# The bearing problem?

1. Nov 1, 2014

### David Carroll

I remember daydreaming one day (is that redundant?), imagining that I'm some technician in a cylinder bearing factory. At some point, I'm given a hollow metal cylinder of some given cross-sectional diameter. Next the foreman gives me a solid metal cylinder with a smaller diameter. This solid metal cylinder fits inside the hollow metal cylinder. The foreman then gives me the task of finding other solid metal cylinders such that when the first solid metal cylinder is fitted exactly in the center of the hollow one, the other solid metal cylinders all of which a diameter equal with one another must all fit around the center one with an exact fit.

The problem is: with a given initial solid metal cylinder, how do I know if there is even a solution to an integer number of other solid metal cylinders to fit around it all inside the hollow metal cylinder?

Is there a general way of solving this problem?

2. Nov 1, 2014

### Dr.D

Sounds like you are describing a roller bearing. The way you do it is that you don't try to completely fill the space. Rather, the bearing elements are spaced around the circumference with gaps between them. Then a spacer ring is introduced that maintains the spaces between the rollers.

3. Nov 2, 2014

### Stephen Tashi

Maybe you mean "wall thickness" instead of "diameter" ?