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
Just checked my Turbonetics catalog and a T3 "60" trim which is a similar size to the stock 2nd gen turbo goes to 154,700 max RPM.
Did you have any small leaks in the turbo intake manifold that you know about? Unlikely but that would increase the turbine RPM. Also if the compressor
is undersize for the amount of engine combustion air required that too will
drastically increase the turbine RPM.
As I said however I don't believe this is the root cause of failure.
Paul Lamar
Hi Paul,
If your formula & calculations are correct for the 15,000 rpm case where you come up with a centripetal stress of 48 psi; then for a 150,000 rpm case where V is 10 times as large, then V
squared is 100 times as large and the stress increases from 48 psi to 4800 psi which is very close to the extrapolated 5 Ksi strength at 1750 F exhaust temp. That would seem to indicate that if the
conditions allow the turbo to overspeed to the 150,000 rpm range, then a simple fatigue failure is quite likely without the assistance of any exotic resonance conditions.
Have I overlooked something here?
Cheers...........Gary
Oh right!!! I missed that. I think that is what Dave was trying to tell me. Sorry Dave.
I dropped a zero there.
Well you hit the nail on the on the head Gary. Thanks for checking my work.
I take it back. Over temp and over speed would do it!
Two bad things are happening here. The loads and stress are going up
with the square of turbine RPM and the max stress is on a very slippery
temperature slope indeed.
Paul Lamar
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