The abstract diagram of the cogwheel split torque drive is shown in Figure 1. The transmission direction shown in Figure 1 is the ideal state, which is also the state that the system needs to reach in normal operation. When the system parameters such as error, backlash and external load of tail transmission gear change, the transmission direction may also change. For the transmission direction shown in Figure 1, the problem of load sharing in the system exists in two places: the first place: the problem of load sharing of the upper and lower gears at the input gear; the second place: the problem of load sharing between the idler gear 3 and the idler gear 4 when the power of the lower gear is transmitted back.
In the ideal state, the power flow direction of the gear on the same shaft surface is shown in Figure 2. In Figure 2, the white arrow shows the upper power transmission path; the gray arrow shows the lower power transmission path; KT is the average meshing stiffness of the orthogonal straight face gear pair; KZ is the axial stiffness of the flange where the face gear and the cylindrical gear mesh; k1-k5 are the radial support stiffness of gear 1-5; K6 and K7 are the axial support stiffness of gear 6 and gear 7 respectively (for the sake of clarity, see Fig S1-S7 are the support deformation of gears 1-7, e u1-e U5 are the tooth side clearance of gears 1-5 meshing with the upper end face gear, e l1-e L5 is the tooth side clearance between gear 1-5 and gear 1-5; lz1-lz5 is the axial deformation of the flange where gear 1-5 is meshed with gear 1-5; uz1-uz5 is the axial deformation of the flange where gear 1-5 is meshed with gear 1-5; L1-L5 is the meshing deformation of gear 1-5 and gear at lower end along the meshing line; u1-u5 is the meshing deformation of gear 1-5 and gear at upper end The meshing deformation of the wheel along the direction of the meshing line.
When loading, the system components produce elastic deformation and rigid body displacement of the wheel body. As shown in Figure 4, the engagement of the two input gears with the upper / lower face gears is considered to be parallel, and the engagement of the idler gear, the tail gear and the upper / lower face gear is considered to be parallel. Neglecting the coupling relationship between the upper and lower branches, there is one meshing deformation and backlash in the upper power transmission path, and one axial deformation of the face gear body. In the lower power transmission path, there are three meshing deformations and backlash, and three axial deformations of face gear body. Obviously, the lower power transfer path is longer than the upper power transfer path, and the upper and lower power transfer paths are asymmetric.
In order to more accurately explain the mechanism of the uneven load of the cogwheel transmission, the concepts of equivalent displacement and equivalent stiffness are defined by projecting the deformation and stiffness of the components of each parallel branch along the direction of the engagement line. In this paper, it is agreed that the meshing deformation of each meshing position is positive in the direction of power transmission as shown in Figure 4; the axial deformation of each gear support and face gear flange is positive in the vertical direction, and the gear support ignores the deformation in the horizontal direction. The following assumptions are made:
(1) For the upper and lower branches, the parameters of input gear 1 and input gear 2 are identical, and their deformation and stiffness are in parallel.
(2) There is no external load on the tail gear, and the idler gear and the tail gear are identical.
Based on the above assumption, the equivalent displacements of the upper and lower branches are defined as
Where α is the angle between the engagement line and the horizontal plane.
The equivalent stiffness of the upper and lower branches is
Therefore, the meshing forces Fu and fl of the two branches are respectively
The load transmitted by the two branches is represented by the meshing force, and the ratio of the load transmitted by the two branches is obtained
In general, unless the backlash, meshing stiffness, support stiffness and the axial stiffness of the face gear rim in the system are specially designed to make δ UKU = δ lkl, the ratio ζ of the load transmitted by the upper and lower branches is not equal to 1. Based on the above analysis, it can be seen that the load of the two power transmission paths is not uniform.