In article ,
says...
In article ,
Ned Simmons wrote:

In article ,
says...
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,

It's not. Show me a reference to a blowgun that produces a supersonic
air jet with shop air and I'll reconsider.

I didn't say supersonic, I said sonic (as the upper limit). The airflow
chokes in the orifice, being limited to the speed of sound, so this is
the upper limit (unless one has a nozzle that looks like the back end of
a rocket engine, with an expansion bell).


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

Okay, since this keeps coming up, despite what seems common sense to me,
I set up a test myself. That's a 6204 bearing with the seals removed,
the grease washed out, and relubed with a few drops of light spindle
oil. There's a paint mark on the race and the ball cage.

It appears to have eight balls. What's the OD?

47mm - 1.85"



http://www.suscom-maine.net/~nsimmon.../Bearing01.JPG
http://www.suscom-maine.net/~nsimmon.../Bearing02.JPG

I see one problem in the photos: That long thin copper tube will not
achieve anything like the airspeed that a proper nozzle will achieve.

I would suggest using a piece of 3/8" tubing with a machined brass
nozzle hard soldered into one end. The brass nozzle would have a
60-degree (included angle) cone inside, going from 3/8" to 0.014"
diameter at the face.

I would put around the bearing a piece of heavy metal pipe lined on the
inside with wooden staves, to stop the shrapnel. Even if you believe
that the bearing won't burst.


I have no interest in exploding a bearing g. I just wanted to get it
spinning fast enough to run the tests described.


I spun the bearing up and measured the difference between the speed of
the ball cage and the outer race at several speeds between 1400 and 5500
RPM. The difference in the angular velocity in all cases was 100~200RPM,
i.e., the race was going 5-10% faster than the balls. Exactly as you'd
expect in an unloaded bearing with internal clearance where the balls
are free to slip relative to the races. As I've said at least twice
before, this clearance will only increase with speed.

These are very low rotational speeds. As the speed increases, won't
centrifugal force pin the balls against the inside of the outer race,
reducing or eliminating slippage?

Even at these speeds I don't imagine there's much slippage between the
balls and the outer race - clearly there isn't. Where the balls *are*
slipping is relative to the inner race, minimizing any speedup due to
planetary action.



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.

I checked this as well just to make sure the assumption that the
frequency of the sound from the bearing does in fact correspond to the
ball passing frequency. I got my teenage son, who's involved in
composing synthesized music, to set up his laptop with an FFT to monitor
the bearing siren tone. Agreement was within a few percent, probably as
good as could be expected with me getting a strobe fix while asking him
to read the frequency.

Good. The "siren" theory is confirmed.

So, how do we explain the reports that the tone went ultrasonic just
before the bearing exploded? With eight balls, this implies 20000/8=
2,500 rps, or 150,000 rpm, a factor faster than the 20,000 rpm discussed
here.

I can't. Maybe Eric's hearing is worse than he thinks. I wouldn't know
how low my upper limit is in one ear (starts rolling off at a few kHz)
if I didn't fail the hearing test in grammar school every year.


Also unexplained is the essentially perfect symmetry of the explosions.

As I said before, it's easier to explain the lack of serious injuries if
the available energy is much lower. Perhaps the bearings that exploded
with bad consequences has selectively thinned the reporters g.



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.

Because it's well known that, for the sort of bearing we're talking
about, speeds in the few tens of thousands of RPMs are the lubrication
limit for properly mounted bearings with elaborate mist lube systems.
It's no surprise at all that a loose bearing that's just had all its
lubrication removed would fail at somewhat higher speeds.

While I don't doubt that being run bare at such high speeds chews the
bearing up pretty fast, the guy I was mentioning also used the long thin
air tube, and so didn't achieve full airspeed.

I agree that higher speeds than 20 KRPM should be attainable, but the
deterioration will limit the speed, and that may be why he couldn't go
faster. As the bearing gets beat up it'll take more power to keep it
spinning at a given rate.

Ned Simmons