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Structural Integrity Analysis and Life Estimation of a Gas Turbine Bladed-Disc
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Procedia Structural Integrity 17 (2019) 758–765
ICSI 2019 The 3rd International Conference on Structural Integrity ICSI 2019 The 3rd International Conference on Structural Integrity
Structural Integrity Analysis and Life Estimation of a Gas Turbine Structural Integrity Analysis and Life Estimation of a Gas Turbine Bladed-Disc Bladed-Disc Shahnawaz Ahmadaa, A Sumanbb, T Sidharthbb, Ganesh Pawarbb, Vikas Kumaraa, N. S. Vyasbb Shahnawaz Ahmad , A Suman , T Sidharth , Ganesh Pawar , Vikas Kumar , N. S. Vyas Defence Metallurgical Research Laboratory Kanchanbagh, Hyderabad, India b Defence Metallurgical Kanchanbagh, Hyderabad, India Indian Research Institute ofLaboratory Technology, Kanpur, India b Indian Institute of Technology, Kanpur, India
a a
Abstract Abstract Turbine blades in an aero-engine are subjected to severe conditions of high temperature and pressure, which cause high levels of Turbine bladestoin crack an aero-engine to severe highhave temperature and pressure, whichofcause levels of stress leading formationare andsubjected subsequent failureconditions in service.ofWe investigated the influence crackhigh on vibration stress leading crack aero-engine formation and failure in service. We ahave investigatedapproach the influence of crack on vibration parameters of atotypical gassubsequent turbine blade and have described life assessment for blades and bladed discs. parameters of a typical aero-engine gas turbine Mission blade andTest) havecycle described a lifeutilized assessment approach for blades and bladed discs. A typical transport aircraft AMT (Accelerated has been for getting operating parameters. Material A typical transport aircraft AMT (Accelerated Test) cycle has disc beenofutilized for getting operating parameters. Material data is taken from tests conducted on specimensMission extracted from turbine a transport aircraft. Initial studies are carried out dataidealizations is taken from tests conducted specimens extractedcross-section; from turbine the discprocedures of a transport aircraft. Initialtostudies are carried out on involving cantileveronbeams with uniform are then extended free-standing turbine on idealizations involving cantilever uniform are then extended to free-standing blades with asymmetric airfoil cross beams sectionwith mounted at across-section; stagger anglethe on procedures a rotating disc. Dynamic characteristics of theturbine blade blades with asymmetric airfoil cross sectionhas mounted at a stagger angle on a rotating disc.those Dynamic of the sizes. blade are estimated and free vibrations analysis been carried out for healthy blades and withcharacteristics cracks of different are estimated and size freeon vibrations analysis has for healthy blades those with cracks different sizes. Influence of crack natural frequencies andbeen modecarried shapesout is studied. Results showand a difference of less thanof1% in frequency Influence crack on in natural frequencies mode shapes studied. Results show a difference of results less than in frequency for cracks of less thansize 1mm length; for larger and crack lengths the is frequency shifts are higher. Analytical are1% compared with for cracks lesstests than 1mm length; for larger crack lengths the frequency shifts forced are higher. Analytical results comparedand witha experimental on a inLaser Doppler Vibrometer set-up. Subsequently, vibration analysis is are performed experimental tests a Laser Doppler Vibrometer Subsequently, forcedthevibration analysis is blade performed and a methodology, using on Lazan’s law,is developed to extractset-up. modal damping ratios from strain energy of the under nozzle methodology, using fluctuations. Lazan’s law,is developed to extract dampingare ratios from thethe strain energy of the blade nozzle excitation pressure Modal damping ratios, modal thus obtained, indicative energy dissipation in theunder component excitation pressure fluctuations. Modal damping ratios, thus obtained, are indicative the energy dissipation in the component under such stress conditions. The ratios show differences of the order of 5% between healthy and cracked blades for the second under such conditions. ratios show differences of the 5% between and cracked blades The for the second mode. Thesestress observations leadThe illustrate that modal damping has order strongofcorrelation withhealthy blade structural integrity. possibility mode. These observations lead illustrate modal damping strongof correlation with blade structural integrity. The possibility of employing these modal damping ratiosthat as indicators for thehas presence cracks / defects is discussed. of employing these modal damping ratios as indicators for the presence of cracks / defects is discussed. © 2019 The Authors. Published by Elsevier B.V. © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Authors. Published by Peer-review under responsibility of Elsevier the ICSI organizers. Peer-review under responsibility of the ICSI 2019 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers. Keywords:Aerodynamic load assessment, Massing hypothesis, Paris Law Keywords:Aerodynamic load assessment, Massing hypothesis, Paris Law Corresponding author Email: [email protected] Corresponding author Email: [email protected]
2452-3216© 2019 The Authors. Published by Elsevier B.V. 2452-3216© 2019 The Authors. Published Elsevier B.V. Peer-review under responsibility of the ICSIby2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.101
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
759 2
1. Introduction The gas turbine is a complex unit of the power generation machinery of an aero engine. The turbine module of a gas turbine, experiences very high temperature-pressure conditions, resulting in high stresses throughout the run of the engine which in turn damages the components and thus limits the life of the engine. The gas turbine components are subjected to some of the harshest conditions inside the engine. The turbine blades are prone to damage and crack formation as they experience extreme pressures and temperatures resulting in high stress. Various aspects of the problem of blade vibrations have been subjects of extensive research, and the overall review of the problem has been done by Rao, Srinivasan and Rieger[1]. The transient vibration analysis using strain life approach following the methodology mentioned below (Figure 1) has been undertaken by Irretier and Vyas [2]. The turbine blades are prone to high cycle fatigue failures, and these failures are primarily due to resonance that occurs at the blade critical speeds during startup and shutdown conditions. As the blade passes through critical speeds, even if it does not fail catastrophically, it accumulates fatigue. There are several theories that estimate the damage in the structure as it passes through resonance and these theories prove to be significant in studying transient loading on the structures. Rao, Pathak and Chawla [3], compared various cumulative damage theories of predicting blade life. Since a crack is a discontinuity, its presence alters the stiffness and consequently the natural frequency of the component. W. M. Ostachowicz and M. Krawczuk[4] studied the effect of cracks on natural frequencies of the cantilever beam. Ming-Chaun Wu et. al.[5]examined the effect of crack on rotating cantilever beam. We adopted the FEA approach to study the effect of crack on the natural frequencies of the blade and performed sweep tests on an LDV setup to validate the analytical results. Presence of discontinuity may also lead to change in the damping parameters. An algorithm is also developed with the help of FEA software and Lazan’s law to compute the modal damping and explore if cracks influence modal damping in any significant manner. 2. Life Estimation The methodology adopted in this study for life prediction is shown in the flowchart (Figure 1)
Figure 1 Methodology for estimating life of a turbine blade
2.1. Aerodynamic Load Assessment on the Turbine Blade Turbine blades are exposed to relatively high levels of aerodynamic and centrifugal forces. The steady and periodic aerodynamic loads due to steady and unsteady components of gas, coupled with steady centrifugal forces due to rotation create distributed loads along the blades. These distributed loads have steady and periodic components. The gas dynamic forces on the blades are periodic with the instantaneous nozzle passing frequency, v = ns where, ns is the number of nozzles, and is the rotational frequency of the bladed disc. For determining this periodically varying force for the bladed disc, a coupled analysis was carried out on the ANSYS 14.5 workbench. The flow through two nozzles was modelled in ANSYS fluent under appropriate boundary conditions. The flow model involves the blade moving through a control volume between two nozzle inlets (Figure 2) and the pressure variation on the blade surface is approximated by a FLUENT analysis in ANSYS 14.5 environment. The flow was taken as glazing to the leading edge, Figure 3. The pressure variation is periodic as the blade passes through all the nozzles, one by one, experiencing the same pressure variation. The pressure distribution in the control volume around the blade profile is shown in Figure 3. The variation of maximum pressure on blade surface is shown
Shahnawaz AhmadStructural et al. / Procedia (2019) 758–765 Shahnawaz Ahmad/ IntegrityStructural Procedia Integrity 00 (2019)17000–000
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3
in Figure 4. Time has been normalized as = tnss 100 where s is the rotational frequency of the rotor in rev/sec. Forcing frequency, for this simulation is taken as 100 Hz. The maximum pressure on the blade’s pressure surface was observed to be approximately 1.8 MPa, and the minimum was 1.2 MPa Table 1Flow Conditions Parameters Design mass flow rate Ambient temperature Tinlet Toutlet Pinlet Poutlet Number of nozzles
Value 105 kg/s 288.15 K 1348 K 1144 K 12.06 bar 5.49 bar 53 Figure 2Flow across a blade passing through 2 nozzles
Figure 3Pressure distribution of air around the blade profile
The periodic nozzle forces F(t) on the blade can be expressed in terms of pressure in Fourier form as:
F
aerodynamic
F + {F }cos mvt + {F = m
0
m
m+ 6
}sin mvt …
(1)
m
The Fourier components are listed in Table 2. Table 2Fourier components of forcing function m 0 1 2 3 4 5 6
Fm (bars) 15.410 1.306 0.144 -0.192 0.071 0.340 0.059
Fm+6 (bars) 0 2.996 -0.833 0.288 0.491 0.270 -0.025
Figure 4Maximum pressure variation on the blade surface
2.2. Transient and steady state stress analysis A gas turbine engine undergoes both -constant rotor speed operation and variable rotor speed operation as in the case of starting up or shutting down or while performing other maneuvers. The equation of motion for the forced vibration can be rewritten as: (2)
The gas turbine engine generally operate at two speeds; (i) the idle speed, and (ii) the cruising speed, which for the engine in analysis are10400 rpm and 12300 rpm respectively. A typical transport aircraft AMT (Accelerated Mission Test) cycle has been utilized for getting operating parameters. The operating cycle with initial takeoff conditions in focus, are shown in Figure 5 and Figure 6, respectively. Stress computation, under flow path excitation forces is carried out for resonance conditions. Damping was calculated as 2% i.e. 0.02, by the half power bandwidth rule from the frequency response curve obtained by the experiments. These centrifugal force caused due to rotation of the bladed disc, is determined as
F= m 2 (R + z) (3) centrifugal where is rotational speed of the shaft (in rad/s), m is the mass of the element, R radius of the rotor disc and z distance from the root to the center of gravity of element. The variation of centrifugal stresses with the rotational
speed is quadratic. This force adds to the mean stress load carried by blade, which are computed at rotating speeds of 10400 rpm (idle speed) and 12300 rpm (max. cruising speed). All material data was taken from tests conducted on
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
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specimens extracted from turbine disc of transport aircraft. The structural analysis shows very high stresses at blade roots. The centrifugal stresses were found to be 243 MPa at 10400 rpm and 340 MPa at 12300 rpm, while the stresses due to the steady component of the flow field were found to be 70 MPa (Figure 7).
Figure 5Accelerated Mission Test cycle for the Gas Turbine Engine
Figure 6Zoomed view of the take-off cycle
Figure 7Centrifugal and steady flow stress (at blade root)
During acceleration from an initial speed to a final speed the rotor may pass through several critical speeds. While under acceleration the flow path forcing function can be expressed as, t2 t2 Faerodynamic ( t ) = F0 + {Fm }cos mns 0 t + (4) + {Fm+6 }sin mns 0 t + 2 m 2 m
where m is the harmonic number (1-6 generally), 0 is the initial rotating frequency (in rad/s), and is the acceleration of the rotor (in rad/s2). This unsteady transient loading with the harmonic components that were obtained from the flow path excitation force evaluation, was applied on the blades, in ANSYS Graphical user interface environment. Acceleration values were obtained from the operating cycle shown in Figure 5. Stresses computed for this transient numerical problem with accelerating periodic forcing are shown in Figure 8.
Figure 8 Alternating Stress Amplitude for the operating cycle
Figure 9 von Mises stress at Blade root as rotor goes from 0 to 10400 rpm
Figure 10 von Mises Stress at Blade root as rotor goes from 10400 to 12300 rpm
Stress amplitudes at the blade root near the fir-tree section, at critical speeds that the rotor passes as it accelerates from rest to its operating speed can be seen for 0-10400 rpm in Figure 9 and for 10400-12300 rpm in Figure 10. These stresses are used in the life estimation algorithm. 2.3. Life prediction algorithm The life estimation algorithm is developed based on the combination approach by Dowling [7]. It combines the local strain concepts to predict the crack initiation life and fracture mechanics principles to predict the propagation life. The combinational approach based on strain-life concepts for prediction of initiation life avoids the inherent difficulty that would have been faced in the application of LEFM (Linear Elastic Fracture Mechanics) to describe the short crack behavior at the defect root. The total life of a component consists of two parts- initiation life and propagation life.
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N t (total life) = N i (initiation life ) + N p ( propagation life)
5 (5)
The step by step procedure for estimation of the Crack initiation life, is summed up as: with the nominal stress (from stress analysis) as input true stresses are obtained in the vicinity of the defect using Neuber’s rule[8] using equation (7). This true stress is then used for solving elasto-plastic strains using iterative technique, coupling with material hysteresis curve and Massing’s hypothesis[9],equation (6). The initiation life of the blade is assessed by accounting for the mean stress using Morrow’s hypothesis [10], equation (8). 1/ n (6) ò 2 = 2 E + ( 2 K ' )
{
((
∆σ ∆σ E + 2 ∆σ 2 K ' ò 2 =
( (
' f
)
1/ n
)} = ( K ∆S ) / E 2
t
− m ) E ) ( 2 Ni ) + òf ' ( 2 Ni ) b
c
(7) (8)
Number of cycles required for propagation of a fatigue crack until it reaches its critical size is the fatigue crack propagation life N p . The crack growth behaviour of the material is represented by da dn vs. K on a log-log plot (Figure 11), where K is the amplitude of the stress intensity factor and da dn is the crack propagation rate. The sigmoidal curve is characterized by three distinct regions- region I, in which almost no crack propagation takes place, region II, where there is slow crack propagation and a linear log( K ) – log( da dn ) relation holds, and, region III, where the crack growth rate curve rises and the maximum intensity factor K max . in the fatigue cycle becomes equal to the critical stress intensity factor K c , leading to catastrophic failure.
Figure 11 Typical fatigue crack growth behaviour in metals(source: Anderson, “Fracture mechanics”[11])
The crack growth rate, from an initial crack size ai to a final size a f , is written in terms of number of propagation cycles, by Paris formulation [12]; Miner’s rule [13] is then utilized to predict the fatigue life under variable stress amplitude loading. The Miner’s rule states that if the average number of cycles to failure at the stress amplitude corresponding to the i th stress block, S i is N i , then the damage occurred to the component, Di , is; Di = ni N i
(9)
where, ni is the number of cycles accumulated at the stress amplitude S i . Di is the corresponding fraction of life consumed,. The crack propagation life (Np) can be estimated asaf
= Np da C ( K ) (10) ai C and m are known as Paris constants [6]. The stress intensity factor K defines the magnitude of the where, local stresses around the tip of crack for a given nominal stress, S , near a crack of length a , and is given by;
K = FS a
m
(11)
In terms of stress amplitudes, the fluctuating stress intensity factor, K , can be written as; K = Kmax − Kmin = F S a (12) where F is the geometry correction factor and S is the remote stress applied to the component. The initial
crack length ai is the smallest detectable crack length, which is limited by the measuring techniques. Analysis has
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
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been performed for various values of initial crack size ai , and the value of F is 1.12 (surface elliptical crack). The final crack length is evaluated by the onset of unstable fracture. Using Equation (11), by substituting K c in place of
K , we get ; Kc = FS ac
a= a= f c
K
(13)
FSmax 2
c
(14)
The material fatigue parameters used for the assessment of life were generated in the laboratory from specimens extracted from actual aero-engine components and tensile properties are taken from earlier published work [6] Table 3Properties of Bladed disc material Cyclic properties Modulus of Elasticity, E Paris constants
C m
Fracture Toughness, Kc Cyclic yield strength Cyclic strength coefficient, K ' Cyclic strain hardening exponent, n'
Fatigue strength coefficient, f ' Fatigue strength exponent, b Fatigue ductility coefficient, ò f ' Fatigue ductility exponent, c
Values 160 GPa 3.5e-10 3.83 112.4 MPa√m 676 MPa 1179 MPa 0.08 2139 MPa
Table 4Effect of initial flaw size on bladed disc life Initial crack size 0.10 (mm) 0.20 0.30 0.40 0.45
Ni (operating cycles) 3379 2122 1266 876 786
Np (operating cycles) 30 15 10 8 7
Nt (operating cycles) 3409 2137 1276 884 793
Nt (hours) 10438 6451 3905 2706 2427
-0.17 1.75 -0.52
3. LDV Test This results from the FE modal analysis of healthy and cracked blades were validated by performing sweep test on the Laser Doppler Vibrometer setup. Blades with different crack depths,[Figure 12-14], are investigated. Electrodynamic shaker frequency is swept linearly from 10 Hz to 3000 Hz in 2.25 seconds. The value of / p 2 for this test, is[14], 0.00014. For this value of / p 2 peak occurs at p = 1.024 , inferring that the recorded value of natural frequency using the sweep test is 1.024 times actual natural frequency. The FFT of the acceleration response is shown in Figure 15 for the healthy blade and in Figure 16 and Figure 17 for blades with 1.5 mm and 2.5 mm deep cracks, respectively. The measured and corrected values along with those obtained from FE simulation are listed in Table 5.
Figure 12 Healthy Blade
Figure 13 Blade with 1.5 mm deep crack
Figure 14 Blade with 2.5 mm deep crack
4. Modal Damping Estimation The methodology developed for the estimation of modal damping is shown Figure 18. This is implemented on a healthy blade and one with 0.5 mm deep crack shown in [Figure 19-21]. The Table 6 shows the modal damping ratio for healthy and cracked blade for second mode. The results shows a 5.2% change in the modal damping ratio due to the presence of crack.
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
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Figure 15FFT of Healthy Blade
7
Figure 17 FFT for blade with 2.5 mm deep crack
Figure 16 FFT for blade with 1.5 mm deep crack
Table 5Variation of Fundamental Natural Frequency with Crack Size in Hz (& % change) Natural Frequency (Hz) Experimental Corrected FE SIMULATION
Beam Healthy Cracked
Healthy 2565 2504.8 2502.7
1.5mm Crack 2531 (1.33%) 2471.6 (1.33%) 2476.2 (1.05%)
2.5mm Crack 2490 (2.92%) 2431.6 (2.92%) 2426.9 (3.09)
Table 6 Mode 2 Damping Ratio for Healthy and Cracked Blade Damping Ratio Iteration No. Initial Value 1 1.00 E-3 1.72 E-4 1.00 E-3 1.64 E-4
2 1.73 E-4 1.64 E-4
5. Conclusion A workable structural integrity analysis and life estimation procedure for aero-engine blades and bladed discs has been implemented. The stress map under flow path excitation and centrifugal stresses has been constructed for a typical AMT (Accelerated Mission Test) to test the integrity of the engine during service. The maximum stress has been observed at the blade root region, which can serve as a crack nucleation site. The life of the bladed disc was estimated using strain-life approach (initiation life) using Massing’s and Morrows hypothesis and Paris’s law (propagation life). The linear damage accumulation model by Miner was used to find the damage done to the system in one AMT cycle, which is then used to estimate the life of the bladed disc. The total life has been estimated to be 3409 operating cycles of the engine, or 10438 hours of flight time for initiating and propagating a flaw size of 0.1 mm at blade root. The variation in the natural frequency is approximately of the order of 0.25 % for each percent of crack depth/blade width ratio. These changes were estimated using FEA software COMSOL and further verified through more sophisticated measurement by using Laser Doppler Vibrometer setup. Crack size greater than 1 mm could be detected by using the vibration signature of the blade and therefore could be a good technique to detect larger cracks. However, in case of tight cracks, the shift in the natural frequency may be smaller and would require a better controlled test environment. Damping ratio calculated for healthy and cracked blade show a difference of 5.20% for the second mode. Modal damping apparently bears good correlation with blade structural integrity can be further explored as a viable tool for damage assessment. 6. Acknowledgement The authors are thankful to Director DMRL for giving opportunity to carry out this work. They express their gratitude to officers and staff of MBG for timely help whenever required. Authors are also thankful to IIT Kanpur
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
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and IISc Bangalore for extending their lab facilities for carrying this work. Authors would like to thank DRDO for funding this work.
Figure 19 Boundary Conditions on the Turbine Blade
Figure 20 Location of crack on the turbine blade
Figure 18Methodology for the calculation of Modal Damping Ratio
Figure 21 Magnified view of crack
7. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
F. Rieger N, J.S.Rao. Some service problems of turbine blades: Factors affecting diagnosis and correction. in EPRI conf. on NDE of steam turbines and electrical generator components. 1985. Irretier H, V. Transient vibrations of turbine blades due to passage through partial admission and nozzle excitation resonances. J S Rao, A.P., A. Chawla, Blade life: A comparison by cumulative damage theories. Transactions of the ASME, 2001. 123: p. 886-891. Ostachowicz, W.M. and M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beam. Journal of Sound and Vibration, 1991. 150(2): p. 191-201. Wu, M.-C. and S.-C. Huang, On The Vibration of a Cracked Rotating Blade. Shock and Vibration, 2014. 5(5-6): p. 317-323. Ahmad, S., Master Thesis, 2014. Normal, E.D. Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. H, N., Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress strain laws. J. Appl. Mech., Trans. ASME, 1964. 28: p. 544,-544. Massing, G. Proceedings of 2nd international congression applied mechanics, Zurich. Morrow, J., Fatigue design handbook, Advances in Engineering, Vol. 4, Warrendale, 1968. Anderson, T.L., Fracture mechanics : fundamentals and applications. 2nd ed. ed. 1995, Boca Raton: CRC Press. Rao, J.S., Vyas, N. S., Determination of Blade Stresses Under Constant Speed and Transient Conditions With Nonlinear Damping. Journal of Engineering for Gas Turbines and Power, 2008. 118(2): p. 424-424. Jr, M.A.M., Applied Mech. A, 160 (1945), p. 159. Vyas, N.S., Vibratory Stress Analysis and Fatigue Life Estimation of Turbine Blade, PhD Thesis. 1986.
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Procedia Structural Integrity 17 (2019) 758–765
ICSI 2019 The 3rd International Conference on Structural Integrity ICSI 2019 The 3rd International Conference on Structural Integrity
Structural Integrity Analysis and Life Estimation of a Gas Turbine Structural Integrity Analysis and Life Estimation of a Gas Turbine Bladed-Disc Bladed-Disc Shahnawaz Ahmadaa, A Sumanbb, T Sidharthbb, Ganesh Pawarbb, Vikas Kumaraa, N. S. Vyasbb Shahnawaz Ahmad , A Suman , T Sidharth , Ganesh Pawar , Vikas Kumar , N. S. Vyas Defence Metallurgical Research Laboratory Kanchanbagh, Hyderabad, India b Defence Metallurgical Kanchanbagh, Hyderabad, India Indian Research Institute ofLaboratory Technology, Kanpur, India b Indian Institute of Technology, Kanpur, India
a a
Abstract Abstract Turbine blades in an aero-engine are subjected to severe conditions of high temperature and pressure, which cause high levels of Turbine bladestoin crack an aero-engine to severe highhave temperature and pressure, whichofcause levels of stress leading formationare andsubjected subsequent failureconditions in service.ofWe investigated the influence crackhigh on vibration stress leading crack aero-engine formation and failure in service. We ahave investigatedapproach the influence of crack on vibration parameters of atotypical gassubsequent turbine blade and have described life assessment for blades and bladed discs. parameters of a typical aero-engine gas turbine Mission blade andTest) havecycle described a lifeutilized assessment approach for blades and bladed discs. A typical transport aircraft AMT (Accelerated has been for getting operating parameters. Material A typical transport aircraft AMT (Accelerated Test) cycle has disc beenofutilized for getting operating parameters. Material data is taken from tests conducted on specimensMission extracted from turbine a transport aircraft. Initial studies are carried out dataidealizations is taken from tests conducted specimens extractedcross-section; from turbine the discprocedures of a transport aircraft. Initialtostudies are carried out on involving cantileveronbeams with uniform are then extended free-standing turbine on idealizations involving cantilever uniform are then extended to free-standing blades with asymmetric airfoil cross beams sectionwith mounted at across-section; stagger anglethe on procedures a rotating disc. Dynamic characteristics of theturbine blade blades with asymmetric airfoil cross sectionhas mounted at a stagger angle on a rotating disc.those Dynamic of the sizes. blade are estimated and free vibrations analysis been carried out for healthy blades and withcharacteristics cracks of different are estimated and size freeon vibrations analysis has for healthy blades those with cracks different sizes. Influence of crack natural frequencies andbeen modecarried shapesout is studied. Results showand a difference of less thanof1% in frequency Influence crack on in natural frequencies mode shapes studied. Results show a difference of results less than in frequency for cracks of less thansize 1mm length; for larger and crack lengths the is frequency shifts are higher. Analytical are1% compared with for cracks lesstests than 1mm length; for larger crack lengths the frequency shifts forced are higher. Analytical results comparedand witha experimental on a inLaser Doppler Vibrometer set-up. Subsequently, vibration analysis is are performed experimental tests a Laser Doppler Vibrometer Subsequently, forcedthevibration analysis is blade performed and a methodology, using on Lazan’s law,is developed to extractset-up. modal damping ratios from strain energy of the under nozzle methodology, using fluctuations. Lazan’s law,is developed to extract dampingare ratios from thethe strain energy of the blade nozzle excitation pressure Modal damping ratios, modal thus obtained, indicative energy dissipation in theunder component excitation pressure fluctuations. Modal damping ratios, thus obtained, are indicative the energy dissipation in the component under such stress conditions. The ratios show differences of the order of 5% between healthy and cracked blades for the second under such conditions. ratios show differences of the 5% between and cracked blades The for the second mode. Thesestress observations leadThe illustrate that modal damping has order strongofcorrelation withhealthy blade structural integrity. possibility mode. These observations lead illustrate modal damping strongof correlation with blade structural integrity. The possibility of employing these modal damping ratiosthat as indicators for thehas presence cracks / defects is discussed. of employing these modal damping ratios as indicators for the presence of cracks / defects is discussed. © 2019 The Authors. Published by Elsevier B.V. © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Authors. Published by Peer-review under responsibility of Elsevier the ICSI organizers. Peer-review under responsibility of the ICSI 2019 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers. Keywords:Aerodynamic load assessment, Massing hypothesis, Paris Law Keywords:Aerodynamic load assessment, Massing hypothesis, Paris Law Corresponding author Email: [email protected] Corresponding author Email: [email protected]
2452-3216© 2019 The Authors. Published by Elsevier B.V. 2452-3216© 2019 The Authors. Published Elsevier B.V. Peer-review under responsibility of the ICSIby2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.101
Shahnawaz Ahmad et al. / Procedia Structural Integrity 17 (2019) 758–765 Shahnawaz Ahmad/ Structural Integrity Procedia 00 (2019) 000–000
759 2
1. Introduction The gas turbine is a complex unit of the power generation machinery of an aero engine. The turbine module of a gas turbine, experiences very high temperature-pressure conditions, resulting in high stresses throughout the run of the engine which in turn damages the components and thus limits the life of the engine. The gas turbine components are subjected to some of the harshest conditions inside the engine. The turbine blades are prone to damage and crack formation as they experience extreme pressures and temperatures resulting in high stress. Various aspects of the problem of blade vibrations have been subjects of extensive research, and the overall review of the problem has been done by Rao, Srinivasan and Rieger[1]. The transient vibration analysis using strain life approach following the methodology mentioned below (Figure 1) has been undertaken by Irretier and Vyas [2]. The turbine blades are prone to high cycle fatigue failures, and these failures are primarily due to resonance that occurs at the blade critical speeds during startup and shutdown conditions. As the blade passes through critical speeds, even if it does not fail catastrophically, it accumulates fatigue. There are several theories that estimate the damage in the structure as it passes through resonance and these theories prove to be significant in studying transient loading on the structures. Rao, Pathak and Chawla [3], compared various cumulative damage theories of predicting blade life. Since a crack is a discontinuity, its presence alters the stiffness and consequently the natural frequency of the component. W. M. Ostachowicz and M. Krawczuk[4] studied the effect of cracks on natural frequencies of the cantilever beam. Ming-Chaun Wu et. al.[5]examined the effect of crack on rotating cantilever beam. We adopted the FEA approach to study the effect of crack on the natural frequencies of the blade and performed sweep tests on an LDV setup to validate the analytical results. Presence of discontinuity may also lead to change in the damping parameters. An algorithm is also developed with the help of FEA software and Lazan’s law to compute the modal damping and explore if cracks influence modal damping in any significant manner. 2. Life Estimation The methodology adopted in this study for life prediction is shown in the flowchart (Figure 1)
Figure 1 Methodology for estimating life of a turbine blade
2.1. Aerodynamic Load Assessment on the Turbine Blade Turbine blades are exposed to relatively high levels of aerodynamic and centrifugal forces. The steady and periodic aerodynamic loads due to steady and unsteady components of gas, coupled with steady centrifugal forces due to rotation create distributed loads along the blades. These distributed loads have steady and periodic components. The gas dynamic forces on the blades are periodic with the instantaneous nozzle passing frequency, v = ns where, ns is the number of nozzles, and is the rotational frequency of the bladed disc. For determining this periodically varying force for the bladed disc, a coupled analysis was carried out on the ANSYS 14.5 workbench. The flow through two nozzles was modelled in ANSYS fluent under appropriate boundary conditions. The flow model involves the blade moving through a control volume between two nozzle inlets (Figure 2) and the pressure variation on the blade surface is approximated by a FLUENT analysis in ANSYS 14.5 environment. The flow was taken as glazing to the leading edge, Figure 3. The pressure variation is periodic as the blade passes through all the nozzles, one by one, experiencing the same pressure variation. The pressure distribution in the control volume around the blade profile is shown in Figure 3. The variation of maximum pressure on blade surface is shown
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in Figure 4. Time has been normalized as = tnss 100 where s is the rotational frequency of the rotor in rev/sec. Forcing frequency, for this simulation is taken as 100 Hz. The maximum pressure on the blade’s pressure surface was observed to be approximately 1.8 MPa, and the minimum was 1.2 MPa Table 1Flow Conditions Parameters Design mass flow rate Ambient temperature Tinlet Toutlet Pinlet Poutlet Number of nozzles
Value 105 kg/s 288.15 K 1348 K 1144 K 12.06 bar 5.49 bar 53 Figure 2Flow across a blade passing through 2 nozzles
Figure 3Pressure distribution of air around the blade profile
The periodic nozzle forces F(t) on the blade can be expressed in terms of pressure in Fourier form as:
F
aerodynamic
F + {F }cos mvt + {F = m
0
m
m+ 6
}sin mvt …
(1)
m
The Fourier components are listed in Table 2. Table 2Fourier components of forcing function m 0 1 2 3 4 5 6
Fm (bars) 15.410 1.306 0.144 -0.192 0.071 0.340 0.059
Fm+6 (bars) 0 2.996 -0.833 0.288 0.491 0.270 -0.025
Figure 4Maximum pressure variation on the blade surface
2.2. Transient and steady state stress analysis A gas turbine engine undergoes both -constant rotor speed operation and variable rotor speed operation as in the case of starting up or shutting down or while performing other maneuvers. The equation of motion for the forced vibration can be rewritten as: (2)
The gas turbine engine generally operate at two speeds; (i) the idle speed, and (ii) the cruising speed, which for the engine in analysis are10400 rpm and 12300 rpm respectively. A typical transport aircraft AMT (Accelerated Mission Test) cycle has been utilized for getting operating parameters. The operating cycle with initial takeoff conditions in focus, are shown in Figure 5 and Figure 6, respectively. Stress computation, under flow path excitation forces is carried out for resonance conditions. Damping was calculated as 2% i.e. 0.02, by the half power bandwidth rule from the frequency response curve obtained by the experiments. These centrifugal force caused due to rotation of the bladed disc, is determined as
F= m 2 (R + z) (3) centrifugal where is rotational speed of the shaft (in rad/s), m is the mass of the element, R radius of the rotor disc and z distance from the root to the center of gravity of element. The variation of centrifugal stresses with the rotational
speed is quadratic. This force adds to the mean stress load carried by blade, which are computed at rotating speeds of 10400 rpm (idle speed) and 12300 rpm (max. cruising speed). All material data was taken from tests conducted on
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specimens extracted from turbine disc of transport aircraft. The structural analysis shows very high stresses at blade roots. The centrifugal stresses were found to be 243 MPa at 10400 rpm and 340 MPa at 12300 rpm, while the stresses due to the steady component of the flow field were found to be 70 MPa (Figure 7).
Figure 5Accelerated Mission Test cycle for the Gas Turbine Engine
Figure 6Zoomed view of the take-off cycle
Figure 7Centrifugal and steady flow stress (at blade root)
During acceleration from an initial speed to a final speed the rotor may pass through several critical speeds. While under acceleration the flow path forcing function can be expressed as, t2 t2 Faerodynamic ( t ) = F0 + {Fm }cos mns 0 t + (4) + {Fm+6 }sin mns 0 t + 2 m 2 m
where m is the harmonic number (1-6 generally), 0 is the initial rotating frequency (in rad/s), and is the acceleration of the rotor (in rad/s2). This unsteady transient loading with the harmonic components that were obtained from the flow path excitation force evaluation, was applied on the blades, in ANSYS Graphical user interface environment. Acceleration values were obtained from the operating cycle shown in Figure 5. Stresses computed for this transient numerical problem with accelerating periodic forcing are shown in Figure 8.
Figure 8 Alternating Stress Amplitude for the operating cycle
Figure 9 von Mises stress at Blade root as rotor goes from 0 to 10400 rpm
Figure 10 von Mises Stress at Blade root as rotor goes from 10400 to 12300 rpm
Stress amplitudes at the blade root near the fir-tree section, at critical speeds that the rotor passes as it accelerates from rest to its operating speed can be seen for 0-10400 rpm in Figure 9 and for 10400-12300 rpm in Figure 10. These stresses are used in the life estimation algorithm. 2.3. Life prediction algorithm The life estimation algorithm is developed based on the combination approach by Dowling [7]. It combines the local strain concepts to predict the crack initiation life and fracture mechanics principles to predict the propagation life. The combinational approach based on strain-life concepts for prediction of initiation life avoids the inherent difficulty that would have been faced in the application of LEFM (Linear Elastic Fracture Mechanics) to describe the short crack behavior at the defect root. The total life of a component consists of two parts- initiation life and propagation life.
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N t (total life) = N i (initiation life ) + N p ( propagation life)
5 (5)
The step by step procedure for estimation of the Crack initiation life, is summed up as: with the nominal stress (from stress analysis) as input true stresses are obtained in the vicinity of the defect using Neuber’s rule[8] using equation (7). This true stress is then used for solving elasto-plastic strains using iterative technique, coupling with material hysteresis curve and Massing’s hypothesis[9],equation (6). The initiation life of the blade is assessed by accounting for the mean stress using Morrow’s hypothesis [10], equation (8). 1/ n (6) ò 2 = 2 E + ( 2 K ' )
{
((
∆σ ∆σ E + 2 ∆σ 2 K ' ò 2 =
( (
' f
)
1/ n
)} = ( K ∆S ) / E 2
t
− m ) E ) ( 2 Ni ) + òf ' ( 2 Ni ) b
c
(7) (8)
Number of cycles required for propagation of a fatigue crack until it reaches its critical size is the fatigue crack propagation life N p . The crack growth behaviour of the material is represented by da dn vs. K on a log-log plot (Figure 11), where K is the amplitude of the stress intensity factor and da dn is the crack propagation rate. The sigmoidal curve is characterized by three distinct regions- region I, in which almost no crack propagation takes place, region II, where there is slow crack propagation and a linear log( K ) – log( da dn ) relation holds, and, region III, where the crack growth rate curve rises and the maximum intensity factor K max . in the fatigue cycle becomes equal to the critical stress intensity factor K c , leading to catastrophic failure.
Figure 11 Typical fatigue crack growth behaviour in metals(source: Anderson, “Fracture mechanics”[11])
The crack growth rate, from an initial crack size ai to a final size a f , is written in terms of number of propagation cycles, by Paris formulation [12]; Miner’s rule [13] is then utilized to predict the fatigue life under variable stress amplitude loading. The Miner’s rule states that if the average number of cycles to failure at the stress amplitude corresponding to the i th stress block, S i is N i , then the damage occurred to the component, Di , is; Di = ni N i
(9)
where, ni is the number of cycles accumulated at the stress amplitude S i . Di is the corresponding fraction of life consumed,. The crack propagation life (Np) can be estimated asaf
= Np da C ( K ) (10) ai C and m are known as Paris constants [6]. The stress intensity factor K defines the magnitude of the where, local stresses around the tip of crack for a given nominal stress, S , near a crack of length a , and is given by;
K = FS a
m
(11)
In terms of stress amplitudes, the fluctuating stress intensity factor, K , can be written as; K = Kmax − Kmin = F S a (12) where F is the geometry correction factor and S is the remote stress applied to the component. The initial
crack length ai is the smallest detectable crack length, which is limited by the measuring techniques. Analysis has
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been performed for various values of initial crack size ai , and the value of F is 1.12 (surface elliptical crack). The final crack length is evaluated by the onset of unstable fracture. Using Equation (11), by substituting K c in place of
K , we get ; Kc = FS ac
a= a= f c
K
(13)
FSmax 2
c
(14)
The material fatigue parameters used for the assessment of life were generated in the laboratory from specimens extracted from actual aero-engine components and tensile properties are taken from earlier published work [6] Table 3Properties of Bladed disc material Cyclic properties Modulus of Elasticity, E Paris constants
C m
Fracture Toughness, Kc Cyclic yield strength Cyclic strength coefficient, K ' Cyclic strain hardening exponent, n'
Fatigue strength coefficient, f ' Fatigue strength exponent, b Fatigue ductility coefficient, ò f ' Fatigue ductility exponent, c
Values 160 GPa 3.5e-10 3.83 112.4 MPa√m 676 MPa 1179 MPa 0.08 2139 MPa
Table 4Effect of initial flaw size on bladed disc life Initial crack size 0.10 (mm) 0.20 0.30 0.40 0.45
Ni (operating cycles) 3379 2122 1266 876 786
Np (operating cycles) 30 15 10 8 7
Nt (operating cycles) 3409 2137 1276 884 793
Nt (hours) 10438 6451 3905 2706 2427
-0.17 1.75 -0.52
3. LDV Test This results from the FE modal analysis of healthy and cracked blades were validated by performing sweep test on the Laser Doppler Vibrometer setup. Blades with different crack depths,[Figure 12-14], are investigated. Electrodynamic shaker frequency is swept linearly from 10 Hz to 3000 Hz in 2.25 seconds. The value of / p 2 for this test, is[14], 0.00014. For this value of / p 2 peak occurs at p = 1.024 , inferring that the recorded value of natural frequency using the sweep test is 1.024 times actual natural frequency. The FFT of the acceleration response is shown in Figure 15 for the healthy blade and in Figure 16 and Figure 17 for blades with 1.5 mm and 2.5 mm deep cracks, respectively. The measured and corrected values along with those obtained from FE simulation are listed in Table 5.
Figure 12 Healthy Blade
Figure 13 Blade with 1.5 mm deep crack
Figure 14 Blade with 2.5 mm deep crack
4. Modal Damping Estimation The methodology developed for the estimation of modal damping is shown Figure 18. This is implemented on a healthy blade and one with 0.5 mm deep crack shown in [Figure 19-21]. The Table 6 shows the modal damping ratio for healthy and cracked blade for second mode. The results shows a 5.2% change in the modal damping ratio due to the presence of crack.
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Figure 15FFT of Healthy Blade
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Figure 17 FFT for blade with 2.5 mm deep crack
Figure 16 FFT for blade with 1.5 mm deep crack
Table 5Variation of Fundamental Natural Frequency with Crack Size in Hz (& % change) Natural Frequency (Hz) Experimental Corrected FE SIMULATION
Beam Healthy Cracked
Healthy 2565 2504.8 2502.7
1.5mm Crack 2531 (1.33%) 2471.6 (1.33%) 2476.2 (1.05%)
2.5mm Crack 2490 (2.92%) 2431.6 (2.92%) 2426.9 (3.09)
Table 6 Mode 2 Damping Ratio for Healthy and Cracked Blade Damping Ratio Iteration No. Initial Value 1 1.00 E-3 1.72 E-4 1.00 E-3 1.64 E-4
2 1.73 E-4 1.64 E-4
5. Conclusion A workable structural integrity analysis and life estimation procedure for aero-engine blades and bladed discs has been implemented. The stress map under flow path excitation and centrifugal stresses has been constructed for a typical AMT (Accelerated Mission Test) to test the integrity of the engine during service. The maximum stress has been observed at the blade root region, which can serve as a crack nucleation site. The life of the bladed disc was estimated using strain-life approach (initiation life) using Massing’s and Morrows hypothesis and Paris’s law (propagation life). The linear damage accumulation model by Miner was used to find the damage done to the system in one AMT cycle, which is then used to estimate the life of the bladed disc. The total life has been estimated to be 3409 operating cycles of the engine, or 10438 hours of flight time for initiating and propagating a flaw size of 0.1 mm at blade root. The variation in the natural frequency is approximately of the order of 0.25 % for each percent of crack depth/blade width ratio. These changes were estimated using FEA software COMSOL and further verified through more sophisticated measurement by using Laser Doppler Vibrometer setup. Crack size greater than 1 mm could be detected by using the vibration signature of the blade and therefore could be a good technique to detect larger cracks. However, in case of tight cracks, the shift in the natural frequency may be smaller and would require a better controlled test environment. Damping ratio calculated for healthy and cracked blade show a difference of 5.20% for the second mode. Modal damping apparently bears good correlation with blade structural integrity can be further explored as a viable tool for damage assessment. 6. Acknowledgement The authors are thankful to Director DMRL for giving opportunity to carry out this work. They express their gratitude to officers and staff of MBG for timely help whenever required. Authors are also thankful to IIT Kanpur
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and IISc Bangalore for extending their lab facilities for carrying this work. Authors would like to thank DRDO for funding this work.
Figure 19 Boundary Conditions on the Turbine Blade
Figure 20 Location of crack on the turbine blade
Figure 18Methodology for the calculation of Modal Damping Ratio
Figure 21 Magnified view of crack
7. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
F. Rieger N, J.S.Rao. Some service problems of turbine blades: Factors affecting diagnosis and correction. in EPRI conf. on NDE of steam turbines and electrical generator components. 1985. Irretier H, V. Transient vibrations of turbine blades due to passage through partial admission and nozzle excitation resonances. J S Rao, A.P., A. Chawla, Blade life: A comparison by cumulative damage theories. Transactions of the ASME, 2001. 123: p. 886-891. Ostachowicz, W.M. and M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beam. Journal of Sound and Vibration, 1991. 150(2): p. 191-201. Wu, M.-C. and S.-C. Huang, On The Vibration of a Cracked Rotating Blade. Shock and Vibration, 2014. 5(5-6): p. 317-323. Ahmad, S., Master Thesis, 2014. Normal, E.D. Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. H, N., Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress strain laws. J. Appl. Mech., Trans. ASME, 1964. 28: p. 544,-544. Massing, G. Proceedings of 2nd international congression applied mechanics, Zurich. Morrow, J., Fatigue design handbook, Advances in Engineering, Vol. 4, Warrendale, 1968. Anderson, T.L., Fracture mechanics : fundamentals and applications. 2nd ed. ed. 1995, Boca Raton: CRC Press. Rao, J.S., Vyas, N. S., Determination of Blade Stresses Under Constant Speed and Transient Conditions With Nonlinear Damping. Journal of Engineering for Gas Turbines and Power, 2008. 118(2): p. 424-424. Jr, M.A.M., Applied Mech. A, 160 (1945), p. 159. Vyas, N.S., Vibratory Stress Analysis and Fatigue Life Estimation of Turbine Blade, PhD Thesis. 1986.