My Chinese drilling machine also has a taper, and the chuck has now giving up. All of my stock of Jacobs chucks have threaded, straight throats….so a careful set up to machine a taper in one is now called for……just need to time to get down to it between all the other jobs.
Jacobs chucks in the large/medium size are easily available for not very much at carboots and on ebay etc……they usually go for about £5……..roughly the same as for a NEW Chinese chuck, which are rubbish, by the way! My Chinese drilling mach. was a fantasic buy from Aldi annd cost £32 (3 pulley multispeed 16mmcapacity700watts) I was told at the time that I had wasted my money but for general (and some accurate stuff too) drilling it has been excellent for the last 5 years!….so, although the chuck has given up now it does not owe me much if anything!…….Only one minor modification has been neccessary(no lube/bearing in idler pulley)