A design to allow for "realignment" before exceeding a given bending moument is to have the bearing housing bolt with a smooth face and use springs under bolt heads. Thus when misalignment bending moument exceeds friction of the housing face, the housing slips to relieve.
If you don't want the friction, you could support the bearing with 3 radial springs
I think byrdj ideas catch the jest of my limited defined problem statement ssnh. I have incorporated 3 radial springs to allow for the shaft misalignment. The true problem is that I have a shaft with two sections that will be joined with a treaded joint. Due to the type of configuration it places four bearings needing to be concentric, which is over constraining, hence my need for two of the bearings to be allowed freedom to move in an orbital motion as a result of any misalignment.
A consideration with a spring supported bearing would be its natural frequency with respect to the shaft speeds. The friction faced bearing surport would allow the bearing to align itself as the conditions changed
If the (2 middle bearings) are going to be supported by springs soft enough to ride the misalignment, how much support can they offer? Ebe if one shaft is fully supported, how much can the nearby sprung bearing offer?
A fairly traditional approach is to eliminate 1 middle bearing and provide a radially stiff, easy to bend coupling (Disc coupling, single element gear, u-joint) at the shaft joint. That way one end of one shaft is "hung" off the fully supported second shaft. No wobble or constrained bearing fight.
Vertical multi-stage pumps often use a threaded coupling at the motor attachment. Ground shoulders or shaft ends run pretty true when butted together (but installed runout MUST be checked). The first pump bearing is still usually many shaft diameters away from the coupling.
Great stuff Guys thank you. One aspect I did not point out is both shafts are hollow allowing high pressure fluid to be pumped threw the center bore. This requires the joint to be sealed ruling out couplings.