Taper rollers are extremely common on lathe spindles, they are probably the worst choice though. During use the spindle will heat up more than the supporting structure, usually cast iron or epoxy granite. Steel, cast iron and EG of optimal mixture all have similar expansion coefficients so the hotter spindle will expand more which loosens the bearings. That is not good. If the bearings are fitted the other way around then they will tighten. That is not good.
Frank mentioned how it should be done. At least two opposed, preloaded angular contact bearings at the business end and a simple radial load carrying bearing at the back. The back bearing should be allowed to move as the shaft expands, often this is a common deep groove ball bearing with a fit in its housing which allows sliding, sometimes this is loaded axially with a spring. I prefer to use a parallel roller for this task. You can have proper fits for the races but the inner race is free to float axially. This is a more expensive option than two taper rollers. It has been on my to-do list for a long time to convert my lathe to this arrangement. Maybe I should make a new headstock out of EG, it might be easier?
Another way, probably cheaper is to have two taper rollers back to back with some preload at the front and simple ball or roller bearing at the rear.
Have you seen the video of Dan Gelbert's granite high precision lathe

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