| dc.description.abstract | Planetary gear sets can achieve higher power density levels, because of multiple parallel power paths by each planet branches. However, load sharing among planets are usually even, due to the manufacturing errors, assembly errors and deformation of parts in planetary gear sets. Therefore, load balancing mechanisms are widely used in multi-planet system. The most common load balancing mechanism is floating sun gear design. In the recent studies, simplified mathematical models are often used for analysis of load sharing in planetary gear system. The goal of the thesis is to establish an approach based on the involute gear geometry for analysis of load sharing among the planet gears, possibilities for assembly, and movable area of the sun gear.
Mesh relation for the planetary gear set is at first derived based on two-dimension involute gear geometry. The possibility to assembly of the planetary gear train under consideration of various design parameters and errors is determined according to the assembly process. The movement of the sun gear is restricted by planets in two different types, i.e. restriction by single planet with double contact tooth pairs, and restriction by double planets with single contact gear tooth pair. In order to find out the movable area of the sun gear center, maximum movable distance of the sun gear in any direction will be obtained according to both the restriction types.. The shared loading among the planets in the planetary gear train is analyzed in the study by using an analytical approach as well as a numerical method. A jumping behavior of the load sharingin the planetary gear set with a fixed sun gear is also explained in the thesis based on the change of the meshing stiffness of the contact gear tooth pair due to the change of the number of the contact tooth pair. The study also introduced object-oriented programming for anakysis to enhance the calculation efficiency.
The analysis result for the movable area of the floating sun gear center in the planetary gear train with 3 to 5 planets showed that the boundary of the movable area is a polygon and the number of the borders is twice the number of the planets. Double planets with single contact tooth pair is the most likely restriction type of the floating sun gear. Furthermore, the movable area of the floating sun gear is proportional to the backlash corresponding to the tooth thickness tolerance.
Acoording to the the analysis result of the assembly condition of the planetary gear set with three planets under consideration of tooth thickness errors, radial pinhole position errors and tangential pinhole position errors, the maximum tolerable error value for assembility is linearly proportional to the backlash.
The analysis of the load sharing in the planetary gear set under consideration of the influences of various types of errors and design parameters shows that the tangential pinhole position error is the critical influence tolerance. Second is the tooth thickness error. The radial pinhole position error has little effect on the load sharing behavior. In addition, the uneven load sharing due to a tangential pinhole position error can be compensated with installation of a planet gear on the pinhole position with specific tooth thickness. Furthermore, increased input torque is also ablbe to reduce the uneven load sharing. In case of floating sun design, the even load sharing among planets can be achieved for the planetary gear train with three planets. Similary the load sharing in the gear trains with four or five planets can be also improved, but uneven.
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