To eliminate stiffness excitation, this paper proposed an approach of design and analysis for actively modified gears with zero amplitude of loaded transmission error (ALTE). Firstly, the maximum bearing deformation of mesh cycle was obtained based on tooth contact analysis and loaded tooth contact analysis (LTCA) for predesign modified gears. Secondly, taking bearing deformations of meshing period being equal to the maximum value as the known condition, a novel equation for LTCA was developed, then compensating tooth gaps from pitch error (additional modifications) were determined by solving the equation in reverse. Thirdly, the compensating gaps characterized by equal values along instantaneous contact line of tooth were constrained according to the meshing positions, and was added to the predesigned modified pinion to produce novel modified gears with zero ALTE. The method integrated geometric analysis and mechanical analysis of tooth, and it can accurately and quickly obtain any modified gears with zero ALTE. The results show that shape and size determined by the compensating gaps surface are related to the locations of tooth, the predesign modification and load. On the one hand, when the differences of predesigned modification is small, the rule of compensation modification curve is basically opposite to the ALTE of predesigned tooth modification, that is, the larger the bearing deformation is, the smaller the compensation gaps is. Then the overall compensation modification is also small due to only compensating the bearing deformation differences actually. On the other hand, when the differences of the predesigned modification is large, the overall compensation modification is also large due to compensating the differences of both bearing deformation and predesigned modification at the meshing position. Besides, the tooth contact pattern is not changed with the compensation modification and ALTE are reduced on wider loads for gears with zero ALTE based on preset topology modification. Appropriate locations and predesign modifications make the additional modification well integrate into the predesigned and modified surface, so as to obtain the machinable modified pinion with zeros ALTE. It provides a theoretical reference for design and analysis of tooth with vibration reduction and high performances.

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.