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

Joseph Gwinn wrote:

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.

Think of rotation as the average motion and resonant acoustic vibration
as the instantaneous motion. The stress from the maximum vibration
excursion can be much greater than that from the rotation.

--
Fred R
"It doesn't really take all kinds; there just *are* all kinds".
Drop TROU to email.

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

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.


Joe Gwinn

- IF - The surface speed is what really matters, not the diameter,
what would be the force with a surface speed of 1047 MPH or 1535 feet
per second?

An intersting number that is... It is very roughly (check my math) the
surface speed at the equator. How much reduction in weight do we expect
with that much surface speed?
Aparently, 1535 feet per second is not enough speed at that diameter(?)

Thus the diameter -And- the surface speed are important,
or:
Something strange needs to be explained.

Someone please educate us all.
Pete

In article .com,
wrote:

Joseph,

The balls of the bearing whizzing around do not carry any hoop stress,
but produce a radial outward force on the outer bearing ring analogous
to the internal pressure of a pressure vessel.

Since you are into the arithmetic and I am too lazy to figure it out,
what is the fraction of the outer ring hoop stress due to the orbiting
balls?

None, I think, because the flywheel theory depended only on the surface
speed at the rim of the flywheel, and not at all on what was inside.

Joe Gwinn

wrote:
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.


Joe Gwinn

- IF - The surface speed is what really matters, not the diameter,
what would be the force with a surface speed of 1047 MPH or 1535 feet
per second?

An intersting number that is... It is very roughly (check my math) the
surface speed at the equator. How much reduction in weight do we
expect with that much surface speed?
Aparently, 1535 feet per second is not enough speed at that
diameter(?)

Thus the diameter -And- the surface speed are important,
or:
Something strange needs to be explained.

Someone please educate us all.
Pete

From Machinery handbook - 22nd edition. (page 226)
"The bending stresses in the rim of a flywheel may exceed the centrifugal
(hoop tension) stress predicted by the simple formula s = V(squared) divided
by 10 by a considerable amount.
See relevant section for further edification.

Have fun.
Ken.

--
Volunteer your idle computer time for cancer research
http//www.grid.org/download/gold/download.htm
Return address courtesy of Spammotel http://www.spammotel.com/

In article ,
Eric R Snow wrote:

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.

I think the guy claiming 20,000 rpm max is wrong, and the actual
rotational rate is ten times that. So, it would take a microsecond
light pulse to stop the pieces, which are moving at Mach 2. This is
high-powered rifle bullet speed.

An easier way to measure the speed of the fragments is two curtains of
fine wire - measure the time delay between disruption of the inner
curtain and the outer curtain. One can also use disruption of a curtain
to trigger a flash.

Joe Gwinn

In article ,
"Ken Davey" wrote:

wrote:
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.


Joe Gwinn

- IF - The surface speed is what really matters, not the diameter,
what would be the force with a surface speed of 1047 MPH or 1535 feet
per second?

An intersting number that is... It is very roughly (check my math) the
surface speed at the equator. How much reduction in weight do we
expect with that much surface speed?
Aparently, 1535 feet per second is not enough speed at that
diameter(?)

Thus the diameter -And- the surface speed are important,
or:
Something strange needs to be explained.

Someone please educate us all.
Pete

From Machinery handbook - 22nd edition. (page 226)
"The bending stresses in the rim of a flywheel may exceed the centrifugal
(hoop tension) stress predicted by the simple formula s = V(squared) divided
by 10 by a considerable amount.
See relevant section for further edification.

That's if you try to change the axis of rotation while the flywheel is
madly rotating.

Joe Gwinn

In article ,
says...
In article .com,
wrote:

Joseph,

The balls of the bearing whizzing around do not carry any hoop stress,
but produce a radial outward force on the outer bearing ring analogous
to the internal pressure of a pressure vessel.

Since you are into the arithmetic and I am too lazy to figure it out,
what is the fraction of the outer ring hoop stress due to the orbiting
balls?

None, I think, because the flywheel theory depended only on the surface
speed at the rim of the flywheel, and not at all on what was inside.


The formula in MH is an approximation that works for steel and materials
with similar specific gravity. The real formula is:

stress = (density / gravity) * radius^2 * angular velocity^2

or

angular velocity = sqrt((stress * gravity) / (density * radius^2))

where angular velocity is in radians/s and density in weight/unit
volume.

You *must* account for the balls, which is why I've been using 1300FPS
as the limit for 300 ksi steel rather than 1700FPS. Based on a SWAG that
the balls weigh a bit less than the race I used a density of 0.5lb/in^3
in the formula, rather than steel's actual 0.28lb/in^3.

Ned Simmons

In article ,
says...
In article ,
"Ken Davey" wrote:

wrote:
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.


Joe Gwinn

- IF - The surface speed is what really matters, not the diameter,
what would be the force with a surface speed of 1047 MPH or 1535 feet
per second?

An intersting number that is... It is very roughly (check my math) the
surface speed at the equator. How much reduction in weight do we
expect with that much surface speed?
Aparently, 1535 feet per second is not enough speed at that
diameter(?)

Thus the diameter -And- the surface speed are important,
or:
Something strange needs to be explained.

Someone please educate us all.
Pete

From Machinery handbook - 22nd edition. (page 226)
"The bending stresses in the rim of a flywheel may exceed the centrifugal
(hoop tension) stress predicted by the simple formula s = V(squared) divided
by 10 by a considerable amount.
See relevant section for further edification.

That's if you try to change the axis of rotation while the flywheel is
madly rotating.


No, that's if you're talking about a real flywheel with a thick rim and
spokes. The formulas we've been bandying about are only strictly
applicable to thin cylinders.

Ned Simmons

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.

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.

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

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.


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.


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.

Ned Simmons

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?


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 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?


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.

Also unexplained is the essentially perfect symmetry of the explosions.


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.

Joe Gwinn

In article ,
Ned Simmons wrote:

In article ,
says...
In article ,
"Ken Davey" wrote:

wrote:
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.



- IF - The surface speed is what really matters, not the diameter,
what would be the force with a surface speed of 1047 MPH or 1535 feet
per second?

An intersting number that is... It is very roughly (check my math) the
surface speed at the equator. How much reduction in weight do we
expect with that much surface speed?
Aparently, 1535 feet per second is not enough speed at that
diameter(?)

Thus the diameter -And- the surface speed are important,
or:
Something strange needs to be explained.

Someone please educate us all.
Pete

From Machinery handbook - 22nd edition. (page 226)
"The bending stresses in the rim of a flywheel may exceed the centrifugal
(hoop tension) stress predicted by the simple formula s = V(squared)
divided by 10 by a considerable amount.
See relevant section for further edification.

That's if you try to change the axis of rotation while the flywheel is
madly rotating.


No, that's if you're talking about a real flywheel with a thick rim and
spokes. The formulas we've been bandying about are only strictly
applicable to thin cylinders.

Hmm. On second thought, I think you're right.

With balls rolling on the outer ring at very high speed, we should see
some metal fatigue effects from the cyclic bending seen as the balls
pass by.

Wonder if we are running through the fatigue life of the steel, which
then cracks, precipitating the burst? One problem with this theory is
that one would not expect this mechanism to lead to the essentially
symmetrical explosions that have been universally reported.

Joe Gwinn

In article ,
Ned Simmons wrote:

In article ,
says...
In article .com,
wrote:

Joseph,

The balls of the bearing whizzing around do not carry any hoop stress,
but produce a radial outward force on the outer bearing ring analogous
to the internal pressure of a pressure vessel.

Since you are into the arithmetic and I am too lazy to figure it out,
what is the fraction of the outer ring hoop stress due to the orbiting
balls?

None, I think, because the flywheel theory depended only on the surface
speed at the rim of the flywheel, and not at all on what was inside.

My theory was that the balls are less dense than solid disk, and more or
less equivalent to (moving) spokes), so the MH formula would apply.


The formula in MH is an approximation that works for steel and materials
with similar specific gravity.

Yes, MH is full of practical approximations, and they do say that steel
is assumed.


The real formula is:

stress = (density / gravity) * radius^2 * angular velocity^2

or

angular velocity = sqrt((stress * gravity) / (density * radius^2))

where angular velocity is in radians/s and density in weight/unit
volume.

What's "gravity", and how does it differ from "density"? This theory
cannot depend on the presence of a planet or its gravitational field.

Where are you getting these better formulas? I'd like to read up on it.


You *must* account for the balls, which is why I've been using 1300FPS
as the limit for 300 ksi steel rather than 1700FPS. Based on a SWAG that
the balls weigh a bit less than the race I used a density of 0.5lb/in^3
in the formula, rather than steel's actual 0.28lb/in^3.

If the balls weigh less than the race, the 0.5 lb/in^3 sounds wrong, as
it's more than that of solid steel, 0.28 lbs/in^3. Perhaps some more
explanation is in order.

Joe Gwinn

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



Yes, MH is full of practical approximations, and they do say that steel
is assumed.


The real formula is:

stress = (density / gravity) * radius^2 * angular velocity^2

or

angular velocity = sqrt((stress * gravity) / (density * radius^2))

where angular velocity is in radians/s and density in weight/unit
volume.

What's "gravity", and how does it differ from "density"? This theory
cannot depend on the presence of a planet or its gravitational field.

Gravitational acceleration, to account for the fact that a pound mass
exerts a pound force in a gravitational field of 386 in/s^2 and we're
calculating the forces exerted by a lump of material in a rotating frame
with a different acceleration.


Where are you getting these better formulas? I'd like to read up on it.

I got the formula from "Roark's Formulas for Stress and Strain", but
that's not the place to go for an explanation of the derivation.
"Elements of Strength of Materials" (Timoshenko) has the derivation for
the stress in a cylindrical pressure vessel, which is a very similar
problem.

As an intuitive approach, you can think of the problem as two
semicircular segments joined together. What's the force required at the
joints to hold the two halves together? Divide that by cross section to
get stress.



You *must* account for the balls, which is why I've been using 1300FPS
as the limit for 300 ksi steel rather than 1700FPS. Based on a SWAG that
the balls weigh a bit less than the race I used a density of 0.5lb/in^3
in the formula, rather than steel's actual 0.28lb/in^3.

If the balls weigh less than the race, the 0.5 lb/in^3 sounds wrong, as
it's more than that of solid steel, 0.28 lbs/in^3. Perhaps some more
explanation is in order.


It's a fudge. As Wolfgang said, the balls are exerting a force on the
race but don't increase it's strength. To account for the balls'
additional mass I added it to the outer race's mass, but didn't change
the cross section (strength) of the race. In other words, I decreased
the strength to density ratio of the race to account for the loose
balls.

Ned Simmons

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

In article ,
Ned Simmons wrote:

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.

How fast did you get it to go?


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.

So the balls and outer race spin together more or less as a unit? I
guess I don't quite trust that so small a clearance will really always
do the job. All it would take to get some real traction would be for
the human holding the inner race to move slightly, twisting the axis of
rotation a few degrees, causing the balls to come up against the sides
of the groove in the inner race, pushing against the gyroscopic forces
keeping the outer race from turning with the inner race.

The lack of lubrication will make for more traction, especially if the
balls are galling with the races.

A test jig where the bearing is clamped to a bench would never see this
effect.


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.

I bet your Son can test your hearing limit.


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.

Darwinism in action. But don't you think we would have heard the
stories, if there were stories to be heard?


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.

Will deterioration really be that much of a limit on an unloaded
bearing, especially if it isn't in contact with the inner race all that
much? And, the airjet has plenty of power.

Joe Gwinn

In article ,
Ned Simmons wrote:

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



Yes, MH is full of practical approximations, and they do say that steel
is assumed.


The real formula is:

stress = (density / gravity) * radius^2 * angular velocity^2

or

angular velocity = sqrt((stress * gravity) / (density * radius^2))

where angular velocity is in radians/s and density in weight/unit
volume.

What's "gravity", and how does it differ from "density"? This theory
cannot depend on the presence of a planet or its gravitational field.

Gravitational acceleration, to account for the fact that a pound mass
exerts a pound force in a gravitational field of 386 in/s^2 and we're
calculating the forces exerted by a lump of material in a rotating frame
with a different acceleration.

Ah. The conversion from pounds (a unit of weight) to slugs (a unit of
inertial mass) is partly buried in the formula. In the MH formula, all
this disappears into a single unexplained constant.


Where are you getting these better formulas? I'd like to read up on it.

I got the formula from "Roark's Formulas for Stress and Strain", but
that's not the place to go for an explanation of the derivation.
"Elements of Strength of Materials" (Timoshenko) has the derivation for
the stress in a cylindrical pressure vessel, which is a very similar
problem.

Thanks. I think I have both books.


As an intuitive approach, you can think of the problem as two
semicircular segments joined together. What's the force required at the
joints to hold the two halves together? Divide that by cross section to
get stress.

And as one increases the number of segments, the formula will approach
the continuum case.


You *must* account for the balls, which is why I've been using 1300FPS
as the limit for 300 ksi steel rather than 1700FPS. Based on a SWAG that
the balls weigh a bit less than the race I used a density of 0.5lb/in^3
in the formula, rather than steel's actual 0.28lb/in^3.

If the balls weigh less than the race, the 0.5 lb/in^3 sounds wrong, as
it's more than that of solid steel, 0.28 lbs/in^3. Perhaps some more
explanation is in order.

It's a fudge. As Wolfgang said, the balls are exerting a force on the
race but don't increase its strength. To account for the balls'
additional mass I added it to the outer race's mass, but didn't change
the cross section (strength) of the race. In other words, I decreased
the strength to density ratio of the race to account for the loose balls.

Ahh. OK.

Joe Gwinn

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


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

How fast did you get it to go?

About 6500 RPM. I didn't have the needle valve opened all the way, but I
don't think it would have gone much faster with the small tube.


I bet your Son can test your hearing limit.

He tests many limits.


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.

Will deterioration really be that much of a limit on an unloaded
bearing, especially if it isn't in contact with the inner race all that
much? And, the airjet has plenty of power.


There's lots of power in the compressed air - transferring it to the
bearing is another matter. Even air motors are notoriously inefficient.

Based on the numbers, and 25 years of machine design experience, I'm
very confident that the bearings did not explode from centrifugal force
alone. The reports of the noise going ultrasonic do give me pause, but
not enough to make me believe that the bearings were spinning at 1300
FPM. I guess someone needs to volunteer to explode a few properly
instrumented bearings. Not me, I'm off to Boston for college visits with
the boy tomorrow.

Ned Simmons

In article ,
Ned Simmons wrote:

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


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

How fast did you get it to go?

About 6500 RPM. I didn't have the needle valve opened all the way, but I
don't think it would have gone much faster with the small tube.

Sounds about right. And needle valves can slow things down too.


I bet your Son can test your hearing limit.

He tests many limits.

Heh...



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.

Will deterioration really be that much of a limit on an unloaded
bearing, especially if it isn't in contact with the inner race all that
much? And, the airjet has plenty of power.

There's lots of power in the compressed air - transferring it to the
bearing is another matter. Even air motors are notoriously inefficient.

Even if it's inefficient, it may be sufficient. How much power does it
really take to spin that little steel ring?


Based on the numbers, and 25 years of machine design experience, I'm
very confident that the bearings did not explode from centrifugal force
alone. The reports of the noise going ultrasonic do give me pause, but
not enough to make me believe that the bearings were spinning at 1300
FPM. I guess someone needs to volunteer to explode a few properly
instrumented bearings. Not me, I'm off to Boston for college visits with
the boy tomorrow.

OK.

One quick test would be a cheap electret microphone near the bearing,
the whole affair being down under a pile of sandbags for safety, to
convert the siren tone into an electrical signal one can display on an
oscilloscope and measure the frequency. Knowing that the siren tone is
ultrasonic would very much constrain the problem.

Joe Gwinn