Subject: Tire Beads

 
Paul was telling us about tire beads, free moving weights  inside a tire that continuously seek the location which counterweights a tire imbalance.
I wondered why they helped as opposed to making matters worse.

So here goes.

First I want to frame the question.  Wide low profile tires and wheels entail three dimensional complications which we should leave out.  Also, the beads are recognized as not solving "lateral imbalance".
Also I think we should exclude out-of-round tires.

So, if a tire is geometrically circular and properly centered in its axle but is out of balance so that a segment has greater mass than other geometrically equal segments, do the beads self-locate so as to correct the imbalance?

Yes.

The beads feel the so-called centrifugal force in the rotating tire and, if they can, they will role to the place farthest from the Axis of rotation (like rolling downhill).  We have said, however, that the tire is properly round and centered, so, at first glance, we can see no preferred collection point for the beads.  Each spot around the tire is equidistant from the axle.

Now, if the axle was hard fixed in a bearing with no chance of movement that would end the discussion.  The bearing would be forced to handle the imbalance and the beads would do nothing significant.

But our vehicle has a suspension system and the axle moves as required.  As the vehicle speeds up, the force of the imbalance increases.  This is the tire's increasing preference to rotate around its own centre of mass, and, because the tire is out of balance, its centre of mass is not exactly at the centre of the axle.

At sufficiently high speed, the axis of rotation moves away from the axle centre towards the centre of the rotating mass.

Obviously, the centre of mass is on the heavy side of the wheel with respect to the centre of the axle.

So we have our whole wheel and tire rotating around a spot that is slightly off the axle centre, and the part that is farthest away from the new axis of rotation  is on the opposite side from the overweight sector.  But this is precisely where the beads will roll...  to the spot farthest from the axis of rotation.

To repeat: it is because the centre of mass becomes the axis of rotation that the points around the tire are no longer equidistant from the axis of rotation.

So we have a positive result.