AEåøóâñüêèé òåõíîëîã³÷íèé óí³âåðñèòåò, AEåøóâ, Ïîëüùà Âèêîíàíî ÷èñåëüíèé ðîçðàõóíîê íàïðóaeåíü ó ãíó÷êîìó ñïëàéí³ çóá÷àòî¿ ïåðåäà÷³ ãàðìîí³÷íîãî (õâèëüîâîãî) ðåäóêòîðà. Çóá÷àòå ê³ëüöå ó ãíó÷êîìó ñïëàéí³ ÷åðåç ñêëàäíó ãåîìåòð³þ ìîäåëþâàëîñü ó âèãëÿä³ ê³ëüöÿ. Âèñîòó ê³ëüöÿ ïðèéìàëè ç óðàõóâàííÿì íàïðóaeåíîñò³ â çóáöÿõ. Äëÿ âèâ÷åííÿ âïëèâó ð³çíèõ òèï³â õâèëüîâèõ ãåíåðàòîð³â íà ðîçïîä³ë íàïðóaeåíü ó ãíó÷êîìó ñïëàéí³ ðîçãëÿäàëè ìîäåë³ ç äâîìà òà ÷îòèðìà ðîëèêàìè, åêñöåíòðèêîì àáî äèñêîì. Ðîçðàõóíîê íàïðóaeåíü âèêîíóâàëè äëÿ äâîõ âàð³àíò³â: áåç îáåðòàëüíîãî ìîìåíòó òà ç îáåðòàëüíèì ìîìåíòîì, ùî â³äïîâ³äຠðåàëüíèì óìîâàì ðîáîòè ãåðìåòè÷íîãî ãàðìîí³÷íîãî ðåäóêòîðà.Êëþ÷îâ³ ñëîâà: ãåðìåòè÷íèé ãàðìîí³÷íèé (õâèëüîâèé) ðåäóêòîð, ðîçïîä³ë íàïðóaeåíü, ñê³í÷åííîåëåìåíòíèé àíàë³ç.
Purpose This paper aims to present a comparison of numerical methods for determining the contact pattern of Gleason-type bevel gears. The mathematical model of tooth contact analysis and the finite element method were taken into consideration. Conclusions have been drawn regarding the usefulness of the considered methods and the compatibility of results. The object of the analysis was a bevel gear characterised by an 18:43 gear ratio and arc tooth line, and manufactured according to the spiral generated modified-roll method. Design/methodology/approach The mathematical model of tooth contact analysis consists of both the mathematical model of tooth generating and the mathematical model of operating gear set. The first model is used to generate tooth flanks of the pinion and the ring gear in the form of grids of points. Then, such tooth surfaces are used for the tooth contact analysis performed with the other model. It corresponds to the no-load gear meshing condition. The finite element method model was built on the basis of the same tooth flanks obtained with the former model. The commercial finite element method software Abaqus was used to perform two instances of the contact analysis: a very light load, corresponding to the former no-load condition, and the operating load condition. The results obtained using the two models, in the form of the contact pattern for no-load condition, were compared. The effect of heavy load on contact pattern position, shape and size was shown and discussed. Findings The mathematical models correctly reproduce the shape, position and size of the contact pattern; thus, they can be reliably used to assess the quality of the bevel gear at the early stage of its design. Practical implications Determination of the correct geometry of the flank surfaces of the gear and pinion teeth through the observation of contact pattern is a fundamental step in designing of a new aircraft bevel gear. Originality/value A possibility of the independent use of the mathematical analysis of the contact pattern has been shown, which, thanks to the compatibility of the results, does not have to be verified experimentally.
The article presents the numerical analysis of the impact of geometry errors on the motion transmission of dual path gearing. The strength calculations of the elements of the drive were made by means of the Finite Elements Method (FEM). The calculations were made for the two-dimensional models of the dual path gearing. In the first place, the drive of the error-free (theoretical) geometry was tested. Next, the modifications of the selected teeth were introduced to the calculation models. The aim of the modifications of the tooth profile was to simulate pitch errors in compliance with the admissible values defined by PN-ISO 1328-1:2015 norm "Cylindrical gears -ISO system of flank tolerance classification". Finally, all the results were put together for comparison. The obtained results confirm the high irregularity of work gear as a result of errors tooth geometry.
Purpose – The analysis, carried out for this publication, concerned checking the nature of mating of gear wheels with different load conditions. The computation was made applying FEM in Abaqus 6.10-1 program and concerned spur gears in dual-power-path gears made of ABS. The same geometrical models, material parameters and boundary conditions were assumed for all the analysed stages of the computation. However, the values of torque transmitted from active wheels to passive wheel of the gearing were changed. The paper aims to discuss these issues. Design/methodology/approach – Observing changes of stress levels for toothed wheel and pinions allows to state that for relatively low load values, bending stresses at tooth root change proportionally to the change of the applied load. Findings – Values of contact stresses on mating teeth flanks were also defined for the most loaded part of the dual-power-path gearing, namely for a pinion. In case of contact stresses, it was observed that together with constant increase of torque value, the values of stresses change but the nature of these changes is not proportional to the applied load. Out of all the analysed variants, the most favourable, from the point of view of durability, was the situation in initial (theoretical) model with regular power division on all mating wheels. Originality/value – Conclusions drawn as a result of numerical computation are helpful in defining the nature of work of dual-power-path gearing in different load conditions and will be compared to results of stand tests of the analysed gearing.
The article presents the course of the calculations and conclusions from the analysis of a bevel gear motion transmission using FEM. The motion transmission graphs show the angular variation of the driven gear in the case of a driving pinion that rotates with a constant angular velocity. In contrary to the classical Tooth Contact Analysis, which is carried out on stiff bodies, FEM analysis includes deformations of mating gears. Thus, it brings more realistic information on dynamic behavior and noise characteristic of analyzed gear drive.
Outer space presents construction challenges that are completely different from the terrestrial environment. They should be characterized by high resilience and indefinite durability because there is no possibility of repair during exploitation. There are drives in spacecraft control systems that are necessary to move solar panels, robotic arms, and manipulators, and also to position antennas. In these devices, they have applications where harmonic drives are characterized by high kinematic accuracy but relatively low mechanical strength. The analysis presented in this study is aimed at modifying the shape of the harmonic drive to increase its durability and reliability. In this study, the most vulnerable damage element of the harmonic drive is the flexspline. The calculation was carried out using the finite element method (FEM) in the computer program ABAQUS. A standardized shape was tested as a basic model, and several other design solutions were proposed. For each of them, the mechanical strength was determined, which allowed the selection of the most preferred shape for the flexspline of the harmonic drive. The specific environmental requirements of the expectations for sand for gear used in spacecraft control systems were included in the analysis. The selected construction solutions of the flexspline allow for longer work and transfer of greater loads by the harmonic driver than the solutions currently used. The choice of harmonic driver design shape allows for failure-free and maintenance-free work in space vehicle control systems.
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