Determination of the optimum depth of relief for planetary gear reducers
DOI:
https://doi.org/10.5944/ribim.29.1.44287Keywords:
Planetary gears, Transmission error, Dynamic load, Profile reliefAbstract
In geared power transmission, load-induced tooth deformations cause an earlier start of contact and a delayed end of contact. This shows the existence of a mesh-in impact and a mesh-out push. Both contacts occur outside the pressure line and therefore between non-conjugate points of the profiles, which negatively influences the smoothness and continuity of the meshing. However, they are not both equally harmful, because the mesh-in impact involves the presence of a shock between the root of the driving tooth and the tip of the driven tooth, which causes dynamic overload, noise and vibrations. To avoid the mesh-in impact, a tip relief can be applied in the driven gear teeth, which delays the start of contact, the deeper the relief the more so. The ideal depth is the one that shifts the effective inner point of contact to the theoretical location, since smaller depths reduce, but do not eliminate, the mesh-in impact, and greater depths, although they eliminate it completely, reduce the contact interval and, therefore, the contact ratio. This poses a problem in the case of planetary gears because the ideal depth of relief –also called adjusted depth– in the planet-ring gear does not have to be the same that as in the planet-sun gear. In the case of a multiplier stage, such as those in wind turbines, the input torque is applied to the planet carrier and the planet is the driving gear in both gears, planet-ring and planet-sun, so that, as the reliefs have to be applied in the driven wheels –the ring and the sun–, they can be made with the required depth in each case. On the contrary, in planetary reducer stages, very frequent in electric vehicles with in-wheel motors, the relief has to be applied to the planet, and the depth of relief can be adjusted, at most, for one of the gears, but not for both. This work presents a study of the influence of the depth of relief of the planet in reducer stages of spur planetary gears, because of which a proposal for an optimal depth of relief is established, understood as the one that minimizes the peak-to-peak amplitude of transmission error, and therefore the induced dynamic load.
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