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V magistrski nalogi smo reševali vezan termomehanski problem cikličnega obremenjevanja konzolno vpetega polimernega nosilca. Upogib nosilca smo opisali s pomočjo Euler-Bernoullijeve teorije upogiba nosilcev, vpliv lokalne pritisne sile pa smo modelirali s pomočjo Boussinesqove rešitve linijske obremenitve na pol-ravnini. Z enačbo vezanega prevoda toplote smo določili temperaturno porazdelitev na obravnavanem območju. V matematični model smo s pomočjo določenih predpostavk vključili tudi druge prispevke generacije toplote, kot so trenje, viskozna disipacija energije in temperaturna odvisnost elastičnega modula. Razvili smo teoretični model, ki se ga lahko uporabi tudi za reševanje vezanega termomehanskega problema obremenjevanja polimernih zobnikov. Predstavili smo različne kriterije določanja maksimalne frekvence obremenjevanja in primerjali različne prispevke na generacijo toplote v nosilcu. Z magistrsko nalogo smo pokazali uporabnost analitičnih modelov pri reševanju termomehanskih problemov in alternativni način obravnave polimernih zobnikov. In the master thesis, we solved coupled thermomechanical problem of cyclic loading of a polymer cantilever beam. The beam bending was described using Euler-Bernoulli theory, and the influence of the local compressive force was modeled using Boussinesq solution of the line load on a half-plane. The temperature distribution over the considered region is determined using coupled heat transfer equations. With the help of certain assumptions, we also included other contributions to heat generation in the mathematical model, such as friction, viscous energy dissipation, and the temperature dependence of the elastic modulus. We have developed a theoretical model that can also be used to solve coupled thermomechanical problems of polymer gears in service. We have presented different criteria for determining the maximum loading frequency and compared different contributions to the heat generation in the beam. With the master thesis we showed the usability of analytical models in solving thermomechanical problems and an alternative way of addressing the heating problem in polymer gears. |
