ELECTROMECHANICAL IMPEDANCE METHOD FOR DAMAGE DETECTION IN MECHANICAL STRUCTURES

Transcription

1 ELECTROMECHANICAL IMPEDANCE METHOD FOR DAMAGE DETECTION IN MECHANICAL STRUCTURES MATEUSZ ROSIEK *, ADAM MARTOWICZ, TADEUSZ UHL, TADEUSZ STĘPIŃSKI, TOMASZ ŁUKOMSKI Department of Robotcs and Mechatroncs Faculty of Mechancal Engneerng and Robotcs AGH Unversty of Scence and Technology, Krakow Abstract Non-destructve measurements of an electromechancal mpedance allow for the effectve assessment of the state of mechancal structures. Pezoelectrc transducers, whch are dstrbuted n montored constructon, ntroduce couplng between mechancal propertes and drectly measured electrc enttes. Therefore ncpent mechancal damage can be detected and ts growth followed. The changes of mechancal propertes are found wth the comparson between plots of mpedances measured for both orgnal healthy system and the system whch s operatng n a current state. Ths paper presents the results of Fnte Element analyses performed for a cantlever alumnum beam wth bonded pezoelectrc transducer. Modelled structure was excted to vbrate at hgh frequency range and electromechancal mpedance plots were obtaned from the harmonc analyss. Vertcal notch was ntroduced n the beam and the damage metrcs were used to asses qualtatve changes n structural propertes of the system. The numercal results were confrmed expermentally usng laboratory equpment. Wth obtaned numercal and expermental results there has been ntroduced the dea of a Structural Health Montorng (SHM) system.

2 Introducton to electromechancal based measurement Amongst a number of applcatons of Non-Destructve Evaluaton (NDE) there are Structural Health Montorng (SHM) technques based on the measurement of electromechancal mpedance. Montorng of materal ntegrty can be performed wth pezoelectrc transducers bonded to mechancal structure [1,2]. Transducers are powered wth alternatng voltage and change ther frequency characterstcs of electrcal mpedance accordngly to fluctuatons of mechancal propertes of montored structure. Appearng damage causes local change of stffness and dampng propertes whch n turn modfes plots of mpedance [4,5,6]. It can be acheved snce the feature of electromechancal couplng n pezoelectrc transducer s present. Therefore measured electrc mpedance of the transducer s commonly called as electromechancal mpedance. For the range of lnear relatonshp between mechancal and electrcal propertes of the pezoelectrc materal the followng matrx equaton can be formulated [7]: E S s = D d d T t T ε E (1) where: S - vector of mechancal strans, T - vector of mechancal stresses, E - vector of electrc feld, D - vector of electrc dsplacement feld, s - matrx of mechancal complance, d - matrx of pezoelectrc stran constants, ε - matrx of electrc permttvty. Indexes E and T are used for the enttes measured wth electrodes connected together and at zero stress respectvely. Operator t stands for the transposton. Equatons whch defne S and D descrbe respectvely drect and converse pezoelectrc effects. Converse effect allows for the exctaton of vbratons n montored structure snce appled alternatng voltage makes the transducer deformed. Drect effect n turn enables the measurement of electromechancal mpedance as already vbratng structure nfluences measured frequency plot. Usually a group of transducers s dstrbuted to cover crtcal localzatons n mechancal structure. Data acquston unts gather data measured wth transducers, perform data processng and fnally create reports on the state of montored constructon. It s based on the nformaton whether assumed thresholds for damage ndexes are exceeded. The measurements of electromechancal mpedance are performed wthn the range of frequency 10kHz 500kHz [4,5]. The range of hgh frequences enables for hgh senstvty to ncpent damage as t dsturbances local normal modes of small sze. Moreover the results of such measurement can therefore be ndependent from external operatonal loads,.e. low-frequency exctatons from ral and

3 road vehcles. However damage detecton can be effectve only wthn neghborng area of transducer localzatons. The process of damage detecton s performed wth the comparson between mpedance plots obtaned for healthy system as well as for ts current state [3]. There has been defned a number of damage ndexes, ncludng based on statstcal data, whch are used to assess the growth of damage. Some exemplary ones are ntroduced n the followng sectons. Fg. 1a presents commonly appled electrc crcut whch s used for the electromechancal measurements. a) b) Mechancal structure Pezoelectrc transducer V C V P V C I V IN R V OUT V I Fg.1. Scheme of electrc crcut used for measurement of electromechancal mpedance (a), resultant model of pezoelectrc transducer (b) The electrc crcut conssts of the followng elements connected n a seres: power suppler electromotve force V, pezoelectrc transducer and referental resstor R. Electromechancal mpedance formula: ( V V ) IN Z E s found wth the V IN OUT VIN Z = = = 1 E R V (2) I OUT VOUT R The current I s ndrectly measured wth the referental resstor R. Voltage V measured on the transducer can be calculated wth known voltages V IN and V OUT. The pezoelectrc transducer can be substtuted wth the seres connecton of capactor C and electromotve force V P as shown n fg. 1b. Indrectly measured voltage V depends on the value of V P generated n pezoelectrc transducer accordngly to drect pezoelectrc effect. Hence any change of mechancal propertes caused by damage fnally nfluences Z. E

4 Descrpton of numercal model For numercal analyses the fnte element model of freely suspended alumnum beam has been created n ANSYS software. The model s presented n fg. 2. The sze of fnte elements used n the mesh has been assumed to equal 0.5 mm. Fg. 2. Fnte element model of analyzed structure The dmensons of the beam were: 100mm, 16mm and 1mm. A smple pezoelectrc transducer of szes 10mm, 10mm and 0.3mm, made of the materal PIC151 followng the specfcaton of PI Ceramc has been bonded to the beam to allow the electromechancal mpedance evaluaton. The transducer was located 5mm far from the beam end n ts left hand sde. The model was consderng also a thn layer of epoxy adhesve. All components of the model were buld wth 3D and 20-node parabolc fnte elements. Elements used to model transducer addtonally consders the feature of pezoelectrc couplng. Addtonal FE elements were enabled for the ntroducton of electrc crcut,.e. voltage source and referental resstor. The alternatng voltage wth the magntude of 1V has been appled to power electrc crcut. The resstance of referental resstor was equal 100Ohms. The damage n the model has been ntroduced as a 1mm wde ncson wth varyng depth - from 1mm to 4mm. The damage was localzed 55mm far from the left vertcal edge of the beam. Non-central localzaton of the ncson has been assumed not to dsturb the node lnes of the fundamental bendng and plate mode shapes of the beam. As reported n the lterature mentoned above case could cause problem wth correct nterpretaton of the sze of damage [8]. Numercal analyses Multphyscs harmonc analyses have been performed wth elaborated fnte element model to generate the frequency plots of electromechancal mpedance for both healthy constructon and wth ntroduced damage (Fg. 3).

5 Fg. 3. Real part of smulated electromechancal mpedance The real part of electromechancal mpedance has been consdered snce t s more senstve to changes of montored mechancal propertes [1]. Growng damage causes shft of most of resonances towards lower values of frequences. It results from ncreasng complance of the structure when ncson s ntroduced. Moreover for the largest damages new resonance peaks are observed because of sgnfcant structural changes. To montor the sze of damage the followng damage ndexes have been taken nto account: n ( Re( Z0, ) Re( Z ))( Re( Z0, ) DI1 = (3) = ( Re( Z ) Re( Z ))( ( Z )) ) n 2 2 = 0, Re 0, = 1 DI (4) n = 1 1/ 2 1/ (( ( ) ( ))( ( )) ) 2 1 Re Z 0, Re Z Re Z 0, DI 3 = (5) n (( 0, 0 ) ( ) ( ) ) 1 (( n 1) s s) Re( Z ) Re( Z ) ( Re Z Z ) DI 4 = 1 0 Re (6) = 1 where: Z 0, and Z -respectvely referental and current value of mpedance for -th frequency, Z 0, s 0 and Z, s -mean values and standard devatons of referental and current mpedances, n -number of consdered frequences. Fg. 4 presents values of damage ndexes calculated for all szes of ntroduced ncson.

6 Fg. 4. Relatons between depth of ncson and damage ndexes numercal results For all tested damage ndexes there have been obtaned monotonc relatons between ther values and depth of ncson. Ths observaton justfes the effectveness of the assessment on the propagaton of damage ntroduced n montored constructon. Expermental verfcaton For the mechancal structure mentoned prevously expermental measurements of electromechancal mpedance have been performed usng hgh precson HP/Aglent 4395A Impedance Analyzer. Fg. 5 presents results obtaned for the alumnum beam n the same frequency range as for the smulatons. Fg. 5. Real part of measured electromechancal mpedance

7 Fg. 6. Relatons between depth of ncson and damage ndexes expermental results Fg. 7. Comparson between numercal smulatons and expermental results for healthy structure Analogcally to the results of FE analyses growth of damage sze causes the ncrease of values of the damage metrcs. Impedance plots obtaned from experments were compared wth the smulatons and there was a good concdence between numercal and expermental data. Some mnor changes n resonance peaks and ampltudes can be observed due to the fact that FE model was not updated after performng the measurements.

8 Summary and concludng remarks In ths work a utlzaton of electromechancal mpedance measurements for damage detecton n mechancal structures was ntroduced. Numercal results were compared wth expermental data and good agreement was reached between smulatons and measurement. It was proven, that mpedance based technque can be used successfully n structural health montorng, however ths method should be treated as qualtatve assessment rather than quanttatve one. Acknowledgements The work was supported by the Polsh Grant POIG /08-00 Montorng of Techncal State of Constructon and Evaluaton of ts Lfespan- MONIT. Bblography 1. Inman D J, Farrar C R, Lopes V Jr and Steffen V Jr 2005 Damage Prognoss. For Aerospace, Cvl and Mechancal Systems (Chchester, England: John Wlley & Sons, Ltd.) 2. Park G, Farrar C R, Rutherford A C and Robertson A N 2006 Pezoelectrc Actve Sensor Self-Dagnostcs usng Electrcal Admttance Measurements ASME J. Vb. Acoust. 128 (4) Gurgutu V 2008 Structural Health Montorng wth Pezoelectrc Wafer Actve Sensors (Amsterdam; Boston: Elsever Academc Press) 4. Yan W, Lm C W, Chen W Q and Ca J B 2007 A coupled approach for damage detecton of framed structures usng pezoelectrc sgnature J. Sound Vb Nadu A S K and Soh C K 2004 Damage severty and propagaton characterzaton wth admttance sgnatures of pezo transducers Smart Mater. Struct Sun F P, Chaudhry Z, Lang C and Rogers C A 1995 Truss structure ntegrty dentfcaton usng PZT sensor actuator. J. Int. Mater. Syst. Struct Park G and Inman D J 2007 Structural health montorng usng pezoelectrc mpedance measurements Phl. Trans. R. Soc. A Rosek M., Martowcz A. and Uhl T.: Uncertanty and senstvty analyss of Electro- Mechancal Impedance based SHM system. IOP Conf. Seres: Materals Scence and Engneerng,10, 2010, do: / x/10/1/012207