experimentální modální analýza (cze)

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University lectures on experimental modal analysis. Czech language.

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  • VB - Technick univerzita Ostrava Fakulta strojn Katedra mechaniky

    EEEXXXPPPEEERRRIIIMMMEEENNNTTTLLLNNN MMMOOODDDLLLNNN AAANNNAAALLLZZZAAA

    Alena Biloov

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    OBSAH

    1. vod ...............................................................................................................................7 1.1 Aplikace modlnch zkouek..................................................................................7 1.2 Strun o teorii modlnch zkouek........................................................................8 1.3 Rzn typy frekvennch odezvovch funkc.......................................................10 1.4 Strun o mcch metodch ...............................................................................11 1.5 Strun o analze..................................................................................................12

    2. Dvoukanlov analza..................................................................................................13 2.1 Autospektrum .......................................................................................................13 2.2 Vzjemn spektrum ..............................................................................................14 2.3 Koherence.............................................................................................................15 2.4 Deskriptory systmu .............................................................................................17

    2.4.1 Frekvenn odezvov funkce (FRF - Frequency Response Function)..........18 2.4.2 Impulsn odezvov funkce (IRF - Impulse Response Function) ..................20

    2.5 Vliv umu na FRF.................................................................................................21 2.6 Digitln zpracovn signlu.................................................................................23

    2.6.1 Chyba typu aliasing ......................................................................................25 2.6.2 Chyba nikem (leakage) ...............................................................................27 2.6.3 Frekvenn lupa (zoom)................................................................................30 2.6.4 Prmrovn..................................................................................................31

    3. Teoretick zklady modln analzy ............................................................................32 3.1 Systm s jednm stupnm volnosti (SDOF) .........................................................32

    3.1.1 Netlumen systm s 1 volnosti ...................................................................32 3.1.2 Systm s 1 volnosti s viskznm tlumenm.................................................33

    3.1.2.1 Voln kmitn ...........................................................................................33 3.1.2.2 Vynucen kmitn .....................................................................................35 3.1.2.3 Uren rezonannho naladn ..................................................................39 3.1.2.4 Urovn tlumen z graf frekvenn odezvov funkce............................39

    3.1.3 Systm s 1 volnosti s hysterznm (strukturnm) tlumenm........................41 3.1.3.1 Vynucen kmitn .....................................................................................41

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    3.1.3.2 Urovn tlumen z graf frekvenn odezvov funkce............................44

    3.1.4 Rzn formy FRF pro systm s 1 volnosti..................................................44 3.2 Systm s vce stupni volnosti (MDOF) ................................................................45

    3.2.1 Netlumen systm s vce stupni volnosti......................................................45 3.2.1.1 Voln kmitn ...........................................................................................46 3.2.1.2 Ortogonln vlastnosti vlastnch vektor ..................................................49 3.2.1.3 Normovn vlastnch tvar .......................................................................50 3.2.1.4 Odezvov analza systmu s vce stupni volnosti ....................................51

    3.2.2 Charakteristiky a znzornn FRF dat s vce stupni volnosti .......................53 3.2.3 Tlumen systm s vce stupni volnosti .........................................................57

    3.2.3.1 Proporcionln viskzn tlumen...............................................................57 3.2.3.2 Proporcionln hysterzn tlumen............................................................59 3.2.3.3 Hysterzn tlumen - obecn ppad..........................................................59 3.2.3.4 MDOF systm s obecnm hysterznm tlumenm - odezvov analza ....60 3.2.3.5 Systmy s vce stupni volnosti - shrnut pro rzn typy tlumen ..............61 3.2.3.6 Buzen obecnm silovm vektorem .........................................................62 3.2.3.7 Buzen vektorem soufzovch sil .............................................................62

    4. Modln zkouka ..........................................................................................................64 4.1 Pprava.................................................................................................................64

    4.1.1 Pprava men struktury.............................................................................64 4.1.1.1 Voln uloen............................................................................................64 4.1.1.2 Pevn uloen............................................................................................64 4.1.1.3 Uloen in situ...........................................................................................65

    4.1.2 Pprava experimentlnho modelu...............................................................65 4.2 Men a mc metody........................................................................................66

    4.2.1 Zkladn sestava men ...............................................................................67 4.2.1.1 Mechanismus buzen ................................................................................68 4.2.1.2 Snmae k men budc sly a odezvy ....................................................77 4.2.1.3 Analyztor.................................................................................................77

    4.2.2 Pprava men.............................................................................................78 4.2.2.1 Men v referennm bod.......................................................................79

    4.3 Experimentln modln analza - identifikace modlnch parametr .................80 4.3.1 Metody aproximace systmem s 1 volnosti ................................................81

    4.3.1.1 Metoda pika-amplituda (sbrn piek)................................................81 4.3.1.2 Metoda aproximace krunic (circle-fit)...................................................82

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    4.3.2 Metody aproximace systmem s vce stupni volnosti ..................................85 4.4 Modln model......................................................................................................86

    4.4.1 Prezentace zskanho modlnho modelu.....................................................86 4.4.2 Kontrola zskanho modlnho modelu........................................................88 4.4.3 Srovnn experimentln zskanho a vpotovho modlnho modelu......89

    4.4.3.1 Srovnn vlastnch frekvenc ....................................................................90 4.4.3.2 Grafick srovnn vlastnch tvar .............................................................91 4.4.3.3 Numerick srovnn vlastnch tvar .........................................................92

    5. Provozn tvary kmitu - ODS (Operation Deflection Shapes) .......................................95

    6. Provozn modln analza - OMA (Operational Modal Analysis) ...............................99 6.1 Metody identifikace ............................................................................................101 6.2 Prezentace vstup .............................................................................................103

    Pouit literatura: ...............................................................................................................104

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    1. vod Dve ne pistoupme k oblasti samotnho modlnho zkouen, je vhodn seznmit se s

    rznmi pstupy k men vibrac. Z metodickho i praktickho hlediska je vhodn rozliovat dva rzn experimentln pstupy zabvajc se vibracemi:

    1) Uren povahy a rovn vibranch odezev - analza signl 2) Zskn nebo oven teoretickch model a pedpoklad - analza systm

    Tmto dvma pstupm odpovdaj i dva typy men: ad 1) M se vibran odezvy za provoznch podmnek stroje nebo zkouman

    struktury. Touto oblast se zabv vibran diagnostika. ad 2) Struktura nebo soust je rozkmitna znmmi budcmi inky, asto mimo sv

    pracovn prosted. Tento proces je podstatou modlnch zkouek. Je zejm, e pi zench podmnkch jsme schopni zskat pesnj a detailnj informace o menm systmu ne pi pouhm men odezev.

    V nsledujcm textu se budeme podrobn zabvat druhm pstupem. Provedenm tzv. modln zkouky jsme schopni zskat modln parametry systmu a na tomto zklad eit mnoh problmy vyvolan strukturlnmi vibracemi. Problmy strukturnch vibrac pedstavuj vznamn riziko a omezen pi nvrhu irokho rozsahu strojrenskch produkt. Mohou bt pinou poruen strukturln integrity (nap. ulomen turbnov lopatky), nebo mohou sniovat vkon strojnho zazen. Nadmrn vibrace vdy zpsobuj minimln nadmrnou hlunost a nepohodl pi provozu.

    Modln zkouka : "Procesy aplikovan na testovan sousti nebo struktury

    s clem zskat matematick popis jejich dynamickho chovn."

    1.1 Aplikace modlnch zkouek Dvod pro proveden modln