SIM: How to reach mesh convergence with bonded Multi-component arrangement

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Hi everybody,
I am fairly amazed by the usability of the Simulation environment. However, I'm really stuck trying to reach mesh convergence and gaining trust in the results of my linear static analyses.
1. Adaptive mesh refinement doesnt converge, probably because it gets stuck on refining areas with singularities. So I am trying to do my own mesh convergence study. Editing geometrical features such as fillets on every edge of the cylinder doesnt change that.
2. The function "Scale mesh size per part" does not seem to work. All components (cylinder,arms,sandwich layers) are meshed with the same size which is too coarse for the cylinder (you can see it in the attached picture).
Any possible reasons for that? I have defined every one as a own component. Insert and sandwich fit perfectly together (as a result of a boolean cutout) and are using bonded contact (since seperation doesnt converge anyways). In another variant without arms (based on the same model) the mesh is much finer on the cylinder than on the sandwich faces.
3. General methodology:
I apply a out-of-plane pullout force on a cylindrical insert with arms that is fit into a three-layer sandwich (mid layer is hidden)
I am looking at the influence of the number of arms on the "pullout resistance" and the stress concentrations in the sandwich (do they conform to the safety margins or are they gonna get destroyed).
I try to compare pullout resistance between models by the smallness of the theoretical displacement. Could that be a valid indicator? If not, any ideas?
Glad for any help or feedback!
Jonas