Comments by "El Ectric" (@electric7487) on "driving 4 answers"
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Using a longer rod length not only helps to reduce secondary vibrations, but also helps to reduce higher-order oscillations that can be difficult to suppress.
Most people know that, in any piston engine, the piston's secondary motion can be broken down into a primary component (one that varies at the same speed as the crankshaft) and secondary component (varying at twice the engine speed). However, what most people don't realise is that the secondary vibration itself is not perfectly sinusoidal and will have harmonics (whole number multiples of the fundamental frequency).
The secondary motion becomes more "pointed" at mid-stroke (less sinusoidal) with lower rod ratios, and as the secondary motion gets more and more "pointed" both the secondary oscillation itself and its harmonics (4th order, 6th order, et cetera oscillations) increase in amplitude.
The peak-to-peak amplitudes of the secondary oscillation's fundamental and harmonics can be calculated by:
A = 2 / π * ∫(cos(nθ) * √(L^2 – (S sin(θ) / 2)^2) dθ, –π to π)
Where n is a non-zero even number, L is the rod's centre-to-centre distance, and S is the stroke length.
This effect is most prevalent on large two-stroke low-speed marine Diesel engines, where the rod ratio is often around 1 or less than 1. (to the point where they need crossheads to take up the lateral thrust). The reason is that these engines have extremely long strokes, so by using crossheads and short rods they can make the engine shorter in height.
Most of these engines also lack balance shafts, so they transmit almost all of their external forces and external rocking moments to the ship (for a marine application) or foundation (for stationary land-based power generation). This problem is aggravated by the fact that the components are all very heavy, which makes the forces even greater.
Take a look at MAN Diesel's project guides for their two-stroke engines (K-model, L-model, S-model, and G-model engine families, though as of 2022 they don't make K or L engines anymore), and on the section where they list the firing orders of each of the variants they will also list not only the first- and second-order vibrations, but also the second- and third-order harmonics of the secondary vibrations (fourth- and sixth-order vibrations). For example, although the 12G90ME has perfect primary balance, they do not have perfect secondary balance. Although there is no second-order rocking moment, the second harmonic of the secondary vibration is still significant and produces a fourth-order rocking moment of 724 kN•m (534000 lb-ft) at 84 RPM (which is conveniently twice that of the 6G90ME's fourth-order rocking moment of 362 kN•m).
The greatest offenders are the secondary rocking moments on five- and six-cylinder engines, which is why they sometimes are fitted with balance shafts.
Large six-cylinder engines also have a sixth-order vertical shake. The heavy components and short rods already make fourth- and sixth-order oscillations a problem, and the 60° spacing between crank throws doesn't help either, as the sixth-order forces (the secondary vibration's third harmonic) for each cylinder all point in the same direction. The sixth-order vertical shake on the 6G90ME has a magnitude of about 32 kN (7200 lbf) at 84 RPM. The same is true for four-cylinder engines, as regardless of the firing order the secondary vibrations' second harmonics all point in the same direction, resulting in a fourth-order vertical shake.
You'll also notice that the 10- and 11-cylinder engines have non-zero net external forces. This makes me suspect that the 10- and 11-cylinder engines are odd-firing, because if they were even-firing the net forces should all be zero.
The reason you only have to deal with primary and secondary vibrations on most engines you'll come across is because their rod ratios are relatively high and their components are relatively light. So not only are the secondary vibrations smaller, they are also much closer to being sinusoidal, which means the higher-order harmonics of the secondary vibrations are negligible.
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7:38 Not really—the R1's crank clearly has counterweights. Obviously the purpose of the weights is to reduce vibration, but the way the weights reduce vibrations is by translating the fundamental vibration (a straight front-to-back rocking moment) into a different imbalance that is more manageable.
The reason that many engines use balance shafts is because they not only have external forces or moments, but the vibration's horizontal and vertical components are different. Engine configurations that have this problem are:
- Inline twins (360° has 1st and 2nd order forces and no moments, 180° has a 1st order moment and 2nd order force, 270° has 1st order forces and moments and a 2nd order moment)
- Inline triples (120° even-fire has 1st and 2nd order moments and no forces, 180° flat plane has 1st and 2nd order forces but no moments, and Triumph's 90° T crank engines have 1st order forces and moments and a small 2nd order force)
- Any even-firing inline engine with an odd number of cylinders (3, 5, 7, 9, _et cetera_)
- Most 2-stroke even-firing inline engines with an even number of cylinders, such as the crossplane I4 (which is essentially a two-stroke I4 modified to run as a 4-stroke)
- Most even-firing V twin, V6, V10, V14, and V18 engines with V angles that aren't 90°
Real-world examples:
- 72° V10's (with non-split crankpins)
- 90° even-fire V10's (+18° split crankpins, residual primary couple is greater in the vertical direction)
- 90° even-fire V6's (–30° split crankpins, residual primary couple is greater in the horizontal direction)
- 60° crossplane V8's like the Caterpillar 3508 (60° V angle, also with –30° split crankpins; this may be the largest displacement piston engine ever built with split crankpins)
The crossplane I4 shares the same problem as even-firing inline engines with odd cylinder counts in the sense that its primary rocking moment (that is of the most concern) has a vertical component that is much greater than the horizontal component.
The crank weights "average out" the vertical and horizontal imbalances (so that the corrected imbalance's horizontal and vertical components are the same) by providing a circular imbalance of their own that is one-half of the sum of the vertical and horizontal components. And now, because the corrected imbalance is approximately circular, it can then be taken care of by a counter-rotating balance shaft which provides a circular force or moment that is one-half of the difference of the components.
There are only two exceptions I'm aware of:
- Detroit Diesel and EMD two-stroke Diesel engines: The crank weights cancel out only the horizontal portion of the imbalance and most of the vertical component is taken by two pairs of weights on the camshaft (since they are 2 stroke the crank and cams rotate at the same speed)
- MAN 32/40 marine Diesel engines: The crank weights on the V engines are the same as those on the inline engines, and as a result they cancel out only half of the average imbalance. This results in the residual imbalance on the V14 and V18 engines still being greater in the vertical direction. In general, on large marine Diesel engines external forces and moments are left unchecked and the ship's structure must be designed to take these vibrations into account.
Even on engines that are inherently balanced, like almost all 4-stroke V12's, you'll often still see counterweights because the weights help reduce the engine's internal stresses and increase the crankshaft's torsional stiffness.
The reason why 90° V engines (with with non-split crankpins, except maybe flat-plane V8's) don't need counterbalance shafts is because the primary imbalance's vertical and horizontal components are the same to begin with, so crank weights are all that are needed.
The same is true, in fact, of the 60° V6's used to power so many cars and SUV's. The 60° V angle with –60° "flying arms" also makes the primary rocking moment's horizontal and vertical components nearly identical, which is why 60° (4-stroke) V6's don't need balance shafts but 90° (even-firing) V6's do. On a 60° V6, the secondary rocking moment is apparently deemed to be not significant enough to warrant further vibration reduction measures, so it is left unchecked.
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(Posting this here so that hopefully people will see it) I'd like to add a few extra points in addition to what you pointed out in the video:
Most people don't know this, but another reason that most V6's are 60° is because this V angle offers perfect primary balance while maintaining even firing intervals.
120° and 90° even fire V6 have bigger horizontal imbalances than vertical for each pair of cylinders resulting in a rocking moment. If the peak primary force of each piston is 1, the peak horizontal and vertical imbalances are 1.5 and 0.5 respectively for a 120° V6. The crank weights are sized to balance out the average of the imbalances so that the remaining imbalance is circular. In this case the remaining imbalance has magnitude 1, so a single balance shaft generating a force of 0.5 (with weights 180° out of phase) would have to be used. But as D4A mentions in the video, a 120° V angle is very wide, and you might as well use a boxer 6 at this point.
For a 90° odd-fire V6, primary balance is perfect as a 90° V-twin has perfect primary balance, and crankshaft weights can be used to balance out primary vibrations. The problem is that when you have non-split crankpins on a V engine, at least one of the firing intervals must be equal to the V-angle, and what happens in the case of an odd-fire V6 is that the engine's firing intervals alternate between 90° and 150°, as he explains in the video. (This is also why the 90° V10's used in the E60 M5, Viper, R8, and Huracan are odd-firing, as their use of a 90° V angle and non-split crankpins results in firing intervals alternating between 90° and 54°.)
For 90° even-fire V6, each crank pin has a –30° split to give 120° firing intervals. Vertical imbalance is 2 * cos(90° / 2) * cos((90° – (–30°)) / 2) = sqrt(2) / 2 = 0.7071 (again relative to a peak piston primary force of 1) and horizontal imbalance is 2 * sin(90° / 2) * sin((90° – (–30°)) / 2) = sqrt(6) / 2 = 1.2247. The average of the imbalances is cos(15°) = (sqrt(6) + sqrt(2)) / 4 = 0.965925, so the crank weights are sized to generate that force. The balance shaft weights are then sized to generate a force of (sqrt(6) – sqrt(2)) / 4 = 0.258819 and are again 180° out of phase with each other.
For a 60° V6 with –60° flying arms, both the horizontal and vertical imbalances are 2 * sin(60° / 2) * sin((60° – (–60°)) / 2) = 2 * cos(90° / 2) * cos((90° – (–30°)) / 2) = sqrt(3) / 2 = 0.866. This means that primary forces on a 60° V6 can be almost completely cancelled with crank weights without needing balance shafts.
All 3 configurations will also have a slight secondary rocking moment, but this does not appear to be an issue in V6's as the magnitude of the vibrations is normally pretty small.
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The Ford V10's have crankpins split forward by 18° so that each pair of cylinders fires 72° apart. The same is true for the older 5.0 Lambo V10, which is why you can make a Gallardo sound like F1.
Even fire V10 pros: Even firing, less torsional vibration (instantaneous torque goes between 1.58 and 0.36 times the mean torque), smoother, lighter flywheels can be used.
Even fire V10 cons: Perfect primary balance requires a boxer configuration or 108° V angle with +36° split crankpins. 90° and 72° angles have a significant primary rocking moment. Split-pin crank not as strong or stiff as common-pin crank.
The Dodge Viper, BMW S85, and 5.2 Lambo engines have non-split crankpins and thus fire unevenly (with firing intervals alternating between 90° and 54°). This is why the Huracán sounds like a 5 cylinder and can't sound like F1.
Odd fire (90°) V10 pros: Perfect primary balance with only crank weights needed (no balance shaft), stiffer crankshaft.
Odd fire V10 cons: More torsional vibration (instantaneous torque goes from 1.91 times to 0.012 times the mean torque, and you have more high-order harmonics, with the 7.5 and 12.5 orders being the worst offenders in this engine), rougher running, heavier flywheel required.
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Let's say you have a 32L Diesel engine and an engine from a Kawasaki ZX-25R. Your Diesel can make 3,000 ft-lbs of torque while the ZX-25R's engine only makes 16.89 ft-lbs. You want 1,200 HP out of both these engines. How fast would both of these engines need to spin at in order to make 1,200 HP at max torque?
Diesel: 1200 / 3000 * 16500 / π = 2100.8
Zx-25R: 1200 / 16.89 * 16500 / π = 373152
As you can see, the Diesel, if it's making 3,000 ft-lbs of torque, would have to get up to 2,100 RPM in order to make 1,200 HP. The little motorcycle engine, on the other hand, would have to get up to 373,000 RPM.
Good luck with that.
In this example, one can see that an engine that can generate lots of torque can easily make power even at very slow speeds. They are typically much more limited, though, in how fast they can turn because they often have heavier components and will often run, in their cylinders, longer stroke lengths than bore diameters.
Smaller engines with high power-to-weight or power-to-displacement ratios cannot produce lots of torque, but they can make up for their lack of torque by spinning at fast speeds using very lightweight components, along with (generally) short strokes and big bores.
They sacrifice longevity, though, as fast speeds generally mean a lot more wear and tear, so those small high-revving engines generally will not (and cannot) last 1,000,000 miles like a Diesel can.
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One other benefit of the 60° V6 that he didn't mention is that, when combined with –60° flying crankpins, it has perfect primary balance when crank weights are used. It does not need balance shafts, since for each pair of cylinders the vertical and horizontal imbalances are roughly the same.
With the 90° V angle, non-split crankpins result in uneven 90° and 150° firing intervals, but it does have perfect primary balance with crank weights. To make it even-firing, the easiest way to do so is to split the crankpins by –30° so that each pair of cylinders hits TDC 120° apart. However, by doing this you lose the perfect primary balance as now the imbalances for each pair of cylinders has a greater horizontal component than vertical component. Here, the crank weights "average out" the imbalances, and by doing so that they undercompensate the horizontal vibrations and overcompensate the vertical vibrations. The crank weights are sized such that the residual vibration from the over- and under-compensation is roughly circular, which means only one balance shaft is needed. The balance shaft adds to and subtracts from the crank weights alternately so that the vertical and horizontal vibrations are properly cancelled out.
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