Investigation of Candidate Features For Crack Detection in Fan and Turbine Blades and Disks

Transcription

1 Visit the SIMULIA Resource Center for more customer examples. Investigation of Candidate Features For Crack Detection in Fan and Turbine Blades and Disks Michelle Meier, Oleg V. Shiryayev, and Joseph C. Slater Wright State University, Dayton, OH Identification of fatigue cracks in turbo-machinery components is a vital but costly effort. This work focuses on nonlinearities in the response behavior resulting from the opening and closing of cracks that results in super-harmonic resonances due to harmonic excitations. Experimental results for a cracked cantilever beam are presented as well as the results from numerical simulations of an integrally bladed compressor disk FE model. Identification of sensitive vibration features is expected to contribute to the development of automated crack detection techniques for aircraft engine disks. I. Introduction Damage detection in engines and subcomponents is an important challenge for cost, performance, and safety of systems. Degradation in structures generally involves corrosion, cracking, delamination of composite layers, and loosened fasteners. In turbine engine disks, blades, and other components we are primarily concerned with damage in the form of fatigue cracks. Due to the large amount of kinetic energy stored in the moving parts of the engine, fatigue cracks can cause uncontained engine failures, which may have catastrophic consequences. Debris flying out of the engine may damage vital aircraft systems leading to loss of control and consequent crash, 1 or fatalities on board the aircraft after penetrating the fuselage. 2 Therefore, development of reliable techniques for detection of damage is highly critical. Research in the area of damage detection has intensified with the development of new sensing and actuation capabilities. Detection of damage can be performed optically, or using x-ray, ultrasound, and vibration methods. Detection of damage based on sensing and detecting changes in vibration characteristics of structures has struggled due to the focus on behaviors that can be caused not only by damage, but by thermal or other effects. A wide variety of techniques have been developed using time, frequency, and modal concepts to identify structural damage. 3 6 However, very few have taken advantage of the inherent nonlinear behavior of cracks to isolate fatigue damage from other effects. Vibration testing for damage identification has struggled to move forward in many instances because the many types of damage cause only very localized behavior changes while in their infancy. Further, common vibration features such as mode shapes, and especially natural frequencies, are typically very insensitive to damage until the damage is near catastrophic. In the case of cracks, sufficient variation in blade linear vibration behavior typically does not occur until the damage is far beyond acceptable. Visible damage, such as removal of material by FOD, is identifiable through visual inspection. However, fatigue cracks typically have very little if any loss of material, and thus they don t provide for easy inspection of visual change. They do become observable, however, when looking at the characteristic of a crack: opening and closing of the crack. Opening and closing of the crack results in a very localized nonlinear elastic behavior. A model of such behavior is a bilinear local modulus. Beams with cracks are well known to have such nonlinearities. 7, 8 Therefore, introduction of nonlinearities and other nonlinear phenomena can be exploited for structural health monitoring (SHM) purposes. Shiryayev and Slater have developed and experimentally verified a method to detect fatigue cracks based on monitoring changes in statistics of the Randomdec signatures caused by the onset of nonlinearity due to a Research Assistant, Department of Mechanical and Materials Engineering. Research Associate, Department of Mechanical and Materials Engineering. AIAA Student Member Professor, Department of Mechanical and Materials Engineering, joseph.slater@wright.edu. AIAA Associate Fellow 1 of 17 Visit the SIMULIA Resource Center for more customer examples.

2 crack. 9, 1 SHM community have also investigated other nonlinear response features (see for example ). Selection of a particular feature for damage detection is application specific. Certain features may work reliably in one application, yet perform poorly in another. The goal of this work is to identify candidate features that can be used to detect fatigue cracks in fan or turbine disks from vibration data. To the best of authors knowledge, during engine overhauls fan and turbine disks are inspected for cracks via one or another non-destructive evaluation (NDE) technique. These procedures are time consuming and expensive. Hence, it is desirable to replace these inspections with techniques that will allow detection of the onset of damage during engine operation. Even if not possible, a validated automated inspection technique using vibration analysis may prove faster and more cost effective. Determining whether that will be true is a significant goal of the research. According to the report from the joint NASA/FAA/NAWC research group, 16 such in situ techniques are still in their infancy and cannot provide definitive results. This work investigates the dynamics of a cracked beam and a model of a compressor disk. We describe the nonlinear vibration phenomena that occur due to the presence of breathing cracks and demonstrate them using experimental data from the cracked beam and numerical models of a compressor disk. This is a first step towards developing effective automated monitoring techniques. II. Nonlinear Response Features The bilinear type weak nonlinearity that occurs due to the presence of an opening and closing crack can be roughly approximated by a system that has a quadratic stiffness term in addition to the linear one as shown in Equation (1). Higher polynomial terms can also be included in the approximation to improve the approximation. Only terms that are even functions will have non-zero coefficients. ÿ + 2ζω ẏ + ω 2 y + αy 2 = F (t) (1) In this equation ω is the natural frequency of the linear system, and α is small relative to ω 2. One of the differences between responses of linear and nonlinear systems due to harmonic excitations is that responses of nonlinear systems may contain harmonics other than those at the driving frequencies. Nayfeh and Mook 17 provide a detailed analysis of systems with quadratic and cubic nonlinearities under harmonic excitations. If the system with quadratic nonlinearity is excited by a two term harmonic excitation such as in Equation (2), F (t) = F 1 (t) + F 2 (t) = A 1 cos(ω 1 t + Θ 1 ) + A 2 cos(ω 2 t + Θ 2 ) (2) then besides the primary resonance (Ω 1 or Ω 2 close to ω ) several interesting phenomena can be observed in the response depending on the relationships between driving frequencies Ω 1 and Ω 2, as well as the linear natural frequency of the system ω. Superharmonic resonance can be excited if Ω 1 or Ω 2 1/2ω. Subharmonic resonance can be excited when Ω 1 or Ω 2 2ω. Combination resonance occurs when Ω 1 + Ω 2 ω, or Ω 1 Ω 2 ω. In this paper we demonstrate the occurrence of super-harmonic resonance in experimental data obtained from a cracked cantilever beam and numerical simulation data obtained from finite element models of a hypothetical integrally bladed compressor disk. III. Experimental Results From a Cantilever Beam The beam is made of 224-T351 aluminum. Figure 1 shows the schematic of the experiment. The beam is 3 inches long with solid rectangular 1 1/2 in. cross-section. The specimen is mounted on the Unholtz- Dickie S32 shaker using a clamp machined out of 775 aluminum. High rigidity and low weight are desired characteristics for vibration fixtures because they allow to minimize the dynamic effects of the fixture on the test results. Heavy fixtures and specimen may significantly limit shaker performance. The clamp was designed to provide durability, high rigidity, and reduced weight. 2 of 17

3 Figure 1. Cantilever beam experiment. Acceleration measurements were obtained using five PCB 333B32 accelerometers placed along the beam. Data were recorded using LabView BNC-212 adapter with PCI-624E DAQ card. An Agilent 3312A function generator provided harmonic excitation signal. The damaged specimen was produced by growing a crack from a very sharp notch made on the top surface of the beam at the axial location that was about 1 inches away from the edge of the clamp. A similar size notch was produced in the baseline specimen, but with a dull cutter to avoid creating a sharp stress concentrator. Sonntag SF-1-U fatigue testing machine with a bending fixture was used to grow a crack in the damaged specimen (Figure 2). The crack produced in the beam is located between two black lines (Figure 3) with a penny coin serving as a dimensional reference. Clearly, the crack is very thin and difficult to see with the naked eye on an unpolished surface. Figure 2. Beam specimen mounted in a 4-point bending system. 3 of 17

4 Figure 3. Crack in the damaged specimen. We considered the 2nd, the 3rd, and the 4th modes of the beams that occur at approximately 14 Hz, 4 Hz, and 77 Hz. Experimental results are presented for accelerometers located at the free end of both beams. Figure 4(a) illustrates the data obtained when the excitation frequency was approximately half of the second resonant frequency. One can observe that the response level at the excitation frequency is the same for both intact and the cracked beams. The response level at 14 Hz is approximately 11 db higher for the cracked beam compared to the intact one. The response spectrum of the cracked beam also contains a harmonic at 3 times the excitation frequency. Figure 4(b) contains the spectrum of both beams excited at half of the 3rd resonant frequency. In this case the response of the cracked beam is about 2 db higher than that of the intact beam at 4 Hz. The most significant difference between the spectra of the cracked and intact beams can be observed in Figure 4(c). In this case the difference is approximately 88 db at 77 Hz. A case was run when both beams were excited at approximately twice the frequency of the second mode Hz. From Figure 4(d) one can observe that the spectra of both beams are distorted at 14 Hz, but there is no clear sub-harmonic resonance at that frequency for the cracked beam. Theoretically the spectrum of the intact beam should not contain any significant response components at the resonant frequencies when it is excited at half of those frequencies. This is because linear systems will produce response only at the excitation frequency. We believe that the reason for significant response of the intact beam in this case was due to the rocking motion of the shaker because it was not possible to clamp it to the floor in our experiment. At higher excitation frequencies this motion is greatly reduced and experimental results appear to be in close agreement with theory as evident from Figure 4(c). 4 of 17

5 power spectrum density, db Hz CH 4 cracked intact frequency, Hz (a) Excitation at 7Hz, 1/2 of the 2nd resonant frequency. power spectrum density, db Hz CH 4 cracked intact frequency, Hz (b) Excitation at 2Hz, 1/2 of the 3rd resonant frequency. power spectrum density, db Hz CH 4 cracked intact power spectrum density, db Hz CH 4 cracked intact frequency, Hz frequency, Hz (c) Excitation at 385Hz, 1/2 of the 4th resonant frequency. (d) Excitation at 281Hz, x2 of the 2nd resonant frequency. Figure 4. Spectral densities of cracked and intact beams. IV. Analytical Study of a Compressor Disk A. Finite Element Model of a Compressor Disk It was decided to create a model of a hypothetical integrally bladed compressor disk in Abaqus. 18 The disk geometry was created by making revolved and extruded cuts in a cylindrical solid. Figure 5 illustrates the geometry of the disk created in Abaqus. The disk has 16 integrated blades. Ti-6Al-4V is the material used in the model (E = GPa, ν =.342, ρ = 443 kg/m 3 ). 5 of 17

6 Y Z X Figure 5. Disk geometry in Abaqus. Two cases of damage were considered. In the first case the crack is located in the flange on the rear (downstream) side of the disk. In the second case the crack is located near the root of one of the blades on the front (upstream) side of the disk. Figures 6 and 7 illustrate the locations of the crack and crack geometries in both damage scenarios. (a) Crack geometry. Figure 6. Damage case 1: crack in the flange. (b) Crack location. 6 of 17

7 (a) Crack geometry. (b) Crack location. Figure 7. Damage case 2: crack near the root of a blade. In both cases fairly large cracks (length wise) were considered. This was done to see if nonlinearities introduced by these large cracks will noticeably affect the response. The width of the cracks at their widest point is set to be very small to represent realistic situations. Significant nonlinear effects observed in the response suggest that nonlinear features may be useful for detection of damage in the disks. If little or no nonlinear effects are present, when one may conclude that the studied SHM features aren t useful for detection of fatigue cracks in these disks. Contact interaction in Abaqus is described by selecting the surfaces that come into contact and prescribing normal and tangential interaction properties. In this work we utilized hard contact formulation for the normal direction. This formulation implies that the surfaces come into contact once the clearance between them reduces to zero at which point any contact pressure can be transmitted between the surfaces. Rough contact interaction was prescribed in the tangential direction. This implies that no slippage occurs between the surfaces while they are in contact. This is equivalent of a friction coefficient of infinity. This choice was driven by the assumption that the crack surfaces are rough and irregular, which will prevent slippage. Baseline undamaged state was modeled by replacing the contact interaction between the surfaces with a mesh tie constraint. Dynamic analysis of disks can be performed either in tuned or mistuned configuration. Real world disks always have a certain degree of mistuning due to variations in geometry and material properties. It was decided to consider mistuned case because it is more representative of reality. For the case when the crack is in the flange, linear 8-node brick elements were used in the mesh of the flange, while the rest of the disk was meshed using tetrahedral elements. In the case when the crack was near the root of the blade the entire disk was meshed using tetrahedral elements. It was not possible to partition and mesh the blades independently of the hub using brick elements due to complex geometry. In both cases most of the hub is meshed using mapped meshing due to its cylindrical shape. The blades are meshed using free meshing technique since their geometry is rather complex. Mistuning is introduced by variations in the size and shape of the elements in the regions meshed using free meshing technique. It must be noted that the mesh is refined near the regions that contain cracks. 7 of 17

8 Y Z X Y Z X Figure 8. Restrained surface near the front side of the disk. (a) Damage case 1: crack in the flange. (b) Damage case 2: crack near the root of a blade. Figure 9. Excitation locations for the two damage cases. To prevent rigid body motion, the nodes on the surface near the front side of the hub were prescribed zero displacement boundary condition. This surface is highlighted in red color in Figure 8. The same boundary condition was used in both damage cases. Figure 9 shows the locations of the loads in the models. In the case with the damage in flange, the load is applied in the form of pressure on the surface of the cracked flange in the radial direction. The locations where the pressure is applied undergo large motions in the mode of interest. In the case with the crack in blade the blade is excited by a point force at the tip in the horizontal 8 of 17

9 direction. Displacement and acceleration measurements were taken at several locations near the damage sites. All three directions (X, Y, Z) were measured. The data was antialiased by Abaqus. In the case when the damage was in the flange, the measurements were taken at the points on the edge of the flange approximately 1.5 cm to the left and to the right from the crack. In the case when damage was near the root of the blade, measurements were recorded at the points on the edges of the blade about 1 cm above the crack, and also at the point on the tip of the blade. B. Results from FEM Simulations The results presented in this section illustrate the presence of nonlinear response features that are caused by the cracks. 1. Case 1: crack is located in the flange on the rear side of the disk The mode at 122 Hz appeared to have significant motion in the region of the flange that contained the crack. In this case the goal was to detect the presence of harmonics at multiples of the excitation frequency, which arise due to bilinear stiffness characteristic introduced by the crack. The total force magnitude was increased to 16 N. In this case excitation was large enough so that contact interaction occurred during the entire simulation time history. Figures 1-12 show the PSD of the cracked and healthy disks from the time histories without significant startup transients obtained in the 16 N excitation case. One can observe the harmonics present in the spectra of the cracked disk model that do not exist in the spectra of the healthy disk. X direction PSD, db x 1 4 X direction PSD, db Linear, left point Cracked, left point x 1 4 Figure 1. PSD of acceleration, (m/s 2 ) 2 /Hz db, X-direction, steady state case. 9 of 17

10 Y direction PSD, db x Linear, left point Cracked, left point Y direction PSD, db x 1 4 Figure 11. PSD of acceleration, (m/s 2 ) 2 /Hz db, Y-direction, steady state case. 1 of 17

11 15 Z direction PSD, db x Linear, left point Cracked, left point Z direction PSD, db x 1 4 Figure 12. PSD of acceleration, (m/s 2 ) 2 /Hz db, Z-direction, steady state case. 2. Case 2: crack is located near the root of the blade on the front side of the disk Modal analysis of the disk model with the crack near the blade root indicated that there is a mode at 1184 Hz, in which the motion of the cracked blade is uncoupled from motion of the rest of the disk (see Figure 13). In this study we demonstrate the presence of super harmonic resonance effect in the cracked disk due to bilinear stiffness introduced by the crack. Super harmonic resonances in nonlinear systems are excited when excitation frequency is a fraction of the resonant frequency. In this case the system is bilinear, hence the excitation frequency is set to be half of the resonant frequency. 11 of 17

12 U, Magnitude Scale Factor:.97.e e e e e e e e e e e e e+ ODB: Job 1 EigAnalysisC.odb Abaqus/Standard Version Wed Nov 12 14:16:58 EST 28 Y Z X Step: Step 1, eigen analysis of the disk Mode 19: Value = E+7 Freq = (cycles/time) Primary Var: U, Magnitude Deformed Var: U Deformation Scale Factor: e 2 Figure 13. Vibration mode of the cracked blade at 1184 Hz. Time histories of acceleration and displacement for t [,.6]s were obtained for locations at the tip of the blade. It was found that the motion in the time period t [.3,.6]s has not settled into the steady state mode. This is due to the very small amount of damping in the system. Much longer simulation time history must be obtained to study the steady state vibration regime, but this is a computationally expensive task. The time history presented here is only.6s long, which required approximately 4 days of CPU time on a computer with a modern dual-core processor. Figures and show the power spectrum densities of acceleration and displacement measured at the tip of the cracked blade. On these plots one can observe the main peak due to harmonic excitation at 592 Hz, as well as the peak that corresponds to the mode of interest at 1184 Hz. While the magnitude of the main peak is approximately equal in both linear and cracked cases, the magnitude of the peak at 1184 Hz is higher in the cracked disk model data compared to that in the baseline model by approximately 1-15 db. Note that the peak that corresponds to the mode at 2 Hz has the same magnitude in both cracked and baseline cases. 12 of 17

13 15 1 X direction PSD, db Figure 14. PSD of acceleration, (m/s 2 ) 2 /Hz db, X-direction, 592 Hz case Y direction PSD, db Figure 15. PSD of acceleration, (m/s 2 ) 2 /Hz db, Y-direction, 592 Hz case. 13 of 17

14 15 1 Z direction PSD, db Figure 16. PSD of acceleration, (m/s 2 ) 2 /Hz db, Z-direction, 592 Hz case X direction PSD, db Figure 17. PSD of displacement, (m/s 2 ) 2 /Hz db, X-direction, 592 Hz case. 14 of 17

15 15 2 Y direction PSD, db Figure 18. PSD of displacement, (m/s 2 ) 2 /Hz db, Y-direction, 592 Hz case Z direction PSD, db Figure 19. PSD of displacement, (m/s 2 ) 2 /Hz db, Z-direction, 592 Hz case. V. Conclusions and Suggestions for Future Work 15 of 17

16 Structural systems with bilinear type stiffness characteristic exhibit several interesting response features depending on the excitation frequency. These features include the presence of sub-harmonic, super-harmonic, and combination resonances. The presence of these features in the response can be exploited for detection of opening and closing fatigue cracks in turbomachinery components or other structures. In this work we demonstrated the presence of super-harmonic resonances in the experimental data from a cracked cantilever beam and simulated response data from the models of a compressor disk. Experimental data showed that the magnitudes of the response spectra of the cracked beam was 11 db, 2 db, and 88 db higher that that of the baseline beam in the cases when super-harmonic resonance was excited for the 2nd, 3rd, and the 4th mode correspondingly. The most vivid illustration of super-harmonic resonance was recorded for the case of the 4th mode. In this case the shaker rocking motion was minimized due to relatively high excitation frequency. Additional experiments need to be performed to investigate the presence of combination resonances. This will require generation of excitation signal that is a sum of two sinusoids with different frequencies. One possible way of implementing this in the experiment is two generate the signal numerically using available LabView software and hardware. Another potential implementation route is to employ two function generators and build a signal summer circuit. In this experiment the beam contained a fairly large crack that was approximately 35% of the crosssection deep (judging by the crack length on the sides of the beam). More experiments will have to be done to investigate the effect of the crack size. Currently, work is being done to develop a numerical model of a cracked cantilever beam with base excitation. It is expected that this model will help interpreting experimental results and quantifying the effects of crack size and location. Using FEM simulation data it was shown that the spectrum of the cracked disk contains harmonics at multiples of excitation frequency when contact occurs between the surfaces of an opening and closing crack. A super-harmonic resonance was demonstrated on a cracked blade when the excitation frequency is half of the resonant frequency. Note that the disk models had large amounts of mistuning and modal families were spread over wide frequency ranges, but it was still possible to observe the nonlinear features in the responses. It appears to be easier to detect the presence of harmonics at multiples of excitation frequency when looking at acceleration measurements rather than displacement measurements. However, the super-harmonic resonance was easily observed in both types of measurements. The numerical simulations presented in this paper utilized excitations that were strategically placed such as to excite the disk mode that will result in the motion with the crack opening and closing causing nonlinear response. Also, the magnitude of excitations was intentionally set to be rather high because nonlinearities are easier to observe at high excitation magnitudes. In reality there are significant constraints with respect to the locations and magnitudes of excitations that can be applied to the disk due to limitations of test equipment (e.g. electrodynamic shakers, or acoustic excitation systems). It is desirable to apply the lowest possible excitation magnitude to reduce accumulation of fatigue damage, while still be able to detect the nonlinearity caused by the crack. Future studies need to investigate realistic test scenarios when the disk is mounted on the shaker and excited in the axial direction, as well as when the disk is excited by the acoustic system. A range of excitation magnitudes that can be achieved in practice without over-stressing the disk should be considered. Another important factor that has to be investigated is the length of the crack. In the studies presented here, very large cracks were considered (about 1 cm long). It is necessary to evaluate sensitivity of nonlinear effects to the size of the crack to approximate the limitation of the technique with respect to this parameter. Similarly, it is necessary to investigate sensitivity of the technique with respect to the proximity of sensors to the crack because it is more likely that nonlinear response features will be observed when measurement locations are closer to the crack. The studies on the effects of excitation method (shaker vs. acoustic system) and magnitude, as well as the study on the sensitivity with respect to the length of the crack will allow to point out the potential limitations of the proposed detection method, as well as its practical payoffs. 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