Abstract : In the internal meshing transmission of a planetary reducer with a small tooth difference, multiple pairs of small-clearance tooth surfaces are close to the theoretical meshing point. The minute deformation caused by the force on the teeth causes some tooth surfaces to come into contact and enter a meshing state. The simultaneous meshing of multiple pairs of teeth significantly improves the transmission capacity, but its mechanical calculation is a statically indeterminate problem. This paper introduces the use of the finite element analysis software COSMOSDesignSTAR to calculate the difference in load-bearing capacity between a single-tooth mesh and multiple-tooth mesh, illustrating the improvement in load-bearing capacity of a planetary reducer with a small tooth difference compared to that obtained by conventional algorithms. Keywords: Planetary reducer with small tooth difference, internal meshing, contact stress, bending stress, multiple pairs of teeth meshing, load-bearing capacity, statically indeterminate, finite element method. Introduction Compared with ordinary cylindrical gear reducers and worm gear reducers, involute planetary reducers with small tooth differences have advantages such as small size, light weight, large transmission ratio, high efficiency, large load-bearing capacity, reliable operation, and long service life. Compared with cycloidal pinwheel planetary reducers, in addition to the above advantages, they can be machined using general-purpose tools on general-purpose gear machining tools. Therefore, it has advantages such as lower cost. But what about its load-bearing capacity? This article uses the finite element method to analyze and discuss the load-bearing capacity of a two-tooth-difference planetary reducer. A small-tooth-difference planetary reducer is an internal meshing transmission. It is generally believed that its pair of meshing tooth surfaces are a convex tooth surface and a concave tooth surface, with their curvature centers on the same side of the tooth surface, the same concave direction, and a very small difference in curvature radius. Contact deformation results in a larger contact area. Therefore, the contact stress of the gear teeth is greatly reduced, and the contact strength is correspondingly increased. At the same time, the bending stress can be reduced by decreasing the tooth tip height, thereby increasing the bending strength. Furthermore, due to the small tooth difference, around the theoretical meshing point, there are multiple pairs of small-clearance tooth surfaces that are close to meshing. The small deformation caused by the force on the gear teeth makes these small clearances disappear, causing these pairs of tooth surfaces to contact each other and thus enter a meshing state. If this judgment is consistent with reality, then multiple pairs of teeth will mesh simultaneously, which obviously can greatly reduce transmission impact, making the operation smoother and the noise lower. Furthermore, when the module is the same, the transmission capacity should be significantly improved compared to ordinary external meshing cylindrical gear reducers: practical engineering applications have confirmed this judgment. A smaller module transmits greater power, which is the value of involute planetary reducers with fewer tooth differences. However, determining exactly how much the load-bearing capacity is improved by multi-tooth meshing compared to single-tooth meshing becomes crucial. As mentioned above, the increase in load-bearing capacity is mainly due to the participation of multiple pairs of teeth in meshing. How the force is distributed among each pair of teeth is a statically indeterminate problem, and an analytical solution cannot be found. Therefore, traditional algorithms can only calculate based on a single-tooth meshing. Although they fully consider factors such as tooth profile, they cannot account for the changes brought about by multi-tooth meshing, resulting in calculations that are highly conservative and fail to develop the load-bearing potential of multi-tooth meshing. This problem can be effectively solved using the finite element analysis software COSMOSDesign-STAR. This article introduces the use of the finite element method to illustrate the difference in load-bearing capacity of a two-tooth differential planetary reducer calculated based on a single-tooth meshing configuration versus a multi-tooth meshing configuration, when the maximum stress is equal. 1. Calculated basic parameters of the reducer [b]For details, please click: Calculation of the load-bearing capacity of a two-tooth differential planetary reducer[/b]