The magnitude value of your loads can certainly affect convergence. Small loads are generally easier to converge. Mesh size can certainly affect convergence also. A minimum time step that would only allow 50 total substeps is not much in a model that's having problems converging. I would only have such settings in a model that runs easily. With highly distorted elements, the model probably has some ill conditioning, and small time steps can somtimes overcome this, but there are probably some more core problems in the model. It may be material properties. It may be connections. The Newton Rapshon residuals help show the problem locations. Transient structural analysis can have a hard time running when there are significant forces/accelerations in small gaps, so that parts "chatter." You usually need to add some damping either globally, or more locally through material definition or damping on a spring or revolute joint.
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