 Open Access
 Total Downloads : 1315
 Authors : M. K. Naidu, D. Santharao, J. Kantharao
 Paper ID : IJERTV2IS2280
 Volume & Issue : Volume 02, Issue 02 (February 2013)
 Published (First Online): 28022013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Stress Analysis of Gas Turbine Wheel
M. K. Naidu1, D. SanthaRao2 , J. KanthaRao3
[PG Student1, Associate Professor2 , Assistant Professor3 , Dept. of Mech. Engg, BVC Engg. College, Odalarevu 533210,Abstract
A Turbine wheel (rotor) plays a significant role in gas turbine. The rotor on which the blades are mounted transmitting this motion holds a key point to better efficiency of gas turbine. Thus more focus should be given to the design of the turbine rotor.
Gasturbine discs are normally operated at high temperatures. The hot gases contact the blades and the rim of the turbine rotor and thus maintain the rim at high temperature. The temperature gradient at rim and central portion of rotor causes the sources for thermal stresses. The disc is expected to perform well in spite of all the stringent operating conditions [1]
.The Advancement in gas turbine materials has been always a major concernhigher their capability to with stand elevated temperature service, produce lower stresses, light weight and more the engine efficiency.
In this paper, an attempt is made to determine the stresses like Thermal, Structural, Radial and other stresses with different materials. The Analytical analysis is carried out by using ANSYS to determine the intensity of stresses.

Introduction
The important role of the turbine wheel in the gas turbine has directed much attention to the analysis of stresses in rotating turbine wheels with temperature gradient. Since heat is conducted from the buckets into the disc, a radial temperature gradient exists in the disc. The outer portions are at a relatively high temperature and would expand if free, but they are held back by the cooler inner portions. This results in tensile thermal stresses in the radial direction but compressive thermal stresses in the tangential direction. Thermal gradients developed during thermal transients are the key sources of stresses generation in the rotor [2].
Thermal stresses may also result from an axial temperature gradient. At the rim the centrifugal stresses are all tensile but thermal tangential stresses takes on large
compressive values. The low margin of the safety at the rim is due to the presence of resultant compressive stresses. Excessive values of such stresses often cause plastic flow of disc during the engine operation and when the disk cools, a system of tensile stresses is set up that can cause rim cracking. Because such cracks usually progress rather slowly, serious troubles from this source can, in most cases, be forestalled by removal of the wheel from service. The thermal and centrifugal stresses are both tensile at the center; in the event that these stresses become excessive, a sudden rupture of the rotor would probably occur. Discs are therefore usually designed to have larger margin of safety at the center than at the rim.

STRESS ANALYSIS OF ROTATING GAS TURBINE WHEEL
In a thin rotating disc of variable thickness, the state of stress at any radius can be completely defined by the two principal stresses, the radial and tangential stresses r and t respectively. Two equations are therefore necessary to determine the two unknown stresses. The first of these equations can be obtained from the conditions of the equilibrium of the element of the disc. The second from, the compatibility conditions, which are
mathematical statements of the interrelation between the radial and tangential strains in a symmetrical disc. The equilibrium and compatibility equations results in differential form defining the relations between the stresses at radius r and those at radius infinitesimally removed from r. The unknown stress can be determined by the boundary conditions at the rim of the disc where the radial stress is equal to the centrifugal blade loading [3].
Lets
r = radial stress, N/m2 t = hoop stress, N/m2
r = radius of disc at any point, m t = thickness of disc at radius r, m = poisons ratio
= density of rotor material, Kg/m3
E = Youngs modulus
= Angular velocity R1 = Inner radius
R2 = Outer radius Radial stress
r = E [a r2 (3+ ) + b1(1+ ) b2(1 )/r2]
1 2
Tangential stress
t= E [ a r2( 1+ 3 ) + b1( 1+ ) + b2( 1 )/r ] 1 2
2 2 1/2
2 2 1/2
Equivalent stress v = ( r – r t + t ) Radial dis placement y = a r3 + b1 r + b2/r Where,
b1 = [ 2 (1 2)R22/E a(3+ )(R24R14) ]
1
1
(1+ )(R22R 2)
temperature or low temperature environments, especially the resistance against oxidation at the high temperature.
Chemical composition:
1
1
b2 = R12 [a R
1
2 (3+ ) + b1 (1+ )]
Ni
Cr
Fe
Mo
Mg
C
Si
S
52.5
19.0
Bal
3.0
0.35
0.08
0.35
0.015
Ni
Cr
Fe
Mo
Mg
C
Si
S
52.5
19.0
Bal
3.0
0.35
0.08
0.35
0.015
a = – 2 (1 2)/ 8E

Turbine wheel materials:
Many thousands of supercharger turbine discs were made of Cyclops 17W, alloys such as A286 are used. Later Timken 16 256 steel was used extensively. Now Alloy 718 Nickel Base alloys are using and alloy 706 is the advanced material.

Alloy 718:
Alloy 718 is a precipitation hardenable nickel based alloy designed to display exceptionally high yield, tensile, and creep rupture properties at temperature up to 1300F Alloy 718 is Austenitic structure, precipitation hardening generate "" made it excellent mechanical performance. Grain boundary generate "" made it the best plasticity in the heat treatment. This alloy has extreme resistance to stress corrosion cracking and pitting ability in high
Characteristics of alloy 718: Workability
High tensile strength, endurance strength, creep strength and rupture strength at 700.
High inoxidability at1000. Good welding performance
Steady mechanical performance in the low temperature.
The elevated temperature strength, excellent corrosion resistance and workability at 700 properties made it use in a wide range of high requirement environments.
Steam turbine
Liquidfuel rocket
Cryogenic engineering Acid environment
Nuclear engineering

Timken steel:
Timken steel is fine grained alloy steel that combines medium carbon content with a robust balance of chromium, nickel and molybdenum for enhanced hardenability. It was originally developed as an alloy to provide ultra high transverse strength and toughness for air craft applications with excellent wear resistance. Typical applications include Drive shafts, crank shafts, turbine components, connecting rods etc.
Chemical composition:
Cr
Ni
Mo
C
Mn
Si
N
Fe
16
25
6
0.08
1.5
0.5
0.15
Bal.

Alloy 706:
This Nickelbased, pecipitation hardened alloy is the newest to be used in turbine wheel application. It has very significant increase in stress rupture and tensile yield strength compared to other alloys. This alloy is similar to Alloy 718 and it contains somewhat lower concentrations of alloying elements than alloy 718 and is therefore possible to produce very large ingot sizes of turbine wheels. It is a precipitation hardened alloy that provides high mechanical strength in combination with good fabricability. It
has excellent resistance to post weld strain age cracking.
Chemical composition:
Ni
Cr
Fe
Ti
C
Cu
Mn
Si
S
co
42
15
6
1.7
0.06
0.3
0.35
0.35
0.015
1.0
Characteristics:
Good machinability
High creep rupture strength Excellent weldebility
4.1 Turbine wheel materials and their properties:
Timken Steel
Alloy 718
Alloy 706
Yield stress N/mm2
620
1375
1300
Density Kg/m3
7850
8190
8080
Poisson ratio
0.3
0.35
0.382
Youngs modulus N/mm2
2.1 x 1011
2.1 x 1011
2.1 x 1011
Thermal conductivity w/mk
3.6
11.4
12.5
Specific heat J/Kg/ 0 c
486
435
444


Turbine wheel specifications:
Mass of each blade : 0.92 kg
No. of blades 100
Inner radius of TW (R1) : 0.0445m Outer radius of TW(R2) : 0.45355m Angular velocity of TW : 534 rad /sec

Theoretical stress calculations for different materials:

Steel:
Radius mm
Tangential stress N/mm2
Equivalent stress N/mm2
Displacement mm
45
233.68
233.68
0.09
116
221.46
203.50
0.11
225
199.82
186.35
0.14
450
118.075
104.92
0.19
Radius mm
Tangential stress N/mm2
Equivalent stress N/mm2
Displacement mm
45
219.81
219.813
0.083
116
207.19
190.273
0.095
225
183.18
170.354
0.127
450
91.34
86.192
0.139
Radius mm
Tangential stress N/mm2
Equivalent stress N/mm2
Displacement mm
45
219.81
219.813
0.083
116
207.19
190.273
0.095
225
183.18
170.354
0.127
450
91.34
86.192
0.139

Alloy 718:

Alloy706:
Radius mm
Tangential stress N/mm2
Equivalent stress N/mm2
Displacement Mm
45
179.45
179.45
0.062
116
167.68
153.69
0.078
225
143.26
132.05
0.095
450
85.5
80.85
0.102


FEM analysis through ANSYS:

Boundary conditions

Deformation of Turbine Wheel for steel.
The deformation of turbine wheel is found maximum 0.214mm at the rim.

Over all stresses of gas turbine wheel for Timken steel.
The maximum stresses are found to be 258.537N/mm2.

The Maximum temperature dissipation for steel is 61.66 0 C/meter.

Deformation of Wheel for Alloy 718
The deformation of Turbine Wheel is found maximum 0.144mm at the rim.

Overall stresses of gas turbine wheel for alloy 718.
The maximum stresses are found to be 252.219N/mm2.

The Maximum temperature dissipation for alloy 718 is 61.66 0C/meter.

Deformation of Turbine Wheel for Alloy 706
The deformation of Turbine Wheel is found maximum 0.123mm at the rim.

Overall stresses of gas turbine wheel for alloy 706.
The maximum stresses are found to be 206.142N/mm2.

The Maximum temperature dissipation for alloy 718 is 121.461 0C/meter.


Results and Discussion:
Deformation mm
Stress N/mm2
Temp. dissipation 0C /m
Strength N/mm2
Steel
0.214
258.539
61.66
620
Alloy 718
0.144
252.219
61.66
1375
Alloy 706
0.123
206.141
121.46
1300
Table: 1 Results obtained by ANSYS
Deformation mm
Stress N/mm2
Strength N/mm2
Steel
0.190
233.68
620
Alloy 718
0.139
219.813
1375
Alloy 706
0.100
179.45
1300
Table.2. Results obtained by Mathematical Approach

From the table 1, it was found that the results obtained by ANSYS are nearly equal to the theoretical calculations.

From the table 1, it is found that the deformation of Alloy 706 is low as 0.123 mm, which is nearly equal to the mathematical approach, while the deformation of Alloy 718 is 0.144 mm and Timken steel is 0.139 mm.

From the table 1, it is found that the overall stress of Alloy 706 is 206.141 N/mm2 which is small comparing to the Timken Steel (258.539 N/mm2) and Alloy 718(252.219 N/mm2).

Temperature dissipation of Alloy 706 is high 121.46 co/m which is good when comparing to Timken Steel and Alloy 718( both 61.66 o c/m)

The yield strength of Alloy 706 is also high i.e. 1300 N/mm2 which is good comparatively Timken Steel (620 N/mm2) and Alloy 718(1300 N/mm2 )

The Alloy 706 has good machinability character with moderate cost.


Conclusion:
The analysis was carried out for gas turbine wheel which was done using ANSYS. It is concluded that Inconel 706 alloy was found better results than other two alloys, 718 alloy and Timken steel.
References:

G Sukhvinder kaur bhatti, Shyamala kumara, M L Neelapu, Dr. I N Niranjan Kumar, Transient state stress analysis on an axial flow gas Turbin Blades and Disk using Finite Element procedure .August 2123,2006(pp323330).

Homeshwar G.Nagapure, Dr.C.C.Handa
Analysis of stresses in Turbine Rotor using finite element method a past review, ISSN: 09755462.

John F Lee Theory and design of steam and gas turbines Mc. Graw Hill Book Company, Inc
Graw Hill publishing company limited

Tirupathi R Chandraputla and Ashok D Belegundu
Introduction to finite elements in engineering, 3rd edition, PHI publications

P Ravinder Reddy Computer aided design and analysis 2nd edition, Pearson education.