1
2
1,2 Department of PG Studies, VTU, Gulbarga, Karnataka. chetanchougule.a10@gmail.com
, babureddy.dh@gmail.com
Abstract: Now a day’s the fir-tree joint is very much evident from the literature that not much work carried out on effect of cooling passage of fir-tree root joint of turbine disk. The method of attaching the blades to the turbine disk is of considerable importance, since the stress in the disk around the fixing or in the blade root has an important bearing on the limiting rim speed. On earlier days, whittle engine were attached by the devotail fixing but this design was soon superseded by the fir-tree fixing that is now used in majority of gas turbine engines. The fir-tree fixing type involves very accurate machining to ensure that the loading is shared by all the serrations. When the turbine is stationary, then the blade is free in the serrations and is stiffened in the root by centrifugal loading when the turbine is rotating. This paper proposed the work on the development of geometric model of disc and blades for turbine.
Keywords— FIR-TREE, SOLID BLADE, HOLLOW BLADE,
CATIA V5.
I.
INTRODUCTION
The Gas turbine engine design is the most highly advanced design. A good design is one which provides all the strength and rigidity to meet all its design requirements. The structural components of the gas turbine engine consist of compressor, combustor, turbine, exhaust system and a convergent-divergent nozzle. The sectional view of the gas turbine engine as shown in Figure 1. the chamber. The mixture is burned at high temperatures to generate the maximum possible heat energy. The burning process is initiated by igniter plugs, isolated after start-up, and remains continuous until the fuel supply is shut off.
In a gas turbine engine, the output of the turbine is used to turn the compressor (which may also have an associated fan or propeller). The hot air flow leaving the turbine is then accelerated into the atmosphere through an exhaust nozzle to provide thrust or propulsion power.
The exhaust system passes the turbine discharge gases to atmosphere at a velocity, and in the required direction, to provide the resultant thrust [1-2].
II.
LITERATURE SURVEY
Wenbin Song et al [3] has carried out automation and optimization of the design of a turbine blade fir-tree root by incorporating a knowledge based intelligent computer-aided design system (ICAD_) and finite element analysis. The firtree joint used to hold a blade in place in a turbine structure is usually identified as a critical component which is subject to high mechanical loads. Most often the attachment is a multi-lobe construction used to transfer loads from blade to disk. The loading on the root is mainly due to centrifugal load which is dependent on the mass of the whole blade.
The design of the fir-tree root involves an iterative process of controlling the blade mass, which incorporates the root mass. Also some key features, such as the fillet radius, play very important roles in the stress distribution in notch regions.
Fig.1: Sectional view of the gas turbine engine
The thermodynamic process requires a supply of air under pressure. The purpose of the compressor is to raise the pressure of the air besides a small rise after air intake. A compressor includes a
(mobile blades) which imparts motion to a mass of air and a stator (stationary vanes) which transforms the velocity into pressure.
In the mobile blades the velocity of the flow increases because of the motion imparted to the air and the pressure increases because of the configuration of the blades (divergence). In the stationary vanes the velocity is transformed into pressure because of the divergent air path, and the flow is straightened.
The combustion chamber receives air from the compressor, which mixes with fuel sprayed from nozzles in the front of
H. D. Conway et al, [4] developed a numerical method for finding the distributions of contact stresses between two and three-dimensional elastic bodies which were pressed together, the area of contact either being free from or subjected to frictional forces. The method was first applied to the plane stress problem of a strip which was compressed by a rigid, axially-loaded, flat-ended indenter where the contact surfaces were either free to slide over one another
(zero friction coefficient) or locked together (large friction coefficient). Numerical values of the contact stresses and displacements were computed in each case of several indenter width vs strip depth ratios.
G. D. Singh and S. Rawtani [5] discussed that in a blade root several parameters are involved and also the number of steps may vary. Hence the study of the effect of these parameters individually on the deformation pattern of the blade root was conducted. They studied a three step Fir Tree root individually for stiffness characteristics at the top and bottom neck for normal step load, tangential friction load due to contact between the blade and disc studs and the distributed centrifugal body force due to rotation. Used the

stiffness of a fir-tree joint to characterize that load sharing.
Deformations of the root for different values of applied load were determined based on a simplified finite element model.
Subsequently, a regression analysis was employed to characterize the stiffness of the different teeth.
IV.
SYSTEM DESIGN
The work carried out in this paper is to development of geometric model of Disc and Blade for turbine. Geometric modeling will be carried out by using Catia tool. Further
Geometric model will be converted into FE model using commercially available too Ansys workbench. Figure 2 shows structural view of turbine disc.
Cheng-Hung Huang and Tao-Yen Hsiung[6] in their paper have discussed an inverse design problem is solved to determine the shape of complex coolant flow passages in internal cooled turbine blades by using the conjugate gradient method. The CGM together with the BEM was successfully applied for the solution of the inverse design problem to estimate the optimal shape of the internal cooling passages in turbine blades. Several test cases involving different design considerations were examined.
III.
RELATED WORK
A fir-tree joint may be used in turbine structures to attach a blade to the rotating disk. Mechanical loads are transferred through the joint from the blade to the disk. The overall aim of fir-tree structure optimization program is to enable the designer to explore different candidate geometries at the preliminary stage, ranging from relatively simple designs to rather complex ones, at a reduced cost compared to using previous manual methods (such costs have often prevented the exploration of more complex profiles and different size and shape teeth). This process involves the use of feature- based parametric geometry construction tools such as
CATIA and large-scale structural finite analysis packages, along with an optimization program implementing various search strategies. Although this problem is basically a structural analysis problem, the strategy employed here is rather different. The use of the CATIA system and finite element analysis software together gives it the capability to model the variations parametrically both for dimensions and in the topology used, and to analyze the e ffect of geometric features on the stress distribution based on the finite element analysis results. Further- more, the above process may be incorporated into a search loop to automatically find the best solution against predefined constraints. As considered here, this is a 2D problem nested in the overall 3D blade/disc optimization procedure and uses well established 2D criteria modified from 3D analysis. The overall architecture of the
CATIA based design optimization used is illustrated in
Fig. 2. In this structure, CATIA is used to generate the model definition based on rules which may be stored in a knowledge database. The model is defined in a descriptive form using the CATIA design language which is a derivation of and extension to common LISP, aimed at geometric modeling capabilities. This model is used to produce geometry and related information. The geometry is then passed to the analysis code along with any geometry dependent properties to evaluate the design performance.
The optimizer is used to find the best solution for a particular set of design parameters. Parallel processing can be achieved by using facilities provided by the OPTIONS search systems.
Fig.2: Structural view of turbine disc
The major function of the turbine is to extract energy from the hot gas flow to drive the compressor and the accessory gearbox. Gas turbine disc works mostly at high temperature gradients and are subjected to high rotational velocity. High speed results in large centrifugal forces in discs and simultaneous high temperature reduces disc material strength.
The joint between the turbine blade and the disc usually represents the most critical area from the point of view of the static and fatigue approaches. The loads associated with these regions are mainly the centrifugal forces and thermal stresses.
The turbine discs basically have three critical regions for which lifetime certification is necessary: the fir-tree rim region, the assembly holes or weld areas and the hub region.
Fig. 2 shows these areas dong with their associated loads.
In this study, attention is devoted to examining the effect of the critical geometric parameters upon the contact stress distribution and load sharing between the different teeth of a fir-tree joint. These features, include the number of fir-tree teeth n i
, flank length 1, contact angle a, and flank angles P

and y which define the tooth pitch. In addition, interface conditions in the fir-tree region will be studied by varying the coefficient of dry elastic Coulomb friction p.
4.1 DESIGN IN THE PRESENCE OF UNCERTAINTIES
Although a part is designed to deliver the desired structural performance for its service life, existence of uncertainties in different parameters may have an effect on its life expectancy. From a structural point of view, uncertainties or variations may arise due to fluctuations in loading and boundary conditions, environmental conditions, geometric parameters, or deviations in material properties such as the yield strength, Poisson’s ratio, etc. Uncertainties may also result from assumptions made while modeling a real engineering problem. Variations due to manufacturing may result in a final part which has deviations with respect to the nominal geometry. This uncertainty in the geometric parameters may result in a scatter in the overall efficiency, performance and hence life expectancy of the part. Recently a lot of e ff ort has been made to include such uncertainties in the system variables while performing design studies both in academia and industry. It has become essential to understand and quantify the e ff ects these uncertainties have on the performance of the part, while designing it, with a goal to minimize them. For this reason the two most commonly used approaches used by researchers are robust design and reliability-based design.
4.1.1 RELIABILITY BASED DESIGN OPTIMIZATION
(RBDO)
To prevent catastrophic failure while designing a critical component in a structural sys- tem, reliability-based design optimization can be adopted. The constraint conditions of the optimization problem are characterized by the probability of its structural failure.
Reliability-based design optimization can be considered as the process of minimizing the cost function under the observance of probabilistic constraints instead of the conventional deterministic constraints. The inclusion of probability of failure in the reliability analysis can be achieved using various di ff erent methods. The simplest and most direct method to gather such information is to perform
Monte Carlo simulation on a large amount of sampled data which can be a computationally expensive exercise. The first and second order reliability methods require an additional nonlinear con- strained optimization procedure for locating the most probable point of failure making the
RBDO a two-level optimization process. Weighted regression based response surface methods have been adopted for structural reliability analysis to overcome some of these computational burdens. However, the approximation methods used for the constraint functions can su ff er in accuracy when the constraint functions are highly nonlinear.
4.1.2 ROBUST DESIGN OPTIMIZATION
Engineering components can be designed by optimizing the parameter values with respect to a single or multiple objective functions. These parameter values are then de- livered to the manufacturing unit in the form of engineering drawings with tolerances on the geometric entities.
However, these manufactured components are subject to variations due to the processes used for producing them.
Variations in designed parameters may also occur during the operation period. Robust design is the field of research that aims to tackle such problems by minimizing the e ff ect, of variations in the design parameters, on the performance of the component. The optimum design is sought with- out eliminating the source of uncertainty or variation. Instead of designing a component based just on the nominal performance, the variations occurring because of the inaccuracies in modeling, variations due to manufacturing tolerances and operating conditions are given due consideration. The robust designs have slightly worse nominal performance as compared to an optimization on nominal performance alone. Some designs can show improvements in both nominal performance as well as the extent of variation in performance, however these are not properly optimized to begin with. In their survey, Beyer and
Sendoff have given a comprehensive list of di ff erent approaches to perform robust design optimization.
Taguchi’s work on developing a design methodology that accounts for the uncertainties in the framework of quality engineering has been regarded as one of the earliest works on robust design.
4.2 DIFFERENT METHODS ADOPTED IN FASTENING
BLADES TO DISCS
Fig.3: Different blade fastening arrangements
Fig. shows the different methods adopted in fastening blades to discs. These are: pin joint, dovetail and fir-tree. Dove-tail joints are commonly used for the disc blade attachments in compressors whereas fir trees are used for the turbine disc blade attachments. . Fir-tree fasteners have ken commonly implemented in turbines because they provide adequate multiple areas of contact over which large centrifugal stresses can be accommodated.

V.
FIR TREE JOINT WITH BLADES
Two types of blades used in this work such as
5.1. Solid Blade
5.4.Hollow Blade
Fig.6: Catia model of solid blade
Fig.4: Solid Blade
5.2.Holow Blade
Fig.5: Hollow Blade
VI.
MODELING RESULTS
The following figure shows CATIA model of solid and hollow blade.
5.3. Solid Blade
Fig.7: Catia model of hollow blade
CONCLUSION
The following conclusions can be drawn from the results obtained
1. The maximum stress occurs at the fillet location on the blade due to more load is accumulated at the location.
2. The displacements of hollow blade and fir tree root of hollow blade are comparatively little bit lesser than solid blade and fir tree root of solid blade respectively.
3. The stress distribution of hollow blade is greater than solid blade and both stresses are lie within the limiting stress.
4. As hollow blade will have less mass compared to solid blade with not more rise in the stress as we are observed in the results obtained, so as the mass is reduced the efficiency is increased in the turbine.
FUTURE WORK
As turbine blade flank length & depth is very imported dimension in the turbine rotor. The optimized dimension should be made to have minimum stress & displacement at the root of the blade & disc.
As turbine blade require cooling to reduce the thermal stresses, the size of the cooling passage is very important.
The optimized size should be made to have maximum cooling of the blades but there should not be over cooling as it affects the thermal efficiency.

The pseudo-elements are used to decrease the analysis time.
The pseudo-elements are dead elements so that we can easily increase or decreases the size of the blade’s hole there by reduces the time for re-meshing of the whole blade.
REFERENCES
[1] Jack Janes P.E
California Energy Commission
“A FULLY
ENHANCED GAS TURBINE FOR SURFACE SHIPS
”
The
International Gas Turbine And Aeroengine Congress & Exhibition
Birmingham, U.K. June 10-12, 1996 .
[2] Travis R. Doom , “ Case studies on the Government’s role in energy technology innovation aeroderivative Gas turbines .” America Energy council, August 2013.
[3] Wenbin Song a, Andy Keane, Janet Rees, Atul Bhaskar, Steven Bagnall,
“Turbine blade fir-tree root design optimisation using intelligent CAD and finite element analysis”, Computers and Structures 80 (2002)
1853–1867.
[4]
H. D. Conway and K. A. Farnham, “The contact stress problem for indented strips and slabs under conditions of partial slipping,” Journal of International Engineering Science, Vol. 5, 1967 pages 145-154 .
[5] G. D. Singh and S. Rawtani, “Fir Tree Fastening Of Turbo machinery
Blades –I” International Journal of mechanical science vol 24, no 6,
1982, Pages 377-384.
[6] Cheng-Hung Huang and Tao-Yen Hsiung “An inverse design problem of estimating optimal shape of cooling passages in turbine blades”,
International Journal of Heat and Mass Transfer 42 (1999) 4307-4319.
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