Monday, April 27, 2015

Transfer matrices and torsional vibes continued...

One of the engineering things I really enjoy is engine and drive train integration and synthesis whether that's considering vehicle mobility, tractive effort, efficiency, hybrid drives or just good old gear box design! Some of the more interesting challenges power train and drive train engineers face these days is what to do with a big rotor (called an electric motor)...  But I digress.  Here's sort of a intro into transfer matrices and how they work as applied to torsional vibration modeling.

So where did this idea come from?  The oldest reference I have to solving this class of problem with matrix methods is from a 1942 Applied Physics paper written by one L.A. Pipes.  A paper titled: "The Matrix Theory of Torsional Oscillations." Targoff looked at it again in 1947 and included bending with torsion which I thought was pretty cool.  In practice however it's hard to get good uncoupling of torsion from bending because  a lot of the structure your amidst has its own modal characteristics.  I have used methods to de-couple these... it can be as simple as doing an fft on a shaft mounted stain gage to capture run-up, or critical mode frequencies.  If you design something that has the ability to run through bending and torsional modes concomitantly, be mindful that barring certain operational speeds may be prudent... gosh I like this stuff!

So it's origins as far as I know are in WW2 era engineering efforts.  I would also add here that W. Ker Wilson, one of my heroes... was very active in this area around the same time.  His motivation was learning how to keep from breaking crankshafts and or busting gearboxes in radial engines in the aircraft of the day and in marine propulsion systems using higher power density diesels. The forcing functions of the new engines made excitation at various speed ranges something that could cause amplitude magnification if you dwelled on a certain speed.  Dwelling on a resonance is usually a very bad thing unless your playing a viola...  in which case it's a pretty amazing thing.

So where to begin.  As with any dynamical system you will need to descritize the assembly into discreet parts.  There's some value to experience in this.  Deciding how equivalent spring rates are calculated from classical methods or by high fidelity FEA really fit into the real world system often involves some judgement. I'll leave this discussion for another time, but I do want to mention the mathematical solution you come up with is dependent on reasonable approximations for inertia (perhaps entrained inertia) and stiffness which could include part of a spline... and it's after all an approximation. But enough of that.  Here's the deal!

Let us take the system in my earlier post: This is a 5 inertia, 4 spring system.  Think of it as a 4 cylinder engine with generator bolted to the flywheel.  It could be lots of things, but this I think is easy to visualize.

The inertia components are in units of [lb-in-s**2] and the torsional springs are in units of [lb-in/radian]  They can be in N-m-s**2 or a dozen other inertial units as long as the associated spring rate units are correct.

In this little engine we have the following:

I1 = 10     K1 = 1.5E6
I2 = 10     K2 = 1.5E6
I3 = 10     K3 = 1.5E6
I4 = 10     K4 = 2.0E6
I5 = 20

These physical values will eventually be incorporated into a column vector called the state vector [z] and transfer matrix [f]. The state vector has two components: the angle of twist and torque that exist at a discreet point.  Call this initial point, 'i.'  So [z]i = [f]*[z]i-1 

A little math...

I'll come back and make this a bit more readable when I get a chance!


Miss ya NLO and JRO!

Tuesday, April 21, 2015

A Classic Worth Remembering!


By Rudyard Kipling

If you can keep your head when all about you   
    Are losing theirs and blaming it on you,   
If you can trust yourself when all men doubt you,
    But make allowance for their doubting too;   
If you can wait and not be tired by waiting,
    Or being lied about, don’t deal in lies,
Or being hated, don’t give way to hating,
    And yet don’t look too good, nor talk too wise:

If you can dream—and not make dreams your master;   
    If you can think—and not make thoughts your aim;   
If you can meet with Triumph and Disaster
    And treat those two impostors just the same;   
If you can bear to hear the truth you’ve spoken
    Twisted by knaves to make a trap for fools,
Or watch the things you gave your life to, broken,
    And stoop and build ’em up with worn-out tools:

If you can make one heap of all your winnings
    And risk it on one turn of pitch-and-toss,
And lose, and start again at your beginnings
    And never breathe a word about your loss;
If you can force your heart and nerve and sinew
    To serve your turn long after they are gone,   
And so hold on when there is nothing in you
    Except the Will which says to them: ‘Hold on!’

If you can talk with crowds and keep your virtue,   
    Or walk with Kings—nor lose the common touch,
If neither foes nor loving friends can hurt you,
    If all men count with you, but none too much;
If you can fill the unforgiving minute
    With sixty seconds’ worth of distance run,   
Yours is the Earth and everything that’s in it,   
    And—which is more—you’ll be a Man, my son!

Friday, April 17, 2015

One of the most Amazing things I've seen recently...

Almost as cool as the FORD 6 degree of freedom driver simulator on the tri-axial base! (That took me back to my vehicle simulator days at a place called "Pontiac North."  Fun!  A long time ago I worked on replication of road profiles into vehicle structure using servo-hydraulics and a giant array processor called a VAX PDP-11.... LOL, that thing kept the whole control room warm when it ran.

So what's this groovy thing... I went to an art show and saw so many amazing things a few weeks ago.  This one stood out as something special.  As an engineer I was amazed at how this actually could work with any accuracy at all.  Then I marveled at the craftsmanship.  This is a fusion of mechanical stuff, hand made craftsmanship, ingenuity - bearings that are really suspended shafts with strings (no rotational loss, just the flexure of a string - very cool bearing idea)  So I present for your awesome enjoyment...

This art is amazing!  The pendulums, the friction loss solutions, the accurate pairing of the inertial characteristics with the mechanism and the perfect finish of the pieces.  A pleasure to see!


Thursday, April 16, 2015

The age of the Airship...

WOW, I had the great fortune to see the museum in Lakehurst.  What a gigantic building!

These are some huge doors! The base of the doors are attached to giant cement counterweights to off set the weight and keep them centered on two railroad tracks that run under the structure!

A 1936 arrival almost a year to the day before the fateful crash...

Hangar 1 is shown here at the left.  This enormous building was finished during the summer of 1921.  Imagine all of the rafters, supports, beams etc analyzed by hand or slide-rule.  Then built by shear courage...

The only time the Hindenburg was in the Lakehurst hangar - 1936.

This is the marker commemorating where the ship's gondola came to rest.

Oops, sorry about the wing tips! 
I had no idea that the Graf Zeppelin had already sailed a million miles by this time and had actually visited Lakehurst four times. The airship business was really a viable way to transit the oceans in comfort and speed - relative to a ship at sea.  Here's a really interesting page that details the Hindenburg and the accident

and this uber cool movie- Around the World in a Zeppelin (1929) ... 

AML, N and J!

Sunday, April 12, 2015

Blessed Pascha for my friends who celebrate the Eastern Orthodox Traditions

Yes the word is Pascha NOT Easter!  A most wonderful day and a beautiful Liturgy.

I hope all have had a peaceful Pascha and a time to reflect on our faith and our lives. Never forget what is important to you.   Hold dear those things and never waiver.

The Dome of St Mary's is so beautiful...

I arrived a bit early.  St Mary's was home to a dear VRev Fr Lecko (ret)

I always enjoy the Liturgy, and remember the things I am grateful for, and keep the people who are so important to me in my prayers.

Christ is Risen!
Christus ist auferstanden!
Christus is opgestaan!
Kristus er opstanden!
Христос Воскресе!

All my love Nick and Johanna,


Sunday, April 5, 2015

First hike of 2015...

The weather is still cold but I did get a chance to make a few short treks this weekend.  After preparing to pack my gps and camera - I promptly forgot both!  So no topo maps this time and no zoom or high def pictures - sorry.  Just iPhone snaps of some of the beautiful scenery.

This trek was to see the 4th highest waterfall East of the Rockies!
Walking down the trail to Big Manitou Falls... another beautiful day!
There are two falls on this part of the Black River, this is the Big Manitou, a drop of 165 ft.
There was still a lot of ice on the rocks and in the areas the sun is only shines briefly...

This is the Little Manitou, it's up river from the big falls and has a drop of around 30 feet.
Borrowed from the Pattison State Park website, here is the upper falls in winter.
Experimenting with a panoramic...
I'll be returning to the NCT soon.  Hope you all enjoyed the pics.  AML Nick and Johanna!