The development of the slider crank equation

Something for the torsional vibes folks who discover my blog... I've been meaning to put this up for some time!  I used to teach a grad course at MTU on the design of internal combustion engines.  Part of the background needed to understand torsional vibration in slider crank mechanisms is the complex description of the motion of the piston with crank angle (time if you will).  So here you go!

For offset pins Lichty is a good reference.

So cool! So here we start with the angle the connecting rod makes with the crank arm...

CFT is Charles Frederick Taylor and his book published from the MIT Press on Design of Engines

Generally the error of a truncated expansion is easily accepted when you consider cylinder to cylinder pressure variation due to porting, standing waves, blow down, volumetric efficiency etc... Ultimately what we want from these equations is gas torque.  The turning power created by the engine.

My O-Speed note was for an example of an overspeed consideration not discussed further in these lecture notes

The differentiation is straight forward...

So here you have the kinematic relationships.  Next - what good are they - really cool if you want to figure out the gas load forces.

To make these equations yield meaningful side forces, and piston scuff calcs you will need a gas pressure v crank angle vector to apply with proper phase angle.

This is the heart of the torsional gas load.  Turning effort.  This complex wave can be reduced to frequency (by crank order) and phase.  It always acts in the opposite direction of the inertia torque so they form the complex turning effort. That then becomes the forcing function for an ordal superposition forced torsional response. YEE-HAAW!

The radial force can be used to calculate bearing fluid film thickness - but that's another story...

Hope the math folks liked the post!

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A visit to Clem Studebaker's house...

What an excellent day this was!  Every now and then we all get to visit some amazing places. Having dinner at the Clement Studebaker Mansion in South Bend Indiana was one of those really memorable experiences for my wife and I. 

It was a cold rainy afternoon with rain turning to snow.  Such was the welcome we had when we drove into South Bend.  We were there to see the Studebaker Museum, and finding the mansion open on such a horrible night was pure luck.  As the afternoon turned into the evening,  the snow and the wind picked up, and nobody was outside. 

The view of Tippecanoe as you arrive, it is nearly 24000 sq ft, has 40 rooms and cost Mr Studebaker $350,000.00 in 1889. The house got its mane from Pres Harrison's grandfather William.  William fought in the 1811 Battle of Tippecanoe, and seeing as how Clem and Benjamin Harrison aka President Harrison were pals, this seemed a fitting tribute.

Work started on Clem's house in 1885 when Clem picked Henry Cobb to be the architect.  The home resembles many of the mansions built in this time frame.  At this point in Clem's life the company he and his brothers founded had built 1 million horse drawn wagons!  These days the entire home is a restaurant.

The rooms are beautiful

You can tour the entire house while you are waiting for your dinner to be prepared.

One can imagine the Studebaker family entertaining guests in these rooms...

The craftsmanship is superb.

Whoa, the office where Clem did all that thinking!  Oak paneling throughout with a stained glass window of a blacksmith's shop.

Hmmm, 38 - 42- 12... nope

I can imagine the company treasures that must have been stashed away in his safe...

Oh what's this?  One of my favorite TV shows as a kid was Mr Ed...  Gee I never knew Mr Ed (the talking horse) was a Studebaker fan!

Ahhh, dinner finally arrived and it was delicious!

What a great evening.  We were the only two for dinner this evening!

One of the oddest roadside oddities I have ever seen...  A naval gun battery on a cement platform...

Not a roadside oddity, but a building side message...

It's been wintery up here so not much hiking or wandering going on just yet.  We've started our garden seeds and are hopeful things will warm up soon!

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Update... Hazel Graduates!

Yay!  Our English Setter pup has made it through obedience class!  She graduated at the top of her class too (she was the only student at the time...) LOL...

We are very thankful to the really amazing trainers at Georgia K9! Hazel learned all of her hand signal commands, and was a riot to work with during the training.  We learned a lot about the cognitive ability and behavior of canines with very positive results from balanced training.  Dogs can learn to do amazing things when treated kindly and the trainer knows what they're doing.  GK9, you guys and gals are the best!

The graduate...

Off leash chasing bird shadows on the beach...

On leash running - because she can!

Hope you got a smile from the pics,  Hazel is a lot of fun. She's about half grown now, I'll post something this spring to update all.

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The Studebaker Museum in South Bend Indiana....

I've been working on restoring our '47 Studebaker truck and knew I would have the chance to visit the Studebaker museum and National Archives early this year.

So the day came!  I have to say, South Bend is a city rich in history.  The car business is just one chapter.

It looks like any abandoned factory

But the old Studebaker assembly plant is being re-purposed...

Cars and trucks rolled off the line in this plant since the 1920's

A 160M USD renovation project has started.  New companies - high tech companies, low tech companies, business incubators, and apartments are to be created in this old venerable building!

The old logo sits in front of the museum

Ok... here we go!  Welcome to the Studebaker National Museum!

One of many of the wagons on display.  Studebaker manufactured over 1 million horse drawn wagons before they ever made an automobile.

Many US Presidents had Studebaker carriages built just for them.

A "Bullet Nose"

The bread and butter of the wagon era

The size of the older touring cars surprised me.

On a radiator, the company badge is quite elegant

The "Wheel Logo"

Fisher Body had nothing on South Bend

Thermometer and logo that thousands of workers passed under every day at the plant shown in the first set of pics...

Gear driven speedo

My favorite car in the collection...

Reliability and craftsmanship were part of the Studebaker DNA

Beautiful

A 1920's hood ornament / thermometer

Gosh the cars from the 30's were beautiful...

Elegant hood ornament

The Bendix concept car.  Look familiar?

The last Studebaker ever built.

Dodge came out with the Airflow in '34.  This was a car made by Studebaker employees in their off hours for Bendix.  It was a demonstrator and was built in 1934.  Me thinks Chrysler learned a lot from Studebaker in their Airflow.

This was the car that they bet it all on!  The Avanti.

One of the concept cars that never made it into production.  I see Pontiac GTO with concealed headlights here...

Another beautiful Studebaker. Studebaker and Packard merged in the 1950's

Raymond Lowey fingerprints

A woody...

The cars from the 30's have always been my favorites

Oh Boy!  I hope my '47 looks like this when I'm finished!

From an old dealership... the LARK was one of the success stories

Parking is shared with another museum.

Alas I must go.  What a great museum!

Hope you liked the pics!

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