Deformation of a polymer gear tooth

V zaključni nalogi smo analizirali deformacijsko stanje zoba polimernega zobnika, ki je posledica sil v kontaktu gonilnega in gnanega zobnika. Zob zobnika obravnavamo kot konzolno vpeti nosilec, ki po svoji dolžini ima spremenljivo geometrijo. Silo v kontaktu, ki se s časom premika po boku zoba poenostavimo kot vertikalno silo, ki deluje na koncu nosilca. Deformacijo smo preračunali po Euler­Bernoullijevi in Timošenkovi teoriji nosilcev ter primerjali rezultate izračunov. Enačbe za opis spreminjanja lege nevtralne osi najprej izpeljemo ob predpostavki elastičnega nosilca s konstantnimi mehanskimi lastnostmi. S pomočjo definiranja temperaturnega polja zoba zobnika in določenih predpostavk smo v matematični model vključili pomembno lastnost polimernih materialov - odvisnost mehanskih lastnosti od povišane temperature, ki je posledica izgub zaradi viskoelastičnosti gradiva. Ovrednotimo količino generirane toplote v zobu in upogib nosilca s temperaturno odvisnimi mehanskimi lastnostmi primerjamo z upogibom nosilca s konstantnimi mehanskimi lastnostmi. S tem smo želeli pokazati ustreznost posameznih deformacijskih teorij v različnih okoliščinah in poudariti pomen upoštevanja vpliva temperature pri zagotavljanju zanesljivosti polimernih zobnikov.In the final thesis, we analyzed the deformation state of a polymer gear tooth, which is a result of the forces in contact with the driving and driven gear. The gear tooth is treated as a cantilever beam with variable geometry along its length. The contact force, which moves along the tooth flank with time, is simplified as a vertical force acting at the end of the beam. The deformation was calculated according to two deformation theories (Euler-Bernoulli and Timoshenko beam theory), which were compared. The equations that describe the change in position of the neutral axis are first derived assuming an elastic beam with constant mechanical properties. With the help of defining the temperature field of the gear tooth and certain assumptions, we included an essential property of polymer materials in the mathematical model - dependence of mechanical properties on elevated temperature, which is a consequence of losses due to viscoelasticity of the material. We evaluated the amount of heat generated in the tooth and compared the deflection of the beam with temperature-dependent mechanical properties to the deflection of the beam with constant mechanical properties. The aim was to demonstrate the suitability of both deformation theories under different circumstances and emphasize the importance of considering the influence of temperature when ensuring the reliability of polymer gears