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