A vibration specification of 2 mm/sec can be translated into acceleration and displacement if it is at a single frequency. This is only rarely the case.
A simplified model of a simple rotating machine, such as a simple hydro turbine is as follows:
A lumped mass representing the rotor
A spring representing the shaft
A spring representing the bearing
A lumped mass representing the bearing housing
A spring representing the machine frame
A lumped mass representing the machine frame
A spring representing the machine foundation
Vibration measurements are typically made on bearing housings, and sometimes on machine frames. Given all of the springs and masses in a simplified model, calculating bearing forces from a measurement made on the bearing housing is only rarely possible.
If you have an unusually simple machine where all stiffnesses are "large", and there is a known unbalance, then bearing forces can be calculated from the unbalance moment and speed. This would be the case in, for example, a one cylinder engine or reciprocating air compressor.
The real world solution is to do a two plane dynamic balance, then calculate the hydrodynamic forces. If it is properly balanced, the unbalance forces will be small compared to the hydrodynamic forces. Note that hydrodynamic forces can vary at the blade passing frequency, which is a cause of vibration.
