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Structural integrated active damping system: optimal layout design strategy of functional elements based on overall strain

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  • Save International Journal of Composite M aterials 2013, 3(6B): 53-58 DOI: 10.5923/s.cmaterials.201310.06 Structure-integrated Active Damping System: Integral Strain-based Design Strategy for the Optimal Placement of Functional Elements Pawel Kostka, Klaudiusz Holeczek*, Werner Hufenbach Institute of Lightweight Engineer ing and Polymer Technology (ILK), Technische Universität Dresden, Dresden, 01307, Germany Abstract In this paper a design strategy is presented for the identificat ion of optimal positions and orientations of composite-integrated actuating/sensing elements for the purposes of an active vibration damping suppression. This publication address mainly the problem of structure’s critical natural v ibrations damping that cannot be achieved by conventional passive measures. This approach is based on the mathematical analysis of strain fields on the surface of a vibrating with an eigenmode structure with the goal of identifying regions with the maximal strain integrated over the size of selected actuating/sensing element. The required strain fields of the investigated structure can be obtained either from a simu lation using a numerical model or fro m measurements using, e. g. image sequence analysis or strain gauging technique. The proposed procedure is presented in a step-by-step manner on an examp le of a co mplex-shaped fibre reinforced composite structure although it can be applied for other materials allowing element integration. Keywords Active Damping System, Function Integration, Smart St ructure, Design Strategy 1. Introduction Every in-service structure is to a greater or lesser extent exposed to vibrations. These can be either structure born – for example resulting fro m realised process characteristics – or have external causes like wind, noise etc. The vibrations can, in the worse case, lead to the structure’s catastrophic failure due to e. g. fat igue or dynamic overload. An increase of vibration-caused issues can arise fro m the applicat ion of materials with relatively low damping properties like the high-performance lightweight polymer-based composites. Typically, to moderate the vibrations of composite structures, three types of measures can be utilised: application of high damping matrix and fibres, incorporation of external damp ing elements, or application of additional active elements which functionally mimic an increase of damp ing[1, 2]. The applicat ion range of the first option – application of damping materials – is constrained by the fact that it is not practically possible to increase the damping with stiffness and strength properties remaining unaffected. Therefore, often an increase in structure’s mass is necessary in order to preserve the primary load bearing capabilit ies. The second measure – incorporation of external damping e le ments – can be only used when the structure’s surface is accessible and there are no restrictions regarding good wear resistance or aerodynamics. The last abovementioned possibility of damp ing increase – application of damp ing mimicking elements – overcomes all disadvantages of the previously mentioned measures since the vibrations are suppressed by generation of counteracting forces using embedded elements. Such solutions normally consist of material-integrated actuating/sensing elements (ASE), appropriate electric circuits to asses the induced force characteristics, and – if needed – devices for energy trans mission. Such solutions are, depending on the configuration of the electric circuit, referred to as active, semi-active or semi-passive damping s ys tems . The main challenge of successful application of such systems lies in the proper identification of position and orientation of necessary material-integrated functional elements since it directly determines the damping system performance. Even though for elementary shaped structures respective positioning strategies have strong closed-form foundations, for complex-shaped structures methods are utilised wh ich require co mprehensive datasets of potential solutions. This gap between co mplexity of the structure and the simp licity of procedure is bridged in the proposed approach. * Corresponding author: (Klaudiusz Holeczek) Published online at Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved 2. State of the Art The progress in miniaturisation of actuator and sensor 54 Pawel Kostka et al.: Structure-integrated Active Damping System: Integral Strain-based Design Strategy for the Optimal Placement of Functional Elements elements comb ined with the h igh maturity of co mposite manufacturing processes as well as recent advances in the signal analysis have stimulated the development of so-called smart structures[3, 4]. Since the introduction of this modern group of structures, the topic of optimal p lacement and orientation of actuator and sensor elements was identified as vital for their performance. Hence, a large nu mber of papers dealing with the topics of ASE position optimisation can be found. In general, the strategy for the development of smart structure can be presented as three step decision process[5]: • determination of the functional e le ments quantity, • optimisation of the ASE placement, • evaluation of the ASE performance. Some authors[6] include in that classification the shape assessment of the ASE, the tuning of the electronic units, and the determination of A SE – host structure bonding layer. One of the main strategies of solving the problemat ic of ASE placement base on the concept of assessing all locations of an candidate ASE set against some objective function and subsequently iteratively removing those ASE that perform least well until some acceptable value of objective function is reached[5]. Based of that concept, the effective independence (EI) method was introduced in[7]. In the EI approach, the objective function is a contribution of functional elements in maintaining the determinant of the Fischer informat ion matrix. The ASE that contributes the least at each iteration step is deleted from the candidate set. At the end, an optimal set of ASE by means of quantity, position and performance is identified. Similar examp les of such iterative approach base on following objective functions: eigenvalue vector product[8], driving-point residue[9], effective independence driving-point residue[10] or modal assurance criterion[11]. This group of approaches is characterised by large co mputational effort especially since the initial candidate set have to be very extensive in order to include all relevant eigenforms. This disadvantage can be eliminated by a reverse approach where a minimal initial ASE candidate set is extended until the acceptable value of objective function is reach. Nevertheless, an essential characteristic o f all this methods is posed by the fact that the analysis of data collected fro m exhaustive search is very often complex and time -consuming – although the correct result is always obtained. Another group of methods for the ASE position optimisation is constituted on the grounds of artificial intelligence (AI) theory[12-14]. Using that theory, an approximate reasoning about optimal integration position of ASE based on limited amount of information is possible. The main advantage of these methods, in co mparison with the aforementioned iterative approaches, lies in the avoiding of the time-consuming exp loration. Nevertheless, the final performance of this group of methods is connected with the informat ion-content – and therefore typically with the size – of the utilised dataset of examp les. In the proposed strategy for optimal positioning and orientation of ASE, the characteristics of both above presented approaches are combined: the correctness of the iterative methods with the simplicity of AI-based ap p ro ach es . 3. Integral Strain-based Design Strategy The proposed strategy originates fro m the fact that the vibration suppression using a material-integrated active damping s ystem can be achieved only when the detrimenting vibrations are observable (sensing) and controllable (actuation). Since the typically used ASE induce or acquire mechanical strain, the position of ASE integration need to be associated with the strain distribution in every detrimenting vibration condition. Taking into account the finite, non-zero size of every ASE, its optimal position have to be determined based on structure’s surface strains integrated over the size of the ASE. Additionally, a match of ASE axis of action (cf. Fig. 1) with angle of maximal integral strain on the structure (v. Fig. 5) needs to be assured. Figure 1. Example of a low-profile strain sensing/inducing ASE with marked axis of action[17] Figure 2. T ransformation of the global strains to local strains. (A) Complex shaped structure with exemplary position of ASE integration. (B) ASE principal axis of action in global and local coordinate system The structure’s strain field required for the analysis can be obtained either fro m a simu lation using a nu merical model or fro m measurements using, e. g. image sequence analysis or strain gauging technique. Since the spatial resolution of the strain fields determines the accuracy of the optimisation procedure, while using data obtained fro m experimental techniques a special emphasis has to be placed on sensing International Journal of Composite M aterials 2013, 3(6B): 53-58 55 element distribution. In the here p roposed strategy, an assumption is made that the strains on the surface layer and immediately under it – where the ASE will be integrated – do not differ s ig n ifican tly . Due to possible arbitrary shape of an analysed structure and limited ASE drapability, an ASE integration angle would be different in each structure-conform coordinate system and therefore specification of one integration angle is not possible. Therefore a general integration angle (φ) is defined in the global coord inate system and the structure-conform integration angle (α) is calculated for every local coordinate system (cf. Fig. 2). Since the strain field have to be calculated fo r the integrated ASE – what means in structure-conform coordinate systems – a reorientation of every strain tensor in surface-conform local coordinate system to the integration angle (α) have to be performed. Such transformation is made using the following equation: εP' = T ⋅ εl (1) where: εl are the strains in structure-conform coordinate system defined as: εx    ε y   εl = εεxzy    (2) ε  yz   ε xz  where εx, εy, εz, εxy, εyz, εxz are co mponents of elastic strain for every investigated integration position defined in surface-conform coordinate system; εP’ are the strains in structure-conform local coordinate system in the defined structure-conform integration angle α; and T is the transformation matrix defined as:  c2 s2 0 cs 0 0    s2 c2 0 − cs 0 0    T = 0 − 2cs 0 2cs 1 0 0 c2 − s2 0 0 0  0 (3)   0 00 0 c − s  0 0 0 0 s c  where: c=cos(α); and s=sin(α); with α defined as: ( ) α = arctan Xp' (4) here X p ' is the axis of action of an ASE after integration defined as: X p ' = Rz ⋅ Rx ⋅ Ry ⋅ a (5) with rotational matrixes Rx Ry and Rz defined as: 1 0 0 Rx = 0 cos (ηx ) − sin (ηx ) (6a) 0 sin (ηx ) cos (ηx )  ( ) ( ) Ry =    cos η y 0 0 1 sin η y 0    (6b) − sin (η y ) 0 cos (η y ) cos (ηz ) 0 − sin (ηz ) Rz =   sin (η z ) cos (ηz ) 0   (6c)  0 0 1  where ηx, ηy, ηz, are the orientation angles of a given surface-conform coordinate system in the global coordinate system; and a is the directional vector defining line of intersection of two planes as: a = n1 × n2 (7) where: n1 and n2 are directional vectors of a plane tangent to the structure’s surface in g iven point, and a plane normal to the XY-p lane of global coordinate system and intersecting that plane in general integration angle φ (cf. Fig. 2). In the next step, the rotated strain tensors for every detrimenting vibration condition are summed over the assumed size of the ASE separately for every general integration angle. lw = εint (φ) ∑ ∑ εP' (φ) (8) 00 where: l and w are length and width of an assumed ASE. Finally, a reg ion and angle with maximal integral strain is selected for the integration position and orientation of the ASE: ( ) max εint (ϕ ) (9) 4. Case Study: Composite Fan Blade Figure 3. Structure investigated in case study. (A) Pressure side. (B) Suction side Co mposite materials are assumed – due to their 56 Pawel Kostka et al.: Structure-integrated Active Damping System: Integral Strain-based Design Strategy for the Optimal Placement of Functional Elements outstanding strength and stiffness properties – to be used in the propellers of a next generation turboprop airplane engines. Hence, in the case study, a co mposite fan blade (Fig. 3) was selected as an exemplary structure for the validation of the design strategy proposed in this article. The selected structure is characterised by: ● comp lex, mu lti-curved geometry, ● anisotropic, locally varying material properties due to complex co mposite layup including dropped layers, ● low intrinsic material damping. 4.1. Numerical Model of the Composite Fan Blade The simu lation with fin ite-element model of the composite fan b lade was performed in order to obtain strain field for the first modeshape. The necessary model was developed using commercial finite element software with application of a 3-dimensional 8-node element based on the Mindlin-Reissner shell theory with enhanced strain formulat ion[15]. The necessary material properties were obtained from the materia l database available at the Institute of Lightweight Engineering and Poly mer Technology (ILK). Selected degrees-of-freedom in the model were constrained in order to simu late the existing boundary conditions of the investigated structure. The main v ibration problem of fan blades is associated with the aeroelastic flutter phenomena. Flutter is a self-driven and potentially destructive vibration condition where aerodynamic forces couple with a structure natural mode. The underlying natural mode is typically the first eigenmode (Fig. 4) of the structure therefore this modeshape was selected as the detrimenting v ibration condition in this an aly s is . 4.2. Data Transformati on Firstly, a structure-conform integration angle α was determined according to Eq. 4. The strain field oriented in general integration angle φ equal to zero is presented on Fig. 5. Subsequently, the strains were rotated in order to calculate the strains in actuator's axis of action for every possible global integration angle. An examp le of strain distribution for t wo angles – 45° and 90° – are presented on the Fig. 6 for pressure and suction side of the fan blade. Finally, the strains for every co mbination o f angle and position of an assumed ASE are integrated aver the size of the ASE. Initially for this study, a commercially availab le low-p rofile ASE with known dimensions was selected. As a characteristic parameter o f integration the middle and axis of action of the ASE were selected. Figure 6. Distribution of the mechanical strains in local coordinate system after rotation. (A) On the blade’s pressure side rotated by 45°. (B) On the blade’s suct ion side rotat ed by 45°. (C) On the blade’s pressure side rotat ed by 90°. (D) On the blade’s suction side rotated by 90° 4.3. Determined Position of the AS E Fi gure 4. Eigenforms of the invest igated composite fan blade The surface strain fields of the identified modeshape for pressure and suction side are depicted on the Fig. 5. The numerical values of the presented strains were subsequently an aly s ed . Figure 5. Distribution of the mechanical strains for the first modeshape presented in structure-conform local coordinate systems. (A) On the blade’s pressure side. (B) On the blade’s suction side Out of all candidate positions and orientations of ASE those are selected which are characterised by globally maximal integral strains on the pressure and suction side. In order to compare the potential damp ing performance a factor was defined as: ( ) p = εint (ϕ ) max εint (ϕ ) (10) Based on the calculated integral strains the p-values are equal 1 for the pressure side and 0.95 for the suction side. Here, it is important to notice the fact that trough the complex shape and layup the position of the ASE on pressure and suction side differ, therefore it is necessary to analyse both sides independently. Therefore, it is possible to assess the optimal position of the ASE on the pressure side in the position as depicted on the Fig. 7 Subsequently, in order to validate the obtained position and orientation of the ASE an experimental study was conducted. International Journal of Composite M aterials 2013, 3(6B): 53-58 57 (4). The blades were excited to vibrat ions with the first modeshape, and subsequently – with persisting excitation force – the ASE were actuated with signals ca lculated using a control algorith m developed by the authors in[16]. Fi gure 7. Est imat ed opt imal posit ions of ASE. (A) On the pressure side. (B) On the suction side 4.4. Experi mental Vali dati on The experimental validation was conducted on two identical co mposite fan blades – the first one with the ASE applied on the surface and the second one with structure-integrated ASE. The co mposite fan blades were manufactured in resin-transfer-mould ing technology from carbon fibre rein forcement infiltrated with epo xy resin. A ll quality-relevant fabrication parameters were set according to the specifications of the fabric and resin manufacturers. The investigations were conducted in order to co mpare the assumption that the difference between the performance of the active damping system with surface applied and integrated ASE optimised using surface input strain is negligible . 4.5. Results and Discussion The measured via ASE timeseries of strain signals for the cases with and without activated damping system for both analysed blades are depicted on the Fig. 9. The results confirm that: ● the difference in the perfo rmance of the active damping system for surface-applied and integrated ASE is, as assumed, neglig ible ● the vibration suppression performance estimated fro m the following equation: pdamp = Apass − Aact Apass ⋅100 (11) where Apass and Aact are vibration amp litudes of a structure with and without active damping system respectively is high. The pdamp equals to 96 and 93 for the surface applied and integrated ASE respectively. These values can be interpreted as the percentage reduction of vibration amp litude. Figure 8. Experimental set-up. (A).General overview: (1) – Electromagnet for vibration excitation; (2) – Composite fan blade with surface mounted ASE; (3) – Diffuse field microphone; (4) – Clamping; (5) – Surface mounted MFC. (B) Detailed view of surface mounted magnet (6) On the surface of the co mposite fan blade (c. f. Fig. 8 - 2) an ASE in the form of a Macro Fibre Co mposite with the dimensions 85 x 28 mm2 was applied (5) using epoxy-based adhesive. Independently, a second blade was fabricated with an identical ASE albeit integrated into the structure under the first reinforcement layer. Additionally, s mall magnets (6) were applied on the tip of both blades in order excite the selected modeshape using externally placed electro magnets (1). Finally, both blades were clamped by the root using a specially constructed and manufactured affixing mechanism Figure 9. Strains measured using integrated ASE. (A) Of the composite blade with surface applied ASE. (B) Of the composite blade with integrated ASE Additionally, the acoustic radiation of the vibrating structure with and without activated damping system was measured. For that purpose a diffuse field microphone was placed in the immediate vicinity of the blade with surface applied ASE (Fig. 8 - 3). The results – presented on the Fig. 10 – confirm significant reduction of vibrat ion and acoustic pressure amplitudes without spin over effects. 58 Pawel Kostka et al.: Structure-integrated Active Damping System: Integral Strain-based Design Strategy for the Optimal Placement of Functional Elements REFERENCES [1] Huang, S., Inman D., Austin E., 1996, Some design considerations for active and passive constrained layer damping treatments, Smart M aterials and Structures 5 (3) , 301. [2] Schürmann, H., 2008, Konstruieren mit Faser-KunststoffVerbunden, Springer Verlag. Figure 10. Acoustic pressure measured with using externally placed microphone on a vibrating blade with surface applied ASE 5. Summary A novel design strategy for the identification of optimal positions and orientations of structure-integrated actuating/sensing elements (ASE) of an act ive damping system was presented in this paper. Since the ASE are always characterised by a finite, non-zero size, the optimal integration-position was determined based on the strains integrated over the size of the ASE. Addit ionally, a match of ASE axis of action with angle of structure’s surface integral strain was addressed. The proposed strategy is based on the mathemat ical analysis of strain fields of a vibrat ing structure with the goal of identify ing regions with the maximal strain integrated over the dimensions of selected actuating/sensing element. This strategy was validated in the case study on examp le of complex, mult i-curved geometry with anisotropic, locally varying material properties, and low intrinsic material damping. The input data for the strategy – strain field occurring while a structure vibrated with first modeshape – was extracted fro m a nu merical simu lation. Alternatively, the same data can be acquired fro m experimental investigations. Since here typically only the surface strains are accessible in the case study two composite fan blades were analysed – with surface applied and integrated ASE. The results confirmed negligib le influence of the through-thickness integration position on the overall performance of the active damping system. Summarising, the assumptions of the proposed strategy for optimal, positioning and orientation of arb itrary shaped ASE of an active damping system were proven to be valid. ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of the European Union of the research under Grant No. DREAM – FP7-211861 ‘Validation of rad ical engine architecture systems’ as well as the European Centre for Emerging Materials and Processes Dresden (ECEMP) funded by the European Union and the Free State of Saxony. 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Journal of Guidance, Control, and Dynamics, 14(2), 251-259 [8] Jarvis B., 1991, Enhancements to modal testing using finite elements, In 9th Conference International M odal Analysis Conference (IM AC), Vol. 1, 402-408. [9] Penny J., Friswell M ., Garvey S., 1994, Automatic choice of measurement locations for dynamic testing, AIAA journal, 32(2), 407-414. [10] Imamovic N., 1998, Validation of large structural dynamics models using modal test data, Imperial College of Science, Technology & M edicine. [11] Breitfeld T., 1996, A method for identification of a set of optimal measurement points for experimental modal analysis, MODAL ANALYSIS–The International Journal of Analytical and Experimental M odal Analysis, 11(1), 1-9. [12] Han J.-H., Lee, I., 1999, Optimal Placement of Piezoelectric Sensors and Actuators for Vibration Control of a Composite Plate Using Genetic Algorithms, Smart M aterials and Structures, 8(2), 257–267. [13] Sadri A., Wright, J., Wynne, R., 1999, Modelling and Optimal Placement of Piezoelectric Actuators in Isotropic Plates Using Genetic Algorithms, Smart M aterials and Structures, 8, 490–498. [14] Sheng L., Kapania, R., 2001, Genetic Algorithms for Optimization of Piezoelectric Actuator Locations, AIAA Journal, 39(9), 1818–1822. [15] ANSYS® Academic Research,2009, Release 12.0, Help System, Elements reference, ANSYS, Inc. [16] Hufenbach W., Langkamp A., Kostka P., Holeczek K., Schreiber K., 2009, Cylindrical Shaped Composite Rotors with M aterial Integrated System for Active Damping of Bending Vibrations, In: Proceedings of ISPA 2009, Dresden. [17] “Datasheet M acro Fiber Composite M FC” Smart M aterial Corp .

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