The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotational mode response is shown to be more sensitive to input torque than translational mode response. [S1050-0472(00)00403-7]
SUMMARYA method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the Bousinesq solution. Numerical examples of contacting hypoid gears are presented.
Effect of flexibility of an internal gear on the quasi-static behavior of a planetary gear set is investigated. A state-of-the-art finite elements/semi-analytical nonlinear contact mechanics formulation is employed to model a typical automotive automatic transmission planetary unit. The model considers each gear as deformable bodies and meshes them to predict loads, stresses and deformations of the gears. Actual support and spline conditions are included in the model. The rim thickness of the internal gear is varied relative to the tooth height and gear deflections and bending stresses are quantified as a function of rim thickness. Influence of rim thickness on the load sharing amongst the planets is also investigated with and without floating sun gear condition. The results are discussed in detail and guidelines regarding the design of a planetary internal gear are presented.
In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.
Vibration and debris monitoring methods are being increasingly used to detect gear tooth breakage. In this paper an alternate method of detecting gear tooth cracking is investigated. It is based on the phenomenon of acoustic emission (AE). The detectability of growing cracks using AE is established. Before this method can be used to detect crack growth in real systems, the transmissibility of these waves has to be studied. These waves have to propagate across a number of mechanical interfaces as they travel from the source to the sensor. The loss in strength of these waves at various interfaces commonly encountered in mechanical systems is studied in this paper.
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