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Ortur YRC-1 Chuck: Tube Reinforcement
Tuck a neatly laser-cut disk into a flimsy cardboard tube:

Ortur YRC-1 – cardboard tube reinforcement Put a big conical center in the tailstock:

Ortur Chuck Rotary conical center – front Whereupon the tube remains nicely tubular on both ends and aligned along the chuck axis:

Ortur YRC-1 – chucked cardboard tube Which is why you save all that scrap material …
Yes, it’s the core from a toilet paper roll, which is way cheaper than burning through tumblers / mugs / shot glasses / whatever while figuring this stuff out.