If I understood your question correctly, you already have vibration spectra from a running machine and the machine is undergoing abnormal radial/axial stresses on the radial bearings (or at least you suspect). You are trying to find a sign in the vibration spectra that will tell you if the load is excessive in the radial or axial direction. Correct?
This is a generic question. I assume you'll receive only generic comments.
If the bearings are normal journal bearings, it's difficult to relate radial vibration data to axial load on the bearing. Radial loads on journal bearings can sometimes be detected by shaft average centerline plots.
If the bearings are rolling element bearings, they can take static loads (e.g. misalignment) or dynamic loads (e.g. unbalance) in both radial and axial directions. Generally speaking, the fundamental frequency and its first harmonics are related loads. If the spectra you have do not show high amplitudes at 1X, 2X, or 3X, then most likely there is no excessive load.
But I could be totally wrong as in many cases in the past.
Regards- Ali M. Al-Shurafa