Loaded Tooth Contact Analysis for Double-Helical Planetary Gear Sets with Floating Components

Considering coupling characteristics of forces and contact gaps of tooth between planet gear pairs for double-helical planetary gears sets (DHPG) with one set planet gears whose free axial movement is restricted by sun gear and ring gear, this paper proposed a numerical method of loaded tooth contact analysis (LTCA) for DHPG, which provides theoretical references of tooth design and performance analysis for the important application of power split and convergence double helical gears. Firstly, based on the meshing theory, finite element method and optimization method, it established the equations of the deformation coordination, the balance of the meshing total force, and the forces balance of the radial and axial floating components. Secondly, precise geometric and mechanical characteristics of left and right tooth of each inner and outer gear pair were integrated closely, which can better reflect the mutual coupling effect of the distribution force system of gear pairs. Finally, load distribution, bearing deformations, load sharing coefficients and floating displacements of each gear pair were obtained quickly based the LTCA with finite element numerical calculation once. The result show that Radial floating of the sun and ring gear is contributed to load sharing of the planet gears, while axial free floating of planet gear is contributed to load sharing of left and right tooth of planet gears. In case of opposite axial forces on both tooth flank of planet gear without floating, namely overall axial force of the planet gear being greatly offset, the axial floating displacements are a little for planet gear with floating, so the load sharing of left and right tooth is improved a little. Conversely, in case of axial forces from the same direction on both tooth flank of planet gear without floating, the axial floating displacements are much for planet gear with floating, and the load sharing of left and right tooth is improved significantly. Besides, both the amplitude and mean value of loaded transmission are reduced, which are contribute to improving dynamic performances of DHPG with floating components. Furthermore, the geometric transmission error, load sharing coefficient and axial force of the inner gear pair are basically the same as the outer gear pair. It is the key to ensure the free axial movement of the planet gear based on structure to improve the uneven loads sharing between left and right teeth for DHPG.