Finally I managed to remove the chuck from my lathe. The screws were in very bad shape. I want to use some kind of collet, preferably ER type, to avoid the lack of repeatability of the 3 jaw chuck. I discovered that is had an MT5 spindle. I measured the runout on different positions on the internal taper. To my surprise the error is very small. I think it is +/- 1µm! There is some wear on the bed and I was expecting the spindle to also have some issues.
I have an ER32 MT5 collet from my milling machine. But it is an no-name AliExpress style. When I put it on the spindle the concentricity error on the collet taper jumped to +/- 10µm. I suppose there must be better holders. What are some good brands?
Until a few days ago I was looking for a small lathe to have more precision on small parts. But now I’m thinking that if I could preserve the small runout of this lathe down to the collet holder then it would make no sense to buy another one. So I have a decent (I think) budget for a good holder.