Optimal sensor distribution for impact loading identification

Transcription

1 11th European Conference on Non-Destructive Testing (ECNDT 2014), October 6-10, 2014, Prague, Czech Republic Optimal sensor distribution for impact loading identification More Info at Open Access Database Jan BARTOŠEK 1, Tomáš KROUPA 1, Robert ZEMČÍK 1, Vladislav LAŠ 1 1 NTIS, Department of Mechanics, University of West Bohemia, Univerzitní 8, Pilsen, Czech Republic Phone: , Fax: ; bartose4@kme.zcu.cz Abstract Problem of optimal sensor distribution for impact loading identification was studied on the composite airfoil segment. The segment is made of glass-epoxy composite with piezoelectric transducers glued on its surface. Numerical model of segment was assembled in finite element software Abaqus. The experimental modal analysis was performed and its results were compared to the results obtained from numerical model. Material parameters were adjusted using optimization where the difference between numerical and experimental results mentioned above was minimized. Furthermore, the segment was loaded by impactor and response was measured by piezoelectric transducer in selected location. The response was compared to one obtained numerically. Adjusted model was used for determination of optimal sensor distribution. Keywords: structural health monitoring (SHM), materials characterization, modeling and simulation, optimal sensor distribution, piezoelectricity, finite element analysis 1. Introduction Composite materials are nowadays widely used in constructions, where high stiffness to weight ratio is needed. However, their use brings new issues and challenges to be solved like non-linear mechanical behavior [1], complicated damage behavior [2] and directional dependence of stress waves propagation [3]. Furthermore, composites are susceptible to transverse loading which can cause delamination and significantly reduce strength of the construction [4]. It can be difficult to find out such failure by common visual inspection, while such failure is often hidden inside material. More advanced non-destruction inspection techniques like ultrasonic waves have to be applied, which is time and cost consuming. Alternatively, the state of the construction can be evaluated during its live by processing of signals from sensors. This principle, structural health monitoring, covers whole area of problems like impact force identification and localization. Several methods were proposed for solving impact force identification problem. Methods based on matrix inversion in time [5] or frequency [6] domain were used. However, matrix inversion in such problems tends to be ill-posted and inappropriate sensor location can significantly reduce quality of force prediction [7]. 2. Numerical model of airfoil segment 2.1 Airfoil segment Airfoil segment analyzed in this paper was fabricated for research purposes by Aerospace research and test establishment inc. using resin transfer molding technology. Its geometry is roughly described in Figure 1 and it consists of two parts, a spar and a skin panel, which are glued together. The segment is made of fiberglass laminate and epoxy resin. Five layers of plain weave fabric with uniform orientation are used in the spar part (L3). The skin panel consists of two parts with the same fabric layouts as used in spar (L1, L2), borders of which are covered on leading and trailing edges by twelve layers of twill weave fabric with uniform orientation (L4, L5).

2 2.2 Numerical modeling Fig. 1 Geometry of airfoil segment. All dimensions in mm. Numerical model of the airfoil segment was assembled in commercial software Abaqus Precise geometry representation of the segment was achieved using 3D laser scanning technology. Linear quadrilateral shell elements with edge length approximately 10 mm and lamina material model with composite layup were used. Number of elements was 7136 in total. Connection of skin panel and spar was considered as ideally stiff and it was realized by Tie constrain. 2.3 Identification of mechanical properties Experimental modal analysis of airfoil segment was performed to adjust mechanical properties of materials. The segment was supported by flexible rubber springs and the response of construction was measured for 97 impact points by impact hammer Brüel & Kjær The analyzer Brüel & Kjær with module Brüel & Kjær 3109 was used for data acquisition and software ME ScopeVES 6 was used for evaluation of the first 20 natural frequencies (Figure 2). The optimal values were searched by optimization technique using software optislang Automatic numerical model generation for Abaqus was implemented using programming language Python 2.7. Firstly, evolutionary algorithm based optimization was utilized to find the starting values for following gradient based algorithm optimization. Objective function for optimization was set as weighted sum of errors of natural frequencies values and natural shapes from numerical simulation compared to measured values: EXP FEA 20 EXP FEA fi f i si s i f s 000 EXP EXP i= 1 fi i= 1 si, (1) o = 5000 e + e = 5 + where f i EXP and f i FEA are i-th natural frequencies, s i EXP and s i FEA are sums of displacements magnitudes of i-th natural shapes over all measured points and upper index denote experimental value (EXP) or value from numerical simulation (FEA). Optimization parameters were elastic properties E 1, E 2 and G 12 of each layup (L1-L5 in Fig. 1). Their optimized values are shown in Table 1. Errors values and comparison of natural frequencies of optimized parameters is in Figure 2.

3 Fig. 2 Comparison of natural modes. Table 1 Optimized material parameters. All values in MPa. L1 L2 L3 E 1 E 2 G 12 E 1 E 2 G 12 E 1 E 2 G L4 L5 E 1 E 2 G 12 E 1 E 2 G Impact response modelling Response of the segment to impact loading was measured and numerically simulated. The airfoil segment was fixed by spar part (Figure 4). Piezoelectric sensor, DuraAct patch piezoelectric transducers P-876.SP1, was glued on outer surface using HBM Z70 adhesive; their response to impact loading was measured and compared with numerical model. The structure was impacted by impact device, which was equipped with force sensor Brüel & Kjær 8200 and was powered by electromagnet. Data acquisition was performed by NI CompactDAQ measurement system with analog voltage input module NI Synchronized measurement of impact force and signal from sensor was performed with sampling frequency 100 khz and was controlled by interface implemented in LabView. The segment fixation was simulated in numerical model by prescribed boundary condition. Explicit solver was used. Sensor response was evaluated as sum of principal elastic strains on corresponding element. Comparison of measured response and response from numerical simulation is shown in Figure 3.

4 Fig. 3 Impact response. 3. Impact force identification and optimal sensor distribution 3.1 Impact force identification method The method considered in this paper for force reconstruction is based on signal deconvolution in time domain. Response of linear system h can be expressed by convolution: h = f g, (2) where f is loading force function and g is transfer function, which represents impulse response and determine system behavior for selected input-output locations. The transfer functions have to be known before force identification and can be obtained from model or measurement. Measurement based approach and matrix representation of deconvolution for time-discreet system is described in detail in [5]. Deconvolution tends to be ill-posed problem and signal noise is then magnified, which leads to oscillating and unrealistic impact force predictions. Regularization technique can solve this problem, but can overdamp the force prediction in contrary [7]. 3.2 Optimal sensor distribution Numerical model of the airfoil segment was used to select optimal sensor distribution. Impact on upper skin and eight possible sensor locations (red in Figure 5) were considered. Impulse response was calculated for 91 impact points (green in Figure 5) to cover whole area of interest. Sum of squared signal time history was measure for sensor location selection and it was numerically determined on each sensor location for all impact locations. Results from numerical simulation are in Figure 6. Three sensor locations from eight possible locations were selected. According to [5], three sensors are adequate number for such geometry. The highest values of signal measure, for majority of impact points, are on sensor location IV. There is decrease in values for impacts behind connection of skin panel to spar. For that reason, sensor location VII was selected to cover impacts in those locations. The last selected location is location III, where signal measure values are noticeable for most of impact locations.

5 Fig. 4 Experimental setup. Fig. 5 Impact and sensor points. Fig. 6 Measure of impulse response for all sensors and impact points.

6 Finally, sensors were glued by adhesive tape on all considered locations and experimental values were compared to numerical ones (Figure 5). 4. Conclusion The numerical model of airfoil segment was utilized for selection of optimal sensor locations based on signal magnitude measure. The results from numerical simulation correspond with some limitations to experimental one. The further work will be focused on improvement of numerical model and optimization of sensor placement with arbitrary location. The criterion for optimal location could be improved by including evaluation of time dependency of signal. Acknowledgements The work has been supported by the European Regional Development Fund (ERDF), project NTIS New Technologies for Information Society, European Centre of Excellence, CZ.1.05/1.1.00/ , grant projects GA P101/11/0288 and SGS References 1 Kroupa T, Laš V, Zemčík R. Improved nonlinear stress-strain relation for carbon-epoxy composites and identification of material parameters. Journal of composite materials, 2011, vol. 45, n. 9, Laš V, Zemčík R. Progressive Damage of unidirectional Composite Panels, Journal of Composite Materials, 42(1), (2008). 3 Červ J, Kroupa T, Trnka J. Influence of principal material directions of thin orthotropic structures on Rayleigh-edge wave velocity. Composite structures 92 (2010), , ISSN: Williams KV, Vaziri R, Poursartip A. A physically based continuum damage mechanics model for thin laminated composite structures, International Journal of Solids and Structures, 40 (2003), Zemčík R, Bartošek J, Lašová Z, Kroupa T, Bartošek J. Reconstruction of Impact on Composite Airfoil Segment Using Piezoelectric Sensors. EWSHM - 7th European Workshop on Structural Health Monitoring (2014). 6 Martin MT, Doyle JF. Impact force identification from wave propagation responses, International Journal of Impact Engineering 18 (1996), Jacquelin E, Bennani A, Hamelin P. Force reconstruction: analysis and regularization of a deconvolution problem, Journal of Sound and Vibration 265 (2003),