The analysis of adaptors’ deformation and stress is an important prerequisite for the design of the adapters. This paper proposed the mathematical description and analytical method for the sponge cylinder and rubber cylinder under pressure. The analytical formulas on deformation and stress of interference fit between adapters and launchers are deduced. Also, the correctness of the analytical formula is verified by numerical simulation. Furthermore, the effect of precompression and the sponge’s thickness ratio on adapter’s deformation and stress is studied. The following results can be concluded: the results of numerical simulation are basically consistent with that of analytical formula. After installing the adapter into the launcher, the rubber layer will move inward as a whole, then the sponge layer and the rubber layer are subjected to radial and tangential compressive stress. When the precompression is smaller than 0.0075 or larger than 0.0015, the deformation and stress of adapter are approximately in proportion to precompression. If the precompression keeps constant, the deformation and stress of adapter will have extremum when the thickness ratio of sponge equals to a certain value.
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