impressed rate.

The books by Prsemienecki and Zienkiewicz and Hoister presented finite element

method as applied to the solutions of stress analysis problems. The book by Zienkiwicz

and Cheung “The finite element method in structural and continuum mechanics”, (Mc-

Graw Hill, London, 1971) presented the broad interpretation of the finite element

method, and its applicability to any general field problem. With this broad interpretation

of the finite element method, it has been found that the finite element equation also

derived by using a weighted residual method or least square method. This led to wide

spread interest among applied mathematicians in applying the finite element method for

the solution of linear differential equations. Over the years several papers, conference

proceedings and books have been published on this subject. With all this progress, today

engineers and scientists consider the finite element method as one of the well established

and convenient analyses tools.



CHAPTER 2 GAS TURBINE

2.1 PRINCIPLE OF GAS TURBINEThe gas turbine is a rotating internal combustion engine, which takes air from the

atmosphere and compresses it to a higher pressure in an axial compressor (compressor

section) and the compressed air flow into combustion chamber where fuel is admitted and

ignited with the help of a sparkplug the products are used as a working fluid for

developing power in the turbine section of the gas turbine.

Fig 2.1 structure of gas turbine

2.2 BASIC THERMO DYNAMIC PRINCIPLES OF GAS TURBINE OPERATION

A schematic diagram for a single shaft, simple cycle gas turbine is shown in

figure 3. Air enters at a point of 1 in schematic at ambient conditions. Since it vary from

day to day from location to location, it is necessary to consider some standard conditions.



The standard conditions used by industry are ISO conditions of 14.7psi and 60% of

relative humidity.

The air is compressed to some higher pressure in the compressor no heat is added;

how ever, the temperature of the air rises because of the compression, so that the air at

the discharge of the axial flow compressor has both its temperature and pressure

increased.

Upon leaving the compressor, the air enters the combustion system at point 2,

where fuel is injected and combustion takes place. The combustion process occurs

essentially at constant pressure, although very high local temperatures are reached with in

the primary combustion zone (approaching stoichiometric conditions), the combustion

system is designed to provide mixing, dilution and cooling. Thus by the time the

combustion mixture leaves the combustion system and enters the turbine at point 3, it is

at some mixed average temperature.

In the turbine section of the gas turbine, the energy of the hot gases is converted

into work. This conversion actually takes into two steps. In the nozzle section of the

turbine, the hot gases are expanded and thus a portion of the thermal energy is converted

into kinetic energy. In the subsequent bucket section of the turbine, a portion of the

Fig 2.2 Gas Turbine Engine Position.



Kinetic energy is transferred to the rotating buckets and is converted into the work. Some

of the work developed by the turbine is used to drive the compressor and the remainder is

available for useful work at the output Flange of the gas turbine, typically more than 50%

of the work developed by the turbine section is used to power the axial compressor.

2.3 THE BRAYTON CYCLE

The thermodynamic cycle upon which all gas turbines operate is called the

brayton cycle. Figure 2.1 shows the classical pressure-volume (p-v) diagram and

temperature- entropy (T-S) diagrams for this cycle.

Path 1 to 2 represents the compression that takes place in the compressor, path 2

to 3 represents the constant pressure addition of heat in the combustion section, and path

3 to 4 represents the expansion that takes place in the turbine.

Fig 2.3 Brayton Cycle

The path from 4 back to 1 on the cycle diagrams is indicative of a constant

pressure cooling process taking place. In the gas turbine this cooling is taken care by the

atmosphere, which provides fresh cool air at point 1 on a continuous basis in exchange



for hot gases exhausted to the atmosphere at a point 4. The actual cycle is an “open”

rather than “closed” cycle as indicated.

Brayton cycle can be characterized by two very significant parameters:

i. Pressure ratio

ii. Firing temperatur

2.3.1 Pressure Ratio

The pressure ratio of the cycle is the pressure at point 2 (compressor discharge

pressure). In an ideal cycle this pressure ratio is also equal to the pressure at point 3

divided by the pressure at point 4. How ever in actual cycle there is some slight pressure

losses in the combustion system and hence the pressure at point 3 is slightly less than at

point 2.

2.3.2 Firing Temperature

The firing temperature is the highest temperature reached in the cycle. As per

company definition firing temperatures as the mass-flow mean total temperature at the

first stage nozzle trailing edge plane.

In gas turbines without first stage turbine nozzle cooling (in which air enters the hot

gas stream after cooling the nozzle) the total temperature immediately down stream of the

nozzle would be the same as the temperature immediately up stream of the nozzle. With

turbine nozzle cooling, this cooling air mixes with the hot gases expanding through the

nozzle and thus tends to reduce the total temperature existing in the nozzle.

From this definition this temperature is the indicative of the point 3 in the cycle. The

pressure ratio resulting in maximum out put and maximum efficiency changes with firing

temperature, and the higher the pressure ratio, the greater the advantage obtained from

increased firing temperature.

2.4 THE COMPONENTS OF A GAS TURBINE

The major components of a gas turbine are the compressor, combustion system

and turbine section. These are dealt in detail in following sections:

2.4.1 Compressor



The gas turbine compressor is an axial flow design of sub sonic type that

efficiently compresses a large volume of air. The compressor consists of many individual

stages operating in series. Each compressor stage consist of a rotating row of blades (air

foil), that increases the velocity of the incoming air there by increasing its kinetic energy,

followed by a stationary row of blades that acts as a diffusers, converting kinetic energy

to pressure increase. The number of stages used for a particular gas turbine compressor

depends upon the design pressure ratio of the turbine. Typical pressure ratio changes

from 6:1 to 14.9:1.

At the compressor inlet there is a row of stationary blades, called inlet guide

vanes (IGV’S) that direct the incoming air on to the first rotating stage in a smooth way.

In some compressor the flow angle of the IGV’s can be changed to control the volume of

air being drawn into the compressor. The variable inlet guide vanes (VIGV’s) are used to

ensure aerodynamically smooth operating compressor through out a large operating

range.

At the compressor discharged, there are several rows of stationary diffuser blades

and a cone shaped diffuser to obtain maximum pressure raise before the air goes into the

combustion system.

2.4.2 Combustion System

The combustion system consists of several liners into which fuel is added and

brunt with a portion of compressed air. The excess compressed air is used to limit the

temperature level usable by the turbine. The individual liners are connected to the turbine

section by transition places. Fuel is injected into each liner by fuel nozzles that atomize

the fuel for effective burning. Electric igniters ignite the fuel initially. Once the fire is

started, the combustion process is self-sustaining as long as the fuel and air are available.

2.4.3 Turbine Section

The turbine consists of a several stages. Each stage comprises of stationary row of

nozzles where, the velocity of the high energy gases is increased and directed towards a

rotating row of buckets (air foils) attached to the turbine shaft. The high velocity gases

impinge on the buckets, converting the kinetic energy of the gas into shaft power.



Varying the amount of fuel injected into the combustion chamber changes the energy

from the combustion system available to drive the turbine.

2.5 GAS TURBINE ROTOR

The gas turbine rotors basically have two major parts:

1) Compressor Part, which is commonly called as ‘compressor rotor’. This part is

made out of individually bladed compressor wheels, which are assembled

together with tie bolts. It may be noted that these compressor wheels are not

mounted on a shaft (like mounting impellers on centrifugal compressor shaft), but

are held together by radially positioning them by press fit (called rabit) near their

bore and axially keeping them compressed by the tie-bolts (18 no’s) running all

along the full length of compressor rotor.

2) Turbine Part, which is commonly called as ’turbine rotor’. The turbine rotor is

made out of ‘distance piece, and turbine wheels (discs), which are assembled

(bolted) together.

The above two parts i.e. the compressor rotor and the turbine rotors are bolted

together to form the gas turbine rotor, which is also known as unit rotor.

A gas turbine rotor generally has the following characteristics:

1) Long life and need little maintenance.

2) No site balancing required.

3) Built up construction so that the damaged parts can be replaced.

4) Highest possible safety factors.

5) Easy approach to various parts of inspection.

In particular the disc type built-up rotors have the following advantages:

1) Reduced size of the forgings which allows exploiting the best properties of the

material.

2) Possibility of designing the discs with uniform strength offering the advantage of

low stresses.

3) Easy replacement of buckets in case of damage.



4) Possibility of pre-stressing the disc by creating plastic strains at the bore by

spinning at high speed.

Fig 2.4 gas turbine rotor disc2.5.1 Critical Issue Related To the Design of the Gas Turbine Rotor Disc



As discussed in the earlier section the gas turbine rotor disc is one of the critical

components of gas turbine rotor because of large diameter and section thickness and also

subjected to high temperature gradients.

In summary, the following are the forces acting on the rotor disc.

1) Centrifugal stresses due to its own rotating mass.

2) Centrifugal stresses due to the mass of the blades mounted on the wheel (disc)

3) The thermal stresses due to the temperature gradients induced during the

operation.

4) Stresses due to the rotor vibration.

In the present work only 1 and 3 types of forces are considered for the stress analysis

of the disc.

As the rotor rotates at a high speed, the stresses at the bore become

critical, as the disc diameter is large. This is the source for centrifugal stresses developed

in the disc.The compressor rotor is subjected to lower temperature and hence relatively

less critical and the turbine rotor is exposed to the hot combustion gases and hence more

critical in the view of thermal stresses.

2.5.2 Turbine Wheel Processes

Each turbine wheel (disc) is spin tested prior to its installation into a rotor. Alloy

steel wheels, because of the brittle-to-ductile transition phenomena, are first spun cold to

verify the absence of critical size defects. All wheels, including cold spun steel wheels,

are hot spun at bore stresses slightly above their yield strength.

To induce residual compressive stresses in the bore region these spinning

operations, in addition to the stringent, non-destructive testing performed both before and

after spin testing provides maximum assurance against brittle fracture in service.

2.5.3 Turbine Rotor Disc Materials

Material selection for these critical rotating applications is dictated by the

operating temperatures and by physical and mechanical property requirements. Including

high proof strength, tensile ductility, low creep extension, fracture toughness, resistance

to crack propagation and high and low cycle fatigue strength. Comparing candidate disc

materials, titanium and its alloy are the strongest available but offer poor oxidation



resistance above 900degF, and are the most expensive. The Ni-Cr-Fe alloys (WASPLAY,

INCONEL ALLOY 718 AND NIMONIC ALLOY 901) offer the most cost effective

range of selection for aircraft engines. Steels are cheaper and are used where power to

weight ratio’s are less important, such as in heavy duty land based engines, even in that

market, the trend is to the high performance nickel base alloy, INCONEL ALLOY 706

and INCONEL ALLOY 718. In the present work the turbine rotor disc is made up of

B50A368 (HY 19467).

The composition of the disc is as follows:

1) carbon – 0.2 to 0.3%

2) chromium – 0.35 to 1.25%

3) molybdenum – 1.0 to 1.5%

4) Vanadium – 0.2%

The yield strength of the material at 0.2% yield = 130N/mm2

CHAPTER 3


3.1 PROBLEM DESCRIPTION

The gas turbine rotor consists of individual discs, stub shafts and distance pieces

stacked and bolted together. As the disc diameter is large and speeds are high and the

centrifugal stresses are high.

The gas turbine discs are normally operated at such high temperatures that the

materials used are at low strength levels. The hot gas contacts the blades and rim of the

turbine rotor and thus maintains the rim at high temperatures. Various cooling methods

have been used to reduce the temperature of the disc but as the rim is always in contact

with hot gases it remains at high temperature whereas cooling decrease the temperature

of the central portion of the rotor and thus increase the temperature gradients. These

temperature gradient gradients are the source for the thermal stresses that causes the



thermal stress distribution in the gas turbine disc to differ widely from those encountered

in the steam turbines which are mainly subjected to centrifugal stresses with small

temperature gradients.

Thus in actual working conditions both these structural as well as thermal stress

are combined acting on the gas turbine rotor disc. If these stresses exceed the threshold

limit of the gas turbine it will cause disc failure.

3.2 PRESENT WORK

The first and foremost task in the present work is the collection of data and

drawings of the gas turbine rotor disc and boundary conditions of the disc to be inputted

are collected and heat transfer coefficients on the disc surface etc.,

As the shape of the gas turbine rotor disc is not simple it is difficult to calculate

the stresses and temperatures of gas turbine rotor disc using analytical methods. Hence

ANSYS a finite element package is used to calculate the temperatures and stresses.

The solution process for finding the resultant stresses which are developed due to

both temperature gradients and structural loads involves two steps. The output of first

solution contains the information about the temperature distribution among all the nodes

of model which is solved by thermal analysis module of ANSYS and can be viewed by

using post processor phase of the ANSYS.

The output of first solution is given as input in the form of .RTH file and the

inertia load for stress analysis of gas turbine rotor disc to calculate the resultant stresses

using structural analysis module.

The cross sectional view of the gas turbine rotor disc which is considered for the

analysis is shown in the figure.

The basic data has been collected from different sources and geometry is drafted

based on the dimensions available in the drawings. The geometry is then meshed property

to divide it into elements and nodes using proper element type. In this work we are using

PLANE 77 element. After meshing the model boundary conditions are applied on the

disc. After applying all boundary conditions the model is solved by using solution

process.

The following are the assumption is made in this project



Steady state flow analysis

3.4 BOUNDARY CONDITIONS

Convection = 0.004 W/m2.K

Reference temperature = 30 0C

Boundary temperatures = 700,1000C

3.5 INPUT DATA USED FOR ANALYSIS

FOR MATERIAL B50A368

Density of material = 7.85x10 -9 kg/mm3

Young’s modulus = 2x105 MPa

Poisson’s ratio = 0.3

Thermal conductivity = 0.036 W/mm.K

Specific heat = 1000 J/kg.K

Operating speed = 450 radians/s

Bulk temperature = 350C

Thermal expansion Coefficient = 12x10-6

FOR MATERIAL 1IN718

Density of material = 8.19 x10 -9 kg/mm3

Young’s modulus = 1.7 x105 MPa

Poisson’s ratio = 0.3

Thermal conductivity = 0.0114 W/mm.K

Specific heat = 435 J/kg.K

Operating speed = 450 radians/s

Bulk temperature = 350C

Thermal expansion Coefficient = 14 x10-6

3.6 PROCEDURE FOR ANALYSIS

Our analysis procedure starts by setting the preferences to structural and thermal

and defining the element type and consider it as an axisymmetric model. Define the

material properties for the materials we are using. As our analysis is a coupled-field

analysis we set the physics environment to both thermal and structural and define loads in



both the environments. The final step in the procedure is solving the model and viewing

the results in post processor through contour plots and list results.

PREFERENCES > STRUCTURAL, THERMAL

PREPROCESSOR >

ELEMENT TYPE > ADD/EDIT/DELETE > ADD > THERMAL

MASS > SOLID > 8node 77 > OPTIONS > ELEMENT

BEHAVIOUR > AXISYMMETRIC

MATERIAL PROPERTIES > MATERIAL MODELS > THERMAL >

THERMAL CONDUCTIVITY > SPECIFIC HEAT

MODELLING > CREATE > KEY POINTS > AREAS



Fig 3.1: 2D Component of Gas Turbine Rotor Disc

MESHING > MESH > AREAS > FREE MESH

PHYSICS > ENVIRONMENT > WRITE > TITLE > THERM > CLEAR > OK

ELEMENT TYPE > SWITCH TO ELEMENT TYPE > THERMAL TO STRUCT> ELEMENT TYPE > ADD/EDIT/DELETE > OPTIONS > AXISYMMETRIC

MATERIAL PROPERTIES > MATERIAL MODELS > STRUCTURAL > LINEAR > ELASTIC > ISOTROPIC > YOUNG’S MODULUS > POISSIONS RATIODENSITY THERMAL EXPANSION > SECANT COEFFICIENT

PHYSICS > ENVIRONMENT > WRITE > STRUCT READ > THERM



LOADS > DEFINE LOADS > APPLY > THERMAL > TEMPERATURE > ON NODESCONVECTION > ON LINES > COVNECTION COEFFICIENT > BULK TEMPERATURESETTINGS > REFERENCE TEMPERATURE

PHYSICS > ENVIRONMENT > READ > STRUCT

LOADS > DEFINE LOADS > APPLY > STRUCTURAL > DISPLACEMENT > ON NODESINERTIA > ANGULAR VELOCITY > GLOBAL

FINISH

SOLUTION > SOLVE > CURRENT LS

GENERAL POST PROCESSOR > PLOT RESULTS > CONTOUR PLOT > NODAL SOLUTIONLIST RESULTS > NODAL SOLUTION

FIG. 3.2 Meshed ComponentFigure 3.2 is the meshed component of the gas turbine rotor disc.



FIG. 3.3 Loads on FE model



CHAPTER 4

FINITE ELEMENT METHOD

The basic idea in the finite element method is to find out the solution of a

complicated problem by replacing it by a simpler one. Since a simple one in finding the

solution replaces the actual problem, we will be able to find only approximate solution

rather than the exact solution. More over, in the finite element method, it will often be

possible to improve or refine the approximate solution by spending more computational

effort.

This is a numerical procedure for obtaining solution to many of the problems

encountered in engineering analysis. In the finite element method, the solution region is

considered as build up of many small inter connected sub regions called finite elements.

As an example consider the milling machine structure, it is very difficult to find the exact

response (like stresses and displacements) of the machine under any specified cutting

conditions. This structure is approximated as composed of several pieces in the finite

element method. In each piece or element, a convenient approximate solution is assumed

and the conditions of over all equilibrium of the structure are derived. The satisfaction of

these conditions will yield an approximate solution for the displacements and stresses.

The finite element method may be divided into two phases. The first phase consists of the

study of the individual element. The second phase is the study of the assemblage of

elements representing the entire body.

4.1 ENGINEERING APPLICATION OF FEM

As stated earlier, the finite element method was developed originally for the

analysis of aircraft structures. However, the general nature of its theory makes it

applicable to wide variety of boundary value problems in engineering. A boundary value

problem is one in which a solution is sought in the domain (or region) of a body

subjected to the satisfaction of prescribed boundary (edge) condition on the dependent



variable or their derivatives. Mostly all engineering problems of the finite element,

method comes under three categories of boundary value problems, namely

1) Equilibrium or steady state or time independent problem.

2) Eigen value problem, and

3) Transient or propagation problems.

In an equilibrium problem, we need to find the steady state displacement or stress

distribution if it is a solid mechanics problem temperature or heat flux distribution if it a

heat transfer problem and pressure or velocity distribution if it is a fluid mechanics

problem and mode shape. In fluid mechanics problem, we have to find stability of

laminar flow and resonance characteristics if it is a electrical problem. The transient or

propagation problems are time dependent problems. This type of problems arises, for

example, whenever we are interested in the area of solid mechanics and under sudden

heating or cooling in the field or heat transfer.

4.2 GENERAL DESCRIPTION OF THE FINITE ELEMENT METHOD

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

liquid or gas is represented as an assemblage of subdivisions called finite elements. These

elements are considered to be interconnected at specified joints, which are called nodes or

nodal points. The nodes usually lie on the element boundaries where adjacent elements

are consider to be connected. Since the actual variation of the field variable (like

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

known. 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 field equation

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

the nodal values of the field variable these approximating functions (also called

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

(like equilibrium equations) for whole continuum is written, the new unknown will be the



nodal values of the field variable will be known. Once, these are known the

approximating function define the field variable through out the assemblage of elements.

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

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

can be stated structural problem can be stated as follows:

Step 1: Discretization Of Structure (Domain)

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

region into sub divisions or elements.

Step 2: Selection of a 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

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

simple from computation point of view, and it should satisfy certain convergence

requirements.

Step 3: Derivation of Element Stiffness Matrices (Characteristic Matrices)

And Load Vectors

From assumed displacement model the stiffness matrix [k (e)] and 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 Overall

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 over

all equilibrium equation have to be formulated as

[k]ø=P

Where, [k] is called assembled stiffness matrix, ø is called vector of nodal

displacements and p is the vector of nodal forces for the complete structure.

Step 5: Solution of System Equations to Find Nodal Values Of The



Displacements (Field Variables)

The over all 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]ø=P

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

involving the modification of the stiffness matrix [k] and / or the load vector p.

Step 6: Computation of Element Strains and Stresses

Form the known nodal displacements ø, 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 the brackets implements for the general

FEM step-by-step procedure.

4.3 EXPLANATION OF FEM STEP-BY-STEP

The steps involved in finite element analysis are stated in previous section.

General explanation for each step of the step-by-step procedure of FEM is given in the

following pages.

4.3.1 Discretization of the Domain

The discretization of the domain or solution region into sub regions (finite

elements) is the first in the finite element method. This is equivalent to replacing the

domain having finite number of degrees of freedom by a system having finite number of

degrees of freedom. The process of discretization is essentially an exercise of engineering

judgment. The shapes, size, number and configuration of the elements have to be chosen

carefully such that the original body or domain is simulated as closely as possible without

increasing the computational effort needed for the solution.

4.3.1.1 Basic Element Shapes



For any given physical body we have to use engineering judgment in selecting

appropriate elements for discretization. Mostly the choice of the type of element is

indicated by the geometry of the body and the number of independent spatial co-ordinates

necessary to describe the system.

Some of popularly used one, two and three-dimensional elements are shown in

figures 1 to 3 respectively. When the geometry, material properties and other parameters

(like stress, displacements, pressure and temperature) can be described in terms of only

one spatial co-ordinate, we can use one-dimensional element shown in fig 1. Although

this element has a cross sectional area it is generally schematically as a line segment.

Using this type of elements the cross sectional area along the length may be varied. When

the configuration and the details of the problem can be described in terms of two

independent spatial co-ordinates, we can use the two-dimensional elements as shown in

fig 2. The basic element useful for two-dimensional analysis is the triangular element.

Although a quadrilateral or its spatial forms, rectangular and parallelogram elements can

be obtained by assembling two or four triangular elements, in some cases the use of

quadrilateral elements prove to be advantageous.

If three spatial can describe the geometry, material properties and other

parameters of the body co-ordinates, we can idealize the body by using the three-

dimensional elements as shown in fig 3. The basic three-dimensional element, analogous

to the triangular elements in the case of two dimensional problems, is the tetrahedron

element. Some problems, which are actually three-dimensional, can be described by only

one or two independent co-ordinates. Such problems can be idealized by using

axisymmetric or ring type elements. The problems that posse’s axial symmetry likes

pistons, storage tanks, valves, rocket nozzles and re-entry vehicle shield fall into this

category. The present problem gas turbine rotor disc comes into this category. So in this

problem the assumed element for descretization of problems involving curved geometry,

finite elements with curved sides are useful. The ability to model A curved boundary has

been made possible by the addition of middle nodes. Finite elements with straight lines

are known as linear elements, while those with curved sides are called high order

elements.



4.3.1.2 Types of Elements

Often the type of elements to be used is evident from the physical problem itself.

For example, if the problem involves the analysis of a truss structure under a given set of

load conditions, the type of elements to be used for idealization is obviously the “bar or

line elements”. How ever, in some cases the type of elements to be used for idealization

may not be apparent and in such cases one has to choose the type of elements judicially.

In certain problems, the given body cannot be represented as an assemblage of only one

type of elements. In such cases, we may have to use two or more types of elements of

idealization.

4.3.1.3 Sizes of Elements

The size of elements influences the convergence of the solution directly and hence

it has been chosen with care. If the size of the element is small, the final solution is

expected to be more accurate. However we have to remember that the use of smaller size

will also mean more computational time. Some times, we may have to use elements of

different sizes in the same body. The size of element has to be varying small near the

regions where stress concentration is expected compare to far away places. In general,

wherever steep gradient of the field variable is expected, we have to use a finer mesh in

that region. Another characteristic related to the size of elements that affects the finite

element solution is the “Aspect ratio” of the elements. The aspect ratio describes the

shape of the element in the assemblage of elements. For two-dimensional elements aspect

ratio is taken as the ratio of the largest dimension of the element to the smallest

dimension. An element with an aspect ratio of nearly generally yields best results.

4.3.1.4 Location of Nodes

If the body has no abrupt change in geometry, material properties and external

conditions (like load, temperature etc.,) the body can be divided into equal sub divisions

and hence the spacing of the nodes can be uniform. On the other hand, if there are any

discontinuities.

4.3.1.5 Number of Elements



The number of elements to be chosen for idealization is related to the accuracy

desired, size of elements and the number of degrees of freedom involved. Although an

increase in number of elements generally means more accurate results, for any given

problem, there will be certain number of elements beyond which the accuracy cannot be

improved by any significant amount. The behavior is shown graphically in fig4. After the

number of elements reaches the point shown in figure no significant improvement will be

found. Moreover, since the use of large number of elements involves large number of

degrees of freedom, we may not be able to store the resulting matrices in the available

computer memory.

4.3.1.6 Simplification Offered By the Physical Configuration Of The Body

If the configurations of the body as well as the external conditions are symmetric,

we may consider only half of the body for finite element idealization. The symmetry

conditions however have to be incorporated in the solution procedure.

4.3.1.7 Node Numbering Scheme

The finite element analysis of a practical problem often reduces to matrix

equations in which matrices involved will be banded. The advantages in the finite

element analysis of large practical systems have been made possible largely due to the

banded nature of the matrices. Further, since most of the matrices involved (like stiffness

matrices) are symmetric, the demands on the computer storage can be substantially

reduced by storing only the elements involved in half band width instead of storing the

whole matrix. The bandwidth of the final systems of algebraic equations, depend upon

the size of the stiffness matrix of the individual elements and upon the system of notation

for the nodes. If we can minimize the bandwidth, we have effectively minimized both the

solution time and the storage requirement for the overall stiffness matrix. There are two

steps that we can take to achieve this minimization. First if the higher order models are

necessary in our analysis, we should avoid, if possible, the use of many secondary

external nodes. Second, we can perform a symmetric sub division and adopt an

appropriate numbering system for the nodes. If the nodes numbers are used as the basis

for numbering the nodal displacements, then the bandwidth of the overall stiffness matrix



depends upon the largest difference between any two external nods numbering for a

single element. The bandwidth B is given by the following equation.

B= (D+1)*F

Where, D= maximum largest difference occurring for the assemblage

F= the number of degrees of freedom

Hence to minimize the bandwidth, the nodal numbering should be selected to

minimize D. As an example, consider the different node numbering system for the nodes

of a simple rectangular mesh shown in fig5a, the ‘D’ for the above node scheme is 8.

Take third element the maximum difference between the node number obtained is 8 (i.e.

11-3=8) and let the degrees of freedom for node are ‘2’.

B= (8+1)*2 = 18

In the same way in fig 2b the d for the node scheme is ‘5’

B= (5+1)*2

=12

So the bandwidth in the second scheme is less than the first scheme. The second

type of node numbering scheme takes less computational time and the less computer core

memory.

4.3.2 Interpolation Polynomials

The basic idea of the finite element method is piece wise approximation i.e. the

solution of method is obtained by dividing the region of interest into small regions (finite

elements) and approximating the solution over each sub region by simple function. Thus

a necessary and important step is that of choosing simple function for the behavior of the

solution within an element are called “interpolation function” or “approximating

functions” or “interpolation models”. Polynomial type of interpolation function has been

most widely used to the following reasons.

1. It is easier to formulate and computerize the finite element equations with

polynomial type of interpolation functions. Specifically, it is easier to perform

differentiation or integration with polynomials.

2. It is possible to improve the accuracy of the results by increasing the order of the

polynomial, as shown in fig 6.



Theoretically a polynomial of infinite order corresponds to the exact solution. But

in practice we take polynomials of finite order only as approximation. In fig 6, an exact

solution for the field variable F(x) is approximated by various degree p polynomials of

the general form

11111F(x) = µ1+ µ2.x+ µ3.x2+ ……+ µn+1.xn

The greater the number of terms included in the approximation the more closely

the exact solution so represented. In equation a, the coefficients of the polynomial µ’s are

known as “generalized coordinates”, and ‘n’ is the degree of polynomial.

The above equation is for one-dimensional model. For two and three-dimensional

finite elements the polynomial forms are below.

Two-dimensional:

F(x, y) = µ1+ µ2.x+ µ3.y+µ4.x2+ µ5.y2+µ6.x.y +……+ µn+1.xn

Three-dimensional:

F(x, y, z) = µ1+ µ2.x+ µ3.y+µ4.z + µ5.x2+µ6.y2 + µ7.z2+ µ8.x.y+ µ9.x.y+ µ10.z.x+

…+ µm.z

From the above three equations, for each order of polynomial we can have three

equations from each one.

In most of the practical application the order of the polynomial in the

interpolation function is taken as one, two or three. The equations a to c reduces to the

following equations for n=1.

One-dimensional case:

a) F(x)= µ1+ µ2.x

Two-dimensional case:

b) F(x, y)= µ1+ µ2.x+ µ3.y

Three-dimensional case:

c) F(x, y, z) = µ1+ µ2.x+ µ3.y+µ4.z

On similar lines we can have the interpolation functions for n=2 and n=3 also.

4.3.2.1 Selection Of The Order Of the Interpolation Polynomial

While considering the order of the polynomial in a polynomial type interpolation

function, the following considerations have to be taken into account:



1. The interpolation polynomials should satisfy as far as possible, the convergence

requirement.

2. The pattern of variation of the variable resulting from the polynomial model

should be independent of the local coordinate systems.

3. The number of generalized coordinate (a) should be equal to the number of nodal

degree of freedom of the element.

The first consideration, the convergence requirement is very important aspect. It is

given in the following separate section. According to the second consideration, the

selection of the order of the model is that the pattern should be independent of the

orientation of the local coordinate systems. This property of the model is known a

geometry isotropy, or geometric invariance. For polynomials of linear order (i.e. n=1) the

isotropy requirement is usually equivalent to the necessity of including constant strain

rates. For higher order patterns, we can see intuitively that it is undesirable to have a

preferential coordinate direction, in other words, the field variable representation with in

an element and hence the polynomial, should not change with in local coordinate system

when a linear transformation is made from one Cartesian selecting the order of terms

involved in the polynomial equal to no of nodal degrees of freedom of element.

4.3.2.2 Convergent Requirement

Since the finite element method is a numerical technique, we obtain a sequence of

approximate solutions as the element size is reduced successively. These sequences will

converge to the exact solutions if the interpolation polynomial satisfies the following

requirements

1. The field variable must be constant with in the elements. The requirement is easily

satisfied by choosing continuous functions as interpolation models. Since

polynomials are inherently continuous, satisfy these requirements.

2. All uniform rates of the field variation φ and its partial derivative up to the highest

order appearing in the function I (φ) (i.e., I(φ))= I(φ,d φ/dx,…). Must have

representation in the interpolation polynomial when in the limit, the element size

reduces to zero. Thus the interpolation polynomial must be able to give a constant



value of the field variable with in the element when the nodal values are numerically

identical.

3. Similarly, when the body is sub divided into smaller and smaller element, the

partial derivatives of field variable unto the highest order appearing in the function

I(φ) approach a constant value with in each element. Thus we can not hope to

obtain convergent to the exact solution unless the interpolation permits this

constant derivative state.

4. The variable φ and its partial derivatives up to one order less than the highest order

derivative appearing in the function I(φ) must be continuous at element boundaries or

interfaces.

The elements whose interpolation polynomial satisfies the requirement (1) and (3)

are called “compatible or confirming” elements and those satisfying condition (2) are

called “complete” elements.

4.3.2.3 Nodal Degrees Of Freedom

The basic idea of FEM is to consider a body as composed of several elements that are

connected at specified node points. The un-known solutions or the field variable (like

displacement, pressure or temperature) inside any finite element is assumed to be given

by a simple function in terms of nodal values of that element. The nodal displacement

rotations are necessary to specify completely the deformation of the finite element or the

degrees of freedom. The nodal values of the solution, also known as nodal degrees of

freedom, are treated as unknowns in formulating the system of overall equations.

The solution of the system of equations (like force equilibrium equations) gives the

value of the unknown nodal degrees of freedom. Once the nodal degrees of freedom are

known, the solution within any element (and hence within complete body) will also be

known to us. For having the results in terms of nodal degrees of freedom the interpolation

function must be derived in terms of nodal degrees of freedom.

4.3.2.4 Coordinate System

A local coordinate system is one that is defined for a particular element and

necessary for the entire body or structure, the coordinate system for entire body is

called as the “global coordinate system”. A natural coordinate system is a local



coordinate system that permits a specification of a point with in the elements by a set

of dimension less numbers whose magnitude never exceeds unity. The derivation of

element characteristic matrices and vectors involves the integration of the shape

functions or their derivative or both over the element. These integrals can be

evaluated easily if the interpolation functions are in terms of local coordinate system.

4.3.3 Formulation of Elements Characteristic Matrices And Vectors

The characteristic matrices and characteristic vectors (also termed as vectors of

nodal actions) of finite elements can be derived by using any of the following

approaches.

Direct approach In this method, direct physical reasoning is used to establish the

element properties (characteristic matrices and vectors) in terms of permanent variables.

Variational approach In this method, the finite element analysis interpolated as an

approximate means of solving variational problems. Since most physical and engineering

problems can be formulated in variation form, the finite element method can be readily

applied for finding their appropriate solutions. The variational approach has been most

widely used in the literature in formulating finite element equations. A major limitation

of the method is that it requires the physical or engineering problem to be stated in

variational form, which may not be possible in all cases.

Weighted residual approachIn this method the element matrices and vectors are

directly formed the governing deferential equations of the problem with out reliance on

the variational statement of the problem. This method offers the most general procedure

for deriving finite element equations and can be applied to almost all practical problems

of science and engineering. Again with in the weighted residual approach different

procedures can be used. They are

i. Collocation method

ii. Sub domain collocation method

iii. Galkerian method

iv. Least squares method

4.3.4 Assemble Of Element Matrices, Vectors and Derivation Of

System Equations



4.3.4.1 Assemblage of Element Equations

Once the element characteristics, namely the element matrices and

element vectors are found in a global coordinate system, the next step is to construct the

overall or system equations. The element matrices are divided by the above stated

methods in previous section. The element vectors are the unknown field variables and the

loading conditions on any element. The process of constructing the algebraic equations

for the assemblage from the equations for the individual elements is routine. The

procedure of assembling the element matrices and vectors is based on the requirement of

“compatibility” at the element nodes. This means that the nodes where elements are

connected, the values of the unknown nodal degrees of freedom of variables are the same

for all the elements joining at the nodes.

Assume that the total number of elements in the assemblage is ‘E’ and ‘N’ is the

total number of equations to be solved for the assemblage. Assume that we know

stiffness matrix and load vectors for each element and that the element load vectors

include all the loading on the body. The nodal displacements that is the unknown for

entire assemblage, may be written as N*1 vectors ‘{r}’.

If we let subscript ‘e’ denote the element number, we can write the expanded

element stiffness and loads as N*1 vectors {R(e)}. These are constructed by inserting the

known stiffness coefficients and loads in their proper locations and filling the remaining

locations with zeros. Thus the global characteristic matrix and the global characteristic

matrix an the global characteristic vector can be obtained by algebraic addition as

E

[K]=Σ [K (e)]

e=1

And E

[R]= Σ [K (e)]

e=1

by applying principle of minimum potential energy to assemblage and extremitization of

condition to the following conclusion.

E E



(Σ [K (e)]){φ}=Σ[R (e)]

e=1 e=1

This may be abbreviated in the form

[K] {φ} ={R}

The above procedure is applicable for any structure having any number of the

finite elements. In fact the procedure is applicable equally top all types of problems.

4.3.4.2 Incorporation of Boundary Conditions

After assembling the characteristic matrices [K (e)] and the element characteristic

vectors [P (e)], the overall or system equations of the entire domain or body can be

written (for an equilibrium problem) as [K] {φ} = {P}

These equations cannot be solved for {f} since the matrix [K] will be singular and

hence its inverse does not exist. The physical significance of this, in the case of solid

mechanics problem, is that the loaded body or structure is free to undergo unlimited rigid

body motion unless some support constraints are imposed to keep the body or structure in

equilibrium under the loads. Hence some boundary or support conditions have to apply to

equation before solving for {f}.In non structural problems; we have to specify the values

of at least one and sometimes more than one nodal degrees of freedom. The number of

degrees of freedom to be specified is dictated by the physics of the problem.

4.3.5 Solution of Finite Elements (Systems) Equations

The finite element analysis of any physical problem led to a system of matrix

equations. After incorporating the boundary conditions in the assembled system of

equations as out lined in previous sections, we obtain the final matrix equations. If the

problem is nonlinear the resulting matrix equations will also be nonlinear irrespective of

the type of the problem. If the problem is nonlinear; some sort of an interactive procedure

has to be used for finding the solution. For example, the matrix equation that results from

the finite element analysis of a nonlinear equilibrium (or steady state) problem can be

solved by using any one of the following schemes:

1. Newton Raphson methods

2. Continuation methods

3. Minimization methods



4. Perturbation methods

4.3.6 Computation of Element ResultsThe solution of the final matrix equations yields the vectors of global nodal

degrees of freedom of the body {f (e)} can be identified for any element ‘e’. If a local

coordinates system was used in deriving the element characteristic matrices and vectors,

the vectors of local degrees of freedom {f (e)} can be found from the transformation

relation. After that we can find the variation of the field variable inside the element ‘e’

from which the element desired resultant gradients of the field variable and associated

quantities (strains and stresses in the case of solid mechanics and structural problems) can

be computed.

The previous sections explain theoretically about the step by step FEM procedure.

The steps are described without going into deep how to solve the equations etc. but this

will provide over all procedure of finite element method regardless type of problem.



CHAPTER 5

FEA SOFTWARE- ANSYS

Ansys

Ansys is general purpose finite element analysis software, which enables

engineers to perform the following tasks

i. Build computer models or transfer CAD models structures, products,

components or systems

ii. Apply operating loads or other design performance conditions

iii. Study the physical response such as stress levels, temperature distributions or

the impact of electromagnetic fields

iv. Optimize a design early in the development process to reduce production costs

A typical Ansys analysis has three distinct steps

1. Pre-processor (build the model)

2. Solution (applies loads and obtains the solution)

3. Postprocessor (review the results)

5.1 ANSYS DERIVED PRODUCTS

In addition to the ANSYS/Multiphysics program and its addition capabilities, a

series of ANSYS derived products are available. These products are subsets of ANSYS

derived from the ANSYS/Multiphysics program.

ANSYS/Mechanical designed for linear and nonlinear, structural and thermal,

static and dynamic/transient analyses. It enables users to solve a wide variety of analyses

in mechanical and civil engineering applications. As mentioned previously,

ANSYS/Mechanical has the linear stress, structural, dynamic analysis, buckling, sub

structuring, heat transfer, thermal, acoustics and piezoelectric capabilities of



ANSYS/Multiphysics but excludes the three additional options: electromagnetic,

LS_DYNA Explicit dynamics and FLOTRON computational fluid dynamics (CFD).

ANSYS/Structural product supports the following types structural analyses,

structural static’s, model, harmonic response, transient dynamic, spectrum, buckling,

nonlinear structural, and p-method structural static analysis. Useful for many civil and

mechanical engineering applications, the product also enable you to solve fracture

mechanics problems and nodal composites and to perform fatigue evaluations. The

ANSYS/Structural product does not include the LS-DYNA explicit dynamics, thermal

electromagnetic, CFD, acoustics or piezoelectric capabilities of ANSYS.

ANSYS/Linear plus product enables you to do linear static and dynamic structural

analyses. Dynamic analyses include modal, harmonic, transient and spectrum analyses.

Although it is limited mostly to linear structural solutions, ANSYS/Linear plus has come

nonlinear capabilities such as large deflection and stress stiffening for some elements and

node to node contact elements.

ANSYS/Thermal product has steady state and transient thermal analysis

capabilities. ANSYS/Thermal allows for combined thermal-electric analyses for the

elements supported in the product, it provides solution capabilities for variety of

mechanical and electrical engineering applications.

ANSYS/Emag is an electromagnetic field simulation product designed for static

and low frequency electromagnetic, electrostatics, current condition, circuit simulation

and coupled electromagnetic simulation. You can use the 3D version for both three

dimensional and two dimensional models. The 2D version supports only two dimensional

(planar or axisymmetric) models. When combined with ANSYS structural or thermal

product, ANSYS/Emag also enables you to do coupled-magnetic thermal analysis (such

as armature motion). If the add on FLOTRON CFD capability is available, you can also

simulate electromagnetic CFD coupling.

ANSYS/FLOTRON is a CFD (computational fluid dynamics) product for fluid

flow and heat transfer analysis. It has the same capabilities as the add ion FLOTRON-

CFD capability described above.



ANSYS/DYNA prep post is a pre-processing and post processing product that,

add on LS-DYNA option described above enables you to perform explicit dynamic

analyses. The difference between ANSYS/DYNA provides the LS/DYNA solver and pre

post offers only an interface to LYDYNA with preprocessing and post processing.

ANSYS/Prep post is a pre-processing product designed for building large models

and moving them to a different usually more powerful computer for solution. It has all

the capabilities of AANSYS/Multi-physics.-

ANSYS/ED is an educational version of ANSYS designed for corporate training

programs, academic institutions and self-study. It has all the capabilities of

ANSYS/Multi-physics, including electromagnetic and FLOTRON CFD. The primary

difference between ANSYS/Multi-physics and ANSYS/ED is that the educational

product limits the size of the model and you can solve. In addition ANSYS/ED does not

include composites and you cannot re-link the product to include user features.

5.2 PERFORMING A TYPICAL ANSYS ANALYSIS

The ANSYS program has many finite element analyses capabilities, ranging from

a simple, linear, static analysis to a complex, nonlinear, transient dynamic analysis. The

analysis guide manuals in the ANSYS documentation set describe specific procedures for

performing analyses for different engineering disciplines. The next few sections of this

chapter cover general steps that are common to most analyses.

A typical ANSYS analysis has three distinct steps:

i. Build the model

ii. Apply loads and obtain the solution

iii. Review the results

5.2.1 Building a Model

Building a finite element model requires more of an ANSYS user’s time

that any other part of the analysis. First job name and analysis titles are specified. Then,



the PREP7 pre-processor is used to define the element types, element real constants and

material properties and model geometry. Specify a job name and analysis titles. This task

is not required for an analysis, but recommended.

5.2.2 Defining the Job Name

The job name is the name that identifies the ANSYS job. When you define a job

name for an analysis, the job name becomes the first part of the analysis creates. (The

extension or suffix for these files names is a file identifier such as .bd) by using a job

name for each analysis, we ensure that no files are over written. If job name is not

defined, all files receive the name FILE or file, depending on the operating system.

5.2.3 Defining Units

The ANSYS program does not assume a system of units for analysis except in

magnetic field analysis, any system of units can be used. (Units must be consistent for all

input data)

5.2.4 Defining Element Types

The ANSYS element library contains more than 100 different element types. Each

element type has unique number and a prefix that identifies the element category:

BEAM4, PLANE77, QLID96 etc.

The following element categories are available:

1. Beam

2. Pipe

3. Combination

4. Plane

5. Contact

6. Shell

7. Fluid

8. Solid

9. Hyper elastic

10. Source



11. Infinite Surface

12. Link User Mass

13. Interface

14. Matrix

15. Visco elastic

The element type determines, among other things

i. Degrees of freedom set (which in turns implies the discipline structural, thermal,

magnetic, quadrilateral, electric, brick, etc.)

ii. Whether the element lies in two dimensional or three dimensional

5.2.5 Defining Element Real Constants

Element real; constant are properties that defined on the element type, such as

cross sectional properties of a beam element. For example, real constants for BEAM3 the

2-D beam element or area (AREA), moment of inertia (IZZ), height (HEIGHT), shear

deflection constant (SHEARZ), initial strain (ISTRN), and added per unit length

(ADDMAS). Not all element types require real constants, and different elements of the

same type may have differential real constant value.

5.2.6 Defining Material Properties

Most element types require material properties. Depending on the application,

material properties may be:

i. linear or non-linear

ii. isotropic, orthotropic or anisotropic

iii. constant temperature or temperature dependent

As with element types and real constant, each set of material properties has material

reference number. The table of material reference numbers versus material property set is

called material table. Within one analysis, you may have multiple material property sets

(to correspond with multiple materials used in the model). ANSYS identifies each set

with a unique reference number.

5.2.6.1 Linear Material Properties

Linear material properties can be constant or temperature dependent and isotropic

or orthotropic.



5.2.6.2 Nonlinear Material Properties

Nonlinear material properties are usually tabular data, such as plasticity data,

magnetic field data, creep data, swelling data, hyper elastic material data, etc.

5.2.7 Creating the Model Geometry

Once material properties have defined, the next step in an analysis is generating a

finite element model nodes and elements that adequately describe the model geometry.

There are two methods to create the finite element model:

1. solid modeling

2. direct modeling

With solid modeling we describe the geometric shape and instruct the ANSYS

program to automatically mesh the geometry with nodes and elements, in direct

generation the location of each node and the connectivity of each element can be

manually.

5.2.8 Applying Loads and Obtain the Solution

5.2.8.1 Applying Loads

Loads applied include the boundary conditions (constraints, supports or boundary

field specifications) as well as other externally and internally applied loads. Loads in the

ANSYS program are divided into 6 categories.

Degrees of freedom constraints forces

Surface loads body loads

Inertia loads coupled field loads

Most of these loads can be applied either on the solid model (key points. Lines

and areas) or the finite element model (nodes and elements) two important load related

terms in ANSYS are load step and sub step A load step is simply a configuration of loads

for which you obtain a solution. In a structural analysis, for example, you may apply

wind loads in one load step and gravity in second load step. Load step are also useful in

dividing a transient load history curve into several segments. Sub steps are incremental

steps taken within a load step. You use them mainly for accuracy and convergence



purposes in transient and nonlinear analyses. Sub steps are also known as time steps-

steps taken over a period of time. Note- the ANSYS program uses concept of time in

transient analyses as well as static analyses.

With solid modeling we describe the geometric shape of model and instruct the

ANSYS program to automatically mesh the geometry with nodes and elements in direct

generation the location of each node and the connectivity of each element can be defined

manually.

5.2.8.2 Specifying Load Step Options

Load step options are options that you can change from load step to load step,

such as number of sub steps, time at the end of a load step, and output controls.

Depending on the type of analysis you are doing, load step options may or may not be

required. The analysis procedures in the analysis guide manuals describe the appropriate

load step options as necessary.

5.2.9 Solution

In the phase of the analysis, the computer takes over and solves the simultaneous

equations that the finite element generates. The results of the solution are:

(a) Nodal degrees of freedom values, which from the primary solution

(b) Derived values, which form the element solution.

The element solution is usually calculated at the elements integration points. The

ANSYS program writes the results to the database as well as to the result file. Several

methods of solving the simultaneous equations are available in the ANSYS program such

as: Frontal solution, sparse direct solution, Jacobi conjugate gradient solution, In

complete cholesky conjugate gradient solution, Pre conditioned conjugate gradient

solution and an automatic iterative solver option.

5.2.10 Post Processing

Post processing means reviewing the results of an analysis, it is probably the most

important step in the analysis, because you are trying to understand how the applied loads



affect your design, how good your finite element mesh is and so two post processors are

available to review your results:

POST PROCESOR 1: The general post processor.

It allows you to review the results over the entire model at

specific load steps and sub steps

POST PROCESSOR 2: The time history post processor

It allows you to review the results at specific time points in the

model as a function of time or frequencies. It has many capabilities, ranging from simple

graphics display and tabular listing to more complex operations such as differential

calculus and response spectrum generation.

It is important to remember that the post processors in ANSYS are just tools for

reviewing analysis results. You still need to use your engineering judgment to interpret

the results.

5.2.11 Results File

The ANSYS solver writes results of an analysis to the results finding during

solution. The name of the result file depends on the analysis discipline:

Job name.RST for a Structural analysis

Job name.RTH for a Thermal analysis

Job name.RMG for a Magnetic field analysis

Job name.RFL for a Flotron analysis

For a Flotron analysis, the file extension is .RFL, for other fluid analysis, the file

extension is .RST or >RTH, depending on whether structural degrees of freedom are

present. Using different file identifiers for different disciplines helps you in coupled field

analysis where the results from one analysis are used as loads for another. This presents a

complete description of coupled field analysis.

5.2.12 Types of Data Available For Post Processing

The solution phase calculates two types of result data:



i. Primary data consist of the degree of freedom solution calculated at each node

displacements in a structural analysis, temperature in a thermal analysis,

magnetic potentials in a magnetic analysis and so on.

ii. Derived data are those results calculated from the primary data, such as

stresses and strains in a structural analysis. Thermal gradients and fluxes in a

thermal analysis, magnetic fluxes in a magnetic analysis and the like.

5.3 ANALYZING THERMAL PHENOMENA

A thermal analysis calculates the temperature distribution and related quantities in

system or components.

Typical quantities of interest are:

(i) The temperature distributions

(ii) The amount of heat lost or gained

(iii) Thermal gradients

(iv) Thermal fluxes

Thermal simulations play an important role in the design of many engineering

applications, including internal combustion engines, turbines and heat exchangers, piping

systems and electronic components. In many cases engineering follow a thermal analysis

with stress analysis to calculate thermal stresses i.e stresses caused by thermal expansions

or contractions

5.3.1 How Ansys Treats Thermal Modeling

Only the ANSYS/ Multi-physics, ANSYS/ Mechanical, ANSYS/ Thermal and

ANSYS/ Flotron programs support thermal analysis. The basic for thermal analysis in

ANSYS is a heat balance equation obtained from the principle of conservation of energy.

The finite element solutions you perform via ANSYS calculate nodal temperatures, and

then use the nodal temperatures to obtain other thermal quantities.

The ANSYS program handles all three primary modes of heat transfer

Conduction

Convection



Radiation

5.3.1.1 Conduction

ANSYS can solve conduction problems by inputting the steady state temperature

values on lines of the model where the conduction takes place.

5.3.1.2 Convection

An ANSYS user specifies convection as a surface load on conduction solid

elements or shell elements. You specify the convection film co-efficient and bulk fluid

temperature at surface, ANSYS then calculates the appropriate heat transfer across that

surface. If the film co-efficient depends upon temperature, you specify a table of

temperature along with the corresponding values of film co-efficient at each temperature.

For use in finite element models with conducting bar elements which do not allow

a convection surface load, or in cases where the bulk fluid temperature is not known in

advance, ANSYS offers a convection element named LINK34. In addition you can use

the Flotron CFD elements to simulate details of the convection process, such as fluid

velocities, local values of film co-efficient and heat flux and temperature distributions in

both fluid and solid regions.

5.3.1.3 Radiation

ANSYS can solve radiation problem, which are non-linear in four ways, by using

the radiation link element, LINK31, by using surface effect elements with the radiation

option. By generating a radiation matrix and using it as a super element in a thermal

analysis, by using radiation boundary conditions in a Flotron CFD analysis.

5.3.2 Special Effects

In addition to the three modes of heat transfer you can account for special effect

such as change of phase and internal heat generation.

5.3.3 Types of Thermal Analysis

ANSYS supports two types of thermal analysis:

(a) A steady state thermal analysis: It determines the temperature distribution and

other thermal quantities under steady state loading conditions. A steady state

loading condition is a solution where heat storage effects varying over a period of

time can be ignored.



(b) A transient thermal analysis determines the temperature distribution and thermal

quantities under conditions that vary over a period of time.

5.4 COUPLED-FIELD ANALYSIS

5.4.1 Definition of Coupled-Field Analysis

A coupled-field analysis is an analysis that takes into account the interaction

between two or more disciplines of engineering. For example a piezoelectric analysis

handles the interaction between the structural and electric fields.

It solves for the voltage distribution due to applied due to applied displacements

or vice versa. Other examples of coupled-field analysis are thermal-stress analysis,

thermal-electric analysis and fluid-structural analysis.

Some of the applications in which coupled-field analysis may be required are

pressure vessels, fluid flow constructions, induction heating, ultrasonic transducers,

magnetic forming, and micro-electromechanical systems.

5.4.2 Types of Coupled-Field Analysis

The procedure for a coupled-field analysis depends on which fields are being

coupled but two distinct methods can be identified: Sequential and Direct.

5.4.2.1 Sequential Coupled-Field Analysis

The sequential coupled-field analysis method involves two or more sequential

analysis each belonging to a different field. There are different types of sequential

coupled-field analysis.

i. Physics analysis

ii. Multi-field solver

5.4.2.1.1 Physics Analysis



In a sequential coupled physics analysis you can couple the two fields by applying

results from one analysis as loads in another analysis. The load transfer occurs external to

the analysis and you must explicitly transfer loads using the physics environment.

An example of this type of analysis is a sequential thermal-stress analysis where

nodal temperatures from the thermal analysis are applied as body force loads in the

subsequent stress analysis. The physics analysis is based on a single finite element mesh

across physics. Physics files can be used to perform coupled-field analysis. Physics files

are created which prepare the single mesh for a given physics simulation. A solution

proceeds in a sequential manner. A physics file is read to configure the database, a

solution is performed, another physics field is read into the database, coupled-field loads

are transformed and the second physics is solved. Coupling occurs by issuing commands

to read the coupled load terms from one physics to another across a node-node similar

mesh interface.

5.4.2.1.2 Multi-Field Solver

The multi-field solver is available for a large class of coupled problems. The

multi-field solver is an automated tool for solving sequentially coupled-field problems. It

is superset of the fluid solid interaction solver and is an alternative for the physics file

based procedure. It provides a robust accurate and easy to use tool for solving

sequentially coupled-physics problems. The solver is built on the premise that each

physics is created as a field with an independent solid model and mesh. Surfaces or

volumes are identified for coupled loads are automatically transferred across dissimilar

meshes by the solver. The solver is applicable to static, harmonic and transient analysis

depending on the physics requirements. Any number of fields may be solved in a

sequential manner.

5.4.2.2 Direct Coupled-Field Analysis

The direct coupled-field analysis method usually involves just one analysis that

uses a coupled-field element type containing all necessary degrees of freedom. Coupling

is handling is handled by calculating element matrices or element load vectors that

contain all necessary terms. An example of this is a piezoelectric analysis using the



PLANE 223, SOLID 226 or SOLID 227 elements. Another example is MEMS analysis

with the TRANS 126 element.

5.4.3 WHEN TO USE DIRECT Vs. SEQUENTIAL

Direct coupling is advantageous when the coupled-field interaction is highly

nonlinear and is best solved in a single solution using a coupled formulation.

Examples of direct coupling include piezoelectric analysis, conjugate heat transfer

with fluid flow and circuit-electromagnetic analysis. Elements are specially formulated to

solve these coupled-field interactions directly. For coupling situations which do not

exhibit a high degree of nonlinear interaction the sequential method is more efficient and

flexible because you can perform the two analyses independently of each other. Coupling

may be recursive where iterations between the different physics are performed until the

desired level of convergence is achieved. In a sequential thermal-stress analysis you can

perform a nonlinear transient thermal analysis followed by a linear static stress analysis.

You can then use nodal temperatures from any load step or time-point in the thermal

analysis as loads for the stress analysis. In a sequential coupling analysis you can perform

a nonlinear transient fluid-solid interaction analysis using Florton fluid element.



CHAPTER 6RESULTS AND DISCUSSIONS

6.1 For Material B50A368



Fig 6.1 Von Mises Stress Distribution

Von Mises is a theoretical measure of stress used to estimate yield failure criteria

in materials.

From figure 6.1 the maximum Von Mises stress is obtained at the inner radius of

the disc at node 1 and the maximum stress value obtained is 1067 kg/cm.s^2. The

minimum Von Mises stress is obtained at the outer radius of the disc at node 172 and the

minimum stress value obtained is 66.908 kg/cm.s^2.

Fig 6.2 X-Component of Stress



The x- component of stress is the measure of stress distribution in x direction.

From figure 6.2 the maximum stress value obtained is 333.434kg/cm.s^2 at node

56 and the minimum stress value obtained is -15.403 kg/m.s^2 at node 230.



Fig 6.3 Y-Component of Stress

The y- component of stress is the measure of stress distribution in y direction.

From figure 6.3 the maximum stress value obtained is 331.731 kg/cm.s^2 at node

120 and the minimum stress value obtained is -44.503 kg/cm.s^2 at node 150.



Fig. 6.4 Stress Intensity

The stress intensity is used to more accurately predict the stress state near the tip

of a crack caused by a remote load or residual stresses. It is a theoretical construct

applicable to materials and is useful for providing a failure criterion for materials.

From figure 6.4 the maximum intensity of stress obtained is 1192 kg/cm.s^2 at

node 1 and the minimum intensity of stress obtained is 71.275 kg/cm.s^2 at node 172.



Fig. 6.5 X-Component of Displacement

The x- component of displacement is the measure of displaced distance in x

direction.

From figure6.5 the maximum absolute displacement value obtained is 2.899 m at

node 235 and the minimum absolute displacement value obtained is 0.1221 m



Fig. 6.6 Y-Component of Displacement

The y- component of displacement is the measure of displaced distance in y

direction.

From figure6.6 the maximum absolute displacement value obtained is -7422 m at

node 220 and the minimum absolute displacement value obtained is -8625 m



Fig. 6.7 Displacement Vector Sum

The displacement vector sum is the vector sum of the displacements in both x and

y directions.

From figure 6.7 the maximum displacement vector sum value obtained is 8.923 m

and the minimum displacement vector sum value obtained is 7.642 m.

6.2 For Material 1IN718



Fig 6.8 Von Mises Stress Distribution

Von Mises is a theoretical measure of stress used to estimate yield failure criteria

in materials.

From figure 6.8 the maximum Von Mises stress is obtained at the inner radius of

the disc at node 1 and the maximum stress value obtained is 1058 kg/cm.s2. The

minimum Von Mises stress is obtained at the outer radius of the disc at node 172 and the

minimum stress value obtained is 66.373 kg/m.s2.



Fig 6.9 X-Component of Stress

The x- component of stress is the measure of stress distribution in x direction.

From figure 6.9 the maximum stress value obtained is 330.623 kg/cm.s2 at node

56 and the minimum stress value obtained is -15.276 kg/cm.s2 at node 230.



Fig. 6.10 Y-Component of Stress

The y- component of stress is the measure of stress distribution in y direction.

From figure 6.10 the maximum stress value obtained is 328.905 kg/cm.s^2 at

node 120 and the minimum stress value obtained is -44.128kg/cm.s^2 at node 150.



Fig. 6.11 Stress Intensity

The stress intensity is used to more accurately predict the stress state near the tip

of a crack caused by a remote load or residual stresses. It is a theoretical construct

applicable to materials and is useful for providing a failure criterion for materials.

From figure 6.11 the maximum intensity of stress obtained is 1182 kg/cm.s^2 at

node 1 and the minimum intensity of stress obtained is 70.718 kg/cm.s^2 at node 172.



Fig 6.12 X-Component of Displacement

The x- component of displacement is the measure of displaced distance in x

direction.

From figure 6.12 the maximum absolute displacement value obtained is 3381 m at

node 235 and the minimum absolute displacement value obtained is 142 m



Fig 6.13 Y-Component of Displacement

The y- component of displacement is the measure of displaced distance in y direction.

From figure 6.13 the maximum absolute displacement value obtained is 123183 m

at node 220 and the minimum absolute displacement value obtained is -1280 m



Fig. 6.14 Displacement Vector Sum

The displacement vector sum is the vector sum of the displacements in both x and

y directions.

From figure 6.14 the maximum displacement vector sum value obtained is 3528

m and the minimum displacement vector sum value obtained is 461 m.



CONCLUSIONS

1. The stress value obtained for material B50A368 is 1067kg/cm2 which is within

the allowable limits i.e. 1000-1200 kg/cm2

2. The stress value obtained for material 1IN718 is 1058 kg/cm2 which crossed the

allowable limits.900-1000kg/cm2

3. If the stress value obtained is greater than within the limits the material tends to

get cracks at the earliest. Hence as the value of stress obtained for material

1IN718 is beyond the limits as a result of which it is not preferable for the usage

in the manufacturing of gas turbine rotor disc.

4. From our analysis we conclude that the material B50A368 is best suited in the

manufacture of gas turbine rotor disc.



References

1. GE Gas Turbine Design Philosophy. D.E. Brandet, R.R. Wesorick.

2. GE Industrial and power systems Schenedty,NY

3. Sawyer, J.W.ed., “Gas turbine engineering handbook”, Turbo machinery international publications, 1985.

4. “Strength of materials: Stephen Timeshenko Advanced theory and problems.

5. Ansys Inc U.S.A.,”Theory Manual”

6. Desai and Abel,”Introduction to finite Element Analysis”

7. Yahya S.M.,” Turbines, compressors and fans”, Tata Mc Graw-Hill publishing company limited, 1997.

8. Chandra Patla T.R., Belegundu A.D.,”Finite Element Engineering” Prentice Hall of India Ltd.,2001.

9. Dr.S.S.Rao,”Introduction to Finite Element Analysis”

10. Sachdev”Heat and mass transfer”

1. www.gepower.com

2. www.specialmetals.com

3. www.materialscience.com 4. www.gooogle.com


http://www.gooogle.com/

http://www.materialscience.com/

http://www.specialmetals.com/

http://www.gepower.com/

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