It looks like you have 1/2 symmetry for this model. Is the model fully axisymmetric? If so, you should do a 2D axisymmetric analysis, it will be much faster to get an accurate result.
If it is axisymmetric, but you want to stay in 3D, take another slice at 90 degrees and do a 1/4 symmetry model. That way you can put symmetry boundary conditions on both planes which will constrain 5 DOF on each body. All you need to prevent a pivot error is to constrain one vertex (or node) in one direction, the axis direction, on each body.
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