REAL-TIME IMPACT FORCE IDENTIFICATION OF CFRP LAMINATED PLATES USING SOUND WAVES

Transcription

1 8 TH INTERNATIONAL CONERENCE ON COMPOSITE MATERIALS REAL-TIME IMPACT ORCE IDENTIICATION O CRP LAMINATED PLATES USING SOUND WAVES S. Atobe *, H. Kobayash, N. Hu 3 and H. ukunaga Department of Aerospace Engneerng, Tohoku Unversty, Senda, Japan, Graduate Schoo of Engneerng, Tohoku Unversty, Senda, Japan, 3 Department of Mechanca Engneerng, Chba Unversty, Chba Cty, Japan * Correspondng author(atobe@ss.mech.tohoku.ac.jp Keywords: Identfcaton, Impact Locaton, orce Hstory, Impact Sound, Noncontact Measurement Introducton Impact force dentfcaton of CRP amnated pates has receved wde attenton because amnates have a ow toerance to transverse mpact forces. In the case of aerospace structures, mpacts by foregn objects, such as ha, brds and toos, nduce mpact damage and degrade the mechanca propertes of the CRP structure. In such a case, the dentfcaton resuts of the mpact ocaton and force hstory gve sgnfcant nformaton whch coud be used to predct the mpact damage. Methods for dentfyng mpact forces have been reported by many researchers thus far []. Generay, sensors that are used to measure the responses of the structure are those that can be bonded or embedded, such as stran gauges [], acceerometers [3], pezoeectrc sensors [] and BG sensors [5]. However, bonded or embedded sensors may compcate the manufacturng and mantenance processes. rom a practca pont of vew, a method whch dentfes the mpact force usng the measured data obtaned from noncontact sensors, such as mcrophones [6, 7], s consdered to be more effectve. Ths paper proposes a method to dentfy the ocaton and force hstory of an mpact force actng on CRP amnated pates usng the radated sound. The mpact ocaton s dentfed usng arrva tmes of the sound wave at the mcrophones. orce hstory s dentfed based on expermenta transfer matrces whch reate the mpact force and the measured sound pressures. In order to verfy the vadty of the proposed method, mpact force dentfcaton of a CRP amnated pate s performed expermentay, and the dentfcaton resuts are compared wth the measured ones. In addton, the effect of the stffness of the mpactor on the accuracy of dentfcaton resuts s aso examned. g. CRP amnated pate subjected to mpact force. Method for Identfyng the Impact orce. Expermenta Transfer Matrx gure depcts a CRP amnated pate subjected to an mpact force. The reaton between the force hstory { f } and the tme hstory of the sound pressure { ζ }, whch s measured by the -th mcrophone, can be expressed n the foowng equaton: where, { ζ } = [ G ( x, y, x, y z ]{ f } (, T { ζ } = [ ζ ( t ζ ( t L ζ ( tn ], T { f } = [ f ( t f ( t L f ( tn ], g 0 L 0 g g O M [ G ( x, y, xs, ys, zs ] =. M M O 0 gn gn L g (

2 Here, ζ ( t n and f ( t n are the sound pressure and force at tme t n = n ts ( n =, K, N, respectvey, t s s the sampng tme, and [ G ] s a transfer matrx composed of the Green s functon. It s worthwhe to note that the transfer matrx s defned by a functon of the mpact ocaton ( x, y and sensor ocaton ( x, y, z, and s not dependent on the force hstory. The transfer matrx s determned expermentay usng the measured data obtaned from mpact tests conducted by an mpuse hammer [8]. By transformng Eq.(, we obtan where, { ζ } = [ ]{ g } (3 f ( t 0 L f ( t f ( t O [ ] = M M O f ( tn f ( tn L T { g } = [ g g L g ]. N 0 M, 0 f ( t ( The components of the transfer matrx { g } are determned so that the estmated sound pressure, whch s gven by Eq.(3 usng the measured force hstory, s adjusted to the measured one. In order to reduce the effect of measurement error, the measured data are obtaned by conductng mpact tests K tmes. Thus, the components are determned by sovng the optmzaton probem as foows: mnmze : { g } K k k { } [ ]{ g }. k = ζ (5 Here, the east-squares method s used to sove Eq.(5. (a (b g. Interpoaton of transfer matrx. As a preparatory work for mpact force dentfcaton, constructon of the expermenta transfer matrces s undertaken. The dentfcaton regon s dvded nto dscrete areas, as shown n g. (a, and mpact tests are conducted at every node. Then, the expermenta transfer matrces are determned for each combnaton of node and sensor by empoyng Eq.(5. Insde four nodes n each area, the transfer matrx s nterpoated usng shape functons smar to those used n fnte eement anayses. When a four-node two-dmensona eement s used, as depcted n g. (b, the transfer matrx nterpoaton s expressed as: [ G ( x, y, x, y, z ] where = = N [ G ( x, y, x, y, z ] N = ( ξ( η, N = ( + ξ ( η, N3 = ( + ξ( + η, N = ( ξ( + η. (6 (7 Here, ( x, y are the coordnates of node, and ( ξ, η are the normazed coordnates of the mpact ocaton.. Impact Locaton Identfcaton The mpact ocaton s dentfed usng the dfference n the arrva tmes of the sound waves. The optmzaton probem soved n the mpact ocaton dentfcaton s as foows: I I ( x, y = j + mnmze: t j ( rj r = v (8 Here, t j s the dfference n the arrva tmes at the -th and j-th mcrophones, r s the dstance between the mpact ocaton and the mcrophone, and v s the speed of sound n the ar. In order to sove the optmzaton probem of Eq.(8, the conjugate gradent method wth goden secton method s used..3 orce Hstory Identfcaton The force hstory s dentfed by mnmzng the devaton between the measured sound pressures and the estmated ones usng the expermenta transfer matrces. Then, the dentfcaton probem reduces to

3 REAL-TIME IMPACT ORCE IDENTIICATION O CRP LAMINATED PLATES USING SOUND WAVES an optmzaton probem that s formuated as foows: mnmze : { f } = subject to : f ( t 0 I { ζ } [ G ]{ f } (9 In order to sove the optmzaton probem of Eq.(9, the quadratc programmng method s used. 3 Expermenta Resuts and Dscusson 3. Expermenta Setup The dmensons of the CRP amnated pate are 300 mm 300mm mm, and the amnate sequence s [ ] s. As to the boundary condtons, the pate s camped at the corners by jgs wth a 35mm square area. The schematc of the expermenta setup s shown n g.. Impact force s apped to the pate by an mpuse hammer (Ono Sokk GK-300, and the radated sound s measured by four mcrophones (Ono Sokk MI-3. The sgna from the mcrophone s ampfed by a preampfer and a sensor ampfer (Ono Sokk MI-3, SR-00, and the sound pressure s recorded by a dgta oscoscope (Keyence GR mutaneousy, the force obtaned from the mpuse hammer s aso measured. Then, mpact force dentfcaton s performed by a computer usng the acqured data. The ocatons of the mcrophones are ndcated n Tabe. As to the mpact tp of the mpuse hammer, two types of tps, one made of hard pastc (hard tp and the other made of rubber (soft tp, are used. The force hstory and the correspondng sensor responses are measured n the tme perod of ms and the sampng tme s set to t s = 0µ s. The dentfcaton regon s a 0mm square area, whose center concdes wth that of the pate. In determnng the expermenta transfer matrces, the dentfcaton regon s equay dvded nto sx n the drectons of the x and y axes, as shown n g. (a. Then, the number of nodes where the transfer matrces are determned s 9. The number of mpact tests conducted for each node s K = 5. In the present study, two types of transfer matrces are constructed by changng the mpact tp used n the mpact tests. g. Expermenta setup Tabe Sensor ocatons Mcrophone ( x, y, z No. (50,50, 8 No. (85,50, 97 No.3 (33,80, 97 No. (33,0, Identfcaton Resuts and Dscusson The dentfcaton resuts of mpact ocaton are shown n g.3. Identfcaton was performed at 36 ponts, and by appyng the force usng the two mpact tps. As can be seen from the fgure, the dentfed ocatons are n good agreement wth the measured ones. The ocatons were dentfed wthn the error of 8.9mm n the case of the soft tp, and.9mm for the hard tp. The dentfcaton resuts revea that the mpact ocaton s dentfed accuratey by the proposed method, and that the accuracy s ndependent of the stffness of the mpactor. Tabe shows the expermenta condtons of the force hstory dentfcaton. The dentfcaton s dvded nto four cases dependng on the mpact tps whch were used for the constructon of the transfer matrces and for the dentfcaton test. gure shows the dentfcaton resuts of the force hstory of an mpact force apped by the soft tp. The mpact ocaton corresponds to pont A n g.3 (a, whch s the pont whose error of the dentfed ocaton s the maxmum. The fgure reveas that the force hstory of the soft tp s dentfed wth suffcent accuracy, regardess of the type of mpact tp used n the constructon of the expermenta transfer matrces. The dentfcaton resuts of force hstory for the hard 3

4 (a Soft tp (b Hard tp g.3 Identfcaton resuts of mpact ocaton. (a Case I (b Case II g. Resuts of force hstory dentfcaton of an mpact force apped by soft tp (Pont A. Tabe Expermenta condtons of force hstory dentfcaton. Case Transfer matrx Identfcaton I Soft tp Soft tp II Hard tp Soft tp III Hard tp Hard tp IV Soft tp Hard tp Tabe 3 Error of dentfed force hstory. Case Error of dentfed force hstory (% Mnmum Maxmum Average I II III IV tp s shown n g.5. The dentfcaton resuts correspond to those of pont B depcted n g.3 (b. The error of the dentfed ocaton for pont B s.9mm. As can be seen from g.5 (a, the dentfed force hstory shows good agreement wth the measured one, athough there s a sma dfference after the mpact force s unoaded. On the other hand, n the case of Case IV whch s shown n g.5 (b,

5 REAL-TIME IMPACT ORCE IDENTIICATION O CRP LAMINATED PLATES USING SOUND WAVES (a Case III (b Case IV g.5 Resuts of force hstory dentfcaton of an mpact force apped by hard tp (Pont B g.6 T resuts of measured sound pressure. the force hstory s not dentfed accuratey. The error of the dentfed force hstory E, whch s defned by Eq.(0, s summarzed n Tabe 3. E MAX MAX f( tm fm( tm = MAX (0 f ( t m m Here, f ( t and f m( t are the dentfed force and the measured force, respectvey, and t MAX m s the tme of the maxmum measured force. The resuts revea that mpact force by the hard tp cannot be dentfed usng expermenta transfer matrces constructed wth the soft tp. Ths s due to the dfference n the frequency components of the radated sound dependng on the stffness of the mpactor. gure 6 shows T resuts of the measured sound pressures for the two mpact tps. In the case of the soft tp, the sgnfcant amptudes are n the frequency range of ess than 5kHz. On the other hand, n the case of the hard tp, the measured sound pressure contans frequency components hgher than 5kHz. Thus, expermenta transfer matrces constructed wth the soft tp cannot estmate the sensor responses accuratey n the case of mpact force by the hard tp. Therefore, n order to obtan sensor responses that have a wde frequency range, constructon of the expermenta transfer matrces shoud be conducted usng a stff mpactor. The tme requred by the proposed method to dentfy the ocaton and force hstory of an mpact force was approxmatey second. rom a practca pont of vew, t can be sad that the proposed method s capabe of dentfyng the mpact force n rea tme. Concuson In ths paper, a method for dentfyng an mpact force actng on a CRP amnated pate has been deveoped. The proposed method uses measured sound pressures obtaned by mcrophones to dentfy the ocaton and force hstory. The vadty of the proposed method has been verfed expermentay. The resuts revea that the ocaton and force hstory can be dentfed n rea tme and accuratey by the proposed dentfcaton method. In addton, t has been found that the accuracy of mpact ocaton dentfcaton s not dependent on the stffness of the mpactor. The force hstory s aso dentfed accuratey regardess of the stffness of the mpactor, when a hard tp s used n the mpact tests conducted for the constructon of the expermenta transfer matrces. 5

6 References [] H. Inoue, J.J. Harrgan and S.R. Red Revew of nverse anayss for ndrect measurement of mpact force. Apped Mechancs Revews, Vo. 5, No. 6, pp 503-5, 00. [] E. Wu, J.C. Yeh and C.S. Yen Identfcaton of mpact forces at mutpe ocatons on amnated pates. AIAA Journa, Vo. 3, No., pp 33-39, 99. [3] M. Sato, T. Onozak, H. Sekne and H. ukunaga Proposton of smpe dentfcaton method for mutpe mpact forces on orthotropc amnated pates. Transactons of the Japan Socety of Mechanca Engneers, A, Vo. 6, No. 67, pp , 998. (n Japanese [] M. Tracy and.k. Chang Identfyng mpacts n composte pates wth pezoeectrc stran sensors, Part I: Theory, Part II: Experment. Journa of Integent Matera Systems and Structures, Vo. 9, No., pp 90-98, , 998. [5] H. Tsutsu, A. Kawamata, J. Kmoto, A. Isoe, Y. Hrose, T. Sanda and N. Takeda Impact damage detecton system usng sma-dameter optca-fber sensors embedded n CRP amnate structures. Advanced Composte Materas, Vo. 3, No., pp 3-55, 00. [6] K. Sekguch, S. Kmura and T. Hanyuu Anayss of sound fed on spata nformaton usng a fourchanne mcrophone system based reguar tetrahedron peak pont method. Apped Acoustcs, Vo. 37, No., pp , 99. [7] T. Tsuj, Y. Kawada, Y. Suzuk, T. Yamaguch and N. Noda Identfcaton of an mpact force by radated sound from the mpacted body. Transactons of the Japan Socety of Mechanca Engneers, A, Vo. 65, No. 63, pp , 999. (n Japanese [8] S. Atobe, N. Hu and H. ukunaga Rea-tme mpact force dentfcaton of CRP structures usng expermenta transfer matrces. Proceedngs of the th US-Japan Conference on Composte Materas, Dayton, 058, 00.