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# Dynamic torque signature6

## Dynamic torque signature

(OP)
Assume that mean piston velocity, displacement, and brake mean effective pressure are constant. Also assume (for the purposes of this discussion) that the crankshaft is infinitely long.

Regarding torsional excitation to the crankshaft, we know that the torque dynamic signature is much greater for an even fire 4 cylinder engine than it would be for an even fire V12 (with everything else held constant).

But we can also readily estimate (from first principles) that the torque signature for a 4 cylinder even fire engine is about the same independent of the stroke-to-bore ratio. That is, a larger bore / smaller stroke engine will have a higher rod force but a smaller moment arm, and the smaller bore / larger stroke engine will have a lower rod force but a larger moment arm.

My question is this: Is anyone aware of any secondary effects that would make the dynamic torque signature (and torsional excitation) different if one differs the stroke-to-bore ratio?

I am trying to determine the expected torsional driveline issues that may occur from a constant mean piston speed and high bmep 4 cylinder diesel engine given everything constant except the stroke-to-bore ratio.

### RE: Dynamic torque signature

Not quite on-topic but if mean piston speed is held constant, the shorter stroke engine will turn at higher rpm and therefore develop more power.

On-topic, you could also consider "inertia torque" - a major component of torsional excitation - particularly in 4 cylinder engines. Piston mass increases in proportion to bore cubed. Velocity (at const rpm) increases in proportion to stroke which decreases in proportion to bore squared (for const displacement).

je suis charlie

### RE: Dynamic torque signature

... and the higher-rpm shorter-stroke engine will have greater inertial torque effects and at a different frequency because everything is happening faster. But if this is a high-BMEP diesel engine, normally the RPM will be constrained by factors other than piston speed and acceleration, which may mean the constant-piston-speed constraint is not a realistic one.

Do you not have a really healthy vibration damper built into the flywheel/clutch/torque-converter/?? If it is a high-inertia load, you're going to need one for an engine like that.

### RE: Dynamic torque signature

(OP)
Thanks, gentlemen, your posts are very helpful. FYI - the application is a flat (boxer) four cylinder diesel engine for an aircraft application. We are looking to use a pendulum damper system either external of the crankshaft (like a Schaeffler CPA) or internal to the crankshaft (classic pendulum torsional absorber). We are looking at a constant speed (direct drive to propellor) of about 2700 rpm which yields a mean piston speed of about 2000 ft/min (not particularly high for automobile engines but in the ball park for constant high bmep constant speed engines). We are looking at a bmep of about 450 psi (about 30 bar). The current engine configuration is oversquare, which makes it different than most all of the automotive diesels (except perhaps the Chevy Duramax). I am trying to determine if we may be exacerbating the torsional signature with the oversquare configuration, but I can't find any reason or published data to support a concern.

### RE: Dynamic torque signature

Is this a new design, or are you torturing an existing design with lots o' boost ?

Longer stroke with the same diameter rod and main journals reduce journal "overlap" which I think generically has greater effect on bending stiffness than torsional stiffness.
Thus a short stroke oversquare design generically has a "stronger" crank.
When Oldmobile diesel-ized their 350 engine they increased the main journal Ø from 2.5" to 3.00". There may have been other upgrades as well.

I'd think a pretty basic FEA model of the crank, flywheel, etc with a nominal concentrated mass at each rod journal, constrained radially in a narrow ring at the center of each main bearing, and with soft springs stuck all over it, would provide pretty good info whether firing pulses are likely to excite any torsional resonances in the operating range. I'd be very concerned about 2nd, 4th and 8th order excitation.

Then again BMEP of 450 psi is likely to make things unpleasant for the crank and rods in any number of ways.
- Crank Bending with high stress at the rod and even main journal fillets
- Crank flange attachment

Probably the crankcase will breaking into a sweat and subsequently fatigue cracking thru the main webs or etc too.

### RE: Dynamic torque signature

So, the upshot is that your RPM will be fixed by the target RPM of the propeller (owing to being direct drive!), and in reality you are thus talking fixed RPM, not fixed piston speed.

There are 2 parts to the torque fluctuation, the part due to the engine's thermodynamic cycle (compression and power strokes), and the part due to inertia of the pistons and rods being transferred to and from the crankshaft. The traditional inline-four layout is bad for the latter, but a boxer-four is no better.

In the absence of being able to put numbers to anything ...

The pistons have to be strong enough to withstand the peak cylinder pressure. This means the pistons of a wide-bore-short-stroke engine will be heavier. First-order approximation, that goes up with the cube of the key dimension (cylinder bore). But it will be making a smaller stroke, and that stroke is going down with the inverse-square of the cylinder bore. In terms of kinetic energy ... that is a function of the square of the velocity and thus stroke. Getting messy ...

Easier to understand to put round numbers to it; nevermind their absurdity because we are only looking for the trend and thus, easy numbers. Start with bore 1 and stroke 1. Then compare to bore 2 and stroke 0.25 to get the same displacement. Piston mass goes from 1 to 8 (cubed). The piston speed goes from 1 to 0.25 (proportional to stroke). The speed-related factor in the kinetic energy equation is speed squared so 1/16th. So the amount of kinetic energy being handed back and forth between the pistons and the crankshaft depends on both the mass and the velocity-squared. Bottom line ... the wide-bore engine has heavier pistons but the much shorter stroke to achieve the same displacement more than offsets it in terms of how much it influences the irregularity of crankshaft rotation.

Furthermore, the crankshaft of the wide-bore engine is going to have to be heavier in order to withstand the combustion forces because that goes up with bore squared. And that further reduces the irregularity of crankshaft rotation.

High-performance engines almost always have a bigger bore than stroke.

I think you're still going to need some sort of way to soak up that irregularity; presumably the blades of the prop won't like being whipped back and forth by the irregular speed of the hub.

### RE: Dynamic torque signature

(OP)

More details below. (If you are getting tired of this, I understand. But I will try to get as much guidance as possible for now.)

As I said above, it is an aircraft application. The engine will be basically new, but the aircraft diesel engine market is not nearly large enough to support the cylinder CFD and combustion technology development as the automotive market (passenger car, personal truck, or commercial truck) supports with the relatively large automotive volume. Hence this aircraft engine will clone the top end combustion chamber config, valve config, etc. of a proven diesel engine design into a boxer four cylinder for aircraft application. I have considered using a six cylinder, as I could likely meet the performance targets with a 3 liter 6 cylinder diesel. The problem is this: all those 3 liter 6 cylinder diesel engines (mercedes, bmw, etc.) that can make the performance targets are overhead cam engines. The application does not have room for the installation of a boxer engine with overhead cams.

The performance targets are simple: full power at 2700 rpm and 270 bhp (about 200 kW). Typical idle speed is 1200 - 1500 rpm. There are NO current emissions requirements, but smoky combustion will clearly be a marketing drawback. The engine will have a two stage turbocharger system to supply adequate air for full power at 17,000 feet standard altitude conditions (about 0F and 15.6 inches Hg absolute).

Tmoose points to potential bearing and crankshaft design issues which I think are very real but treatable. The issue that scares me most is torsional resonance, as any resonant condition and the associated cyclic loads will likely result in early fatigue failure somewhere in the driveline.

So let me pose my question this way: Is there any consideration that should be given to the stroke/bore ratio? Is there any significant difference in the torsional signature between the Duramax cylinder oversquare config (103mm bore, 99mm stroke) versus the Powerstroke cylinder undersquare config (99mm bore, 108mm stroke). I think both configurations are capable of 400 psi bmep (I originally overstated the goal at 450 psi bmep) at 2700 rpm. I think the lack of emissions requirements and transient response requirements make the problem statement a bit easier for the aircraft application than the automotive application.

I have looked at an existing aircraft 4 cylinder diesel engine with a bore of 126mm and a stroke of 100mm, and there appear to be (based on second hand reports of test results) some significant issues with torsional loads. But that may just be a result of the 4 cylinder configuration and the diesel cycle, and not related to the highly oversquare configuration (which is very odd for a diesel engine).

Thanks for taking the time to read and comment.

### RE: Dynamic torque signature

(OP)
Thanks to Brian for his post - he really helped me to think the issue through.

Also just for info (and info that makes Brian's response even more salient) - the engine will have steel pistons (with an aluminum head and aluminum case).

### RE: Dynamic torque signature

Good call on the steel pistons for that BMEP level. Do you have handle on these other aspects:
• exhaust temperature - components that will be exposed to it - i.e. exhaust valves,
exhaust manifolds/pipes, turbine housing
• intake and exhaust manifold pressures - is your high pressure turbo designed for these pressures?
• low pressure compressor out temperature - can high pressure compressor handle this, or will there be an intercooler?

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

### RE: Dynamic torque signature

(OP)
Hemi - very good points, thanks.

1. I agree that exhaust gas temps many get quite high (as compared to a typical diesel). For our relatively low volume application, we can afford to make exhaust system from high temp alloys. We will likely use CRES 321 (so that we can weld pipes without worry of carbide precipitation), but we may consider Inco 625. I expect that we will need to use metal bellows to avoid high thermal growth related stresses. See pic in link for similar example.

https://en.wikipedia.org/wiki/SMA_SR305-230

2. We are planning to use robust thrust bearings on both turbos, but pressures are not much higher than typical sea level high bmep diesel engines. For example, at 17,000 feet, absolute pressures are approximately thus: LP in - 7.5 psia, LP out - 20 psia, HP in - 19.5 psia, HP out - 40 psia.

3. Low pressure compressor out temperature is a bit high, but the tip speed of the HP compressor is low enough so that a forged aluminum wheel should have adequate allowables. (If the turbocharging were done with a single stage, then the tip speed would be much to high for aluminum at the single stage compressor outlet temperature. We would need to use a titanium alloy for the wheel, and the weight of the wheel and the containment qualified housing would increase significantly (per Federal Aviation Reg 14 CFR 33.27).

An example of expected air temperatures, at 17,000 feet: LP in temp - 460 R (0 F), LP out temp - 660 R (200 F), HP in temp - 660 R (200 F), HP out temp 860 R (400 F). The 400 F HP comp out is a concern, but also we would rather not add the cooling drag of an additional air/air intercooler to the package. We may need to consider a air-to-liquid intercooler between the compressor stages (which may require a separate liquid coolant loop to get a liquid coolant temp that makes sense).

And, as may be obvious, system performance at altitude will be better when the altitude ambient air is colder than standard, and will be negatively impacted when ambient air at altitude is warmer than the standard. A very hot day take-off from Leadville, CO will likely not make full power before hitting the HP comp out temp limit, which will be an input used to limit the fuel input.

Thanks for your comments, as they cause us to think through some of these system issues a second and third (or fourth or whatever) time.

PS. This gets a bit long, so you may want to skip this part. We expect to size the turbine A/R (and therefore the turbine flow curve) so that we get similar temperature rise on both compressors at the rated altitude condition. A similar temperature rise equates to a similar true tip speed, while the pressure ratio is a function of Delta T/Tin. So the pressure ratio of the HP compressor is significantly lower that that of the LP compressor because the inlet temperature of the HP is much higher. But the work is about the same for both (work = mdot * Cp * Delta T), and the tip speed of the both compressor wheels are about the same. (Actual total work (reversible and irreversible work) added to the air, as measured by the adiabatic temperature rise, is a function of the tip speed as defined by the Euler equation.)

### RE: Dynamic torque signature

The small difference in bore/stroke ratio that you are talking about ends up as noise. What will actually matter is the real, actual, reciprocating weight of the pistons. Having steel pistons doesn't help your cause but I understand why you want to go that route.

This not being an automotive application, it doesn't necessarily need to spin up to full-load RPM in an instant. A flywheel with a high MOI (heavy rim, biggest diameter you can manage) will help your cause.

A flat-four configuration is short enough that I suspect that torsional vibration in the crankshaft itself will have a frequency outside your operating RPM range (it is sure to be way higher) and that is good.

But I have zero knowledge of how a propeller would cope with it.

### RE: Dynamic torque signature

Oversquare is typical for boxer engines - think packaging.

je suis charlie

### RE: Dynamic torque signature

As I'm sure you know, having an inter(stage)cooler does a couple of things for you:
1. Overall compression work is reduced (assuming the same stage efficiencies), which equates to lower backpressure to the engine, which equates to higher BMEP and thermal efficiency, other things being equal. Higher BMEP and thermal efficiency can allow a reduction in displacement, hence engine mass, and fuel load, all of which offset the mass and space claim of the intercooling.
2. Cooling the first stage compressor out air reduces the required size of the second stage compressor. This effect can be further leveraged by biasing the pressure ratio split toward the HP compressor, which in turn leverages point 1. The resulting smaller HP turbocharger partially compensates for the added mass and space claim of the intercooling. And, for what it's worth, the smaller HP turbo will give faster overall boost response, considering that in a bootstrapping scenario, the HP stage does the initial heavy lifting.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

### RE: Dynamic torque signature

...what is more, a cleverly designed cooling system can offset and possibly negate cooling drag, as was the case with the WWII Mustang fighter. At high forward speeds, expansion of the cooling air through a low restriction cooling core can, in principle, generate net forward thrust.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

### RE: Dynamic torque signature

When you say "the crankshaft is infinitely long", did you mean the connecting rod?

Otherwise, nobody has mentioned the effects of basic engine balancing. For an I4 engine, the level of the 2E out-of-balance is strongly affected by the bore/stroke ratio. And for most automotive I4 engines, inertia forces dominate the torsional behaviour at 2E, above about 2000-3000 rev/min.

Steve

### RE: Dynamic torque signature

(OP)
EHudson - Thanks, I will get a copy. I have not read that text. (And the insert has already answered a question that I had regarding pendulum dampers!)

SomptingGuy - Good catch, and yes, I meant "connecting rod". Sometimes there is a disconnect between my brain and my fingers.

### RE: Dynamic torque signature

Horizontal-opposed engines tend to have short connecting rods, same reason as generally having big bore short stroke. Otherwise the engine gets too wide.

But the good news is that a horizontal-opposed engine of the usual "boxer" arrangement - in which the corresponding pistons on each side are both moving out together or in together - cancels out most of the 2nd-order harmonic that plagues a traditional inline-four layout. (It may not cancel 100% because the cylinders on the left and right bank can't be directly opposite each other - they need separate crank journals, so one bank is always a little forward of the other along the crankshaft.)

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