Something here might work...

http://www.directindustry.com/cat/detection-measurement-position-displacement/incremental-rotary-encoders-AG-1311.html

I am not aware of any equipment that would be permanently installed that would provide real time data of shaft float in the axial plane. However a good millwright should be able to make a one-time measurement while the motor is running through various means.

I suspect you are only trying to figure out just how far the shaft is moving while the motor is running for troubleshooting purposes, in an effort to solve another problem. A motor on ball bearings shouldn't have any axial float, at least not any that would be detectable or that would cause a problem. Sleeve bearing motors that are properly aligned and coupled also should not have any axial float when running. Sometimes failures of the driven equipment can cause axial float of a sleeve bearing motor shaft.

The simplest method for determining whether a shaft is moving or not is to use a strobe light. Additional preparations can be made to enhance the effect of the strobe, such as bluing and marking the shaft with a scribe.

I'd use a vibration sensor. You'll need to establish some criteria to help determine the amount of float.

Shoot the non drive end of the motor shaft with a laser sensor while the motor is running and during load changes.

I am not aware of any equipment that would be permanently installed that would provide real time data of shaft float in the axial plane.

har restoration california

A displacement/proximity probe could be used, but you need something to measure against, like a collar or something equivalent on the rotor. One such probe is made by GE - Bently Nevada, model 3300xl proximity probe. I'm sure there are other cheaper brands out there though