Fatigue Life Estimation of Small Gas Turbine Blisk

Transcription

1 Fatigue Life Estimation of Small Gas Turbine Blisk Chethan R Chandran 1, Dr. T. Rangaswamy 2, Dr. Manjunath K 3 1Student, Dept. of Mechanical Engineering, Govt. Engineering College, Hassan, Karnataka, India 2 Professor and Head Dept. of Mechanical Engineering, Govt. Engineering College, Hassan, Karnataka, India 3Asst. Professor, Dept. of Mechanical Engineering, Govt. Engineering College, Hassan, Karnataka, India *** Abstract - A Small Gas Turbine (SGT) blisk is used for the power generation of a surveillance aircraft. So it is important to predict the fatigue life of a SGT blisk for the scheduling the maintenance and the safety of the aircraft. SGT blisk undergoes mainly four types of loadings. They are centrifugal, thermal, vibrational and aerodynamic loads. In the present work, the fatigue life of a SGT blisk is simulated with the help of an FEA package ANSYS. After defining an operating cycle of 2 hours; thermal, pressure and centrifugal loads are applied on the blisk and stress values at different time steps are extracted. From the analysis results it is observed that the blisk is operating in the elasto-plastic region. So a strain based approach is suitable for the estimation of Low Cycle Fatigue and the same is estimated using Smith Watson Topper mean stress correction theory. Key Words: Life Estimation, Fatigue, Structural analysis, Finite element analysis, Small gas turbine, Blisk 1. INTRODUCTION Fatigue life estimation of a gas turbine blisk is very important in the operational point of view. Failure of a blisk during operation will lead to the failure of the aircraft. Conventional life estimation procedures are time consuming and expensive. A simulation of the blisk under operating conditions can save the time and cost of the life estimation process. The objective of the present study is to estimate the fatigue life of a small gas turbine blisk with the help of a FEA package ANSYS. manufactured as integrally cast or from a single solid piece material or manufactured by welding between disc and blades. The term Blisk is an acronym composed of the words blade and disk which means bladed disc. Blisks are named as IBR (Integrated bladed rotors) Meaning is that joint between root dick and blade is not even required. Initially blisks were used in small engines for helicopters. Blisk was introduced in the years of 1980s for military aircraft engines and later elaborately used in turbofan and turboprop engines. By eliminating the components for the disk-blade attachment weight as well as the drag is reduced. Elimination of fir tree or dovetail will reduce the chance of crack formation and propagation. Blisks possess higher thermal efficiency. A gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber or area, called a combustor, in between. The main aim of the turbine is to extract maximum energy from the working medium to convert into to a useful work and by obtaining maximum reliability, less starting time, minimum cost and less supervision. Fresh atmospheric air flows through a compressor that brings it to higher pressure. Energy is then added by spraying fuel into the air and igniting it so the combustion generates a hightemperature flow. This high-temperature high-pressure gas enters a turbine, where it expands down to the exhaust pressure, producing a shaft work output in the process. 1.1 Turbine Rotor A Blisk is an engine component in which rotor disc and blade is manufactured a single component. The Blisk may be 1.2 Super Alloys Fig 1: Turbine rotor blisk A superalloy or high performance alloy exhibits excellent mechanical strength, resistance to thermal creep deformation, good surface stability, and resistance to corrosion or oxidation. Addition of elements such Aluminium and Chromium will provide oxidation or corrosion resistance. Microstructure of the superalloys slow down the crack propagation and thereby increased fatigue life. Nickel (Ni) based superalloys have emerged as the material of choice for these applications. The properties of these Ni based superalloys can be tailored to a certain extent through 2018, IRJET Impact Factor value: ISO 9001:2008 Certified Journal Page 1118

2 the addition of many other elements, both common and exotic, including not only metals, but also metalloids and non- metals. INCONEL alloy 718 is the alloy considered here. Table 1: Material properties of Inconel 718 Particulars Units Inconel 718 Density Kg/m Tensile Yield Strength Tensile Ultimate Strength MPa (at K) (at K) MPa (at K) (at K) x 10 5 (at K) Young s Modulus MPa x 10 5 (at K) Poisson s Ratio.30 Coefficient of thermal Expansion C x 10 5 (at K) x 10-5 (at K) x 10-5 (at K) fatigue behavior are available. One is Morrows parameter and the other is Smith Watson and topper parameter. The strain life approach is a comprehensive approach which can be applied for the treatment of both low cycle and high cycle fatigue. Morrow Equation: Smith Watson and Topper relationship: In the above equations = Strain Amplitude = Strength coefficient = Mean Stress = Number of cycles to failure = Strain coefficient b = Fatigue strength exponent c = Fatigue ductility exponent Both strain range and maximum stress determine the amount of fatigue damage. Smith, Watson and Topper proposed a theory in 1970 that include both the cyclic strain range and maximum stress this model commonly referred to as the SWT parameter. This method has been used for the present case. 3. ANALYSIS USING FINITE ELEMENT METHOD Thermal Conductivity 2. METHODOLOGY W m -1 c x 10-5 (at K) (at K) (at K) Blade coordinates from CFD analysis for the turbine rotor blisk for SGT is taken. The coordinates are imported to the modelling software Solid works and rotor blade is generated. Based on the engine configuration considered for the analysis the detailed modelling of the disk is done in solid works. For a proper mesh generation and to reduce the overall time for analysis a periodic sector of the blisk is considered for the analysis. The below figure shows the CAD models of the SGT blisk and a periodic sector. Super alloys have the capability to retain its shape at higher stress values even at higher temperatures. Strain based fatigue is applicable for both HCF and LCF. Here because of the special material properties and the deformation in the elastoplastic region, Strain based LCF is estimated. Strain based approach for fatigue life estimation is considered for structures undergoing plastic deformation. The total strain amplitude can be resolved into elastic and plastic strain components from the steady state hysteresis loops. At large strains or short lives the plastic strain component is predominant and at small strains or longer lives the elastic strain component is predominant. Several models dealing with mean stress effects or the strain life Fig 2: CAD model of SGT Blisk and Periodic Sector of Blisk 2018, IRJET Impact Factor value: ISO 9001:2008 Certified Journal Page 1119

3 For getting accurate results an optimized mesh is required. To avoid the issue of stress concentration that may arise due to poor meshing near blade fillet area is overcome by giving a proper face sizing over the blade and the fillet. Maximum face sizing in the disk region is set as 1.25mm and.4mm of maximum face size is set in the fillet region. As a result a mesh of elements with nodes is obtained with an average Jacobian ratio of Fig 5: Imported pressure loads over the blade, Structural boundary conditions Table 2: Rotational velocity over time Steps Time [s] X [rpm] Y [rpm] Z [rpm] Fig 3: Mesh generated on the blisk section The pressure and temperature loads on the rotor blade from a CFD simulation at design point are taken. The nodal temperature values are saved as csv file format and the same is mapped over the blades. The maximum blade temperature is 1080 for the SGT blisk and the temperature at the bore is assumed to be 500 K. Thermo-structural analysis is carried out by considering temperature dependent mechanical properties of the blisk material. The pressure profile, which is also obtained from ANSYS CFX solver is imported to the rotor blades. An operational cycle of 10 time steps is considered with varying RPM. The RPMs at different time steps are listed in the table 4.1 and the same are applied about the axis of rotation. Each time step is divided into 4 sub steps FINITE ELEMENT ANALYSIS RESULTS By finite element analysis ANSYS gives the temperature distribution over the blade as a result of the simulation. From the figure (5.1), it is noticed that maximum temperature is at the middle region of the blade and it gradually decreases towards the center of the disk. Same thermal loads are considered further to carry out structural analysis. The structural analysis is carried out at the steady state condition with varying RPMs at 10 time steps. The maximum equivalent stress (Von-Mises stress), maximum principal stress, equivalent elastic strain, equivalent plastic strain, maximum principal elastic strain are obtained as shown in the following figures Fig 4: Thermal Boundary Conditions, Imported thermal loads over the blade 2018, IRJET Impact Factor value: ISO 9001:2008 Certified Journal Page 1120

4 Fig 6: Temperature distribution over the blisk, Equivalent stress Fig 9: Damage occurred, minimum number of cycles to failure (Life) From the Biaxiality indication results which is ranging from to it is evident that the structure is undergoing bi-axial stresses and the maximum principal stress component has to be taken for predicting the minimum life. As the infinite life cycle value is set at 1e9 and he Design fails at 759 cycles, the Factor of Safety calculated by fatigue tool is Fig 7: Maximum principal stress, Equivalent plastic strain Fig 10: Biaxiality indication, Factor of Safety 4.4 Theoretical Calculation Results Number of Cycles to Failure using SWT Equation Fig 8: Equivalent elastic strain, Maximum principal elastic strain 4.2 Fatigue Analysis Results Considering the value of infinite life as 1e9, the life is evaluated in ANSYS Fatigue Tool with SWT strain life approach. At the maximum loading condition that is at 2160s SWT theory predicted a life of 759 cycles. Maximum damage value observed is e5. The area where the maximum damage is occurred is where the least life is predicted. The value of Damage more than 1 indicates that the design will fail before the infinite life. The SWT equation is given below In the current simulation = 771MPa (Maximum principal Stress developed during the cycle) = x 10-3 = 2355 = Number of cycles to failure =.0128 b = c = E = * , IRJET Impact Factor value: ISO 9001:2008 Certified Journal Page 1121

5 By substituting the above values, we get an equation as follows After solving the numerical equation for N f, N f = By considering the loading history for 40 time steps (4 substeps in each time step), theoretical calculations predicted a life of 1793 cycles. Ansys fatigue tool estimated a life by considering the maximum principal stress value of 771 MPa at 2160 seconds, which must predict a life lesser than the theoretical calculated value and the desired result (759 cycles) is obtained. ACKNOWLEDGEMENT We would also like to thank Mr. Prathapanayaka R, Principal Scientist and in charge of Versatile Turbine Test Rig, Propulsion Division for guiding and inspiring me to carry out this project work with interest. His constant inputs, feedbacks and encouragement were invaluable. REFERENCES Fig 11: Representation of loading cycle. Green line connects the maximum and minimum principal stress values at each time step. Here, there are 40 loading cycles in the operating cycle of 2 hours. So the number of operating cycles = Table 3: Results comparison Calculation method Number of cycles to failure FE Analysis by ANSYS workbench 759 Theoretical calculation 1739 By considering the loading history for 40 time steps (4 substeps in each time step), the average of maximum and minimum stress values are taken for the calculation. Theoretical calculations predicted a life of 1793 cycles. Which is almost the double of estimated life by ANSYS fatigue tool (759 cycles). ANSYS Fatigue tool predicts the least life by considering the maximum principal stress value which is attained at 2160s. So the average of maximum and minimum Principal stress values considered is higher than the theoretical calculations, which will lead to a reduced life compared to theoretical calculations. [1] Deepak Dhar, A M Sharan, J S Rao: Transient stress analysis fatigue life estimation of turbine blades [2] N.S Vyas, J.S Rao: Fatigue life estimation procedure for a turbine blade under transient loads.1994 [3] R. Bahree, A.M Sharan, J.S Rao: The design of rotor blades taking into account the combined effects of vibratory and thermal loads [4] J.S.Rao, N.S Vyas: Determination of blade stresses under constant speed and transient conditions with nonlinear damping [5] Lucjan Witek: Failure analysis of turbine disc of an aero engine [6] Prof. K Gopinath & Prof. M.M Mayuram, Machine Design II- indian institute of technology, madras [7] I.Rychlik. A new definition of the rainflow cycle counting method, International Journal of Fatigue Volume 9, Issue 2, April 1987, Pages [8] P. H. Wirsching and A. Mohsen Shehata, Fatigue Under Wide Band Random Stresses Using the Rain- Flow Method, J. Eng. Mater. Technol 99(3), (Jul 01, 1977) (7 Pages) 5. CONCLUSION The detailed thermal and structural analysis showed that during the operating cycle at design condition and 110% of the design condition the blisk maintains its natural shape. Plastic strain of only is developed. But the presence of plastic strain indicates that strain life approach is suitable for the operating conditions. 2018, IRJET Impact Factor value: ISO 9001:2008 Certified Journal Page 1122