Again in reference to a previous post; What are models?
Strictly speaking a torsional model is a math exercise. The required math runs from very simple for a basic two-element frequency model to quite complex for a Holzer-method analysis of many elements with amplitude. All of it can be found in old books. How to calculate this stuff has been known since well before WWII. Modern developments are mostly methods of using computer power to obtain great accuracy in fully dynamic models.
We don't work for Caterpillar or Toyota, where experts do a torsional analysis of every rotating shaft system as part of the design process. We can reasonably simplify our approach. For the most part we don't need to worry about amplitude at a resonant RPM; our goal is to move it out of the operating range so it doesn't matter.
The process starts with some visualization. Take a look at the images below. The first line is a representation of a simple torsional model, two inertias connected by a single stiffness. The image on the right is the usual represenation found in the textbooks. Large inertias are drawn as disks larger than the small ones, although usually no effort is made to draw them in accurate proportion. The "shaft" represents the connecting stiffness value.
Next we have some reasonable representations of a Lycoming 4-cyl and a BAP/Chevy V6. The Lycoming has a metal fixed pitch prop, assumed (for purposes of this example only) to be quite stiff in bending. The BAP is assumed to have a prop with a ground adjustable hub, ie small blade roots, so I've drawn in an "equivelent torsional stiffness" at the root. The BAP has another equivelent torsional stiffness, the belt connecting the upper and lower sprocket inertias. For both examples we also have inertias for each crankthrow. The BAP includes a flywheel inertia.
The next line would be Ross's Marcotte system on a 4-cyl Subaru. In the left figure, from left to right, we have a prop, propshaft, ring gear reduction, the soft element bushings, a flywheel, the crank stub, and four crankthrows with connecting shafts. The prop hub has been ignored. In this model as well as all the previous I've also ignored the accessory drive(s), things like camshafts and belt-driven alternators. They wouldn't do that at Toyota.
When treated this way, the math model would have seven inertias and six connecting stiffness values. The math gets complex, at least if you do it by hand. For poor homebuilders, it is also difficult to assign individual stiffness and inertia values to the crankthrows. So, we use a simplified model.
As Ross previously dscribed, the Subaru crank is compact and likely quite stiff. For our simplified model, we treat the entire crankshaft and flywheel assembly as a single inertia. Hang it on a bifillar pendulum, time the oscillation, and with a minute's calculation we
know it's inertia.
Now our model only has four inertias and three stiffness values. The results won't be of any practical difference in the context of determining F1 and F2 natural frequencies. To make it really easy use something like the Holzer program I mentioned in a much earlier post. Now that you have a reasonable model of your existing system, you can play with a particular stiffness or inertia and see the shift in natural frequencies. In the case of Ross's drive, the logical place to start would be variations in the stiffness of the coupler.
Wanna make it really easy? Eliminate the equivelent stiffness at the blade roots. Now you have a three-element model, which can be hammered for F1 and F2 with two equations. Nothing in them more difficult than using the square root key on a $10 calculator. The result requires a simple assumption; the actual frequencies will be a little lower than the computed result.
Note to lurking geeks: yeah, you gotta include an adjustment for gearing. One bite at a time <g>.
Now you see why I think it a lot easier to experiment with a model than with an endless cycle of building and installing and running new parts.
Shot at 2007-07-20
