In order to reduce the amount of calculation, the convex dentition and the spherical crown are taken separately and only half of the symmetry is used. Considering that there is an interference connection between the tooth column and the crown, the nodes on the combined surface need to be treated with an auxiliary unit. The normal load is applied at different positions of the tooth column, and the surface force calculated by the interference amount is applied to the corresponding unit. Unit selection and meshing We use 20-node and 16-node isoparametric elements. Due to the complex curve of the upper part of the tooth profile and the intense stress change at the root of the tooth column, the mesh should be dense. The division of the grid is all done automatically by the author's program. The root stress distribution law uses SAPS to calculate the root stress of the tooth column under different loads, different boundary conditions and different geometric shapes. The calculation results show that the maximum stress position is on the root surface, and the geometry of the root has a great influence on the root stress. When the local effect of the concentrated force is not considered, the maximum stress is on the surface of the tooth root, and this stress decreases as the radius of the fillet increases, and is proportional to the load arm.
The effect of interference on the root stress of the tooth column is not obvious, but it has a great influence on the fitting part. The root load radius of the tooth root is within the range of 850~4900N for the internal point of the root section, and the theoretical analysis results are larger than the test value. This is mainly due to the fact that the strain gauge is difficult to stick to the maximum stress and it only reacts to the local average stress value. However, from the finite element analysis, the experimental results are compared with the formula calculation results. In general, the difference is about 10, and there is a similar law. Therefore, the method adopted in this paper is feasible, and the result is also credible. This paper systematically analyzes the principle and strength of the spherical gear transmission, taking full advantage of the flexibility of the spherical gear transmission while taking into account its bearing capacity. It lays a theoretical foundation for the wider application of spherical gears. The method used in this paper is applicable to the strength calculation of spherical gear transmission or ellipsoidal gear transmission of other structures and materials.
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