Abstract:
Abstract: As a novel internal planetary gearing with small tooth number difference, the spider reducer has been found its wide applications in many industrial fields such as energy, mining, electricity and irrigation. Despite its successful applications for decades, the mechanical mechanism of the spider reducer has been rarely investigated. The reason for less investigations of the spider reducer may lie in two aspects. One is the complexity of the reducer's structure and the other is the property of over-constraints in the transmission. The lack of in-depth understanding of system's mechanics results in the premature fatigue of planetary bearings and severe vibrations in some application occasions. In order to obtain a fully understanding of the mechanics principle of this kind of transmission, this paper presents an elasto-static model for the spider reducer by using the method of sub-structure synthesis. With consideration for the structural features of the spider reducer, the overall transmission system is divided into three sub-systems, i.e., the spider gear sub-system, the spider shaft sub-system and the output shaft system. The static equilibrium equations of each sub-system are derived based on Newtonian theory. Since the transmission system is over constrained, some compatibilities are required. Thus, the deformation compatibility conditions for the spider reducer are then derived by analyzing the relationships between the deflections of different component. The considered deflections include those of internal gearings, planetary bearings as well as torsional deformations of spider and output shafts. With the proposed compatibility conditions, the equations of each sub-system are assembled and the global elasto-static governing equations are obtained. By solving the elasto-static governing equations, the static responses on each component in a working cycle can be simulated numerically. The static loads of internal gearings, the planetary bearings and the torques on crank shafts during one cycle are depicted. The simulation results indicate that the meshing forces of internal gearings in two parallel phases change periodically. The two phases of meshing forces share the same variation rules but there exists a 180 degree of phase angle difference. This is coincident with the structural symmetry of the spider reducer whose two parallel phases of mechanism are 180 degree configured. The fluctuations of meshing force curves are very small, which implies that the meshing procedure of the internal gearings in the spider reducer is quite stable. This is agreeable with the long service span of internal gearing in this kind of transmission. On the contrary, the simulations reveal that the load conditions on planetary bearings are quite severe. To be specific, the planetary bearings on input shaft demonstrate high load amplitudes while the planetary bearings on spider shafts come through a remarkable fluctuation during a working cycle. Both the high load amplitudes and the fierce variation shorten the service life of planetary bearings. This gives an explicit explanation for the premature fatigue of planetary bearings in application occasions. The elasto-static analysis of the spider reducer indicates that the dimensions of internal gearings and planetary bearings are open to optimization during the design stage in order to extend serve span of planetary bearings and achieve better transmission performances.