Abstract
This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute–involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 + 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies’ flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.
Highlights
Nowadays, there is a growing demand in the development of more reliable transmission systems, with higher requirements of torque, speed and compactness
There are a great number of models available in the literature that, using a similar approach, obtain the parametric excitation characteristic of gear transmissions by time-varying values of mesh stiffness and/or loaded transmission error
This model feature provides good results, but the approach applied to calculate the local deformations introduces a step in the transition between different contact types, due to the change in the curvature radii
Summary
There is a growing demand in the development of more reliable transmission systems, with higher requirements of torque, speed and compactness. The objective is to construct a planetary transmission model capable of obtaining a sufficient degree of accuracy in the simulated meshing stiffness, without impairing the dynamic modeling capabilities With this aim, analytical solutions are hybridized with finite element models in order to compute the contact forces, making unnecessary the use of mesh stiffness waveform approximations or static transmission error excitation assumptions. Especially key modeling aspects (such as geometric and contact forces calculation) are described in great detail, with the aim to allow for reproducibility of results and implementation by fellow researchers For this reason and for the sake of shortness, only quasi-static results are presented, the model is conceived to be part of a complete dynamic planetary transmission model. Regarding the contact point location algorithm, the model must be capable of simulating the behavior of planetary transmissions with any number of planets, allowing the displacement of gear centers
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