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Designing the gear body structure to control vibration behaviour
Riad Ramadani, 2018, doctoral dissertation

Abstract: This research presents a new approach aiming to reduce gear vibration as well as its weight by modifying the gear body structure. The primary objective was to reduce vibration and noise emission of spur gears. For this purpose, a solid gear body was replaced by a cellular lattice structure, which was expected to raise the torsional elasticity of the gear body. The cellular lattice structure was designed and optimized by FE-based topology optimization software CAESS ProTOp, which is based on strain energy control. For experimental purposes, the optimized gear was produced from Titanium alloy Ti-6Al-4V ELI by using Selective Laser Melting technique. A polymer matrix was added to increase the damping of the structure. In order to test the gears, a new test rig with closed loop was conceived, designed and produced. The test rig is equipped with two gear pairs: with the tested one and with the driving one. The gears have been run and tested at different speeds and torque. The acceleration, strain and sound pressure of a running gear pair was measured. The final processing of the signal was done by a specially developed software based on LabView. By employing the fast Fourier transformation the time signal of acceleration, strain and sound pressure has been converted to the frequency spectrum and time frequency spectrogram. The results obtained by testing the solid and cellular lattice gear body were compared. It was experimentally confirmed that the cellular lattice structure of a gear body and addition of a polymer matrix may significantly reduce the vibration.
Keywords: Gear vibration, cellular lattice structure, topology optimization, test rig
Published in DKUM: 27.02.2018; Views: 1607; Downloads: 164
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Effective topological charge cancelation mechanism
Luka Mesarec, Wojciech Góźdź, Aleš Iglič, Samo Kralj, 2016, original scientific article

Abstract: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.
Keywords: topological defects, topological charge, numerical studies, orientational ordering, nematic liquid crystals, liquid crystalline shells, biological membranes, nanoparticles, Gaussian curvature, electrostatic analogy, annihilation, topology
Published in DKUM: 23.06.2017; Views: 728; Downloads: 308
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Inverse limits in the category of compact Hausdorff spaces and upper semicontinuous functions
Iztok Banič, Tina Sovič, 2013, original scientific article

Abstract: V članku obravnavamo inverzne limite v kategoriji ▫$mathcal{CHU}$▫ kompaktnih Hausdorffovih prostorov in navzgor polzveznih (u.s.c) preslikav. Vpeljemo pojem šibkih inverznih limit in pokažemo, da inverzne limite z navzgor polzveznimi veznimi preslikavami skupaj s projekcijami niso nujno inverzne limite v ▫$mathcal{CHU}$▫, so pa vedno šibke inverzne limite v tej kategoriji. Med drugim gre za realizacijo kategorijalnega pristopa k reševanju problema, ki ga je zastavil W. T. Ingram.
Keywords: topologija, kategorije, navzgor polzvezne funkcije, inverzne limite, posplošene inverzne limite, šibke inverzne limite, topology, upper semi-continuous functions, inverse limits, generalized inverse limits, weak inverse limits
Published in DKUM: 10.07.2015; Views: 772; Downloads: 85
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Inverse limits with generalized Markov interval functions
Iztok Banič, Tjaša Lunder, 2013, original scientific article

Abstract: V [S. Holte, Inverse limits of Markov interval maps, Topology Appl. 123, 2002,421-427] so bile predstavljene markovske preslikave in dokazano je bilo, da sta inverzni limiti z markovskimi veznimi funkcijami z enakim vzorcem homeomorfni. V tem članku predstavimo posplošene markovske preslikave, ki so posplošitev markovskih preslikav na večlične preslikave in pokažemo, da sta inverzni limiti s posplošenimi markovskimi veznimi preslikavami z enakim vzorcem homeomorfni.
Keywords: topologija, inverzne limite, navzgor polzvezne funkcije, posplošene markovske preslikave, topology, inverse limits, upper semi-continuous functions, generalized Markov interval functions
Published in DKUM: 10.07.2015; Views: 917; Downloads: 89
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Inducing functions between inverse limits with upper semicontinuous bonding functions
Iztok Banič, Matevž Črepnjak, Goran Erceg, Matej Merhar, Uroš Milutinović, 2013, original scientific article

Abstract: V članku predstavljamo kategorijo ▫$mathcal{CU}$▫, kjer so objekti kompaktni metrični prostori ▫$X$▫ morfizmi med njimi pa navzgor polzvezne preslikave iz ▫$X$▫ v ▫$2^Y$▫. Vpeljemo tudi kategorijo ▫$mathcal{ICU}$▫ inverznih zaporedij v ▫$mathcal{CU}$▫. Proučujemo inducirane funkcije med inverznimi limitami kompaktnih metričnih prostorov z navzgor polzveznimi veznimi funkcijami. Podamo kriterije za njihov obstoj in dokažemo imajo pod določenimi pogoji surjektivne grafe. Pokažemo tudi da predpis, ki objektom iz ▫$mathcal{ICU}$▫ priredi njihove inverzne limite, ki so objekti v ▫$mathcal{CU}$▫, morfizmom pa priredi inducirane preslikave ni funktor iz ▫$mathcal{ICU}$▫ v ▫$mathcal{CU}$▫, (je pa temu zelo blizu). Na koncu podamo še uporabno aplikacijo dokazanih rezultatov.
Keywords: topologija, inverzne limite, navzgor polzvezne funkcije, inducirane funkcije, inducirani morfizmi, topology, inverse limits, upper semi-continuous functions, induced functions, induced morphisms
Published in DKUM: 10.07.2015; Views: 723; Downloads: 37
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Ważewski's universal dendrite as an inverse limit with one set-valued bonding function
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, Tina Sovič, 2012, original scientific article

Abstract: Konstruirana je družina navzgor polzveznih večličnih funkcij ▫$f:[0,1] rightarrow 2^{[0,1]}$▫, za katere velja, da je inverzna limita inverznega zaporedja intervalov ▫$[0,1]$▫ in ▫$f$▫ kot edine vezne preslikave homeomorfna univerzalnemu dendritu Ważevskega.
Keywords: topologija, kontinuum, inverzna limita, večlična funkcija, dendrit, univerzalni dendrit Ważevskega, topology, continua, inverse limits, upper semi-continuous functions, dendrites, Ważewski's universal dendrite
Published in DKUM: 10.07.2015; Views: 986; Downloads: 142
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Limits of inverse limits
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, 2010, original scientific article

Abstract: Obravnavamo naslednji problem: če zaporedje grafov navzgor polzveznih večličnih funkcij ▫$f_n$▫ konvergira h grafu funkcije ▫$f$▫, ali potem zaporedje pripadajočih inverznih limit, dobljenih s pomočjo funkcij ▫$f_n$▫ konvergira k inverzni limiti, dobljeni z ▫$f$▫?
Keywords: matematika, topologija, kontinuumi, limite, inverzne limite, navzgor polzvezne večlične funkcije, mathematics, topology, continua, limits, inverse limits, upper semi-continuous set valued functions
Published in DKUM: 10.07.2015; Views: 778; Downloads: 24
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The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time
Leila Marek-Crnjac, 2006, original scientific article

Abstract: Pokažemo povezavo med topologijo štiri-mnogoterosti, konformno teorijo, verjetnostno teorijo in Cantorjevim prostorom. Na vseh štirih matematičnih področjih najdemo kot najpomembnejšo skupno povezavo pojav zlatega reza.
Keywords: matematika, topologija, zlati rez, konformna teorija, Cantorjev prostor-čas, E-neskončno teorija, mathematics, topology, golden mean, conformal field theory, Cantorian space-time, E-infinity theory
Published in DKUM: 10.07.2015; Views: 706; Downloads: 87
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