Nastanak zamorne pukotine u korijenu zuba zupčanika s tankim vijencem

doctoral thesis

• Title (english): Fatigue crack initiation in the tooth root of thin-rimmed gears
• Author: Krešimir Vučković
• Mentor: Milan Opalić (mentor)
• Mentor: Jože Flašker (komentor); VIAF: 66191048
• Committee member: Mirko Husnjak (predsjednik povjerenstva)
• Committee member: Milan Opalić (član povjerenstva)
• Committee member: Jože Flašker (član povjerenstva); VIAF: 66191048
• Committee member: Zdenko Tonković (član povjerenstva)
• Committee member: Gordana Marunić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2009-10-29, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering
• Universal decimal classification (UDC): 621 - Mechanical engineering. Nuclear technology. Machinery ; 53 - Physics ; 004 - Computer science and technology. Computing. Data processing

Abstract

U radu je provedena trodimenzijska numerička analiza nastanka zamorne pukotine u korijenu strane zuba zupčanika na kojoj djeluje opterećenje. Usporedo je provedena i analiza najvećeg glavnog naprezanja. Predmet istraživanja su cilindrični zupčanici s tankim vijencem i vanjskim evolventnim ozubljenjem ravnim zubima. Istražen je utjecaj položaja diska, debljine vijenca, okretnog momenta te brzine vrtnje, odnosno centrifugalne sile. \Najveće glavno naprezanje kao i njegovo mjesto u korijenu zuba određeni su primjenom elastične analize pomoću metode konačnih elemenata. Utjecaj slike nošenja uzet je u obzir modeliranjem kontakta između zubi u zahvatu. Numerički model je verificiran eksperimentalnim ispitivanjem pomoću metode tenzometrije, a iskorišten je i za određivanje povijesti stanja naprezanja u korijenu zuba zupčanika. U obzir je uzeta činjenica da se opterećenje prenosi s pogonskog na gonjeni zupčanik mijenjajući svoj pravac djelovanja, položaj i intenzitet zbog čega je stanje naprezanja neproporcionalno. Na osnovu poznatih cikličkih karakteristika materijala, potencijalno mjesto i vrijeme do nastanka zamorne pukotine određeni su numeričkim izračunom pomoću metode ovisnosti amplitude deformacije o vremenu do nastanka pukotine u kombinaciji s metodom kritične ravnine. Izračun je verificiran usporedbom s numeričkim i eksperimentalnim rezultatima drugih autora. Pokazano je da iznos i mjesto najvećeg glavnog naprezanja u korijenu zuba, kada opterećenje djeluje u vanjskoj točki jednostrukog zahvata, ovise o opterećenju, centrifugalnoj sili, debljini vijenca te položaju diska. Dobiveni rezultati odstupaju od istih izračunanih pomoću konvencionalnog proračuna. Potencijalno mjesto nastanka zamorne pukotine znatno se razlikuje od mjesta najvećeg glavnog naprezanja. Za analizirani materijal zupčanika, čelik C45E, ovisi o debljini vijenca i položaju diska. životni vijek zupčanika s obzirom na nastanak zamorne pukotine, ovisi o opterećenju, debljini vijenca te položaju diska, dok centrifugalna sila, pri brzinama vrtnje karakterističnim za prijenosnike opće namjene, ima neznatan utjecaj na njega. Pretpostavkom da zamorna pukotina nastaje na mjestu najvećeg glavnog naprezanja čini se nekonzervativna greška u njegovom određivanju. Trajna dinamička čvrstoća korijena zuba zupčanika s tankim vijencem razlikuje od one kod punih zupčanika, a ovisi o debljini vijenca i položaju diska. Primjenom numeričkog modela te rezultata iz ovog rada može se pouzdanije i točnije procijeniti životni vijek te nosivost korijena zuba zupčanika s tankim vijencem.

Abstract (english)

Three dimensional numerical analysis of fatigue crack initiation and the analysis of maximum principal stress were performed at the loaded side of the gear tooth root. Thin-rimmed cylindrical involute gears with external teeth were analyzed. Effects of the rim thickness, web arrangement, applied torque and rotational speed related to centrifugal force were evaluated. Elastic FEM analysis was used to determine the magnitude and location of maximum principal stress. The influence of load distribution on the face width is taken into account through the modeling of contact between teeth in mesh. The numerical model was validated experimentally using strain gauges. Subsequently, the model was used to determine the stress history at the gear tooth root. We have taken into account the fact that in actual gear operation the magnitude and the position of load change as the gear rotates through the mesh, causing a nonproportional stress state. On the basis of known cyclic material properties, the time to fatigue crack initiation and the potential location of a fatigue crack were determined by numerical computation using a combination of the local strain-life and the critical plane method. The obtained results were compared with other investigators’ numerical and experimental results, and thus validated. When load is applied at the outer point of single-tooth contact, it was shown that the magnitude and the location of the maximum principal stress in the tooth root, depend on the rim thickness, web arrangement, applied torque and centrifugal force. The obtained results deviate from those obtained by conventional calculation. Potential fatigue crack initiation is located away from the location of maximum principal stress. In the case of the analyzed gear material, steel C45E, it depends on the rim thickness and web arrangement. The gear service life, estimated in regard to fatigue crack initiation, depends on the applied torque, rim thickness, and web arrangement, while the influence of centrifugal force is insignificant for rotational speeds of common gear drives. A non-conservative mistake in the determination of gear service life is made by assuming that the initial crack occurs at the location of maximum principal stress. The allowable stress number at tooth root for thin-rimmed gears is different from that for solid gears, and depends on the rim thickness and web arrangement. Service life of gears and the bending strength of toot root can be more accurately and reliably estimated using the numerical model and the results presented in this work.

• Keywords: zupčanik; tanki vijenac; zamor materijala; nastanak pukotine; najveće glavno naprezanje; MKE; metoda kritične ravnine
• Keywords (english): gear; thin rim; fatigue of materials; crack initiation; maximum principal stress; FEM; critical plane method
• Language: croatian
• URN:NBN: urn:nbn:hr:235:117777
• Study programme: Title: Mechanical Engineering and Naval Architecture; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje tehničkih znanosti (doktor/doktorica znanosti, područje tehničkih znanosti)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2021-02-01 10:24:52