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
 
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