Burst speed of rotating disk
Burst speed of rotating disk
(OP)
I am looking for the equations for hoop stress and radial stress in a rotating disk, to calculate the theoretical burst speed. I am not looking for the more complex empirical solutions having to do with fatigue, balance, vibration, temperature, etc...
A link would be great.
I googled, but found WAY too much information, and wasn't able to find the simple equations that I was looking for.
Thank you very much,
-Michael
www.sewellgeneralcontracting.com
ALBANY SCHENECTADY TROY NY
A link would be great.
I googled, but found WAY too much information, and wasn't able to find the simple equations that I was looking for.
Thank you very much,
-Michael
www.sewellgeneralcontracting.com
ALBANY SCHENECTADY TROY NY





RE: Burst speed of rotating disk
http:
RE: Burst speed of rotating disk
RE: Burst speed of rotating disk
Thank you for the link, but it is one of the 100 bzillion pages that I visited on google during the past 3 days with no equation...
-Michael
www.sewellgeneralcontracting.com
ALBANY SCHENECTADY TROY NY
RE: Burst speed of rotating disk
V = sqrt(10 * S)
where
V = circumferential speed in ft/s
S = tensile strength of flywheel material in psi
Don
Kansas City
RE: Burst speed of rotating disk
Exactly what I needed.
Thank you soooo much!
eromlignod,
Not what I was looking for, but maybe even better. It sounds like a "rule of thumb" formula with a built in safety factor. I'm interested in knowing where it comes from.
Thank YOU very much,
-Michael
www.sewellgeneralcontracting.com
ALBANY SCHENECTADY TROY NY
RE: Burst speed of rotating disk
The text reads:
"The bursting velocity of a flywheel, based on hoop stress alone (not considering bending stresses), is related to the tensile stress in the flywheel rim by the following formula which is based on the centrifugal force formula from mechanics."
Don
Kansas City
RE: Burst speed of rotating disk
where
V = circumferential speed in ft/s
S = tensile strength of flywheel material in psi
- cannot be correct in general. It might be right for a particular material, but it has no term for the material density, which is a critical factor for the calculation.
RE: Burst speed of rotating disk
σmax = [(3+ν)/8]ρR2ω2
where
σmax = maximum principal stress
ν = Poisson's ratio of disk material
ρ = mass density of disk material
R = disk radius
ω = angular velocity
Regards,
Cory
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
RE: Burst speed of rotating disk
S is the tensile strength of the material. Class 30 cast iron, for example, would have an s of around 30 ksi, so the critical rim speed would be about
V = sqrt(10 * 30,000) = 548 ft/s
for that material. Unless you need to know *precisely* when the wheel will burst, this is close enough for design work once you have figured in an appropriate safety factor.
Don
Kansas City
RE: Burst speed of rotating disk
RE: Burst speed of rotating disk
Ashby's equation reduces to a rim speed as well, if that's what you like to think about.
?max = [(3+?)/8]?R2?2
V=2*pi*R*?
so
?max = [(3+?)/8]?V^2/4/pi^2
so
V=sqrt(S/([(3+?)/8]?))
V = sqrt(10 * S)
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Burst speed of rotating disk
V=Rω
σmax=(3+ν)ρV2/8
V=√(8S/((3+ν)ρ))
Now, using a sane system of units, we have
ρ=11360 kg/m3 for lead
and with S in Pa, V will be in m/s.
Using S in psi and to get V in ft/s, the factor under the square root becomes (also assuming ν=0.33, that's not really important):
8 x 6894.8 / (3.33 x 11360 x 0.30482)=15
So, if I'm not mistaken, that formula contains a factor of safety of about 1.2 (√1.5) for lead, is unsafe for gold
And of course the bursting speed does depend on density!
prex
http://www.xcalcs.com
Online tools for structural design
RE: Burst speed of rotating disk
I'm not sure why you refer to your metric units as "sane" units in this case, since you needed a calculator to work that formula anyway. How is that easier?
Don
Kansas City
RE: Burst speed of rotating disk
I don't think it is very sane to mix pounds per square inch and feet per second, when the handy meter is available for both measurements (as well as every other length measurement).
Regards,
Cory
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
RE: Burst speed of rotating disk
According to DenHartog,"Advanced Strength of Materials", the tangential stress at the hole edge would be double that quoted by Coreypad for any size hole at the center or
2*rho*w^2*(3+nu)*R^2/8
which looks surprising, in that it is independent of the hole diameter, including a tiny one.