Research of degradation state at the use of the vibration signal

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1 Iteratioal Joural of Egieerig ad Advaced Research Techology (IJEART) ISSN: , Volume-, Issue-1, October 16 Research of degradatio state at the use of the vibratio sigal Bogda Zoltowski, Mariusz Zoltowski, Krzysztof Napieraj Abstract The kowledge of the dyamic state ad structure of system allows to describe its behavior, ad allows a creatig progosis models of the system behavior i the fuctio of dyamic evolutio time, based o the model of the techical state symptoms growth. Most ofte, there are o kow equatios describig behaviors of the system i the fuctio of dyamic evolutio time, which accouts for the eed to apply ew tools to examie the dyamic state. There is, therefore, the requiremet to experimetally verify aalytical techical models as the proper oe is a model which is verified i practice. A experimet is ofte oly a ispiratio for further researches leadig to the optimizatio of the costructio. I this article authors shows chose problems of techical state diagosis with the use of idetificatio ad techical diagostics methods such as experimetal modal aalysis. Relatios betwee methods of dyamic state evaluatio ad methods of techical state evaluatio were idicated. Example modal aalysis results illustrate the complexity of projectig dyamic state researches ito diagostic researches of state evaluatio. Idex Terms techical diagostics, idetificatio, modelig, modal aalysis I. INTRODUCTION Destructio processes of techical systems force the eed to supervise chages of their techical state. It is possible with the use of techical diagostics methods. Methods ad meas of moder techical diagostics are a tool of machie state diagosis, which is the basis of decisios made at each stage of their existece. May previous works [1,,3,4,5] clearly idicate coectios betwee dyamics ad techical diagostics, especially vibratio diagostics. The bases of idetificatio, modelig ad cocludig fully covice towards the domiatig role of vibratios i machie state idetificatio [ ]. Properly plaed ad realized experimet is the base to obtai diagostically sesitive sigals which processed will determie state diagosis procedures. The processig icludes: creatio of umerous sigal measures i time domai, frequecies ad amplitudes, selectio ad reductio of the umber of sigal measures, creatio ad aalysis of effectiveess of cause-ad-effect models, as well as evaluatio of the righteousess of made diagostic decisios. II. DYNAMICS AND DIAGNOSTICS Ito quality measures of machie s techical state, i.e. its dyamics, icluded is the level of vibratio amplitudes, as well of the machies as the lot, ad also of relative vibratios of separate elemets ad parts. Overall vibratios of the machie ca be perceived as a exteral symptom while they are resposible for the level of iterfereces emitted ito the eviromet. Relative vibratios of separate elemets, however, ifluece maily the state of iteral forces i the machie, i.e. at its level of dyamic stress amplitudes. Idetificatio ca cocer both the costructio of models ad the recostructio of the examied model state, which leads straight to the problem of techical diagostics. The process of diagostic idetificatio icludes: modelig (symptom or structural), idetificatio experimet (simulatio ad/or real), estimatio of diagostic parameters (state features or symptoms), diagostic cocludig. The specificity of diagostic idetificatio tasks is differet from geeral idetificatio i the way that it icludes a umber of additioal elemets ehacig this process. They are: - costructig models of diagostic sigals geeratio, - choosig features of object structure state ad diagostic symptoms, - modelig cause-ad-effect relatios, - evaluatig the accuracy of choosig variables for the model, - determiig boudary values of the symptoms, - state classificatio ad determiig of periodicity a diagosis. Methods of idetificatio ca be divided cocerig: the kid of idetified model, the kid of experimet, idetificatio criterio applied, as well as estimatio procedure applied. I geeral these are: methods of aalysis, time, frequecy, correlatio, regressio, factor aalysis, as well as iteratio methods described i works of may authors [,4,6,5,8]. For simple objects a good tool to evaluate their chageable dyamic state are methods of simple idetificatio, which use amplitude - frequecy spectrum. Searchig resoace frequecy ad amplitude value i this frequecy with the use of tests (impulse, harmoic ad radom) are relatively well mastered i research techiques of our eterprises [,5]. Aother way of describig ad aalyzig the dyamic state of machies is a modal aalysis used as a theoretical, experimetal ad exploitatio method. It uses frequecies of ow vibratios, values of suppressio ad forms of vibratios to describe the chagig machie state, ad it is used to improve the fiished elemets method. The preseted procedures are based o the kowledge of the system model, ad the coclusios draw from the actios o the models deped o their quality. Depedig o the aim of the performed dyamic aalysis of the object, differet requiremets are set for the costructed models, ad their evaluatio is coducted with differet experimetal methods. III. DESCRIPTION OF OBJECT STATE CHANGES The dyamic state of the object ca be, i the easiest case, described with a model of 1 degree of freedom Fig.1. A covetioal descriptio of this model are kow relatios 16

2 Amplitude Research of degradatio state at the use of the vibratio sigal idicatig that vibratios well reflect the state of the machie. A descriptio of this model ca be achieved withi m, k, c categories, or through a, v, x researches k Correlatio, Rail : (Force 1, Accel. X) A =.7971 t =.358 [ms] f = 79.7[Hz] Time [s] Fig.1. System model of 1 degree of freedom ad vibratio sigal of real system the state parameters (m, k, c) = vibratio process (a, v, x) x Asi( t ) () dx v A cos( t ) (3) dt d x dv a A si( t ) (4) dt dt Idetificatio of his model (Eq.1) from the experimetal side is the a, v, x measuremets for differet time momets, which reflects the chages of the object state ad is widely applied i vibratio diagostics. The solutio of the task i the m, k, c, categories, however, requires a umber of solutio coversio of the equatio (Eq. 1) for determiig: c kr m c kr 4mf (5) k m k 4 mf Determiig the value (5) requires realizig idetificatio experimet from which the frequecy f or frequecy ω ca be determied. Here is useful the simple idetificatio or modal aalysis directly givig the values of ow frequecies ω from the stabilizatio diagram Fig.. Fig. Stabilizatio diagram for ω determiatio The problem becomes more complicated for models of may degrees of freedom (more tha 3). Here also the problem of object state idetificatio ca be solved from the measuremet side (a, v, x), Chile from the side of determiig m, k, c ow problem eeds to be solved. M q c (1) K (6) Equatio (Eq. 6) presets a liear system of homogeeous algebraic equatios: A solutio for q exists whe the mai matrix determiat ( K ω M ), i.e. det( K ω M ). Solvig the system of Eq. 7 ow values ca be determied, ad from them the frequecies of ow vibratios, idispesable for the object idetificatio λ ω A. Eviromet of experimetal modal aalysis k m For complex systems, oliear ofte used for idetifyig complex moder method of o-ivasive test, which is the modal aalysis. As a result of modal aalysis is obtaied modal model, which is a ordered set of its ow frequecy, the correspodig dampig ratios ad mode shapes. O the basis of kowledge of the modal model of the object ca be predicted respose to ay disorder i both time ad frequecy domais [4,14,18]. Usig the statemet that the destructio of the state of the object (test material) ca be described alteratively [istead of modellig the chages i terms of the (m, k, c) use the descriptio of the vibratio i terms of (a, v, x)] i the study of the developmet of the state of degradatio of the structure or masory vibratio frequecies were evaluated, resultig directly from the applicatio of modal aalysis procedures. The idetificatio of the idividual modal models for extortio i the test sub-elemet ad further aggregatig them for the whole structure of the object is obtaied evolutioary model, clearly describig the chages estimators state variable load coditios. Is revealed by the fractal ature of eergy coversio the processes, ad perfectig possible ways to zoom descriptio of the real world. I most practical applicatios require the aalysis of a multi-modal experimet ad the complex calculatios associated with the processig of the measured sigals ad model parameter estimatio. So welcome the possibility of applicatios allows us to distiguish the followig types of modal aalysis: theoretical MA, which requires the solutio of the problem for the assumed its structural model of the object, experimetal MA, cotrolled experimet requirig idetificatio, durig which forces the movemet of a object (eg. Vibratios) ad measures the force ad measure the resposes i a umber of measurig poits distributed over the examied object, operatioal (exploitatio) MA, based o a real experimet, i which measuremets are made oly i respose to the may poits of measuremet, while the movemet of the subject is due to the actual operatig extortio. The theoretical modal aalysis is defied as the problem of self-depedet mass matrix, rigidity ad dampig. The theoretical modal aalysis requires addressig issues of their ow for the assumed of structural model. Here desigated frequecy sets its ow frequecy atteuatio coefficiets for their ow forms of vibratios ad allow the simulatio of structural behaviour at ay extortio, selectio of cotrols, ad other desig modificatios. It is used i the desig (7) 17

3 Iteratioal Joural of Egieerig ad Advaced Research Techology (IJEART) ISSN: , Volume-, Issue-1, October 16 process, whe there is o possibility of carryig out studies o the subject. Modal aalysis is widely applied Resultig damages removig it from vibratios, modifyig structure dyamics, updatig aalytical model or state cotrol, ad also used for moitorig vibratios i aircraft idustry ad civil egieerig [7,9,1,19]. Theoretical modal aalysis is defied as a matrix eigevalue problem of a depedet matrices of mass, stiffess ad dampig. It requires the eigevalue problems for a Assumed structural model of ivestigated structure to be solved [1,1]. The determied sets of atural frequecies, dampig coefficiets for the atural frequecies ad forms of atural vibratios make it possible simulate behaviour of a structure uder arbitrary excitatios, choice of steerig meas, modificatios ad other structural issues. Aalysis of atural frequecies ad vectors is obtaied o the basis of motio equatios (after eglectig terms Which Cotai exteral dampig matrix ad load vector). The the motio equatio of atural vibratios Help Us obtais the form: B qkq (8) For oe d.o.f. system its solutio is as follows: q( t) q si( t ) (9) where: - vector q of amplitudes of atural vibratios. O substitutio of the above give equatio ad d derivative to the motio equatio the followig is obtaied: ( B )si( qk t ) (1) The equatio is to be satisfied for arbitrary istat t, the the set of algebraic equatios is yielded as follows [14,19]: ( K B) q (11) 11 m11q 1 1 m1 q 1 m1 q m41q 1 4 m4 q m q Fig.3. A set of test equipmet i the experimetal modal aalysis IV. PRACTICE TEST ITEMS A. Experimet modal aalysis Experimet to idetify the state of the tested masory destructio is the primary source of iformatio ad o the basis of measuremet values ca be determied ad the structure of the model. O the oe had, the quality of the experimetal results obtaied deped o the quality of the model, o the other had the way the experimet determies the structure of the idetified model. The experimet of modal aalysis ca be divided ito the followig steps: 1. Plaig the experimet: - the choice of how to force vibratio test piece ad the poits of applicatio, - selectio of measuremet poits ad vibratio measurig equipmet, - selectio of appropriate measurig equipmet, - selectio of the model (reducig the umber of degrees of freedom) of the system.. Calibratio of the measuremet path. 3. Acquisitio ad processig of the results of the experimet. The aim of the experimet is to force modal aalysis of the movemet of the test piece masory by providig eergy ad measurig the aswer to extortio. The geeral procedure for carryig out studies of this work is show i Figure 4. This way was produced the set of liear homogeeous algebraic equatios, which has o-zero solutio oly whe the coditio: det( K B) (1) is fulfilled. O trasformatios the -order polyomial is obtaied. Amog its roots multifold oes may be preset, ad the vector built from the set of frequecies ϖ ordered accordig to icreasig value sequece is called the frequecy vector, ad the first frequecy is called the fudametal oe [19]:,..., ] [ 1 (13) Fig.4. The essece of the measuremet chael usig modal aalysis [19] The test piece subjected to forcig the forced walled correspods to the vibratio sigal, proportioal to the state of destructio. Forcig ad respose sigal is used to determie the fuctio of further FRF ad the stabilizatio of the diagram, ad the frequecy of oscillatios. By the way, these procedures are available for other iterestig cogitive processes vibratio estimators, which are also used i further studies. Test results after processig by differet algorithms are subjected to statistical study. From the viewpoit of experimetal modal aalysis methods ca be divided ito: 18

4 Research of degradatio state at the use of the vibratio sigal - a method of forcig movemet of the multiple actuators for the excitatio of oe form of vibratio; - the method of forcig movemet of the oe or more poits i order to measure the trasfer fuctio. The first group of methods is carried out maually movig the system i such a way as to force the vibratio i accordace with oe embodimet of the vibratio. This requires a complex cotrol system actuator to obtai the appropriate phase shifts force. The secod group is used to force ay depedig o the type of the object. Set of equipmet for the implemetatio of the experimet modal aalysis is made up of compoets: - measuremet of the force of motio ad respose, - sigal coditioig system (pre-processig), - the processig ad collectio of sigals, - forcig sigal geeratio system, - the vibratio excitatio. The simplest due to maiteace solutio is to use sigal aalyser, but the most moder givig the greatest potetial solutio is based o a workstatio, ad a specialized iterface measuremet. The basic operatio performed by all applicable devices measurig modal aalysis is aalogies to digital processig, which eables the use of digital sigal processig techiques to determie the modal aalysis required by the characteristics of estimators. Modal studies do ot care that the size of the kiematic motio measurig, as a respose of the system. I practice, the displacemet measuremets give better results i terms of low frequecy, ad acceleratio of the high frequecy rage. It is widely believed that the velocity measuremets are the most optimal structural dyamics studies due to the fact that the effective value of the vibratio velocity is i some sese a measure of the kietic eergy of vibratio of the system. However, sesors for measurig displacemet ad velocity are relatively heavy ad may affect the behaviour of the test object ad the acceleratio sesors have a cosiderably lower mass ad therefore do ot affect the motio of the system. A additioal advatage of the acceleratio sesor is that the acceleratio sigal a further sigal ca be obtaied by itegratig the velocity or displacemet vibratios. Operatio i the opposite directio, lead to large errors especially i the higher frequecies. O those grouds, acceleratio sesors are the most commoly used trasducers for studies of modal structure. Acceleratio sesors built o the piezo-electric pheomea ca be modelled as a system with oe degree of freedom from suppressio. The weight of this model is the seismic mass aggravatig crystal piezoelectric material durig movemet. Due to the desig of the sesors has its resoace, which reduces the frequecy rage i which they ca be applied [1]. A very importat factor ifluecig the modal test results associated with a variety of sesors, sesor moutig locatio. The sesors should be mouted i such a way as ot to affect the vibratio system ad are secured at the characteristic behaviour of the structure. Curretly, the vibratio measuremet durig the examiatio of the structure modal cotactless sesors, are used ad oe of the feasibility of this type of sesor is the use of a laser beam. Such sesors eable the measuremet of vibratio velocity i the frequecy rage of O to 5 khz, ad amplitudes i the rage of to1 mm / s. A importat factor i the rage of measured frequecy of the sesor is o way for the study of the structure. The sesors ca be attached to the test structure by meas of a special wax, adhesive, maget or screw with the screw. Experimetal modal aalysis requires laboratory coditios for testig. Model is subject to advace well-kow ad established extortio. Forcig these may differ from those that operate o the object durig ormal operatio. Durig the executio of the experimet may ecouter difficulty i keepig i lie with the reality of such boudary coditios, for example method of fixig the test object. I the case of large models the executio of the experimet is very expesive ad ofte impossible. V. MEASUREMENT SOFTWARE For the measuremet waveforms extortio ad respose system ad determie the most used fuctios FRF measuremet equipmet purchased for the project compay uder the ame of LMS LMS TEST.XPRESS. This software eables you to easily perform a modal aalysis of brick elemets, as well as ay other buildig structures. For the purposes of measuremet usig experimetal modal aalysis you defied two measuremet chaels. Accordig to the theoretical experimetal modal aalysis first sesor is reserved for the hammer modal (vibratio force), ad place sesor piezoelectric sesor is coected (the aswer key to force). Fig.5. Calibratio of sesor coectio The figure 5 shows the calibratio widow ad defies the coectio of sesors. Properties, that each sesor is coected to the segmet defied by the widow, visible o the right i the drawig. There are characteristic values of the sesors, which ca chage as eeded. The ext step was to prepare the masory. I the study, it was decided to check is it possible to see a differece i destructio state i bricks, with use of oly FRF fuctio for this purpose, were use types of the samples. There was a full brick tested, ad for compariso a cracked full bricks were also measured. VI. RESULTS Durig the tests it was able to geerate a trasfer fuctios of vibratio sigal by the structure (FRF fuctio). The results are preseted i real time i the ceter of a scree. It s allows visualizig the temporary courses of extortios ad the aswer, as well as the fuctio the FRF ad the fuctio of coherece. 19

5 db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] Time [N] Traces: / Compressed Time [s] Time [m/s] Traces: / Compressed Time [s] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] db/1 [(m/s)/n] Iteratioal Joural of Egieerig ad Advaced Research Techology (IJEART) ISSN: , Volume-, Issue-1, October Fig.8. Compositio of FRF fuctios of full brick i axis X 6 4 Fig.6. Example expositio of results of measuremet - the ow study For a better visualizatio of the results of the ivestigatio, the results are show below separately - 5 times is show the FRF fuctio for good, ad 5 times for destroyed brick elemet. I Figure 9 it is show oce the extortio, ad the aswer of sigal i time domai, which allows to FRF fuctio extortio aswer FRF Fig.7. Compositio of results of measuremets (the temporary course of extortio, temporary course of aswer, fuctio the FRF) the full brick i axis X Graphic results which shows FRF fuctios of good, ad destroyed bricks measured i axel Y are show below i Figures 9, ad 1 5 measuremets for each material sample Fig.9. Compositio of FRF fuctios of destroyed full brick i axis X VII. CONCLUSIONS Methods of idetificatio i the research buildig costructio (icludig costructio materials) are utility methods to estimate chages i operatig structure. Modal aalysis of the varieties for its realizatio is icreasigly beig used by civil egieers ad modal model accurately reflects the destructio of objects. Searchig for mappig models with models of modal vibratio, bech research ad studies o real objects, allows assessig the similarity of the models, the relevace ad effectiveess of decisio methods. The search for methods of o-destructive testig of materials idicates the possibility of usig modal aalysis i the assessmet of their degradatio, as show i this study. Practically verified susceptibility modal aalysis of the degree of degradatio of masory shows to the satisfactio of practice differeces betwee of the structure ca bear ad damaged. It is therefore possible to determie the risks of buildig structures o the basis of the study of atural frequecies ad their characters, usig operatioal modal aalysis. The results poit to the fact that it is possible to distiguish betwee material properties, which has a impact o the ability to distiguish betwee their mechaical properties. The study also cofirmed the usefuless of the LMS test apparatus usig operatioal modal aalysis performed o the actual buildig costructio. By obtaiig

6 Research of degradatio state at the use of the vibratio sigal graphical charts of FRF fuctio, ad a later their compariso it is possible to observe their diversity. These charts are differet for materials that are i good coditio, ad damaged, which demostrates the ability to assessmet of the destructio of a brick elemet. REFERANCE [1] Batel M.: Operatioal modal aalysis aother way of doig modal testig. Soud ad Vibratio, August. [] Bishop R., Johso D.: The mechaics of vibratio. Cambridge Uiversity, Press, 198. [3] Bradt S.: Aaliza daych. Wydawictwo Naukowe PWN, Warszawa [4] Cempel C.: SVD decompositio of symptom observatio matrix as the help i a quality assessmet of a group of applicatios. Diagostyka, r 35, PTDT, Warszawa 5. [5] Formeti D., Richardso M.: Parameter estimatio from frequecy respose measuremets usig ratioal fractio polyomials (twety years of progress). Proceedigs of Iteratioal Modal Aalysis Coferece XX, February 4-7, Los Ageles, CA. [6] Ibrahim S., Mikulcik E.A.: Method for the direct idetificatio of vibratio parameters from the free respose. Shock ad Vibratio Bulleti, Vol 47, Part 4, [7] Peeters B., Vetura C.: Comparative study of modal aalysis techiques for bridge dyamic characteristics.submitted to Mechaical Systems ad Sigal Processig, 1. [8] Pickrel C.R.: Airplae groud vibratio testig omial modal model correlatio. Soud ad Vibratio, November. [9] Richardso M.: Is it amode shape or a operatig deflectio shape? Soud ad Vibratio, February [1] Richardso M.: Structural dyamics measuremets. Structural : Curret status ad future directios, Research Studies Press, Ltd. Baldock, Hertfordshire, Eglad, december, p-341. [11] Shih C., Tsuei Y., Allemag, R., Brow D.: Complex mode idicatio fuctio ad its applicatios to spatial domai parameter estimatio. Proceedigs of Iteratioal Modal Aalysis Coferece VII, Jauary [1] Uhl T.: Komputerowo wspomagaa idetyfikacja modeli kostrukcji mechaiczych. WNT, Warszawa [13] Williams R., Crowley J., Vold H.: The multivariate mode idicator for fuctio i modal aalysis. Proceedigs of Iteratioal Modal Aalysis Coferece III, Jauary [14] Vold H., Schwarz B., Richardso M.: Display operatig deflectio shapes from o-statioary data. Soud ad Vibratio, Jue. [15] Vold H., Kudrat J., Rockli G.A.: Multi-iput modal estimatio algorithm for mii-computers. S.A.E. paper No. 8194, 198. [16] Zoltowski B., Ladowski, B., Przybyliński B.: Desig of machie operatio, ITE - Natioal Research Istitute, Radom, 1. [17] Zoltowski, B., Lukasiewicz M., Kałaczyński T.: Iformatio techology i the research of machie coditio, Ed. UTP, Bydgoszcz, 1. [18] Zoltowski B.: Virtual egieerig methods i the study of, safety ad evirometal risks operated machies, Ed. UTP, Bydgoszcz, 1. [19] Żółtowski M.: Modal aalysis i the testig of buildig materials. ITE-PIB, Radom 11. [] Żółtowski M., Żółtowski B., Castaeda L.: Study of the state Fracis Turbie. Polish Maritime Research No /13, pp [1] Żółtowski M.: Ivestigatios of harbour brick structures by usig operatioal modal aalysis. Polish Maritime Research No 1/14, pp