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VSB – Technical University of Ostrava Faculty of Mechanical Engineering
Department of Applied Mechanics
DIPLOMA THESIS
THE ANALYSIS OF THE TURBINE BLADE FIXTURE CRACK
Student: DHANISHKUMAR LOGANADANEEJIL
Supervisor: doc. Ing. JIŘÍ PODEŠVA, Ph.D.
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Student’s affidavit
I declare that I have prepared the whole diploma thesis including appendices independently under the leadership of the diploma thesis supervisor, and I stated all the documents and literature used.
In Ostrava on
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Dhanishkumar Loganadaneejil Pondicherry, India
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ANNOTATION OF MASTER THESIS
Dhanishkumar Loganadaneejil, The Analysis of the turbine blade fixture crack. Ostrava: VSB Technical University of Ostrava, Faculty of Mechanical Engineering, Department of Applied Mechanics, 2020, 55 p. Supervisor: doc. Ing. Jiří Podešva, Ph.D.
In this thesis, the analysis of turbine blade fixture crack is performed. The main task is to analyse the crack of the turbine blade by using the FEM model and figure out the characteristics. In this case, crack is caused by the fixture of turbine blade root inside the disk grooves when centrifugal force is applied to it and also by its material properties. For the analytical part, the mass of the blade, rotating speed, angular velocity and radius of the centre of mass trajectory are described to find the centrifugal force. For the simulation process, the commercial software Ansys Workbench is used. In the computational analysis, static structural analysis is performed. Static structural analysis is used to determine the deformation and stress in the component caused by loads. This analysis is then compared to criteria that indicate the conditions of failure.
Keywords: FEM analysis, Static structural, Turbine, Centrifugal force, Directional deformation, Equivalent von-mises stress.
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ANOTACE MASTER THESIS
Dhanishkumar Loganadaneejil, Analýza příčin praskání úchytu lopatky turbínového kola.
Ostrava: VŠB-TU Ostrava, Fakulta strojního inženýrství, Katedra aplikované mechaniky, 2020, 55 s. Školitel: doc. Ing. Jiří Podešva, Ph.D.
V této diplomové práci je provedena analýza praskliny upínání lopatek turbíny.
Hlavním úkolem je analyzovat trhlinu lopatky turbíny pomocí modelu FEM a zjistit vlastnosti.
V tomto případě je trhlina způsobena fixací kořene lopatky turbíny uvnitř drážek disku, když na ni působí odstředivá síla, a také svými materiálovými vlastnostmi. Pro analytickou část je popsána hmotnost lopatky, rychlost otáčení, úhlová rychlost a poloměr trajektorie středu hmoty pro nalezení odstředivé síly. Pro simulační proces se používá komerční software Ansys Workbench. Ve výpočetní analýze se provádí statická strukturální analýza. Statická strukturální analýza se používá k určení deformace a napětí ve složce způsobené zatíženími.
Tato analýza je poté porovnána s kritérii, která označují podmínky selhání.
Klíčová slova: FEM analýza, Statická struktura, Turbína, Odstředivá síla, Směrová deformace, Ekvivalentní von-Misesovo napětí.
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CONTENTS
1 INTRODUCTION ... 1
2 PARTS USED IN TURBINES ... 3
2.1 TURBINE CASING ... 3
2.2 TURBINE ROTORS ... 4
2.2.1 DISK TYPE ROTORS ... 5
2.2.2 DRUM TYPE ROTORS ... 6
2.3 TURBINE BLADES ... 6
2.3.1 STATIONARY BLADES AND NOZZLES ... 7
2.3.2 BLADES FASTENING ... 8
2.3.3 TWISTED BLADES ... 8
2.3.4 SHROUDS ... 9
2.4 TURBINE BARRING DEVICE... 9
2.5 BEARINGS... 10
2.5.1 RADIAL BEARING ... 10
2.5.2 THRUST BEARING ... 11
2.6 TURBINE SEALS ... 11
2.6.1 SHAFT SEALS ... 11
2.6.2 BLADE SEALS ... 11
2.7 COUPLING ... 12
2.8 GOVERNOR ... 12
2.8.1 SPEED SENSING GOVERNOR ... 12
2.8.2 PRESSURE SENSITIVE GOVERNOR ... 13
2.9 LUBRICATION SYSTEM ... 13
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3 DIFFERENT TYPES OF BLADE ATTACHMENTS ... 14
3.1 MUSHROOM-TAIL JOINT ... 14
3.2 DOVE TAIL JOINT ... 15
3.2.1 VERTICAL TYPE ... 15
3.2.2 INCLINED TYPE ... 15
3.3 FORK TAIL JOINT ... 16
3.4 T- TAIL JOINT... 16
4 LOAD DISTRIBUTION ON ROOT LANDS ... 17
4.1 CENTRIFUGAL FORCE ... 19
4.2 EQUIVALENT STRESS ... 20
5 CENTRIFUGAL FORCE CALCULATION ... 21
5.1 CALCULATION OF MASS OF THE BLADE ... 22
6 COMPUTATIONAL DESIGN OF THE COMPONENTS ... 24
6.1 T-TAIL WITHOUT VANE ... 24
6.2 ROTOR ... 25
6.3 SHROUD ... 26
6.4 T-TAIL WITH VANE ... 27
6.5 BLADE ASSEMBLY ... 28
6.6 BOTTOM T-TAIL WITH ROTOR ASSEMBLY ... 29
7 FINITE ELEMENT METHOD ... 30
7.1 FEM PROCEDURES ... 30
7.2 STATIC STRUCTURAL ... 31
7.3 GEOMETRY ... 32
7.4 CONTACT 1 ... 33
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7.5 CONTACT 2 ... 34
7.6 MESH ... 35
7.7 LOAD CONDITIONS ... 36
7.7.1 FORCE ... 36
7.7.2 FIXED SUPPORT ... 36
7.8 DIRECTIONAL DEFORAMATION WITH CONTACT 1 ... 37
7.9 EQUIVALENT VON-MISES STRESS WITH CONTACT 1 ... 38
7.10 DIRECTIONAL DEFORMATION WITH CONTACT 2 ... 39
7.11 EQUIVALENT VON-MISES STRESS WITH CONTACT 2 ... 40
8 CONCLUSION ... 41
9 REFERENCES ... 42
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LIST OF FIGURES
Figure 1 Arrangements of blades to the shaft. ... 2
Figure 2 Turbine casing [3]. ... 4
Figure 3 Turbine rotors. ... 5
Figure 4 Disk type of rotor in turbine [4]. ... 5
Figure 5 Drum type rotor in turbine [4]. ... 6
Figure 6 Blades arrangement. ... 7
Figure 7 Different types of blade according to the pressure [5]. ... 7
Figure 8 Twisted blades [6]. ... 8
Figure 9 Shrouded tip of the turbine with crack [7]. ... 9
Figure 10 Turbine barring device to startup [8]. ... 10
Figure 11 Radial Bearing [2]. ... 10
Figure 12 Thrust bearing of turbine [10]. ... 11
Figure 13 Coupling in turbine [2]. ... 12
Figure 14 Lubrication system in turbines [12]. ... 13
Figure 15 Mushroom tail joint of the blade [13]... 14
Figure 16 Vertical type of the dove tail joint [13]. ... 15
Figure 17 Inclined type of the dove tail joint [13]. ... 15
Figure 18 Fork tail joint [13]. ... 16
Figure 19 T-tail joint [13]. ... 16
Figure 20 Load distribution on root glands [14]. ... 17
Figure 21 Forced vibration of the blade due to centrifugal force [15]. ... 19
Figure 22 Equivalent von mises stress [16]. ... 20
Figure 23 Mass of three blades. ... 22
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Figure 24 Mass on light end of the blade. ... 22
Figure 25 Mass on heavy end of the blade. ... 23
Figure 26 Isometric view of T-tail blade. ... 24
Figure 27 Isometric view dimensions of T-tail blade. ... 24
Figure 28 Single part of rotor component. ... 25
Figure 29 Isometric view dimensions of single component of rotor. ... 25
Figure 30 Shroud to form a circular ring. ... 26
Figure 31 Isometric view dimensions of shroud. ... 26
Figure 32 T-tail with vane. ... 27
Figure 33 Right side view and isometric view of t-tail with vane. ... 27
Figure 34 Blade assembly in dimetric view. ... 28
Figure 35 Blade assembly in front view and right side view. ... 28
Figure 36 Bottom t-tail attached with rotor. ... 29
Figure 37 Plastic zone around crack tip [17]. ... 31
Figure 38 Isometric view of geometry of the. ... 32
Figure 39 Front view of the geometry. ... 32
Figure 40 Bonded contact 1 at surfaces. ... 33
Figure 41 Contact body view and target view of 1. ... 33
Figure 42 Bonded contact 2 at surfaces. ... 34
Figure 43 Contact body view and target view of 2. ... 34
Figure 44 Mesh ... 35
Figure 45 Force applied to the top surface of the blade ... 36
Figure 46 Fixed support in bottom side of rotor. ... 36
Figure 47 Front view of directional deformation in y-axis. ... 37
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Figure 48 Isometric view of direction deformation in y-axis. ... 37
Figure 49 Equivalent von-misses stress. ... 38
Figure 50 Equivalent von-misses stress with minimum and maximum points. ... 38
Figure 51 Front view of directional deformation with contact 2 ... 39
Figure 52 Isometric view of directional deformation with contact 2... 39
Figure 53 Equivalent von-misses stress with contact 2. ... 40
Figure 54 Equivalent von-misses stress with minimum and maximum points. ... 40
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LIST OF SYMBOLS
SYMBOL DESCRIPTION UNIT
m Mass [Kg]
Fcent Centrifugal force [N]
ω Angular velocity [rad/s]
e Eccentricity [m]
rn Radius [m]
n Rotating speed [rpm]
Lc Total length [mm]
mt Mass on heavy end [kg]
ml Mass on light end [kg]
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1 INTRODUCTION
A turbine is a rotary mechanical system that extracts and transforms energy from a fluid flow into useful work. When coupled with a generator, the work generated by a turbine may be used to generate electrical power. A turbine is a turbomachine with at least one moving component called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid works on the blades so that the rotor is pushed and given rotational energy.
Gas, steam, and water turbines have a casing that holds and controls the working fluid around the blades. Steam turbine invention credit is granted to both Anglo-Irish engineer Sir Charles Parsons(1854–1931) for reaction turbine invention and Swedish engineer Gustaf de Laval(1845–1913) for impulse turbine invention. In the same unit, modern steam turbines also employ both reaction and impulse, usually varying the degree of reaction and impulse from the blade root to its periphery.
Turbine machinery is a system where there is a continuous transfer of energy between fluid and system part revolving around its axis. This turbine machine part is commonly known as an impeller, a wheel, a rotor, a screw or a driver. Turbine engines are generators, fans, compressors, water turbines, gas turbines, wind turbines, aviation and marine propellers, torque converters, hydrodynamic clutches, etc. Blade failure is a prevalent phenomenon in a steam turbine and has a good connection with the forces acting on the blade, which are centrifugal forces, centrifugal bending, steady steam bending, unstable centrifugal forces due to lateral vibration and alternating bending. The working condition of the turbine blade during operation and deployment also plays an important role in blade failure.[1]
This diploma thesis deals with the analysis of turbine blade fixture crack. The main aim of the thesis is to analysis the crack in the turbine blade by using the FEM model and find out its dynamic characteristics. The FEM model consists of various parts such as high and low pressure compressor, high and low pressure turbine, shaft .etc . In this case, crack is caused by the fixture of turbine blade root inside the disk grooves when centrifugal force is applied to it.
For the analytical part, the mass of the blade, rotating speed, angular velocity and radius of the center of mass trajectory are described to find the crack in the turbine blade.
“Finite element analysis (FEA) is the process of simulating the behaviour of a part or assembly under given conditions so that it can be assessed using the finite element method (FEM). FEA is used by engineers to help simulate physical phenomena and thereby reduce
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the need for physical prototypes while allowing for the optimization of components as part of the design process of a project”.
For the simulation process, the commercial software Ansys Workbench is used. In the computational analysis, static structural analysis is performed. Static structural analysis is used to determine the deformation and stress in components caused by loads in the turbine blade.
This analysis is then compared to criteria that indicate the conditions of failure.
Figure 1 Arrangements of blades to the shaft.
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2 PARTS USED IN TURBINES
The steam turbines are widely used in power generation, refineries and petrochemical industries. Some of the various parts used in turbine are as follows [2],
a) Turbine casing b) Turbine rotors c) Turbine blades d) Stationary blades e) Shrouds
f) Turbine barring device g) Turbine seals
h) Turbine coupling i) Governor
j) Lubrication system
2.1 TURBINE CASING
The form of the casing and the nature of its construction depend on whether it is a case of high pressure(HP) or low pressure(LP). A single shell casing is used for the low and moderate inlet steam pressure up to 120 bar. With an increase in inlet pressure, the thickness of the casing may increase. The turbine too is very difficult to handle such heavy casing as to bring it slowly up to operating temperature. Otherwise, there may be undue internal stress or distortion to the thick casing. Dual casing is used for high pressure and temperature applications. The inner casing of the double casing is for high pressure and the outer casing is for maintaining the low pressure.
The bulk of the turbine has split-type horizontal casings. Because of horizontal splitting it is easy to assemble and dismantle for turbine maintenance. Hold proper axial and radial clearance between the rotor and stationary sections, too.
The turbine casings are normally heavy to withstand the high temperatures and pressures. The thickness of walls and flanges decrease from the inlet to the exhaust end due to the decrease of steam pressure from inlet to exhaust is common practice.
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Figure 2 Turbine casing [3].
2.2 TURBINE ROTORS
The steam turbine rotors must be designed with the most care as it is mostly the highly stressed component in the turbine. The design of a turbine rotor depends on the operating principle of the turbine. The impulse turbine, where the voltage falls into the stationary blades.
The stationary blades are mounted in the diaphragm, and the moving blades on the rotor are fixed. Steam leakage occurs between the stationary blades and the rotor. The leakage rate is controlled by labyrinth seals. This construction requires a disc rotor.
The reaction turbine has decreases in pressure through both the moving and stationary blades.
The rotor of the disk would produce a great axial thrust through each disk. Consequently, disk rotors are not used in the turbine for the reaction. A drum rotor is used for this application to reduce the axial thrust induced by the disks, but not the axial thrust generated by the differential pressure over the moving blades. Regardless of this the reaction turbine configuration is more complex.
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Figure 3 Turbine rotors.
2.2.1 DISK TYPE ROTORS
This rotor style is used extensively in steam turbines. The rotors of the disk form are rendered by way of forging. The forged weight of the rotor is generally around 50 percent higher than that of the final machined rotors.
Figure 4 Disk type of rotor in turbine [4].
6 2.2.2 DRUM TYPE ROTORS
The rotors of the reaction turbines are initially made by a rotor of the solid forged drum. The rotors are strong and rigid in construction. Because of this, the rotor 's inertia is very high as compared with the same-capacity disc-type rotor. The hollow drum-type rotors are used to solve this nowadays, instead of solid rigid rotors. This type of rotor is normally composed of two parts. In certain special cases, multi-piece construction shapes the rotor. Both outside and inside the drums are machined to achieve optimal rotor balance.
Figure 5 Drum type rotor in turbine [4].
2.3 TURBINE BLADES
The efficiency of the turbine depends on more than anything else on the design of the turbine blades. The impulse blades must be designed to convert the kinetic energy of the steam into mechanical energy. The same goes for the reaction blades, which furthermore must convert pressure energy to kinetic energy.
Below are the following factors that can withstand the blade strongly.
• High temperatures and stresses due to the pulsating steam load.
• Stress due to centrifugal force.
• Erosion and corrosion resistance.
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Figure 6 Blades arrangement.
Blades also depends on the rotor pressure region which are as follows,
• High Pressure (HP) blades.
• Intermediate Pressure (IP) blades.
• Low Pressure (LP) blades.
Figure 7 Different types of blade according to the pressure [5].
2.3.1 STATIONARY BLADES AND NOZZLES
The nozzles found in diaphragms are in all stages following the control point. The diaphragms are in halves and fitted into grooves in casing. Anti-rotating pin or locking sections in the upper part of the casing avoid a rotation of the diaphragm.
All the modern diaphragms are of an all-welded construction. For the case halves, the stationary blades for reaction turbines are mounted into grooves, keys can lock the blades. In certain
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situations, on one side of the root the blades have keys or serration, and on the other side of the root a caulking strip is used to firmly lock the blades in the grooves.
Nozzles are used to direct the steam to reach the moving blades and transform the energy from pressure energy into the kinetic energy. For small impulse turbine, the nozzles are in the lower half of the casing. However, in the case of the larger turbine, the nozzles are in the upper half of the casing.
2.3.2 BLADES FASTENING
Through the milling process, blades are machined . The blades are then inserted into the groove of a rotor. The blade root segment varies depending on the application.
Blade roots are subjected into four types of stress
• Tensile stress due to the centrifugal forces.
• Bending stress due to fluid forces act on the blade in tangential direction.
• Stress due to vibration forces.
• Thermal stress also due to the uneven heating of the blade root and the rim.[2]
2.3.3 TWISTED BLADES
This form of blades is used in a large multistage steam turbine's final stage. These are the largest turbine blade and contribute about 10% of the total turbine output. Since these types of blades are larger in size they are subject to strong centrifugal and bending forces. Twisted structure is used to combat these forces.
Figure 8 Twisted blades [6].
9 2.3.4 SHROUDS
The shrouds are used to protect free ends of the turbine blades to minimize friction and leakage. It is achieved by reverting a flat end over the blades. In some cases the shroud can be integral with the blade, particularly at the early stages. When the blades are very long, as in the case of the last LP turbine stage. The rotor blades are further strengthened by the use of lacing wires (caulking wire), which link all blades circumferentially at a desired radius and remove the shrouding.
Figure 9 Shrouded tip of the turbine with crack [7].
2.4 TURBINE BARRING DEVICE
When a turbine is left cold and at a standstill, the rotor weight appears to slightly bend the rotor. If left at a standstill while the turbine is still hot, the lower half of the rotor will cool off more rapidly than the upper half and the rotor will bend "hog" upwards. For both situations it will be hard to power the turbine. To solve the problem the manufacturer provides the larger turbines with a turning or barring gear consisting of an electric motor that turns the turbine shaft at low speed through multiple sets of reduction gears.
The first turning gears turned the shaft at around 20 rev/mm, later increased to 40 and up to 60 rev/mm as it is difficult to achieve sufficient lubrication at low speed. Many turning gears, whether electrical or hydraulic, switch the shaft 1800 over 24 hours at fixed times.
Before a cold turbine is started it should be around three hours on the barring equipment. This will be barring for the next 24 hours when a turbine is shut down. When involving a hydrogen- cooled generator, the turbine should be held on the barring gear to avoid undue loss of hydrogen, all barring gears are interlocked with a lubricating oil pressure switch and an engagement limit switch controlled by the engagement handle.
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Figure 10 Turbine barring device to startup [8].
2.5 BEARINGS
Although bearings are used in a nacelle in many ways, such as in the yaw and pitch bearings and on generators, those on main shafts and gearboxes are the most troublesome.
There are two types of bearing used in turbine. They are as follows,
• Radial Bearing
• Thrust Bearing 2.5.1 RADIAL BEARING
For small turbines often fitted with bearings of the anti-friction kind. The radial bearing will be a form of tilting pad for larger turbines. The pad number per bearing will be chosen based on rotor weight. For forced lubrication these types of bearings is used.
Figure 11 Radial Bearing [2].
11 2.5.2 THRUST BEARING
Thrust bearings retain the rotor 's axial location in spinning equipment, transferring the rotor's axial load to stationary frame. The thrust bearing is positioned at the rotor's free end or at the turbine 's steam inlet. The main two purposes of the thrust bearing are:
• To keep the rotor in an exact position in the casing.
• To absorb axial thrust on the rotor due to steam flow.[9]
Figure 12 Thrust bearing of turbine [10].
2.6 TURBINE SEALS
Seals are used to reduce steam leakage between the steam turbine 's rotational and stationary parts. The seals are classified as two types depending on the location of the seal,
• Shaft Seal
• Blade Seal 2.6.1 SHAFT SEALS
Shaft seals are used to avoid the leaking of steam, as the shafts pass into the container.
For small turbines , carbon rings are used as shaft seals up to a shaft surface. The carbon ring is composed of three segments, butting tightly together under a garter spring pressure. The carbon rings in the housing are free flowing, so an anti-spinning pin is used to keep carbon ring seal from spinning.
2.6.2 BLADE SEALS
Blade seals are used to prevent the release of steam between the diaphragm and the shaft.
Turbine efficiency is largely dependent on blade seals. In the tiny and wide turbines labyrinth
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seals are used as blade seals. In the case of large labyrinth seals charged by steam turbine spring are required.
2.7 COUPLING
Couplings are intended to transfer power from the prime mover to the driven piece of machinery. Flexible couplings of the kind are found in turbines. Coupling hubs are taper bore and a key way to fit the tapered end of the shaft.
Figure 13 Coupling in turbine [2].
2.8 GOVERNOR
One of the basic parts of the steam turbine is the Governor. The principal role is to monitor the steam turbine activity. The governor is generally classified as being of two types,
• Speed-sensing governor.
• Pressure sensing or load governor.
2.8.1 SPEED SENSING GOVERNOR
In power generation applications, speed-sensing governors are used to maintain a constant speed with respect to the governor's change of load. Droop is one of the key features of this selection of Governors. In a digital governor, the program usually executes roles performed by machines such as power motors, solenoids, and location switches in mechanical and analogue governors. Digital devices may be carried out in every configuration, as program improvements or adjustments may be easily rendered without external specifications.
13 2.8.2 PRESSURE SENSITIVE GOVERNOR
These are applied in connection with the speed-sensitive governor on back pressure and extraction turbines.
Three forms of governors are used in steam turbine,
• Mechanical Governor
• Hydro-mechanical Governor
• Electronic Governor
2.9 LUBRICATION SYSTEM
Turbines are almost exclusively lubricated by petroleum mineral oils and the systems described are not necessarily suitable for other types of lubricant.
Oil lubrication is used for small turbines, and bigger turbines are designed for pressurized lubrication. The pressure lubrication device comprises of a lube oil tank, oil pump, filter, cooler, pressure regulating valve, etc. Steam turbine lube oil device is normally needed to provide oil for the trip-and-throttle pump, governor mechanism, power cylinder or related accessories (combined pressure lubrication and oil control unit).
A steam turbine main bearings are simple white metal journal bearings, which are hydrodynamically lubricated by creating a high-pressure oil wedge between the shaft.
Hydrostatic pressure lubrication is required to raise the shaft from the bottom of the bearing, leading to the stress on the bearings of massive turbines at start-up. When the output of the turbine is transmitted through reduction gears, it will be in the form of double helical type and are spray or bath lubricated [11].
Figure 14 Lubrication system in turbines [12].
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3 DIFFERENT TYPES OF BLADE ATTACHMENTS
Attaching the blades to the rotor is achieved by providing machined surfaces on the blade and the rotor that function in a locking system together. The configuration of the blade attachment area differs between suppliers, which on an individual rotor may differ from row to row. The connection region is built to make it fairly convenient to adjust the blades if they should be broken during operation, in addition to the primary task of securing the blade onto the rotor. Also, cutting blades can be highly time-consuming. The method also has the ability to destroy the blades beyond repair. Consequently, blade removal is best avoided when possible.
Some of the commonly used root attachments in turbines is not only steam, but the following are also gas type [13],
3.1 MUSHROOM-TAIL JOINT
In the lower part of the root one incorporates a flange (circular edge) used to prevent the radical segment from being opened during the blade's rotation as a result of the blade 's reaction to the appearance of attachment on the edge of the rotating disk.
It is important to render the relation between the supporting surfaces in ideal proportions in order to prevent the uneven distribution of loads in the root attachments and this condition can be accomplished by minimizing the gap between them to the highest possible precision.
Figure 15 Mushroom tail joint of the blade [13].
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3.2 DOVE TAIL JOINT
Dove tail joint are widely used based on the temperature and loads. The types are classified as follows,
• Reliability work.
• Easy assembly and disassembly.
• Tolerability large centrifugal force of up to 100Tf.
3.2.1 VERTICAL TYPE
The vertical type in which the angle between the axis of symmetry of the root portion and tangent to edge of rotating disc is right angle. This form used in the rotor, which carries relatively limited number of blades, that is, the phase between the blade and the other blade will be equal to the thickness of the air foil of the fixed blades at the edge of the disk, and this is in the turbine's first stages.
Figure 16 Vertical type of the dove tail joint [13].
3.2.2 INCLINED TYPE
Inclined type which are non-right angle. This method is mostly used for the disk carrying a large number of blades in which steps between the blades would be relatively small in the final stages and distinguished by sufficiently large number and length of used blades.
Figure 17 Inclined type of the dove tail joint [13].
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3.3 FORK TAIL JOINT
The root includes complex and similar projections ringing on the edge of the disk with existing rules, as shown in (Figure 18). This type is characterized by the following,
• Installing the blades within the disc be consistent.
• Ease of replacements of blades individually.
• The absence of ruling blade in the fittings.
Figure 18 Fork tail joint [13].
3.4 T- TAIL JOINT
It is the root component in the form of letter T, which has the following characteristic.
Blade root slot on the turbine rotor impeller is divided into T shape blade root slot and fir type groove . Here in this thesis we use T-tail joint for blade.
• Simplicity in design and manufacturing.
• Rigidity in installation.
Figure 19 T-tail joint [13].
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4 LOAD DISTRIBUTION ON ROOT LANDS
Basic principles of load transfer from the blade to the rotor, an impulse blade with a symmetrical T-root, as shown in Figure 10, shall be considered. The blade forces are grouped into centrifugal forces and into axial and circumferential bending forces. For the stiffness effects of both rotor (drum and disc) and the blade root, the reduction of the bending force into its axial and circumferential component is required.
The moment of bending, caused by the circumferential portion of blade force, tends to extract the rotor blades, similar to a centrifugal force action. (Figure 20) shows the load distribution in
Figure 20 Load distribution on root glands [14].
When the centrifugal force is applied on the vane of the blade, there will be a deformation in the platform and root lands of the blade in which stress occurs at the fillet and shank.
Three major types of start-ups,
• From a cold state – when HP and IP inner casing temperature is lower or equal 170°C.
• From a warm start – when HP and IP inner casing temperature is lower or equal 430°C.
• From a hot state – when HP and IP inner casing temperature is greater than 430°C.
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The joint between either a compressor or a turbine blade and the rotor is frequently the weakest part of the entire rotating assembly. It is widely accepted that the two most important ways of loading which work on the blade are the following,
• A radial centrifugal force which pulls the blade away from the joint.
• The bending of the blade as a cantilever.
The bending is created dynamically by the gas pressure motion on the air foil, and by a tangential component of the centrifugal forces due to an air foil tilting. Also, the bending load has a dynamic portion that is generated by blade vibrations. This point of view assumes therefore that stresses due to other factors such as residual and thermal stresses are secondary influences and may be neglected for design purposes. The two basic ways of testing, namely tensile testing and bending loading, were applied to the blade models and the actual blades.
The steady stress at any section of a parallel sided blade is a combination of direct tension due to centrifugal force and bending due to steam force. Both of which are acting on that portion of blade between the section under consideration and the tip. The direct tensile stress is maximum at the blade root and is decreasing towards the tip. [14] The centrifugal force depends on the density of material on the edge, the length of the edge, rotation pace, and blade cross-sectional area.
The impulse turbine blades are, however, prone to bending stresses because of the centrifugal forces, the tangential force of the fluid and the centroids of the edge. Both turbine blades endure vibration loads and pressures due to vibration. The average tensile and bending pressures at the root are optimum and decrease by distance.
For tapered blades the direct tensile stress diminishes less rapidly outwards the tips, while the bending stress can be made to increase at greater radii. It is therefore possible to design the blade as a cantilever, with constant tensile stress (centrifugal stress) and bending stress and by doing so the blade material is much more effectively utilized.
Centrifugal stresses are a function of the mass of the material in the blade, blade length, cross- sectional area of blade (profile area) and rotational speeds. To calculate the centrifugal stresses on a moving blade, assume a single blade fixed to the disc.
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4.1 CENTRIFUGAL FORCE
When an blade is moving in a circular motion which acts outwardly away from the centre of rotation is said to be a centrifugal force. The below-given (Figure 21) represents the vibrating body with the rotating mass, stiffness.
Centrifugal force acts on centre of mass and periphery of the area, allowing tensile stress to concentrate on one side of the blade's centre of gravity and the other is compressive stress. The blade is designed to balance the airflow load in the centre of the blade 's edge, blade designers use the centrifugal bending effect to reduce the effects of airflow bending.
Airflow bending occurs at three levels of HP, IP and LP, but is most pronounced at the HP level where the pressure difference between the blades is the greatest. At the LP level, airflow bending is also prevalent, because the LP blade is much longer than HP or IP.
Figure 21 Forced vibration of the blade due to centrifugal force [15].
Where,
m
rot – the rotating mass in kg,ω
– the angular velocity of the rotating mass in rad/se
– eccentricity in mHere we know the diameter of the blade, therefore we can find the radius, R = 0.5. D + a
Rotating speed of the turbine (n) is given as constant, n = 3000 min-1
20 Angular velocity (𝜔) can be calculated by,
𝜔 = 2. 𝜋. 𝑛
The rotation of the system produces the constant centrifugal force:
Fcent= mrot∙ ω2∙ R
4.2 EQUIVALENT STRESS
An equivalent tensile stress or equivalent von Mises stress σV is used to predict yielding of materials under multiaxial loading conditions. Equivalent stress is used when there is a multiaxial stress state with multiple stress components acting at the same time in the structure.
In this thesis, we can use selected criterion to transform the whole stress tensor into a single equivalent component that can be treated as a tensile stress and thus compared with material’s strength easily. It’s commonly used in engineering as for example Finite Element Analysis programs use it as a default stress measure.
Figure 22 Equivalent von mises stress [16].
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5 CENTRIFUGAL FORCE CALCULATION
𝑔1 = 9.81 𝑚. 𝑠𝑒𝑐 − 2 𝑔 = 9.807 𝑠 − 2
N= Newton kN= 103 newton
𝑚31 = 3.67 𝑘𝑔 The mass of three blades.
𝑚11 =𝑚31
3 𝑚11 = 1.223 𝑘𝑔 The mass of one blade.
𝑚𝑡 = 2.8 𝑘𝑔 The mass on heavy end of the blade.
𝑚𝑙 = 1.5 𝑘𝑔 𝑚𝑡 + 𝑚1 = 3.78 𝑘𝑔 The mass of light end of the blade.
𝐿𝑐 = 205 𝑚𝑚 Total length.
𝑎 =
𝑚𝑙.𝑙𝑐𝑚𝑡+𝑚𝑙 𝑎 = 81.349 𝑚𝑚 The distance from centre of mass to heavy end of the blade.
𝑏 =
𝑚𝑡.𝑙𝑐𝑚𝑡+𝑚𝑙 𝑏 = 123.651 𝑚𝑚 The distance from centre of mass to light end of the blade.
𝐷 = 965 𝑚𝑚 The diameter of the blade fixing on rotor.
𝑅 = 0.5. 𝐷 + 𝑎 𝑅 = 563.849 𝑚𝑚 The radius of centre of mass trajectory.
𝑛 = 3000 𝑚𝑖𝑛 − 1 The rotating speed.
𝜔 = 2. 𝜋. 𝑛 𝜔 = 314.159 𝑠 − 1 Angular Velocity.
𝐹𝑜𝑑 = 𝑚11. 𝜔2. 𝑅
𝐹𝑜𝑑 = 68.078 𝑘𝑁 Centrifugal force
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5.1 CALCULATION OF MASS OF THE BLADE
The basic parameters for the numerical solutions are used such as masses and dimensions, rotating speed and angular velocity. In this analytical calculation, directional deformation and stress can be calculated.
Figure 23 Mass of three blades.
Figure 24 Mass on light end of the blade.
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Figure 25 Mass on heavy end of the blade.
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6 COMPUTATIONAL DESIGN OF THE COMPONENTS
In this chapter, the individual parts of the turbine blade are designed in 3 dimension.
Furthermore, the dimensions of the blade are measured and designed to make crack analysis in shrouds and in T-tail joints. The blade components are collected from the industry and designed using solidworks software.
6.1 T-TAIL WITHOUT VANE
The dimensions are measured and the t-tail blade is designed using the solidworks software. Here the t-shaped blade is used for crack analysis. The bottom face of the t-shape blade is connected with the top surface of the rotor.
Figure 26 Isometric view of T-tail blade.
Figure 27 Isometric view dimensions of T-tail blade.
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6.2 ROTOR
Rotors are connected with rotor blades that are attached to a rotating shaft that runs through turbines, generators and sometimes air compressors (which are present in combined cycle applications). In a turbine, rotor blades are the means by which thermal/kinetic energy is transformed into rotating mechanical energy.
Figure 28 Single part of rotor component.
Figure 29 Isometric view dimensions of single component of rotor.
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6.3 SHROUD
Shroud are placed on the top surface of the twisted blade in order to reduce vibration.
The shrouded tip is placed on the top surface to form a circular ring shape. Two types of the impact vibration that occur in the system are studied
• 1-side impact where only one side of the shroud collides with another shroud.
• 2-side impact where both sides of the shroud collide with the adjacent shrouds.
Comparisons between the two types of the impact vibration show that the amplitude of the 1- side impact is larger than that of the 2-side impact while the resonance frequency of the 1-side impact is smaller.
Figure 30 Shroud to form a circular ring.
Figure 31 Isometric view dimensions of shroud.
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6.4 T-TAIL WITH VANE
In the (Figure 32) shown below, the vane of the blade is on the top surface of the T-tail in which the shroud will be placed on the top surface of the vane. A curved line is formed on the surface and a plane is created from axis to a distance of 207.50mm and similar curved line is drawn in opposite direction. Lofted base is used to form the curved structure of the blade.
This type of blades are connected to the rotor in a circular form. Based on the HP,LP and IP rotors there will be change in structure of the blade.
Figure 32 T-tail with vane.
Figure 33 Right side view and isometric view of t-tail with vane.
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6.5 BLADE ASSEMBLY
The complete structure of the assembly is shown in (Figure 34). The rotor, t-tail blade with vane and shroud are assembled to form a circular form. Since, crack occurs only in t-tail blade without vane and the rotor, we use one part of the t-tail blade without vane in it for analysis. Dimetric, front side and right side views are shown Figure 34 and Figure 35.
Figure 34 Blade assembly in dimetric view.
Figure 35 Blade assembly in front view and right side view.
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6.6 BOTTOM T-TAIL WITH ROTOR ASSEMBLY
Since the crack occurs only in the bottom region of the t-tail blade which is between the shank and the root glands of the rotor. The assembly is made without the vane design and structural analysis is used to perform the directional deformation and stress of the component in order to reduce the crack in the platform. The assembly design which is attached to the rotor in shown in the (Figure 36) below.
Figure 36 Bottom t-tail attached with rotor.
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7 FINITE ELEMENT METHOD
The finite element method (FEM) is the most commonly used technique to solve mathematical models and practical problems. In 1956, the use of finite elements for the study of aircraft structures was proposed and it is considered as one of the main contributions for the advancement of this method. The finite element approach was initially designed for the analysis of airplane stiffness. Subsequently, stress analysis is the most common application of FEM.
Clough introduced the idea of the finite element method in his popular book “The Finite Element Method in-plane stress analysis”. FEM is the computational method used to find approximate results of boundary value problems in engineering. It shows that a component failure, wear out, or perform the way it was made. It is used in the process of design and development to predetermine what will happen when the product is being used.[16]
7.1 FEM PROCEDURES
To summarize in general terms how the finite element method works, the three main steps of FEM analysis procedures are given below,
[1] Pre-processing, [2] Solution, and [3] Post-processing.
The first stage is to divide the whole geometry into several sub-domains to allow mathematical analysis. The material properties, boundary conditions are essential to apply each of the sub- domains. The aim of the pre-processing is to create finite element mesh for better accuracy of results. In the computational method, the user can use any type of material with user-defined properties and boundary conditions may apply with certain constraints and loads to the material. Develop equations for an individual element and assemble all the element equations.
These are all the steps processed in the pre-processing stage.
In this stage, the computational software used for the finite element analysis originates the matrix equations from the geometrical model and solve for all the key measures individually.
Static structural method is used for the solution. Solve a set of non-linear or linear algebraic equations instantaneously to get results such as displacements, stress, strain, temperatures, and so on.
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This is the last stage of finite element analysis. After the FEM model is designed, tested and the entire FEM model is resolved successfully. Users can monitor the solutions and examine the result of all primary quantities such as displacement in a particular direction which are obtained after the solution.
In this thesis, Ansys Workbench is used for the simulation process. Static structural is used to determine the directional deformation and equivalent von-mises stress of the turbine blade fixture crack.
7.2 STATIC STRUCTURAL
A structure refers to a connected body or system of parts used to support a load. If a structure's dimensional requirement has been established , it is important to decide the loads which the structure will bear. There are two types of loads that the structure will withstand.
The first type of loads are dead loads consisting of the weights of the various members of the structure and the weights of any objects permanently attached to the structure. The second form of loads is live loads that differ in magnitude and location.
The finite element method approximates a structure as an arrangement of elements or components with various ways of interaction between them and each of which has a stiffness correlated with it.
In this project, static structure is used by applying the load condition to the blade which attains the crack with deformation and change in stress. So, it is necessary to perform a static structural analysis to perform crack test.
Figure 37 Plastic zone around crack tip [17].
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7.3 GEOMETRY
The geometrical design of the turbine blade which is assembled is attached to make the analysis of directional deformation and stress. Isometric view and front view of the geometry are shown in (Figure 38) and (Figure 39).
Figure 38 Isometric view of geometry of the.
Figure 39 Front view of the geometry.
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7.4 CONTACT 1
As shown in (Figure 40) the left and right surfaces of the t-tail blade which is adjacent to the rotor are made in contact. The t-tail blade surface are contact bodies and rotor surfaces are target bodies.
Figure 40 Bonded contact 1 at surfaces.
Figure 41 Contact body view and target view of 1.
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7.5 CONTACT 2
As shown in (Figure 42), the left and right side of the rotor parts which is interconnected with the t-tail blade are made in contact in order to reduce stress. Rotor surfaces are contact bodies and t-tail blade surfaces are target bodies.
Figure 42 Bonded contact 2 at surfaces.
Figure 43 Contact body view and target view of 2.
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7.6 MESH
The precision that can be achieved from any FEA configuration is directly related to the mesh used for finite elements. The finite element grid is used to subdivide the CAD layout into smaller domains called components. Meshing is more important to obtain an accurate result from an FEA model. The element in the mesh by considering many aspects into reason to be able to discretize stress gradients precisely. Naturally, the smaller mesh size gives more accurate results. Other important aspects of meshing are element types such as 1D, 2D, or 3D. The element size is given as 0.9mm in order to get smaller mesh. Number of elements are 61005 and number of nodes are 218217.
Figure 44 Mesh
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7.7 LOAD CONDITIONS
7.7.1 FORCE
In t-tail blade component the force of 68078 N (or) 68.078 kN is applied to the top surface in upward direction.
Figure 45 Force applied to the top surface of the blade
7.7.2 FIXED SUPPORT
Figure 46 Fixed support in bottom side of rotor.
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7.8 DIRECTIONAL DEFORAMATION WITH CONTACT 1
When applying the force in upward direction and making the bottom of rotor as fixed by using configurations of contact 1, the direction deformation is shown in Figure 47 and Figure 48.
Figure 47 Front view of directional deformation in y-axis.
Figure 48 Isometric view of direction deformation in y-axis.
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7.9 EQUIVALENT VON-MISES STRESS WITH CONTACT 1
In this chapter, the equivalent von- mises stress is calculated based on the force applied to the component. The maximum stress occurs in the t-tail blade of the component’s edge point which leads to breakage of the component when contact 1 is used.
Figure 49 Equivalent von-misses stress.
Figure 50 Equivalent von-misses stress with minimum and maximum points.
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7.10 DIRECTIONAL DEFORMATION WITH CONTACT 2
When applying the force in upward direction and making the bottom of rotor as fixed by using configurations of contact 2 , the direction deformation is reduced in its values when compared to contact 1. Here, both contact 1 and 2 are used to reduce the deformation as shown in Figure 51 and Figure 52
Figure 51 Front view of directional deformation with contact 2
Figure 52 Isometric view of directional deformation with contact 2
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7.11 EQUIVALENT VON-MISES STRESS WITH CONTACT 2
As shown in Figure 53 and Figure 54 there is a maximum stress occurs t-tail blade which leads to crack or even breakage. The stress occurs at certain divisions of the rotor. Since, the material used for this chapter is structural steel there is maximum stress of 830.02 Mpa.
When plastic material model is used there will be a reduced stress when compared to the structural steel to lower the crack in the component.
Figure 53 Equivalent von-misses stress with contact 2.
Figure 54 Equivalent von-misses stress with minimum and maximum points.
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8 CONCLUSION
In this thesis work, the analysis of turbine blade fixture crack is performed by using the finite element method and computer software Ansys Workbench 2019 R3. The first part of the thesis is described as an introduction, load case definition and a brief explanation about the finite element method. In that, the basic concept of the turbine and its parts are explained. The types of blades according to the various aspects are discussed. In chapter 5, the centrifugal force calculations is performed. In chapter 6, the computational design of each turbine blade components and rotor are explained. In chapter 7, the finite element method and the working principle are explained. Furthermore, Ansys Workbench 2019 R3 is used for the simulation process. Static structural is used to determine crack analysis of the turbine blade fixture crack.
In chapter 7, the geometry of the turbine blade and rotor is attached with contacts at the surfaces. Meshing of the component is performed. The crack analysis is performed initially without making contact at the t-tail blade to find the deformation and equivalent von-mises stress with contact 1 and secondary part of the chapter is performed by making contact with both surfaces which is located at the left and right side of the t-tail blade connected with rotor.
The analytical solution of centrifugal force is calculated using the data given by the professor.
In chapter 7, force is applied to the top surface of the component by making the bottom surface of the rotor in fixed support. Furthermore, in the secondary part of chapter 7, the static structural analysis is performed to find the directional deformation and equivalent von- mises stress of the component by applying the load conditions. Centrifugal force is calculated by the use of mass of turbine blade.
The explanation of the directional deformation and stress are discussed each with figures. In this thesis, the material used for the component is structural steel. Therefore, we get the directional deformation and stress at higher state of values in which plastic material model can also be used for the component by inputting the tangent modulus and young’s modulus to get a reduced stress values. The directional deformation and equivalent von- mises stress of the given component are discussed.
Finally, the computational design of the component and analysis performed are also attached with diagrams in this thesis.
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