Paul wrote:
Thanks to Gary Palmer for going through my original calculations
and correcting the math in this message.
Lets see a .3 inch square section of blade that is .1 inch thick
would weigh .0027 pounds. or .0000843 slugs.
At 150,000 RPM and a one inch radius it would be going 471,240 inches per
minute or 7,854 inches a second or 654.5 feet per second.
Centrifugal force is = to mV^2/r
654.5 squared is 428,370. Times .0000843 slugs is 36 pounds.
The area to resist this force is .1 times .3 or .03 square inch.
The stress would therefore be 1,200 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 1500,00 RPM it is going twice 654.5 feet per second or
1309 feet per second
That squared is 1,713,481 Times .0000843 slugs is 144 pounds
Stress is 4,800 psi.
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!
If I extrapolate this loss in strength curve for valve steel out to 1750 F
we are 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
Paul must be a mathematical genius to be able to do this stuff in Slugs and
Inches :)
Anyway, there is no way that well radiused short stubby stiff curved blade
has a strong resonant response at 200Hz. 200kHz maybe.
But an overspeed, combined with an overtemp will happily take off a corner
causing an imbalance. The oversped bearings now have the additional
vibrational load. The overspeed chewed up the shafts critical bending margin
now agravated by additional vibration. Sooner or later the rotor rubs
causing blade damage, bent shaft, broken shaft etc.
It is pretty easy to see how you can chew up a unit which will happily do
10000+ hours in a car, within 5 to 10 hours.
Don't fit stock automotive turbo and waste gate. We should all thank Dave
for his perseverance and dedication, and for still being here. We all wanted
to know, "what if I use the stock turbo", now we know.
Dave please don't just bolt another stock turbo in.
Regards,
Mark Wrathall
Slugs and inches is what I learned back in college when a cycle per second
was a cycle per second and not a Hertz :) As Vance is fond of saying we
got to the moon on inches :)
Intuitively I think you are right but as I recall the modules of elasticity is
also drastically affected by temperature. Also the forcing function does not
have to match the resonant frequency... only some multiple of it.
Having said that I think you are right. It is an unlikely scenario but worth
a look.
I am still not convinced there is that much difference in a stock turbo and a "aircraft"
turbo. I think we are just using a turbo too small for the application.
I suspect if we bolted on a T3 we would have the same problems. As far as I know
(and can find out) the only difference on the "aircraft" turbos is the paper trail.
Inconel and ceramic ball bearings are Inconel and ceramic ball bearings.
You have to admit a car turbo gets far more heat cycles than an aircraft turbo.
Paul Lamar
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