A simple, stiff, statically and dynamically stable linear oscillator incorporating a negative stiffness element is used as a template to provide a generic theoretical basis for a novel vibration damping and isolation concept. This oscillator is designed to present the same overall static stiffness, the same mass and to use the same damping element as a reference classical linear SDoF oscillator. Thus, no increase of the structure mass or the viscous damping is needed, as in the case of a traditional linear isolator, no decrease of the overall structure stiffness is required as in the case of 'zero-stiffness' oscillators with embedded negative stiffness elements. The difference from these two templates consists entirely in the proper redistribution and reallocation of the stiffness and the damping elements of the system. Once such an oscillator is optimally designed, it is shown to exhibit an extraordinary apparent damping ratio, which is even several orders of magnitude higher than that of the original SDoF system, especially in cases where the original damping of the SDoF system is extremely low. This extraordinary damping behavior is a result of the phase difference between the positive and the negative stiffness elastic forces, which is in turn a consequence of the proper redistribution of the stiffness and the damping elements. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the excitation forces. Consequently, a resonance phenomenon, which is inherent in the original linear SDoF system, cannot emerge in the proposed oscillator. The optimal parameter selection for the design of the negative stiffness oscillator is discussed. To further exhibit the advantages that such a design can generate, the suggested oscillator is implemented within a periodic acoustic metamaterial structure, inducing a radical increase in the damping of the propagating acoustic waves. The concept may find numerous technological applications, either as traditional vibration isolators, or within advanced composite materials and metamaterials.

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)

No abstract

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.

No abstract

No abstract

No abstract