[en] Spherical gear couplings are commonly used mechanical components to transmit power between highly misaligned rotating shafts. Their main geometry characteristic is the appearance of undercut sections on the hub when machining a high amount of longitudinal crowning. This possibility is even more significant when gear couplings with a low number of teeth are manufactured directly on the shaft. Current geometry generation models in the literature avoid the generation of undercut sections. Furthermore, it is a matter of disagreement among the existing models, since the generated tooth surfaces of the hub vary depending on the analytical model employed. In fact, these variations influence the contact characteristics and the load distribution of the gear coupling. Moreover, gear couplings working at high misalignment angles cause a drastic decrease in the number of teeth in contact. In consequence, higher tooth-root stresses in those in contact are suffered and result in the failure of the component by tooth root breakage. However, the scientific literature has focused on gear couplings working in applications where the misalignment angles are below 1◦, thus mainly centered on failures other than bending fatigue, such as fretting or surface wear. Thus, there is a lack of sizing methods oriented to higher misalignment angles, therefore current components working at these conditions may be oversized, or which is even more critical, sometimes undersized. This thesis covers the existing gap in the generation of the crowned hub tooth surface geometry, with the development of a novel mathematical model which assesses the complete thread surface of the cutting tool and considers its cutting tool path. Moreover, this model can accurately generate undercut profiles that may appear on the hub. Furthermore, the achievable misalignment angle of this type of gear coupling is discussed, assessing the influence of the geometry and manufacturing variables on this value. It gives an overview of the preliminary design phase and helps the designer to find out the most suitable design parameters to avoid as much as possible further geometrical issues, without compromising the achievable maximum misalignment angle. Finally, a loaded tooth contact analysis is carried out with a finite element model to understand the load distribution among the teeth and the bending tooth root stress in terms of the applied torque and the working misalignment angle. Moreover, the results are experimentally correlated with a real gear coupling which works in such high misalignment applications. The results from the geometry generation model reveal that deviations between the generated crowned tooth surfaces with models existing in the literature are significant and modify the undercut cross sections beginning or even the contact conditions. At the same time, it is proved that the generated geometry is in good agreement with experimental data and highlights that the existing models in the literature to determine the maximum misalignment angle are not applicable for highly crowned gear couplings. Moreover, from the loaded tooth contact analysis, it is observed that different mechanical behaviors arise at low or high misalignment angles since teeth in the pivoting position lose contact. This results in a tooth root stress history change from a sinusoidal cycle to a pulsating cycle, which may affect the fatigue life of the gear coupling. In conclusion, this research analyzes in depth the geometry and mechanical behavior of gear couplings working in applications at high misalignment angles (γ ≥ 3◦) with the developed analytical and numerical models. Also, demonstrates that the attained results differ from those obtained when applying current generating and rating standards.

[eu] Abonbamendu handiko horzdun akoplamenduak desalineazio angeluar handiko ardatz birakorren artean potentzia transmititzeko erabiltzen diren elementu mekanikoak dira. Beraien ezaugarri geometriko nagusia abonbamendua mekanizatzerakoan hortzen oinean agertzen den interferentzia da. Hau gertatzeko aukera handitu egiten da hortz kopuru txikiko akoplamenduak zuzenean ardatzean mekanizatzen direnean. Bibliografian dauden modelo gehienak oineko interferentziak sortzea saihesten dute. Gainera, modelo aurreratuenen artean desadostasunak daude, sortutako hortzaren geometria desberdina baita erabilitako eredu analitikoaren arabera. Izan ere, desberdintasun horiek eragina dute hortzen arteko karga banaketan edota kontaktu baldintzetan. Bestalde, desalineazio angeluar handietan lan egiten duten akoplamenduetan kontaktuan dauden hortz kopurua nabarmen murrizten da, kontaktuan geratzen diren hortzen oineko tentsioak handituz eta ondorioz hortz oinaren haustura eraginez. Literatura 1◦ azpiko desalineazio angeluarretan zentratzen da gehienbat, ondorioz, beste mota bateko akatsak ikertzen ditu, hala nola, higadura edo gainazal nekea. Alabaina, ez dago desalineazio angelu handiagoetara dimentsionatzeko metodorik. Beraz, baldintza horietan lan egiten duten egungo elementuak gaindimentsionatuta egon daitezke, edo are kritikoagoa dena, noizbehinka azpidimentsionatuta. Tesi honetan, aurrez aipatutako baldintzetan lan egiteko behar diren hortzen geometria generatzeko modelo analitiko bat garatu da. Eredu honek, fresa amaren gainazal helikoidal osoa eta beronen ibilbidea hartzen ditu kontuan. Horrez gain, modeloa gai da akoplamenduan ager daitezkeen hortzen oineko interferentziak zehaztasunez sortzeko. Horrez gain, abonbamendu handiko horzdun akoplamenduek era egokian lan egin dezaten gehieneko desalineazio angeluar onargarria eztabaidatzen da, parametro geometrikoek eta fabrikazio prozesuak duten eragina aztertuz. Honek aurretiko diseinu fasearen ikuspegi orokorra eskaintzen du. Bide batez, diseinatzailearentzat erreminta baliagarria da akoplamenduarentzat parametro egokiak hautatzen laguntzen diolako arazo geometrikoak saihesteko. Azkenik, kargapeko kontaktuaren analisia egin da elementu finituen modelo bat garatuz. Honek, aplikatutako momentuaren eta desalineazio angeluarraren arabera karga banaketa eta hortzaren oineko tentsioak nola aldatzen diren ezagutzea ahalbidetzen du. Gainera, emaitzak esperimentalki egiaztatu dira desalineazio angeluar handietan lan egiten duen abonbamendu handiko horzdun akoplamendu batekin. Geometria sortzeko modeloaren emaitzek, literaturako ereduekin sortutako hortzen gainazal abonbatuen arteko desbiderapenak esanguratsuak direla erakusten dute. Gainera, desbiderapen hauek oineko interferentziaren hasieran eta kontaktu baldintzetan eragina dutela frogatu da. Era berean, generatutako geometria neurtutakoarekin bat datorrela egiaztatu da eta agerian geratzen da bibliografian dauden desalineazio angeluar maximoa kalkulatzeko modeloak ez direla aplikagarriak abonbamendu handiko akoplamenduentzat. Bestalde, kargapeko kontaktuaren analisitik abiatuta, desalineazio angelu baxuetan eta altuetan portaera mekaniko desberdinak ikusi dira; izan ere, pibotatze-posizioan dauden hortzek kontaktua galtzen dute desalineazio angelua handitzean. Honek hortzaren oineko tentsioen ziklo mota aldatzea dakar, ziklo sinusoidal batetik ziklo pultsatzaile batera igaroz, eta nekearekiko portaera aldatuz. Laburbilduz, tesi honek sakon ikertzen ditu desalineazio angeluar handietan (γ > 3◦) lan egiten duten abonbamendu handiko horzdun akoplamenduen geometria eta portaera mekanikoa, horretarako garatutako modelo analitiko eta numerikoen bitartez. Horrez gain, lorturiko emaitzak gaur egun indarrean dauden araudiak aplikatuta lortzen diren emaitzekin konparatzen ditu, desberdintasun nabariak daudela ondorioztatuz.