Well, i made it at work under 3 microns, as you can see in my latest video how it is made. At home i have a cheap copy indicator that is called miluloyo, spindle is not tightened properly and bearings are crap. Please comment in english because i have to translate cyrilic and google translate is not the best.
It's short because i designed it to be sandwitched between two bearings (which was a bad design) and if it was longer, i would not be able to grind it because of a placement of a dresser. But i'm planning to build another spindle with better design.
Depends on what are you planning to do but i think that you can both. At company where i work, we use 20MnCr5 because it has a great properties for surface hardening and we produce cnc toolholders and pull studs. 4140 is medium hardenability general purpose high tensile steel and 4340 has beter properties than 4140.
Не самый лучший выбор схемы подшипников для подобного шпинделя. Быстроходность слабая, по нагрузке они избыточны. А результат в 1.5 сотки боя вообще никуда не годится. Хотя полагаю, что в таком биении не только подшипник виноват.