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What features prevent the drum center from moving? It is better to model the features that keep the center of the drum from moving such as three blade flexures arranged around the diameter of the drum.
Same question and suggestion for the wedge. What features allow the wedge to move only radially? It is better to model the features that allow a small motion such as two blade flexures on the wedge.
If there is a radial force on the wedge and there is a small gap between the wedge and the drum, the gap will be closed by the force. Since you know this, it would be much easier to solve if you put the wedge in initial contact with the drum.