In the article research related to the increasing in the scope of application of additive technologies in the construction of machines for the production of gears with involute and sinusoidal profile from polymeric materials was presented. The designed original research stand and with its use carried out a series of preliminary fatigue tests of the obtained polymer gears with an involute and sinusoidal profile was show. The tested gears were obtained in the technology of rapid prototyping by the FFF (Fused Filament Fabrication) method from polymer composites obtained in the form of an ABS (acrylonitrile/butadiene/styrene) -based filament. Based on the results obtained, it was noticed that the temperature in the meshing zone of the gears with involute profiles is higher than for sinusoidal profiles, regardless of the type of composite from which the gears were made. It should also be noted that in the range of nominal load, the sound intensity level of the meshing zone is also lower for gears with a sinusoidal profile than for gears with an involute profile. Based on the tests carried out, an increase in sound intensity was noticed in the case of gears obtained from selected composites (Table 2) compared to the gear obtained from unfilled ABS. However, in the case of gears obtained from the tested composite materials, we observe a decrease in the gear operating temperature (Table 2). The most favorable results of these tests were obtained for gears with a sinusoidal profile obtained from ABS + P2 composite, which show the lowest operating temperature of the gear. It should also be mentioned that slightly worse results were obtained for involute gears.
Przedstawiono matematyczny opis powierzchni boku ślimacz-nicy przekładni ślimakowej globoidalnej. Pokazano układ kinematyczny kształtowania boku zęba ślimacznicy oraz wykorzystano matematyczny opis powierzchni bocznej ślimaka globoidalnego. SŁOWA KLUCZOWE: przekładnia ślimakowa globoidalna, śli-mak globoidalny, ślimacznicaPresented is a mathematical description of tooth flank surface of the wormwheel in globoid worm gear. The kinematic system of tooth formation was performed. The mathematical description of tooth flank of globoid worm was used.
Abstract:In this article, a mathematical description of tooth ank surface of the globoidal worm and worm wheel generated by the hourglass worm hob with straight tooth axial pro le is presented. The kinematic system of globoidal worm gear is shown. The equation of globoid helix and tooth axial pro le of worm is derived to determine worm tooth surface. Based on the equation of meshing the contact lines are obtained. The mathematical description of globoidal worm wheel tooth ank is performed on the basis of contact lines and generating the tooth side by the extreme cutting edge of worm hob. The presented mathematical model of tooth ank of TA worm and worm wheel can be used e.g. to analyse the contact pattern of the gear.
Omówiono wpływ skrajnych krawędzi skrawających frezu globoidalnego na kształtowanie powierzchni zęba ślimacznicy przekładni ślimakowej globoidalnej. Wyprowadzono matematyczny opis tej powierzchni i z modelu matematycznego wyeksportowano ją do systemu CAD. Przedstawiony model zęba ślimacznicy uwzględnia wpływ skrajnych krawędzi skrawających frezu. Na powierzchni zęba ślimacznicy wskazano obszary powstające w wyniku kształtowania środkową częścią frezu oraz krawędziami skrajnymi.
SŁOWA KLUCZOWE: ślimacznica, przekładnia ślimakowa globoidalna
This paper presents the effect of the globoid hob extreme cutting edges on generation of the wormwheel tooth flank profile of globoid worm gear. Mathematical formula for the said flank surface was worked out. The surface drawn from the mathematical model was exported to CAD system. The model of the wormwheel tooth was presented with the effect of the extreme hob edges taken into consideration. The regions on the wormwheel flank as generated by the middle part of the of hob and by its extreme edges were identified respectively.
Przedstawiono sposób hybrydowego modelowania ślimaka globoidalnego z zastosowaniem systemów CAD. Wyznaczono ogól-ny matematyczny wzór na linię zwoju ślimaka globoidalnego, który następnie wykorzystano do modelowania, oraz omówiono tok postępowania przy tym modelowaniu, wyodrębniając operacje zautomatyzowane. Zwrócono uwagę na zalety systemów CAD i ich przydatność w projektowaniu przekładni ślimakowych globoidalnych. SŁOWA KLUCZOWE: przekładnia ślimakowa globoidalna, systemy CAD This paper presents a method of hybrid modeling of a globoid worm using CAD systems. General mathematical formula for the coil line of globoid worm was developed and used in the worm modeling work. The procedure of modeling was presented with the automatically performed operations suitably highlighted. The advantages and possibilities of application of CAD systems in design work of globoid worm gear mechanism were presented.
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