Approach to Operational Experimental Estimation of Static Stresses of Elements of Mechanical Structures

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1 Journal o Physics: Conerence Series PAPE OPE ACCESS Approach to Operational Eperiental Estiation o Static Stresses o Eleents o Mechanical Structures o cite this article: A V Sedov et al 8 J Phys: Con Ser 944 View the article online or updates and enhanceents his content was downloaded ro IP address 4858 on 6//8 at 4:

2 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// Approach to Operational Eperiental Estiation o Static Stresses o Eleents o Mechanical Structures A V Sedov,, V V Kalinchuk and O V Bocharova Departent o Mechanics, Physics and anotechnology, Southern Scientiic Center o ussian Acadey o Sciences, ostov-on-don, ussian Federation Departent o inoration technology and control, Platov South-ussian State Polytechnic University (PI), ovocherkassk, ussian Federation e-ail: Sedov7@listru Abstract he evaluation o static stresses and strength o units and coponents is a crucial task or increasing reliability in the operation o vehicles and equipent, to prevent eergencies, especially in structures ade o etal and coposite aterials At the stage o creation and coissioning o structures to control the quality o anuacturing o individual eleents and coponents, diagnostic control ethods are widely used hey are acoustic, ultrasonic, X-ray, radiation ethods and others he using o these ethods to control the residual lie and the degree o static stresses o units and parts during operation is raught with great diiculties both in ethodology and in instruentation In this paper, the authors propose an eective approach o operative control o the degree o static stresses o units and parts o echanical structures which are in working condition, based on recording the changing in the surace wave properties o a syste consisting o a sensor and a controlled environent (unit, part) he proposed approach o low-requency diagnostics o static stresses presupposes a new adaptive-spectral analysis o a surace wave created by eternal action (ipact) It is possible to estiate iplicit stresses o structures in the eperient due to this approach Introduction Various types o diagnostic control ethods are widely used at the stages o the creation, coissioning and using o echanical structures to evaluate the workanship and the unctioning o individual eleents and coponents A rather coplete review o these ethods, their erits and deerits is given in [-5] here are known works in which attepts were ade to deterine the stress states o structures ro the analysis o responses to serial shock eects [6,7] he eatures o the deterination o the state (without a deect or with a deect) o a vertically suspended physical odel o a periodic welded rod structure were established in [6] his proble is solved by constructing the Fourier transors o linear and nonlinear deoration responses to serial shock eects and coparing the phase diagras o deoration behavior o an intact and daaged odel he qualitative and quantitative eatures o the structure staying in the stressed state are eperientally substantiated based on the analysis o the nonlinear and linear regions o the constructed Fourier transors in [7] he using o Fourier transors liited the possibilities or accuracy o these ethods, as the possibility o adaptation, sel-learning and tuning to a speciic type o response unctions Successul application o these approaches, ensuring the required accuracy, are directly related to the used atheatical ethods o processing o the easured response echanical wave - reactions hus, Content ro this work ay be used under the ters o the Creative Coons Attribution licence Any urther distribution o this work ust aintain attribution to the author(s) and the title o the work, journal citation and DOI Published under licence by Ltd

3 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// the ost eective approaches o atheatical processing o reactions are traditional spectral analysis [6-]; the correlation analysis o signals [9-]; the artiicial neural networks [,]; statistical approaches and odels [4,5,6]; wavelet transor signals [9,5,7]; optial orthogonal decopositions o signals on the adaptively adjusted basis based on training saple [] Eactly the latter approach is a detail considered in the present work as a proising one with a nuber o advantages he ain advantage is the adaptive adjustent o the orthogonal basis, in accordance with the criteria or the best recognition o the stressed state o the structure In the work, the evaluation o the diagnostic observability [8,9] o static stresses o a echanical structure with the using o the ethod o low-requency diagnostics o static stress and recording o the changing in the surace wave properties o a syste consisting o a sensor and a controlled environent (unit, part) was ade In this case, a set o diagnostic state variables in the or o the coordinates o the orthogonal diagnostic space was deined he schee o the research o the approach to estiation o static stresses A ultiunctional easuring cople and a package o atheatical odeling o echanical structures, which akes it possible to conduct research, to copare signals and to build spectral characteristics with sensors o various types, were used or the research and evaluation o the proposed approach he eatures o the dynaic process on the surace o the parallelepiped ade o aluinu aterial were researched (see igure ) Inluences oring static stresses in the saple were applied along three perpendicular aes,, he eect was deterined by the quantity o shortening (copression) i i or etension (stretching) o the saple along the ais he copression and stretching o the saple along the aes were varied Each o the quantities set its static stress in the saple he probing surace oscillations in the saple were ecited by a shock orce action F o constant type at one o the ends he occurred oscillations t, t, H were ied by the sensor S during a tie interval suicient or the arrival o relected waves ro the opposite end o the structure A general view o the ied response unctions t or saples with dierent stress along the aes,, o the structure is shown in igure As ollows ro igure, their shape depends on the presence and agnitude o the stress in the structure and its distribution along the aes,, H Figure hree-diensional representation o the parallelepipedal eperiental structure Figure Graphs o response unctions t Adaptive-spectral analysis o the surace wave in the estiation o static stresses In the case o a discrete ipleentation o the recognition o the agnitude o the stress ro the

4 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// response unctions, the construction o the adaptive eature diagnostic space ξ is carried out as ollows A siilar atheatical apparatus was used or odeling in power engineering [] and lowrequency nondestructive testing o echanical structures [7] Each graph o the unctions o the low-requency response to eternal ipact F in the i t t t diagnostics o structures can be considered as a vector o real values,,, i i i i i o the change o response in tie he sapling step in tie or the nuber o saples in the observation interval is chosen in accordance with the sapling theore [8-] n Conditionally, the nuber o vectors in the saple,,,, n is deterined by the required accuracy o stress identiication in the structure and is dependent on the stress easureent range And it is deterined, as a rule, by the nuber n 5 5 o uniorly distributed stresses throughout the easured range in the structure Initially, the set o vectors,,,, n is linearly dependent his is due to the ecessive diensionality o the vectors i i t, the proiity o the shapes o the graphs and is conired by the n,,,, or which rank value o the rank o the atri n he basis o stress identiication in a structure is the inding o such orthogonal transoration o a atri into a atri, that ecludes an ecessive diensionality associated with poorly inorative, oten rando variations in the graphs he atri [,,,, ] in this case deines a linear subspace n A n A, Moreover, the vectors,,,, or an orthonoral basis in I is true Conditionally, a atri o a linear space o a atri into iages into a space,, and or the atri, can be considered as a atri o orthogonal copressing Vectors i o responses are transored by eans A and, thus, the entire atri o responses is transored into an i iage atri n A A, A, A, A n In the general or, the orthogonal decoposition o the initial vectors i in ters o the basis can be represented in the or i Ai A where is the constant coponent o the transoration An orthonoral basis,,,, is adaptive, trained and dependent on a recognizable saple,,,, n n A In deterination o the basis, a cople o optiization probles is solved, in particular: n providing the best reproducibility: A A in, where A - the atri o constant coponents o the transoration, consisting o vectors A ensuring the orthonorality o the basis: I in realizing the best discernibility: d A a Ai Aj i j, i j he discrete realization o the ethod o recognizing the agnitude o the stress ro the response unctions akes it possible to sipliy the algorithization o the processing o graphs For the siplicity o the graphic and physical interpretation, the recognizing o the stresses o the saples will be carried out in the two-diensional eature space by iages A a, a As the i i i

5 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// two coordinates o the iage, let us choose those that have the aiu varieties o projections o the iages 4 Eperiental research o approach o estiation o the static stress he research showed that a two-diensional eature space is suicient or qualitative estiation o stressed states o structures Dierent in agnitude and sign stresses causing displaceent such as copression or stretching o the saple along three utually perpendicular aes i i,, were considered (see igure ) he values o the displaceents were speciied ro the series 5 ; ;5 he shock ipact was ored and the eerging surace waves i were recorded as a response unction he set o 9 response unctions was received:, s s s r,5,,,,5,,5,,,,,,,,, bd t t t t t r r ss ss ss, t,5 t,5 t, t,5 t t rr rr rr sss sss,,5 t,, t,,5 t,,5 t,, t, sss rrr rrr rrr,5 t,5 t, t,5 t where the designations bd - without stress; s, ss, sss the copression relative to the aes,,,, accordingly; r, rr, rrr - the stretching relative to the aes accordingly; 5; and 5 - the values o the displaceents along these ais he result o the construction o a two-diensional eature diagnostic space and the location o the iages or the speciied saples o the response unctions is shown in igure An iportant act is that all given iages corresponding to dierent stresses along each o the aes,, are located on their ideal parabolas: a, a a a ;, a a a, a a ; his localization o iages greatly sipliies the identiication o the current value o the stress in the structure by the location o the iage he parabolic shape o the iage localization curve is deterined by the shape o the eperiental structure and the eatures o the construction o the diagnostic space s r t and stretching he iages o the copression,5,5 t graphs along the ais are reoved ro igure to increase the scale and to iprove detailing hese iages s5 and r5 are also located higher on the ais parabola Figure wo-diensional eature diagnostic space and iages o response unctions corresponding to copression and stretching o the structure along the aes,, 4

6 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// Each parabola can be viewed as a separate scalable stress transoration along each o the three aes onto the ain ais he ais is the ain one because it is the shortest path between the probing ipact point F and the location o the sensor S his ais covers the longest part o the structure and the signal propagated along this ais is the ain easuring one containing the greatest inoration about the stresses; thereore, the ais will be called the ain projection ais he act o the inversion o the arrangeent o the iages on the parabola takes place or the aes and in relation to the iages obtained or the ais By inversion the authors ean the change in the arrangeent along the branches o the parabola o the stretching and copression patterns his can be eplained by the schee o the changing o the structure at the deoration or the aes and, considered in igure 4 his inversion can also be interpreted by the projection o stresses along the ais (or ) onto the ain projection ais Figure 4 he relationship between copression and stretching o the structure along perpendicular aes, he ollowing notation are used in igure 4: a) - the initial state o the structure; b) - an aial ' ; c) - the copression S stretching, leading to an aial copression along the ais leading to aial stretching he presence o two parabolas in igure or the aes and is eplained by the indicated nonlinear character o the interrelation between copressions and stretching along perpendicular aes he relationship between copression and stretching between the aes and can be eplained siilarly 5 Conclusions A new adaptive-spectral approach to the operative eperiental estiation o static stresses in echanical structures is proposed It is based on the analysis o the response unctions to the ipact low-requency nondestructive action, which allows estiating both the agnitude o the stresses and the direction o the action he principle o constructing spaces or the analysis o response signals in the operative eperiental estiation o static stress based on an adaptive orthogonal basis is proposed in accordance with the criteria or the best recognition o the stressed state o a structure he property o the parabolic distribution o iages o the response unctions or structures is revealed at various stresses caused by the stretching or copressing structure along one or another ais he property o luctuations o the parabolas o the iage distribution is revealed depending on the direction o the applied action causing the stress 5

7 IOP Con Series: Journal o Physics: Con Series (8) doi :88/ /944// he proposed ethod and the principle o constructing diagnostic spaces can be the basis or building trained systes o operational control o stress or various types o structures 6 eerences [] Sharpa 97 on-destructive onitoring ethods (Moscow: Mir) [] Kershenbau V Y 99 on-destructive testing ethods (Moscow: auka i tekhnika) [] McMaster 965 on-destructive esting (Moscow: Energiya) [4] Glagovskii B L and Moskovenko I B 977 Low-requency acoustic ethods o control in echanical engineering (Leningrad: Mashinostroyeniye) [5] Guz A, Mahort F G, Guscha O I and Lebedev V K 974 Fundaentals o ultrasonic nondestructive ethod or deterining stresses in solids (Kiev: aukova Duka) [6] Esipov Y V, Mukhortov V M and Andzhikovich I E Ecological bulletin o BSEC scientiic centers [7] Esipov Y V, Sazanov S and Uzunyan A M Measuring technique -5 [8] Mallat S A 999 Wavelet our o Signal Processing (ew York: Acadeic Press) [9] Gonzales C and Woods E W Digital Iage Processing (ew Jersey: Prentice Hall Publishers) [] ung, Garg A, Kovacs A, Peroulis D and aan A J Microech Microeng 459 [] Sedov A V Modelling Objects with Discrete-Distributed Paraeters: Decoposition Approach (Moscow: auka) [] Dervilis, Choi M and aylor S G 4 J Sound Vib [] Salazar A, Vergara L and Llinares Mech Syst Signal Process [4] ondreau G and Deraeaeker A Mech Syst Signal Process [5] Cogranne and etraint F 4 Signal Process [6] Martinez M, ocha B, Li M, Shi G, Beltepo A, utledge and Yanishevsky M Sart Mater Struct 5 [7] sui P C and Basir O A 6 Ultrasonics [8] Sedov A V 7 he concept and the principle o the diagnostic observability o the object in probles o onitoring and non-destructive testing Materials Science and Engineering 77 4 [9] Bocharova O V, Sedov A V, Andzhikovich I E and Kalinchuk V V 6 ussian Journal o ondestructive esting Acknowledgents he work was supported by the ussian Foundation or basic research (grant ) and the ussian Scientiic Foundation (project ) 6