TENTATIVE OF DAMAGE ESTIMATION FOR DIFFERENT DAMAGE SCENARIOS ON CANTILEVER BEAM USING NU- MERICAL LIBRARY

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1 TENTATIVE OF DAMAGE ESTIMATION FOR DIFFERENT DAMAGE SCENARIOS ON CANTILEVER BEAM USING NU- MERICAL LIBRARY Roger Serra INSA Centre Val de Loire, Laboratoire de Mécanique et Rhéologie, 3 rue de la Chocolaterie, Blois, France roger.serra@insa-cvl.fr Lautaro Lopez INSA Centre Val de Loire, Laboratoire de Mécanique et Rhéologie, 3 rue de la Chocolaterie, Blois, France & University National of Rosario, FCEA, Argentina Guillaume Gautier CEA-Tech Pays-de-la-Loire, Technocampus Océan, 5 rue de l Halbrane, Bouguenais, France & Inria / IFSTTAR, I4S, Campus de Beaulieu, Rennes, France Structural Health Monitoring is a method used during operation to diagnose faults. This is accomplished by placing some type of sensor system on the structure to measure vibration, strain, thermal emission, acoustic emission, The accuracy of detecting and locating damage using vibration measurements depends on the number and locations of accelerometers on the structure but in practical applications, only a limited number of on-board accelerometers will be available. In this context, a tentative of damage estimation was proposed. Different numerical damage scenarios were considered and a damage library was created for typical damages (like hole, crack, notch, etc...) from 3-D correlated to a 2-D finite element models simulation of a cantilever beam considering only bending modes. Thus, a methodology to detect and localize a damage is tested numerically from various classical indicators and a classification is proposed. Experiments were then performed. The damage was detectable but the damage location was found to be sensitive to errors in the experimental measurements and the estimation using a comparison with the damage library was CPU cost higher using 3D model. Suggestions for improving the experimental technique are given. 1. Introduction The main purpose of Structural Health Monitoring (SHM) is to detect damages before they become so severe that they threaten the integrity and functionality of the structure. The damage can be defined as changes introduced into the system that affects it current or future performance. The interest in detecting damage at the earliest possible stage is pervasive throughout the civil, mechanical, and aerospace engineering communities. Thus the predictive technique of Vibration based Structural Health Monitoring (VBSHM) [1] has been developed rapidly for the few last years. The leitmotiv of VBSHM is that the presence of damage changes the dynamic characteristics of the structure. Moreover, this damage induces changes in the physical properties that will be detectable as changes in the modal properties (natural frequencies, mode shapes, etc). Therefore changes in modal parameters are the result of changes in the geometry or the materials properties. VBSHM method consist in five levels 1

2 that are: 1) Detection; 2) Localization; 3) Classification; 4) Assessment and 5) Prediction. Many previous work for most of the levels are available in the literature. For instance, comprehensive surveys have been proposed by Doebling [2,3] and Sohn [4] for structural health monitoring and damage detection techniques in the civil and mechanical engineering communities. Friswell [5] presented a brief overview of the use of inverse methods in damage detection and location from measured vibration data. A review based on the detection of structural damage through changes in frequencies has been discussed by Salawu [6]. Different detection procedures to diagnose damage in rotors with various modelling of the cracked elements have been summarized by Wauer [7]. Dimarogonas [8] gave an extensive review about cracked structures including beam, rotor, shell and blades, plates and pipelines. Sabnavis [9] proposed a review on cracked shaft detection and diagnostics. A review of vibration-based structural health monitoring with special emphasis on composite materials has been described by Montalvao [10]. Gautier [11] proposed a subspace fitting approach for structure identification and damage localization based on a FE model updating procedure. From it, the position of the damage and the amount of it, represented as a reduction of stiffness, can be ensured. However there is not an exact methodology to identify the geometry and the size of the damage with accuracy and low computing-effort. In this paper, the development of a method able to detect, localize and classify the damage on a cantilevered Euler-Bernoulli beam with two degrees of freedom is first presented and a correlation between 2D and 3D finite element models is made to obtain a damage library. Then, the effectiveness of the method is proved. The procedure is tested then with experimental data. 2. Presentation of the model used Our scope on this paper will be concerned about the first three levels of VBSHM. The finite element method in MATLAB (for the 2D model) program will be developed, therefore the structure to be used need to be defined. A cantilevered beam that has only two degrees of freedom is studied, a vertical translation dy and a rotation rot z. The beam is discretized into n elements. The accuracy of an indicator is tested and the built of a Damage library is performed. Figure 1: Studied cantilever beam. The equations of motion of such dynamic systems are easily obtained from Newton's Second Law. This gives an equation for each degree of freedom within the system. Combining these, the equations of motion of the structure, is known as the following: [M]{X } + [C]{X } + [K]{X} = {F} (1) where [M] is the mass matrix of the system, [C] is the damping matrix, [K] is the stiffness matrix.{x } {X },{X} are the vectors containing the accelerations, velocities and displacements in all degrees of freedom of the model; and {F} is the external forces vector applied to the system whose solution is: {x} i = {y } i sin(w i t i ) (2) where w i and i are the natural frequencies and phase angles, respectively, corresponding to the i th mode shape{y } i. After obtaining the elementary local stiffness matrix and local mass matrix as follows: 2 ICSV23, Athens (Greece), July 2016

12 6h 12 6h K e = E.I [ 6h 4h 2 6h 2h 2 h 3 12 6h 12 6h 2h 2 6h Finally the global matrices

3 12 6h 12 6h K e = E.I [ 6h 4h 2 6h 2h 2 h h 12 6h 2h 2 6h Finally the global matrices are: ] M 6h e = 4h 2 ρ.s.h 420 [ h 54 13h 22h 4h² 13h 3h² ] (3) 54 13h h 13h 3h² 22h 4h² K 1 0 M 1 0 K = [ ] M = [ ] (4) 0 K 2 N+2 0 M 2 N+2 Now the equation (1) could be solved, which will result in the dynamic characteristic response of the structure under study, these are the natural frequencies or eigenvalues, and eigenvectors or modal deformed. 3. Methodology 3.1 Strategy The strategy developed is based on a cantilevered Euler-Bernoulli beam with two degrees of freedom simulation and a two-step method: Step 1: Numerical correlation between 2D and 3D finite element models simulation to obtain a damage library comparing %E reduction and geometry Step 2: VBSHM strategy with detection, localization (Position) and classification (Level / Type / Geometry) of the damaged beam. Figure 2: Flowchart of the proposed strategy. 3.2 Step 1: Numerical correlation %E reduction / Geometry First of all, an updated procedure from safe experimental structure is necessary to have a validated model. From a model, the 2D and 3D approaches could be initiate. It is well known that the presence of damage inside the structure modifies its dynamic parameters and different dynamic responses will be obtained. It is observable that changing parameters will modify the dynamic response, this means that the damage can be characterized varying the mass or stiffness matrix of any element. Many experiments have shown that the results were achieved by introducing the damage as a reduction of the Stiffness. Therefore the damage is set as a local reduction of the Young s Module for the 2D finite element model and correlated to the 3D finite element model like showed in Fig. 3. From these correlations, a damage library is created. ICSV23, Athens (Greece), July

Figure 3: Numerical example of correlation %E reduction / damage / geometry. 3.3 Step 2: VBSHM strategy The VBSHM methodology consists in five levels as already mentioned in introduction [12].

4 Figure 3: Numerical example of correlation %E reduction / damage / geometry. 3.3 Step 2: VBSHM strategy The VBSHM methodology consists in five levels as already mentioned in introduction [12]. The main objective is to develop a technique which the detection and location will be accurately performed. As each level requires that the previous one is available, in order to ensure an accurate solution, the previous levels must be precisely upstream. The first two levels indicators (denoted 1 and 2 below) were utilized as (by alphabetic order) [12-13]: -Coordinated Modal Assurance Criterion (COMAC) (1, 2) -Damage Index (DI) (1, 2) -Energy of Deformation (ED) (1, 2) -Flexibility Method (FM) (1, 2) -Local Frequency Change Ratio (LFCR) (1, 2) -Modal Assurance Criterion (MAC) (1) -Modal Shape Curvature (MSC) (1, 2) In the proposed VBSHM strategy, it is necessary to detect a change between a safe structure and the unknown structure. If a damage is detected, then the localization strategy could be performed Detection This level gives the information about the presence of a damage. The beam is scanned and the dynamics properties are analysed, in other words, the health of the beam is assessed [13] Localization Information about the possible position of the damage is given. The most promising indicators were selected within the domain of monitoring methods of structural behaviour. These indicators were chosen due to their high accuracy and their low computing time [13] Classification / Estimation The classification / estimation is made using the damage library defined in the step Numerical example The figures below were obtained numerically simulating a clamped-free beam divided into 10 finite elements. Three modal shapes were taken into account for the calculations. A stiffness reduction of 10% of stiffness in the 7 th and 9 th elements were simulated. In this example, only some indicators are showed but it s clear that the damage is detected and its position in determined. It is the case when the damage are multiples and located closely. To evaluate the size of the damage, the mesh could be increased but the computing time increase too. Then, a compromise should be found. 4 ICSV23, Athens (Greece), July 2016

4. Results Figure 4: Identification and location of damage (10%)

Simulations and Experimental assessments were performed.

the beam is studied like: Influence of the position of one damage

increase since the third mode, so to measure until this level was

5 4. Results Figure 4: Identification and location of damage (10%) in the 7 th and 9 th elements. Simulations and Experimental assessments were performed. In this work, the influence of some parameters in the behaviour of the beam is studied like: Influence of the position of one damage though the entire beam: near the embeddedness, at the free part and in the middle. It is shown how the frequency is affected by the location of the damage. The difference between the simulated and the experimental model increase since the third mode, so to measure until this level was decided Influence of the amount of damage: The amount of damage was varied from 30 to 1% through the entire beam. An assessment with 3 and 5% of damage at the same time was performed. ICSV23, Athens (Greece), July

Influence of the number of damage: three damages through the beam and also the sensibility of the technique was analysed by locating two

1 Simulation test Numerical simulation test is performed to verify the efficiency of proposed VBSHM strategy.

2 Experimental validation test An experimental validation test is performed to evaluate the performance and accuracy of the methodology.

6 Influence of the number of damage: three damages through the beam and also the sensibility of the technique was analysed by locating two consecutive damages elements. Likewise, damages at the two extremes were located and the indicator was tested. 4.1 Simulation test Numerical simulation test is performed to verify the efficiency of proposed VBSHM strategy. Figure 5: Numerical example 2 of correlation damage / geometry. 4.2 Experimental validation test An experimental validation test is performed to evaluate the performance and accuracy of the methodology. A clamped-free beam of steel SAE 1010 (length = 1 m, width = 25.8 mm and thickness = 5.3 mm) is instrumented with 9 accelerometers as showed in Fig. 6 below. The impact testing is chosen and the signals are recorded with a multi-analyser. Figure 6: Experimental validation test. 6 ICSV23, Athens (Greece), July 2016

7 Figure 7: Experimental validation test. The VBSHM strategy have localized a damage at the 31cm of the clamp with a depth of 4mm and a stiffness reduction of 98% with a fixed tolerance of 8% (under this value, the algorithm might not converges). 5. Conclusion Damage cases were studied in different sections of the beam and with different indicators. The proposed methodology has shown to be able to detect and localize a damage (numerically and experimentally) from various classical indicators. A damage library was successfully accomplished by linking 2D and 3D finite element models. The estimation using a comparison with the damage library was CPU cost higher using 3D model. In the future works, multiply experimental tests and simulations (with finer mesh) should be investigated. REFERENCES 1. Worden, K., and Dulieu-Barton, J. M. An Overview of Intelligent Fault Detection in Systems and Structures, Structural Health Monitoring, 3 (1), 85-98, (2004). 2. Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz., D.W. Technical Report LA MS, Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review, (1996). 3. Doebling, S. W., Farrar, C. R., and Prime, M. B. A Summary Review of Vibration-Based Damage Identification Methods, The Shock and Vibration Digest, 30(2), , (1998). 4. Farrar, C. R., Hemez, F. M., Shunk, D. D., Stinemates, D. W., Nadler, B. R., & Czarnecki, J. J. Technical Report LA-UR , A review of structural health monitoring literature: , (2002). 5. Friswell, M. I., and Penny, J. E. T. A simple nonlinear model of a cracked beam, Proceedings of the international modal analysis conference. Society for Experimental Mechanics inc., (1992). 6. Salawu, O. S. Detection of structural damage through changes in frequency: a review, Engineering structures, 19(9), , (1997). 7 Wauer, J. On the dynamics of cracked rotors: a literature survey, ASME Applied Mechanics Reviews, 43(1), 13-17, (1990). 8. Dimarogonas, Andrew D. Vibration of cracked structures: a state of the art review, Engineering fracture mechanics, 55(5), , (1996). ICSV23, Athens (Greece), July

8 9. Sabnavis, G., Kirk, R. G., Kasarda, M., and Quinn, D. Cracked shaft detection and diagnostics: a literature review, Shock and Vibration Digest, 36(4), , (2004). 10. Montalvao, D., Maia, N. M. M., and Ribeiro, A. M. R. A review of vibration-based structural health monitoring with special emphasis on composite materials, Shock and Vibration Digest, 38(4), , (2006). 11. Gautier, G., Mencik, J. M., and Serra, R. A finite element-based subspace fitting approach for structure identification and damage localization, Mechanical Systems and Signal Processing, 58, , (2015). 12. Pandey, A. K., and Biswas, M. Damage detection in structures using changes in flexibility, Journal of sound and vibration, 169(1), 3-17, (1994). 13. Serra, R., and Gautier, G. Detection and localization study for different damages scenarios applied to a beam, Proceedings of the 22 th International Congress on Sound and Vibration, Florence, Italy July, (2015). 8 ICSV23, Athens (Greece), July 2016

FINITE ELEMENT MODELLING OF A TURBINE BLADE TO STUDY THE EFFECT OF MULTIPLE CRACKS USING MODAL PARAMETERS

Journal of Engineering Science and Technology Vol. 11, No. 12 (2016) 1758-1770 School of Engineering, Taylor s University FINITE ELEMENT MODELLING OF A TURBINE BLADE TO STUDY THE EFFECT OF MULTIPLE CRACKS