针对单排人字行星齿轮的轴向自由窜动受太阳轮与齿圈限制及其齿面接触间隙、力的耦合特点，提出考虑构件浮动的齿面承载接触分析数值方法，为重要应用场合人字齿功率分支系统的齿面设计、分析提供理论参考。该方法以啮合理论、有限元及优化方法为基础，建立内、外齿轮副瞬时啮合齿对的变形协调、啮合总力平衡、构件径向和轴向浮动下行星轮的力学平衡等方程；将各齿轮副左、右齿面的精确几何与力学特性紧密融合，更能够反映齿面分布力系的相互耦合作用，仅需一次有限元数值计算可快速获得齿面载荷、承载变形、浮动位移和均载系数等。结果表明：中心轮的径向浮动保证行星轮之间载荷均匀，而行星轮左、右齿面的均载性与其轴向自由窜动位移相关，当行星轮轴向浮动前的内与外啮合副轴向力方向相反即行星轮整体轴向力被抵消大部分时，则浮动后的行星轮的轴向窜动位移较小，其左、右齿面均载性能无大的改善；反之，当行星轮轴向浮动前的两齿侧轴向力方向相同时，则其浮动后的轴向窜动位移相对较大，左与右齿面均载性有较大改善。浮动后的承载传动误差幅值及均值减小，且各内、外齿轮副的几何传误差或均载系数或轴向力数值规律基本相同。从结构上保证行星轮的轴向自由窜动是改善人字齿行星传动系左、右齿面偏载的关键。

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.