In this study the idea of spur gear teeth with circular instead of the standard trochoidal root fillet is introduced and investigated numerically using BEM. The strength of these new teeth is studied in comparison with the standard design by discretizing the tooth boundary using isoparametric Boundary Elements. In order to facilitate the analysis the teeth are treated as non-dimensional assuming unitary loading normal to the profile at their Highest Point of Single Tooth Contact (HPSTC), so that non-dimensional stress vs. Contact ratio diagrams are plotted. The analysis demonstrates that the novel teeth exhibit higher bending strength (up to 70%) in certain cases without affecting the pitting resistance since the geometry of the load carrying involute is not changed. The circular fillet design is particularly suitable in gear with a small number of teeth (pinions) and these novels gears can replace their existing counterparts in any mechanism without any alterations. Finally the geometry of the generating tool (i.e. rack) is determined in order to be able to cut these teeth using a generating method (i.e. hobbing)
Indexing errors are a cause of significant vibration and overloading in gearboxes and require much designer attention, especially in high-speed applications. Furthermore, the continuously varying elastic deflections of the meshing teeth contribute to vibration excitation and tooth profile corrections, which are usually employed to alleviate the ill effects of these errors and further complicate the modelling of the phenomenon. Current gear dynamical simulation models either do not consider indexing errors or do so in a simplified manner.To address this problem, in this article, the exact geometry of tooth meshing is used as a starting point for a comprehensive dynamical modelling of gear systems, seamlessly incorporating the effect of pitch errors, tooth separation, degree-of-freedom coupling, and profile corrections. The resulting model is fundamentally non-linear. A single-stage spur gear reducer is then simulated dynamically using various scenarios of error distributions and profile corrections, and the overload factor is calculated. The results show that there are optimal corrections, which can reduce overload by a factor of nearly 35 per cent; however, with bigger corrections, the benefit diminishes. The sensitivity of different design solutions to manufacturing tolerances is investigated and definitive trends are recognized. Finally, a new design recommendation for profile correction is made on the basis of these findings.
Under the current standardized involute gear systems, meshing of gears of different modules is a practical impossibility. However, by performing a fresh reinterpretation of the well-established fundamental meshing principles, a more insightful form for the compatibility equations that govern involute gear tooth generation and meshing can be obtained. This article reports some first non-standard designs based on this analysis that allows gears of different modules to mesh. By the same token, standard gears can be manufactured with non-standard hobs and vice versa. Initial investigation suggests that practical benefits such as increasing the root bending strength without affecting the pitting resistance and the sliding velocity can be achieved that may justify such deviation from standard designs.
Standard 20 • spur gears are typically generated with a whole depth of 2.2-2.25 times the module. At the nominal centre distance, this leaves a radial clearance, which is in itself redundant from a functional point of view. However, the intrinsic geometry of the cutting process always results in a non-involute root profile (the trochoid), which is even more pronounced in the case of using a rounded cutter tip in order to increase the strength of the cutting edge. Larger tip radii produce stronger tooth fillets, potentially increasing the bending strength, but reducing the involute part of the tooth. Thereby, they increase the risk of interference with mating gears. This paper performs a parametric investigation of the combined effect of the cutter radius and the dedendum on the clearance and the resulting tooth bending strength using analytical calculations, computerised generation and finite element simulations to determine the exact tooth geometry in search of stronger tooth forms. Non-dimensional modelling is used to obtain results applicable to entire gear families.
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