Abstract
Techniques and software tools, which were recently introduced by the authors, allowed for effi-cient automatic generation of 3D gear flanks and selective meshing of the gears of a simple planetary gear system with backlash and manufacturing imperfections. Friction of the meshing gear flanks was neglected. First results were promising and showed that even in geometrically perfect planetary gear systems the torque distribution is not uniform. It was further verified that pitch errors have a strong impact on the load distri-bution and that a self-aligning sun gear significantly enhances the torque distribution among the planets. In the current study, the procedure mentioned above is enhanced in several aspects. First, the tooth friction is considered. The friction coefficient is assumed constant along the path of contact; however different values for the sun-planet and planet-ring gear mesh may be given to account for the different contact conditions. Second, deviations are generated between given limits in a stochastic way. This feature significantly reduces the time needed to setup a model. Third, the entire analysis procedure is further automated by extensively employing Python scripting, enabling the solution of successive snapshots in much shorter time. Besides the torque distribution among the planets, the mesh load factor Kγ and the deformation of the teeth, the planet bearing load is also shown.
Highlights
Planetary gearboxes are widely used in many applications like robotics, automotive, aircraft engines and wind turbines
Load distribution depends on manufacturing and assembly errors, deformation and members support
The sun rotates around a fixed axis. This model corresponds to a sun gear manufactured on the input shaft, which is supported by two bearings
Summary
Planetary gearboxes are widely used in many applications like robotics, automotive, aircraft engines and wind turbines. Even if gears and carrier had perfect geometry, the load would not distribute among the planets, because the meshing stiffness varies along the path of contact. The impact of the sun’s floating capability on the load distribution has been already investigated by the authors [2]. By considering the pitch error of just one active flank of the sun, the resulting load distribution was even more non-uniform. A simulation, considering one floating planetary gear, confirmed the experimental results with an accuracy better than than 10% [5]. The impact of many parameters, such as input torque, number of planets, pin diameter and bearing clearance, on the load sharing was presented. Nejad et al [7] among others investigated numerically and experimentally the effects of a floating sun gear in a wind turbine’s planetary gearbox using a multi-body approach. The friction on the mating gear flanks was taken into account by assuming a constant friction coefficient
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