a b s t r a c tConducting a further analysis on loading sharing among compound planetary gear system in wind turbine gearbox, and making a meshing error analysis on the eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of wind turbine gearbox respectively. In view of the floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of all gears, this paper establishes a refined mathematical model of two-stage power split loading sharing coefficient calculation in consideration of multiple errors. Also obtains the regular curves of the load sharing coefficient and floating orbits of center gears, and conducts a load sharing coefficient test experiment of compound planetary gear system to verify the research results, which can provide scientific theory evidence for proper tolerance distribution and control in design and process. Compound planetary gear system is widely used in the field of wind turbine gearbox, aeronautics and other special precision transmission system. The RENK and SANY company adopts compound planetary gear system used in its wind turbine as main gearbox. Compound planetary gear system uses multiple double planet gear with fixed axes for load sharing. Planet gear does not revolve but rotate, featured in power split, high transmission power, and one-side force bearing. Compound planetary gear system can avoid simultaneous mesh with sun gear and annular gear, instead breaking it down into two stages of external gearing and internal gearing, which can overcome traditional planetary gear transmission's bearing of alternating load, intermittent lubrication between planetary gears and bearings, and centrifugal forces caused by the rotation of planet carrier. The wind turbine gearbox using two-stage and fixed axes gear train with unilateral mesh brings greatly improved strength, stiffness, working life as well as reliability of the system. Scholars from both home and abroad have been constantly exploring and studying planetary gear system load sharing behaviors, and the research findings are as follows. Hidaka T et al. studied the relationship between error and load-sharing in planetary gear transmission [1]; Ma et al. probed into the effects of gear errors on planetary transmission [2]; Krantz et al. discussed the characteristics of load sharing of power-split transmission [3,4]; Kahraman focused on the characteristics of load sharing of planetary gear transmission from the perspective of statics [5e10]; Singh et al. established the analysis model on the characteristics of load sharing of planetary transmission [11,12]; Carlos et al. elaborated on the solutions to load distribution on gear teeth [13]; Zhu Rupeng et al. delved into the characteristics of load sharing of planetary and Encased Differential Herringbone Train transmission systems from the perspective of statics [14,15]; Fang zongde et al. studied the load-sharing characteristics of planetary and two-way power-split gear system [16,17]; Mo Shuai et al. devel...
The load sharing characteristics of the herringbone planetary transmission system are a key indicator for evaluating the bearing stability and reliability of each planet gear in the transmission system. The value of the load sharing coefficient is closely related to the manufacturing error and the assembly error in gear processing and assembly process. Therefore, it is indispensable to study the influence mechanism of these errors on the load sharing characteristics of the transmission system. Nevertheless, researches on the multi-coupling transmission error to the load sharing characteristics of herringbone planetary transmission system did not receive enough attention, but much of the single errors. Based on the centralized parameters theory and the Lagrange method, this research establishes a dynamic model for herringbone planetary transmission system and creatively proposes a study of multi-coupling error which consists of eccentric error, tooth profile error, stagger angle and assembly error. This work shows that the changing regulation of the load sharing characteristics with any one of the above errors is different. However, the load sharing characteristics become worse with the increase of multi-coupling error, in which the eccentric error plays a main role. Therefore, the error control should focus on eccentric error.
Compared with the conventional gear, the asymmetric gear has better root bending stress and tooth contact stress. Taking a pair of asymmetric involute spur gears as the research object, a model of asymmetric gear considering the influence of friction and shear stress on root bending stress is established. Take the upper boundary point of single tooth meshing area as example, the formula for calculating root bending stress of asymmetric gear is deduced under friction, get the rule of root bending stress without neglecting the friction force and the shear stress by MATLAB. At the same time, we design the plane finite element model of conventional gear (20°/20°) and asymmetric gear (20°/35°) by using APDL. The upper and lower boundary points of the double tooth meshing area, the upper and lower boundary points of the single tooth meshing area, the meshing node are systematically studied, get the change rules of root bending stress in the meshing process under the condition that the friction force cannot be ignored.
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