Article citation info:Marciniak, T., Ostrowski, D. Worm gear’s operating barriers. Scientific Journal of Silesian University of Technology. Series Transport. 2015, 89, 79-87. ISSN: 0209-3324. DOI: 10.20858/sjsutst.2015.89.9.Tadeusz MARCINIAK, Dariusz OSTROWSKIWORM GEAR’S OPERATING BARRIERSSummary. The main factor that characterize the durability of worm gears are the materials from which the elements are made. Distinct from toothed gear, in which, in most of cases collaborating elements are made from toughened steel, in worm gears the standard is collaborating of toughened worm and relatively soft worm wheel, made from bronze. Applications of different materials have not given good results. Due to this reason a worm gear operating barriers, which not similar to different types of gears, take place.The article presents the mechanism of worm gears utilization, which in most of cases decide about its durability. Theoretical basis of operating barriers have been given, with particular emphasis on fatigue and abrasive wear barriers, which are most common reason of durability limitation. Operating test results have been presented as well as trials, that were to determine the durability depending on operation conditions. Recommendations have been formulated for proper material selection, operating conditions as well as valuations of gear durability stage.Keywords: worm gear’s, barriers in operating, durability of gearsBARIERY EKSPLOATACYJNE W PRZEKŁADNIACH ŚLIMAKOWYCH Streszczenie. Decydującym czynnikiem określającym trwałość przekładni ślimakowych są materiały, z których wykonane są elementy przekładni. W odróżnieniu od przekładni zębatych, praktycznie w większości przypadków, współpracujące elementy są wykonane z utwardzonej stali. W przekładniach ślimakowych normą jest współpraca utwardzonego ślimaka ze stosunkowo miękkim brązem. Zastosowanie innych materiałów nie przyniosło pozytywnych rezultatów. W związku z tym pojawiają się bariery eksploatacyjne, niewykazujące podobieństw w innych rodzajach przekładni.W artykule przedstawiono mechanizmy zużywania się przekładni ślimakowych, które w większości przypadków decydują o ich trwałości. Podane zostały podstawy teoretyczne wszystkich barier eksploatacyjnych, ze szczególnym uwzględnieniem bariery zużycia zmęczeniowego i ściernego, jako najczęściej ograniczających trwałość tych przekładni. Przedstawiono wyniki badań eksploatacyjnych oraz próby określenia trwałości w zależności od warunków eksploatacyjnych. Sformułowano zalecenia co do stosowanych materiałów konstrukcyjnych, warunków eksploatacji oraz oceny stopnia zużycia przekładni.Słowa kluczowe: przekładnie ślimakowe, bariery w eksploatacji, trwałość przekładni1. WSTĘPJednym z podstawowych zagadnień współczesnych technik wytwarzania jest dążność do podwyższania trwałości maszyn i urządzeń. Wiąże się to głównie z rosnącymi możliwościami udoskonalania stosowanych inżynierskich technik obliczeniowych. Wynikiem tych obliczeń jest takie ustalenie parametrów konstrukcyjnych, aby otrzymać z góry założone, korzystne ze względu na charakter pracy. Dotyczy to również przekładni ślimakowych, gdzie coraz dokładniejsze metody obliczeniowe, bazujące na rozpoznanych zjawiskach zachodzących w strefie kontaktu pomiędzy zwojem ślimaka i zębem ślimacznicy, skutkują wydłużaniem ich okresu eksploatacji. Przekładnie te ze względu na takie zalety, jak:– cichobieżność,– możliwość uzyskiwania dużych przełożeń,– małe wymiary,są masowo wykorzystywane w przemyśle.2. Bariery dopuszczalnego obciążenia przekładni ślimakowych Specyfika pracy przekładni ślimakowej polega na tym, że w jej zazębieniu współpracuje twardy stalowy ślimak i stosunkowo miękki brąz. Próby stosowania innych materiałów w przekładniach mocy nie przyniosły pozytywnych rezultatów. Tak zbudowane zazębienie narażone jest na następujące formy zużycia:– wyłamanie zębów ślimacznicy,– przełom zmęczeniowy rdzenia ślimaka,– zużycie zmęczeniowe powierzchni zębów ślimacznicy,– zużycie zmęczeniowe powierzchni zwojów ślimaka,– zatarcie zazębienia w wyniku przekroczenia dopuszczanej granicy obciążenia cieplnego,– zużycie ścierne zębów ślimacznicy.Pomijając zużycia katastroficzne, które są wynikiem rażących błędów konstrukcyjnych czy eksploatacyjnych, w zależności od wymiarów przekładni, zastosowanych materiałów, sposobu smarowania, prędkości obrotowych i innych cech konstrukcyjno-eksploatacyjnych trwałość przekładni jest ograniczona jedną z następujących barier:– bariera dopuszczalnego obciążenia ze względu na zużycie zmęczeniowe powierzchni zębów ślimacznicy,– bariera dopuszczalnego obciążenia ze względu na zużycie ścierne zębów ślimacznicy,– bariera dopuszczalnego obciążenia zębów ślimacznicy ze względu na złamanie,– bariera dopuszczalnego obciążenia cieplnego.Oznacza to, że o trwałości przekładni, w danych warunkach, zadecyduje ta z wyżej wymienionych barier, która osiągnie krytyczną wartość podczas eksploatacji w przekładni.Na rysunku 1 przedstawiono przykładowy obraz krzywych granicznych przenoszonego obciążenia w funkcji prędkości poślizgu w zazębieniu. Rys. 1. Krzywe graniczne przenoszonego obciążenia w funkcji prędkości poślizgu w zazębieniuJak wynika z rysunku 1, trwałość przekładni ślimakowej głównie uzależniona jest od zużycia zmęczeniowego dla przekładni wysokobieżnych oraz ściernego dla przekładni pracujących w średnim zakresie obrotów. Bariera złamania zębów ślimacznicy jest groźna dla przekładni wybitnie wolnobieżnych i warunek bezpieczeństwa w tym przypadku ma postać: , (1)gdzie: − ugięcie dopuszczalne [mm],− ugięcie wału ślimaka [mm],a dla przekładni szybkobieżnych warunek bezpieczeństwa cieplnego sprawdzamy z zależności: , (2)gdzie: − ciepło odprowadzane [kW], − straty całkowite [kW].W większości przypadków dwie pierwsze bariery eksploatacyjne decydują o trwałości przekładni. 3. Bariera zużycia zmęczeniowegoPodczas eksploatacji przekładni w wielu przypadkach, szczególnie w przekładniach szybkobieżnych, na powierzchni zębów ślimacznicy po pewnym czasie pojawiają się wżery zmęczeniowe. Powierzchnia zajęta przez wżery stopniowo rośnie, aż osiągnie wielkość uznaną za krytyczną. Występuje tu znaczna różnica pomiędzy zachowaniem się klasycznych przekładni zębatych i przekładni ślimakowych. W przekładniach zębatych uznaje się, że przy zajęciu przez wżery zmęczeniowe 3% powierzchni zęba przekładnia taka traci całkowicie swoje walory eksploatacyjne. W przekładniach ślimakowych natomiast znane są przypadki, gdzie powierzchnia wżerów zmęczeniowych wynosiła 70%, a przekładnia nie traciła na sprawności oraz obciążalności. Wytłumaczeniem tego zjawiska jest rozkład prędkości poślizgu, jaki występuje w obu tych zazębieniach oraz w zachowaniu współpracujących materiałów pod wpływem obciążenia. Na rysunku 2 przedstawiono schematycznie rozkład prędkości poślizgu w punkcie styku w zazębieniu przekładni ślimakowej.Rys. 2. Rozkład prędkości poślizgu w zazębieniu: a) przekładni ślimakowej, b) zębatejZ przedstawionego rysunku wynika, że w przekładni ślimakowej dużą rolę odgrywa składowa obwodowej prędkości poślizgu v1 wielokrotnie przewyższając swoją wartością prędkość obtaczania VN, która dominuje w przekładniach zębatych. W rezultacie w tej pierwszej tworzą się naturalne warunki do powstawania filmu olejowego. Na ile skutecznie, za każdym razem zależy to od wielu czynników, do których należy zaliczyć:– zmienność odkształceń w punktach styku,– zmiany podatności elementów przekładni,– wielkości i rozkład nacisków wzdłuż linii styku,– rodzaj współpracujących materiałów,– rodzaj środka smarnego i sposobu smarowania.Przeprowadzono próby określenia wielkości filmu olejowego na podstawie teorii smarowania hydrodynamicznego. Zależność ta ma postać:, (3)gdzie:smin – minimalna wartość szczeliny smarowej [m],ρN – zredukowany promień krzywizny w punkcie styku [m],VB – prędkość śrubowa [m/s],ηo – lepkość dynamiczna oleju [N s/m2],p/l – obciążenie na jednostkę długości [N/m].W rzeczywistości okazało się, że każda przekładnia mocy nie jest w stanie pracować w takich warunkach, gdyż współpracujące elementy nie są doskonale sztywne. W związku z tym poczyniono próby określenia tego filmu na podstawie teorii EHD (Elasto-Hydro-Dynamicznej). Grubość filmu olejowego według tej teorii można obliczyć z zależności: , (4)gdzie: α’ – współczynnik lepkości oleju [m2/N],E’ – zredukowany moduł sprężystości współpracujących materiałów [N/m2].Również zastosowanie tej metody nie przyniosło pozytywnych rezultatów w praktyce, prawdopodobnie ze względu na konieczność stosowania wartości uśrednionych z całej powierzchni współpracy, tak bardzo zróżnicowanej tu w swojej geometrii. Należy zaznaczyć, że obliczenia te prowadzone były dla przekładni obciążonych momentem znamionowym, to jest takim, przy którym przekładnia osiąga maksymalną sprawność. Przy obciążeniu niższymi wartościami momentu film olejowy może się tworzyć i rozdzielać współpracujące powierzchnie. Tłumaczy to występujące czasami minimalne zużycie zazębienia pomimo długiego okresu eksploatacji. Jedyna możliwość, jaka pozostała dla określenia bariery zużycia zmęczeniowego, to przyjęcie metody mającej w swojej podstawie teorię Hertza. Przyjęto tu za podstawę wartość wyrażenia z jednej linii styku o długości l, nazywanego siłą nośną P. Zależność ta ma postać [5]:, (5)gdzie:kH – nacisk powierzchniowy Striebecka [N/m2],τ – kąt pochylenia płaszczyzny ściśle stycznej do płaszczyzny czołowej ślimaka [o].Pozwoliło to na określenie momentu dopuszczalnego, jakim można obciążyć przekładnię, tak aby nie była narażona na powstawanie wżerów zmęczeniowych.Adaptując prawa żywotności łożysk tocznych, podano [1] zależność na trwałość zazębienia przekładni ślimakowej i przedstawiono w następującej postaci:,(6)gdzie: cwm – współczynnik materiałowy, zależny od liczby cykli obciążeń LW2, po której wystąpiły pierwsze wżery zmęczeniowe,Fw   – przyjęta dopuszczalna powierzchnia zęba ślimacznicy, jaka może być zajęta przez wżery zmęczeniowe [%], i    – przełożenie przekładni,n1    – prędkość obrotowa ślimaka [1/min],M2   – moment znamionowy [Nm],LW2 – liczba cykli, po których występują pierwsze wżery zmęczeniowe.Ze wzoru (4) wynika, że trwałość zazębienia w dużej mierze uzależniona jest od liczby cykli LW2. Warunek bezpieczeństwa zazębienia w tym przypadku ma następującą postać:, (7)gdzie: – naprężenie dopuszczalne,Ctm – współczynnik zależny od rodzaju oleju,Ctr – współczynnik chropowatości,Ctv – współczynnik zależny od poślizgu, – naprężenia Hertza w zazębieniu.Jak wspominano wcześniej, nawet zajęcie 70% powierzchni zęba ślimacznicy wykonanej z brązu nie powoduje znaczącej utraty właściwości eksploatacyjnych przekładni. Może to być wynikiem znacznej przewagi prędkości obwodowej ślimaka nad prędkością obtaczania. W takiej sytuacji zachodzą dobre warunki do rozdzielenia współpracujących powierzchni środkiem smarnym. Dopiero znaczne wykruszenia z powierzchni zęba muszą skutkować wyłączeniem przekładni z eksploatacji. Szczególną rolę odgrywa więc proces docierania zazębienia. W przypadku obciążenia niedotartej przekładni momentem znamionowym zachodzą warunki do natychmiastowego tworzenia się wżerów zmęczeniowych. Proces docierania może być bardzo istotny dla trwałości przekładni.4. Bariera zużycia ściernego O ile w przekładni zębatej, pomijając przekładnie z zębami nieutwardzonymi, zużycie ścierne jest praktycznie niedopuszczalne, gdyż może zostać zachwiana zasada Willisa, to w przekładni ślimakowej zużycie ścierne, ale tylko zębów ślimacznicy, jest zjawiskiem w pełni naturalnym. Zużycie to praktycznie rozpoczyna się od momentu uruchomienia przekładni i trwa do osiągnięcia wcześniej założonego stopnia zużycia. Dla określenia bezpośredniego związku pomiędzy dopuszczalnym zużyciem masowym zębów ślimacznicy Δmdop a trwałością zazębienia T wykorzystuje się tak zwaną prędkość zużycia ściernego Δms, rozumianą jako ubytek masy ślimacznicy w jednostce czasu. Zależność ta ma postać: . (8)Wykazano, że prędkość ta jest stała w okresie eksploatacji, o ile nie występuje zużycie zmęczeniowe. W pracy [4] podano zależność dającą dobrą zgodność z wynikami badań i ma ona następującą postać: (9)gdzie: cx – współczynnik związany z warunkami w zazębieniu.Dopuszczalne zużycie ścierne można określać wartością grubości zęba ślimacznicy na wierzchołku, tak jak to pokazano na rysunku 3.Rys. 3. Miejsce pomiaru zaostrzenia zęba ślimacznicyZa minimalną wartość grubości gp wskazanej na rysunku przyjmuje się iloczyn 0,2 m [2]. Drugim sposobem, często stosowanym w badaniach, jest określenie dopuszczalnego ubytku masy ślimacznicy, którą można wyliczyć z powierzchni zęba. Trzecim sposobem, chętnie wykorzystywanym w eksploatacji, jest określenie dopuszczalnego powiększenia luzu obwodowego w zazębieniu. Na rysunku 4 przedstawiono schemat takiego pomiaru przeprowadzonego za pomocą poziomnicy koincydencyjnej.Rys. 4. Schemat pomiaru luzu obwodowego za pomocą poziomnicy koincydencyjnej: 1− poziomnica koincydencyjna, 2− podstawa, 3− ramię, 4− ślimacznica, 5− jarzmo ślimaka, 6− ślimak, 7− ciężar5. PodsumowanieSpecyfika konstrukcyjna przekładni ślimakowych mocy, to znaczy skojarzenie utwardzonego ślimaka i stosunkowo miękkiego brązu, powoduje, że przekładnie te wyróżniają się z grupy przekładni zębatych, gdzie dominuje kontakt dwóch twardych powierzchni. Tworzenie się w czasie eksploatacji wżerów zmęczeniowych na powierzchni zębów ślimacznicy nie powoduje wyłączenia jej z eksploatacji, tym bardziej że znane są przypadki, w których po wystąpieniu wżerów zmęczeniowych w dalszej eksploatacji zanikają one. Oznacza to, że możliwe jest starcie uszkodzonej warstwy w wyniku zużycia ściernego. Jest możliwość określenia trwałości zazębienia ze względu na zużycie zmęczeniowe przy spełnieniu pewnych warunków określonych za pomocą wzoru (4). Zużycie ścierne jest naturalną formą zużycia zazębienia. Tu sprawa jest znacznie bardziej poznana. Znając parametry pracy przekładni, zachodzi możliwość określenia trwałości zazębienia wychodząc ze wzoru (6). Ważny jest tutaj znany fakt proporcjonalności tempa zużycia ściernego w całym okresie eksploatacji. Zużycie graniczne jest stosunkowo proste do określenia.Do inżynierskich obliczeń wcześniej omawianych barier obciążalności można stosować autorski program TESTER [2] w zakładce „Obliczenia”.Rys. 5. Program TESTER – obliczenia wytrzymałościoweW ostatnim czasie dużą popularność zyskują przekładnie przeznaczone do przenoszenia małych obciążeń, gdzie ślimacznica wykonana jest ze specjalnych tworzyw sztucznych [3]. Brak jest jednak miarodajnych wyników badań eksploatacyjnych takich przekładni.ReferencesWinter H., T. Hosel, G. Huber. 1979. „Weiter entwicklte Tragfahigkeitberechung fur Zylinderschneckengetriebe”. VDI Berichte 332. [In German: „Evolved Tragfahigkeitberechung for cylindrical worm gear drives”].Marciniak Tadeusz. 2001. Przekładnie ślimakowe walcowe. Warszawa: PWN. ISBN 83-01-13474-7. [In Polish: Helical Worm Gearboxes].Marciniak Tadeusz. 2013. Technologia przekładni ślimakowych. Radom: Wydawnictwo Naukowe ITE. ISBN 978-83-7789-171-1. [In Polish: Technology of worm gear].Marciniak Tadeusz. 2004. „Obciążalność zazębienia w przekładniach ślimakowych”. Zeszyty Naukowe Politechniki Łódzkiej 329. ISSN: 0137-4834. [In Polish: „Load worm gears meshing in”].Winter H., H. Wilkesmann. 1981. „Calculation of Cylindrical Worm Gear Drives of Different Tooth Profiles”. Journal of Mechanical Design 103: 73-82. ISSN 1050-0472.Sabiniak Henryk Grzegorz. 2001. „Odporność na pitting zazębienia ślimakowego”. Przegląd Mechaniczny 7-8: 26-29. ISSN 0032-2259. [In Polish: “Resistance to pitting meshing of the worm”].Sabiniak Henryk Grzegorz. 2002. „Ścierne zużycie zębów, a grubość filmu olejowego w zazębieniu ślimakowym”. Przegląd Mechaniczny 10: 38-41. ISSN 0032-2259. [In Polish: „Abrasive tooth wear, and the thickness of the oil film on the worm gear”].Received 10.06.2015; accepted in revised form 21.08.2015Scientific Journal of Silesian University of Technology. Series Transport is licensed under a Creative Commons Attribution 4.0 International License PAGE 80T. Marciniak, D. OstrowskiWorm gear’s operating barriers PAGE 87.Scientific Journal of Silesian University of Technology. Series TransportZeszyty Naukowe Politechniki Śląskiej. Seria TransportVolume 89 2015p-ISSN: 0209-3324e-ISSN: 2450-1549DOI: 10.20858/sjsutst.2015.89.9Journal homepage: http://sjsutst.polsl.pl Faculty of Mechanical Engineering, The Lodz University of Technology, Stefanowskiego 1/15 Street, 90-924 Łódź, Poland. E-mail: tadeusz.marciniak@p.lodz.pl Faculty of Mechanical Engineering, The Lodz University of Technology, Stefanowskiego 1/15 Street, 90-924 Łódź, Poland. 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