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I guess the displacer doesn't need lubrication whereas the power piston should?
It looks like a crude attempt at metal spinning? I made several chucks and parts over the years. Brass is quite forgiving so long as it has adequate soap and Paraffin to ease the working.As for the split I would roughen the surfaces and apply a film of Acetate cure Silicone it’s remarkably heat tolerant. Our own Robinson model uses a displacement piston that is stuffed with stainless Steel wool that serves as a regenerator. Graham.