"For the normal working load, the radial reaction force at four-bearing assembly is not over 2000lb ".
- How far off the spindle nose and first bearing is the load applied?
- The fatigue limit (infinite life with excellent cleanliness) for a garden variety 6222 is under 1000 lbs (SKF)or 3000 lbs (FAG). The SKF N222 is good for over 9000 lbs, So as far as life is concerned, you don't need all those bearings.
"As regarding the induced load, it’s a tough part. Probably it’s caused by the different bearing clearances. Is there any special method to figure this out? or just using beam theory?"
- The induced load results as soon as you have a staticially indeterminate problem, and results from stuff like bearing stiffness, bearing line of action, bearing clearance and bearing, shaft, and housing concentricity and eccentricity, which are tough enough to think about, and danged near impossible to really quantify. I'd start by measuring shaft deflection at the spindle nose at 100/200/300/400/500 lb radial load
With a short tool Shaft stiffness is hard to add with more bearings. An approximate weighting is spindle stiffness is 70% shaft/30% bearing stiffness. With an overhung or long tool the shaft stiffness (diameter) is all that will save me.