Lets see a .3 inch square section of blade that is .1 inch thick
would weigh .0027 pounds. or .0000843 slugs.
At 15000 RPM and a one inch radius it would be going 47124 inches
per
minute or 785 inches a second or 65.45 feet per second.
Centrifugal force is = to mV^2/r
65.45 squared is 4284. Times .0000843 slugs is .356 pounds.
The area to resist this force is .1 times .3 or .03 square inch.
The stress would therefore be 12 psi if my math is correct.
Seems like the blade should withstand that no matter what the temp.
Lets try a 2 inch radius.
At 15000 RPM it is going twice 65.45 feet per second or
130.9 feet per second
That squared is 17,135. Times .0000843 slugs is 1.444 pounds
Stress is only 48 psi.
Obviously something else is going on here.
At 6000 RPM the engine is putting out 12000 pulses per minute
or 200 pulses per second. You don't suppose the blades have a
bending resonant frequency of 200 hertz do you? Could be.
The bending force on the blade is not much from the
average pressure of 5 psi. Blade area is only .09 square inches
so this .45 pounds. Peak pressure could be many times this
due to the explosive nature of the rotary exhaust.
Lets say it is 20 pounds.
A cantilevered beam .3 by .3 by .1 inches thick
would have a bending moment of 3 inch pounds at 20 pounds.
(ball park number)
Bending stress with 20 pounds of load would be 30 psi (ball
park number). Not much!
Despite the great loss in strength of the turbine material
at 1750 F I don't think simple centrifugal force and bending
stress on the
blade is causing the failure.
If I extrapolate this loss in strength curve for valve steel
out to 1750 F
we are still looking at a max stress level of about 5000 psi.
Fatigue life can be 5% of max stress or 250 psi or less.
I suspect that the stock 2nd gen 1989 to 1991 turbo has a blade
bending
resonant problem at certain RPM's. Just like a metal prop blade. The
car
never sees 6000 RPM at high power continuously.
If a chunk of blade breaks off and jams between the rest of the
turbine and
housing that will shear the hot shaft due to compressor
rotational inertia.
The resonant condition and magnitude of the pulse can be changed by
many things. Just the shape of the intake manifold can have a major
effect. Small difference in the thickness and shape of the
blade can also
change the bending resonant frequency greatly.
All this is dependent on my arithmetic and physics above being
correct
so by all means check me carefully on this.
I am looking forward to showing this failed turbine of Dave's to
some ME
professor at UCLA.
Paul Lamar
Sorry that should have been "shape of the exhaust manifold".
Paul Lamar
DaveLeonard wrote:
Paul, I am very inclined to agree that there are probably some other
factors
involved. But I think you used the wrong RPM in the above calculation.
All
the turbo maps I could find for a similar sized turbo in similar
conditions
seemed to indicated that the turbine would be turning closer to 70,000
RPM
under those conditions.
Dave Leonard
Well perhaps but that is a small turbine housing.
If it is blade bending resonance that is not going to change the
situation.
All that will do is reduce further the already small amount of stress due
to
centrifugal force alone. That in turn also increases the likelihood of a
blade bending resonant condition as the cause of failure. The main forcing
function for that is still the exhaust pulses at 12,000 per minute or 200
Hertz.
If UCLA has a shake table we could put the turbine on it and see
what the blade resonant frequency is. Heck you could tap it with a small
hammer and use a micro phone hooked to a storage oscilloscope and take
a picture.
Paul Lamar
What is the compressor diameter? The 66mm compressors that the model jet
guys are using run standard at about 100 000rpm.
My guess would be, you oversped the turbine, causing the the shaft to exceed
the resonant critical bending speed, and the resulting imbalance cause a
heavy rub closely followed by the fatigue failure of the rubbed blades.
This is a common failure mode on the model engines, beacause the longer
shaft has less margin to the resonant bending speed. On the other hand these
stock radial inflow turbines have a much greater overhung mass, adversely
effecting the critical bending speed.
Shaft design will also be the big challenge if you want to go to TC
configuration.
Regards,
Mark
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