Efekty histerezowe w tarciu suchym

• Autorzy: Wojewoda J.

Warianty tytułu

EN

Hysteretic effects in dry friction

• Języki publikacji: PL

Abstrakty

PL

W pracy rozważane są zjawiska zachowania histerezowego siły tarcia suchego obserwowanej podczas badań eksperymentalnych. Na podstawie analiz doświadczalnych i teoretycznych postuluje się, że takie zachowanie można uważać za pewną reprezentację dynamiki układu. Zgodnie z takim założeniem, wprowadza się nową klasyfikację modeli siły tarcia, dzieląc je ze wzglę du na ich wrażliwość na charakter ruchu układu. Dyskutowane są ogólne zagadnienia modelowania zjawisk towarzyszących tarciu suchemu oraz zaproponowany jest nowy, prosty lecz efektywny w implementacji numerycz- nej model sily tarcia, zdolny odzwierciedlić efekty histerezowe. Pokazane są wyniki eksperymentalne i ich porównanie z symulacjami numerycznymi zaproponowanego modelu i z wybranymi modelami klasycznymi. W części wstępnej zawarto ogólny opis zjawiska tarcia i historii ba- dań w tej dziedzinie oraz przedstawiono tezę pracy oddającą związek siły tarcia z charakterem ruchu realizowanego przez układ drgający. Przedmiotem rozważań w rozdziale drugim jest opis najbardziej istotnych zagadnień dotyczących tarcia opracowany w kontekście nawiązującym bezpośrednio do układu rzeczywistego będącego przedmiotem badań eksperymentalnych. Największy nacisk położono na takie zagadnienia, jak efekty histerezowe, siłę zrywającą oraz krzywą Stribecka. Są to główne cechy charakteryzujące proponowany w treści rozdziału 5 nowy model tarcia. W rozdziale trzecim przedstawiono wybrane modele tarcia stosowane do- tychczas w klasycznym podziale na statyczne i dynamiczne. Przedstawiony przegląd zawiera najbardziej znaczące etapy rozwoju modelowania tarcia i choć nie obejmuje wszystkich znanych podejść, to odwołania literaturowe pozwalają Czytelnikowi na dalszą eksplorację tego tematu. Szczególny nacisk położono na nowe pomysły, jak modele szczotkowe, modele uwzględniające histerezę oraz nowe charakterystyki dynamiczne tarcia. W kolejnym rozdziale zaprezentowano wyniki badań eksperymentalnych wymuszanego wzbudnikiem drgań oscylatora ciernego, opisano stanowisko badawcze i metody pomiarowe. Przedstawiony zostal model matematyczny oscylatora oraz jego uproszczona wersja, która stanowiła podstawę dalszego modelowania numerycznego. Pokazane zostały wyniki badań eksperymentalnych odzwierciedlających różne zachowania badanego oscylatora. Zebrane wyniki posłużyly do zbudowania nowego matematycznego modelu zjawiska pokazanego w rozdziale 5. Rozdział ten rozpoczyna propozycja nowego podziału modeli tarcia -na układy wrażliwe i niewrażliwe na dynamikę układu. Pomysł pochodzi z zaprezentowanych wcześniej wyników eksperymentalnych i przeglądu z roz- dzialu 3. Zawiera także opis modelu tarcia uwzględniający takie elementy, jak sztywność kontaktową, pamięć tarcia, nieodwracalność, zmienną war- tość siły zrywającej oraz czynniki stochastyczne. Poprawność modelu zweryfikowano poprzez porównanie wyników eksperymentalnych z rezultatami symulacji numerycznych. Wnioskiem jest stwierdzenie, że model pozwala na precyzyjną symulację rzeczywistej dynamiki siły tarcia oraz odpowiedzi układu na wymuszenie. W rozdziale 6 zaprezentowane zostały wyniki kolejnych symulacji numerycznych typowych ukladów mechanicznych, wykorzystując między innymi proponowany model tarcia. Przedmiotem analizy byl klasyczny cierny oscylator samowzbudny z dodatkowym wymuszeniem zewnętrznym oraz nieliniowy oscylator typu Duffinga z zewnętrznym wymuszeniem harmonicznym i z tłumieniem tarciem suchym. Porównań dokonano, używając różnych charakterystyk tarcia od modelu klasycznego, przez Poppa-Steltera, niepowracającą wrażliwą charakterystyką opracowywaną wcześniej z udziałem autora oraz opisaną nowym proponowanym modelem histerezowym. Wyniki pokazano z wykorzystaniem nowoczesnych metod badawczych, z których najważniejsza -nowe podejście do estymacji maksymalnych wykładników Lapunowa poprzez synchronizację map, świetnie sprawdza się w układach z nieciągłością, jaką wprowadza do ruchu tarcie suche. Wnioski zawarte w końcu tego rozdziału są dość istotne z punktu widzenia zarówno inżynierów, jak i badaczy zjawiska. W części końcowej podsumowano rozważania proponowanego wrażliwe- go modelu statycznego tarcia. Istotność uogólnienia polega na możliwości zastosowania w nim dowolnej funkcji modelującej efekt Stribecka przy przejściu do tarcia kinetycznego oraz pokazano ważne zalety -prostotę zastosowania w symulacjach numerycznych, uniwersalność (można łatwo uzyskać inne charakterystyki tarcia), możliwość symulacji różnych zjawisk związanych z tarciem. Z praktycznego punktu widzenia wniosek, że największy wpływ na dynamikę układu z tarciem ma średni poziom siły tarcia kinetycznego, jest ważnym efektem rozważan. Pokazano też kierunki stanowiące drogę dalszego rozwijania modelowania zjawiska tarcia.

EN

In the book phenomena of hysteretic behaviour of a friction force observed during experiments are discussed. A review of friction models and friction phenomena is enclosed. On the basis of experimental and theoretical ana- lyses there is argued that such behaviour can be considered as a representation of the system dynamics. According to this approach, a new classification of friction models, with respect to their sensitivity on the system motion nature, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective model capturing the hysteretic effects is proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model. Also, for the verification purposes the model is applied in two examples of the typical nonlinear applications together with other, classical approaches. New method of calculating Lyapunov exponents for systems with discontinuity is applied. Importance of average level of friction force to the system dynamics is shown.

Słowa kluczowe

PL

efekt histerezy; tarcie suche

EN

hysterectic effects; dry friction

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka
• Rocznik: 2008
• Tom: Z. 366
• Strony: 6--126
• Opis fizyczny: Bibliogr. 140 poz., wykr.

Twórcy

autor

Wojewoda J.

• Politechnika Łódzka. Katedra Dynamiki Maszyn

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