On Mon, 17 Apr 2006 22:05:57 -0400, Joseph Gwinn
wrote:

Machinery Handbook has long had a section of flywheels. In the 20th
edition, on page 346, states that all that matters is surface speed at
the periphery, and the tensile strength of the steel, and gives a
formula: V=Sqrt[10*s], where V is surface speed in feet per second, and
s is tensile strength in pounds per square inch.

Let us assume that s= 300,000 psi, the cited strength of ball bearing
race steel. Sqrt[10*300000]= 1732 fps.

A bearing 1.75 inches in diameter will have a circumference of
(1.75)(3.1416)/12= 0.4561 feet, so 1732 fps implies 3,781 rps, or
226,832 rpm.

The speed of sound is about 300 meters per second at sea level, or about
900 feet per second, so the surface speed of the outer race is 1732/900=
1.92 times the speed of sound at sea level.

If the airjet is at the speed of sound, and is impinging on the balls,
the outer race will go twice the speed of sound.

If the bearing has ten balls, the siren tone will be at 3,781*10= 37,810
Hz, well into the ultrasonic, as people have observed.

The guy that did the experiment showing a max speed of ~20,000 rpm for
whatever reason did not achieve full speed, as 20,000 rpm isn't nearly
enough, and yet people have no problem causing bearings to burst from
overspeed.

Basically, it all fits together. Then it bursts.

Joe Gwinn
I'd love to use a high speed camera to take a picture of the burst. I
wonder if a light beam could be used for this. I'm picturing (sp?) 3
mirrors, a laser pointer, and a photodetector of some sort to trigger
the shutter. Maybe use a very bright halogen light to illuminate the
area. Use the mirrors to make a box shaped area with the laser. Maybe
use more than three mirrors to make a cube shaped area. I guess if the
bearings are exploding at 25000 rpm then if my math is right the
pieces will be moving at about 218 feet per second. With a 1/1000
shutter speed it looks like the parts would travel about 2.6 inches.
Maybe a better solution is to leave the shutter open and use a
flashlamp instead. Hmm.
ERS