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      07-03-2012, 04:39 PM   #100
swamp2
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Let's look at n55 being the base engine for the new M3/M3, specifically the bored vs. stroked issue for a larger displacement. I thought I may be able to conclude that the engine simply can not be bored alone to 3.2 liters, but this quick calculation does not quite show that, neither from pure geometric argument nor from a more engineering based argument. It almost shows it but not quite...

n55/n54
Bore: 84 mm
Stroke: 89.6 mm
Bore spacing: 91 mm
Displacement 2.979 l

Cylinder wall thickness between cylinders = 91 - 84 = 7 mm = .28". Just over 1/4 inch.

To get to 3.2 l (a rumored displacement) with bore change alone requires a bore of:

2*((3.2/2.979)*(84/2)^2)^(1/2)

Or 87.1 mm. Let's call it 87.

That would leave .15 inch of material between the cylinders. A shade more than 50% of what you can see in this picture (n54 block shown, these features are identical on the n55 block). Although this looks and feels too thin, engineering is not about look at feel. The stress in this portion of the engine will be roughly

σ = peak combustion pressure * (bore/2)/(thickness between bores)

(Note: This is the simplest thin walled cylinder approximation, which should be decent in this case.)

The peak combustion pressure (really rough estimate) is probably around 1000 psi (full load, high rpm). Anyone want to help me revise that estimate? This IS NOT BMEP, but peak dynamic combustion pressure.

Thus going from 3.0 to 3.2 liters by bore alone will increase the stress in this region by the same ratio as the wall thicknesses, nearly 200% in this case (x 1.86)!

The wall is certainly strong enough to handle a single combustion cycle. The limiting factor in design here is very likely "high cycle fatigue". This is just the repeated loading of the combustion cycle continuously weakening the material on the thin walled aluminum in this area. A practical limit for the allowable stress in typical aluminum alloys used for heads and engine blocks (say A356 alloy at an elevated temperature of 300 deg F) is in the 13000 psi range.

In the new 3.2 l hypothetical design the cylinder wall stress would be about 11000 psi. Very close the 13000 limit.

So in short, without sleeving, the n55 could likely enable a 3.2 l engine by bore increase alone. However, it appears to be producing a design very near fatigue limits. Thus, unlikely but not impossible.

My prediction for the engine is > 3.0 liter displacement and that will be gained by bore and stroke. I think that was also my prediction before this simple investigation...

As I've noted before even 400 hp from a 3 liter engine is already reaching the same hp/l as the Porsche Turbo. An additional reason I think the displacement must be going up.
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