Mr dan ruggirello wrote:

Hi all,
I goofed.  Note to self - never drink beer while you
are calculating natural frequencies.

I rechecked those numbers for natural frequency of the
bolt and found I made an error using the density
instead of mass/unit length.  Someone please check me
on this calc!

The textbook natural freq formula for a uniformly
distributed beam is:

f=(1/(2*pi))*k^2*sqrt(E*I*g/m)

where
f= natural freq (cyle/s)
k=3.93/l (fixed-pinned)
l=length
E=modulus of elasticity
I=area moment of inertia
m=mass per unit length (lbs/in)
g=gravity constant(386.4 in/s^2)

See attached spreadsheet shot.

The 1st mode frequency is ~440hz, NOT 150hz.

I serve as a reminder to all to take what is posted at
your own risk ;-)

So, if this higher frequency is the case, vibration
may still be an issue.  For those of you familiar with
the "rise time" of an exiting pulse such as a hammer
hitting a plate, or similarly, the firing of a spark
plug and the ensuing explosion, depending on what this
rise time is, it can excite frequencies greater than
the repeating frequency (in this case 5000-6500 rpm).
The question then is how high are the vibration levels
at 440hz?  Has anyone gathered any accelerometer
vibration data on a rotary engine block during flight?

Other potential causes of failure may be
overtorqueing, stress corrosion cracking, thermal
shock, block thermal expansion.......

Dan

I have some data from K. Yamamoto's book Rotary Engine.
Vertical acceleration becomes over 10 G (120 db)  at 5000 RPM. No load.
I will scan in the graph when I get a chance. 

I put a lot of credence into your combustion shock theory Dan.
Considering the changes made by Mazda over the years to the tension
bolt I am almost certain it is the vibratory mode that is causing
the failures.

Paul Lamar
 
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