Bearing Reaction

## Question:

Hello!

I have a large shaft with a flywheel-type disc mounted at its centre point. The shaft runs inside two bearings at its extremities. I believe the assembly is statically and dynamically balanced (as far as my primitive means allow). When I spin the wheel it runs down and eventually stops (as you would hope!); as it it reaches its point of rest, it stops, and rotates backwards approximately half a degree and then stops absolutely. Why would it do this? People have suggested that it is not balanced 100%, but I really don't think this is it - I wondered about reactive forces within the assemlby, which might cause this brief reversal...? But then again...

Any thoughts?

You do not mention whether the shaft is horizontal or whether the bearings are journal, ball or roller. Assuming a horizontal shaft and simple journal bearings, here are some thoughts. If these assumptions are bogus, please let me know.

Imbalance is one possibility. As the assembly coasts to a stop its kinetic energy will at some point be too low to carry the heavy spot over the top. If this were the case we might expect the counter rotation to be up to half a revolution and depending on the damping supplied by the bearing friction, there might be some oscillations rather than a single retrograde motion.

From your description I would sooner suspect bearing reaction. You might think of it this way.

A shaft sitting at rest in horizontal bearings is only in contact at the very bottom since the shaft outer diameter is necessarily smaller than the journal inner diameter. When the shaft begins to turn it rolls part way up the inner surface of the journal, until the component of shaft weight along the inner surface of the journal balances the force of friction in the bearing. The turning shaft then rests not at the bottom of the journal but a little ways up that side on which the shaft surface is descending.

Since the force of friction is pretty much constant as long as the shaft is moving at all, and the weight of the rotating assembly and the geometry of the bearing are fixed, this point of contact stays up the wall of the journal until all motion stops. Then the shaft will roll back down the journal wall.

The half degree of so strikes me as reasonable given that the bearing friction is probably made as low as practical so there would be minimal climbing of the journal wall to find the rolling equilibrium point of contact.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ