Harmonic's In The L Series, In-line 6 Cylinder Engines - a Discussion.

Contributed By: Zorro

The Purpose of this page is to give the reader a simplified understanding of harmonics that effect the L Series, In-line 6 cylinder engines, as used in the first and second generation Z Cars.

The following discussion is reproduced, with permission from the author, from the IZCC's, on-line, e-mail based, Z Car discussion group - "the Z Car List"

To: z-car@taex001.tamu.edu
From: "Zorro Zman"zorrozman@hotmail.com
Subject: Vibration vs harmonics, attempt to clarify
Date: Thu, 21 Jun 2001

Edited Sat, 23 Jun 2001

I've read the vibration / harmonics thread with interest for a while, and would like to throw in a little clarification, at the price of a little more geekiness. It seems to me that there are some less than complete statements being forcefully stated as the absolute and complete truth; it is a mistake to treat engineering textbooks the same way some people treat the Bible, as the ultimate, literal, and complete truth. It also seems to me that there is some incorrect terminology being used. So lets see if we can make this any clearer.

The very first point to understand: Newton's laws tell us that the centre of mass (loosely, centre of gravity) of an object wants to stay put (or move with constant velocity) unless acted on by an external force. That means if you rearrange the mass inside an object, such as by pushing a piston up a cylinder bore, the object itself tries to move in such a direction as to cancel out that mass rearrangement. In our example above, if you push the piston up the bore, the entire engine block tries to move in the opposite direction. If you hooked up an electric motor to a single-cylinder engine and spin it, with no fuel or spark supplied, the engine wants to shake and vibrate due to the moving masses inside.

When the engine is being supplied with fuel and spark, there is an additional shaking force, due to the engines power strokes. The vibration from a running engine comes from both the internal mass rearrangements, and the pulsating force from the exploding air/fuel mix.

As I understand it, in simplified but essentially correct terms, due to the mass of the piston moving up and down in the cylinder, the engine block wants to shake up and down (i.e. along the cylinder bore axis); this is the primary or first order force shaking the engine. Due to the mass of the connecting rod swinging from side to side, the engine block wants to shake from side to side; this is the secondary shaking force.

From what I know at this point, it is these two forces which cancel out in a spinning - BUT NOT FIRING - inline-six, flat six, or V-12. By "cancel" we mean that the interrelated motion of the various pistons and connecting rods act in such a way that no net force acts on the engine block to shake it. As one piston moves down, another moves up; as one piston rod swings left, another swings right. Net result: no shaking force in either the axial direction (along cylinder bore) or at right angles to this.

Here's where the first additional complication comes in. An engine block (or any other chunk of matter in a 3-dimensional universe) is free to move (or shake!) in SIX basic "directions", or more precisely, degrees of freedom. The first three are straight-line motion along three mutually perpendicular directions, usually called the x,y,&z axes. The second three are *rotations*, or twisting motions, once again about three mutually perpendicular axes.

In discussing the "perfectly balanced" inline six above, we have so far only considered two of these six degrees of freedom. The third linear motion is back and forth along the crankshaft axis - and *any* engine that has its cylinder bores truly perpendicular to this axis should not have any shaking force in this direction. So far so good.

Okay, its time to look at the three rotational degrees of freedom. First, the motion where the front of the engine goes up-and-down, and the rear of the engine goes down-and-up, i.e. what is commonly called a pitching motion. For instance, if piston #1 is going down as piston #6 is going up, the engine will want to vibrate in this pitching mode.

If the engine is perfectly symmetric about its midplane, these forces cancel out. It appears that by choosing the correct firing order and matching crank design, this vibration can be eliminated in an inline six. Notice that this doesn't just happen for any inline six, only for correctly chosen firing orders.

The second rotational degree of freedom is what is called "yawing" motion - front of engine goes right-and-left, rear of engine goes left-and-right. Essentially the same arguments apply here as for the paragraph immediately above this one. Symmetry of the engine about its midplane is what is required for cancellation of this force.

The third degree of rotational freedom is twisting along the crank axis, or "rolling". If the engine is spinning over but not firing, it may be possible to arrange things so that there is no net shaking force in this direction, but I am a little skeptical of this. If the valve events were exactly symmetric about TDC then the force needed to push one piston up the bore would be exactly balanced by the force of the compressed air pushing another piston down. But the valve events may not be symmetric in this way...

All the discussion above was for an engine being spun over, but not actually firing. The moment the engine starts to actually be supplied with spark and fuel so that there are power strokes, most of the arguments above no longer hold. The moving masses may counterbalance each other, but what about the force from the rapidly expanding gases on the power strokes? If cylinder #1 in an L6 fires, it wants to push the front of the engine block up; when cylinder #6 fires, it wants to push the front of the block down. That means that cylinders #1 and #6 will tend to set up a pitching force on the engine as they fire. The only way to cancel this pitching force would be for cylinders 1 and 6 to fire *simultaneously*. But if they do fire simultaneously, they *both* push the block down, so now you have a shaking force in the up-and-down direction. Since no cylinders point upwards in an L6, there is no way to cancel this out with other firing strokes! In short, if you try to cancel one of the six degrees of vibration, you only make things worse in another. Not to mention firing off multiple cylinders at one time makes for a very jerky supply of torque! I can imagine a mirror-symmetric flat-four engine with a flat crank and all four cylinders firing off simultaneously - in theory all the sideways shaking forces and two of the twisting forces would cancel, but there is major shaking about the third rotational axis - along the crank - due to only one power stroke every two revolutions.

This third rotational degree of freedom - twist about the crank axis - is *never* balanced in any running (firing) internal combustion engine. It doesn't matter if this is an inline six, a V-12, or any other magical configuration. First of all, all the torque the engine makes is in this direction! If the forces in this direction were perfectly balanced, the engine would not put out any torque, or horsepower. Secondly, if you look in detail at the force in this direction, it is a series of pulses, hammer-blows resulting from the firing of the various cylinders. Any repeating time sequence of pulses like this can be studied using the mathematics of the Fourier series, and it tells you that a train of hammer-blows like this contains harmonics - not just a few harmonics, but hundreds of them.

In light of this, I believe a more correct statement is that inline six, flat six, and V-12 engines have no net shaking force *when they are spinning but not actually firing*. Once actually running (firing), ALL internal combustion engines have both shaking forces AND harmonics acting in at least one degree of freedom, i.e., torsional motion about the crankshaft axis. In most cases there are also shaking forces in several of the remaing five degrees of freedom.

And the purpose of the doohickey on the front of the crank - call it a harmonic balancer or a vibration dampener or the Grand Panjandrum With the Little Round Button On Top, that doesn't change its function - is to reduce the damaging effect of this pulsating, vibrating, harmonic-laden force twisting the crank.

From the discussion above, it also sounds to me as though various other now-defunct engine layouts probably had the same cancellation of the six shaking modes when spinning but not firing. The requirements of fore-and-aft symmetry requires an even number of cylinders or a radial engine, like WWII aircraft engines. I suspect straight-8 engines, flat 8's, and radial engines could all be designed to achieve the same cancellation as an inline six, flat six, or V-12.

One final thing, this one a matter of personal opinion. Don't be so quick to believe that all American engines are poorly designed turds. Don't forget that an American engine - a Ford V8 - in Shelby's Daytona coupe beat the pants off Ferrari's best (not to mention every other manufacturer of race cars that year). Don't forget the total dominance of the Vipers with their American V-10 engines in their racing class these last few years at Le Mans. And if American engine designs are so bad, how come an American design - the Mopar Hemi - is used in all the fastest accelerating race cars on this planet today?

In a follow-up to the discussion thread -Zorro Writes:

To: z-car@taex001.tamu.edu
From: "Zorro Zman"zorrozman@hotmail.com
Subject: {L6}Vibration vs harmonics, edited 2nd post
Date: Thu, 21 Jun 2001
> jpd280z@hotmail.com - Writes:
>....since the engine is firing off those hammer blows (or
>, hamster blows,in my case) about 9K - 18K times per minute
> (about every 1/200th of a second), it seems like the torque
> spike may not get back to the zero mark before the next blow
> pushes the engine around.

Zorro Replies:
Perhaps there's an easier way to look at this: in a 6-cylinder, 4-stroke engine, there are three power strokes per revolution, meaning that there's a power stroke occuring every 120 degrees of crankshaft rotation. Now the entire power stroke (TDC to BDC) occupies only 180 degrees of crank rotation; if the piston were pushing down and making power during its entire power stroke, the torque spike would indeed never drop to zero.

In practice, the piston doesn't really make power all the way down the power stroke, a better guess that it makes significant power only for the first half of the downstroke, or about 90 degrees of crank rotation. That leaves a full 30 degrees of little to no power to the crank before the next cylinder fires. During these 30 degrees when there is no power or torque from the piston - the crank is coasting due to the flywheel effect of all that rotating mass (crank, flywheel, clutch, harmonic balancer, etc). So the torque pulses are indeed pretty darn spiky. Maybe rubber mallet blows instead of steel hammer blows, but still spiky!

The more cylinders you have, of course, the less spiky the torque force gets. If you had a 16-cylinder engine, with a cylinder firing every 45 degrees of crank motion, then the torque might actually never die down to zero. Anyone put a V-16 in a Z-car? :)

>And, I have rubber engine mounts to absorb some of the twisting of
>the blows. Why/how can a rubber ring on a pulley help, other than
>protecting the water pump, alternator, and (on those vehicles
>so-equipped) the A/C compressor, which are connected with a rubber
>belt that slips slightly anyway? And the REAL question, do I hafta
>have that heavy pulley/damper if I balance everything internally
>(pistons, rods, crank, rings, bolts, pins, etc.) in order to have an engine
>that will turn 6,000 rpm safely and last 100,000+ miles?

The rubber engine mounts are there to keep the vibrating engine from shaking the cars body, and eventually the driver; as you say, the water pump, alternator, AC compressor are not really at risk due to the stretchy rubber belt that hooks them to the engine. What IS at risk is the crankshaft itself! Think about it,here's a long skinny forging, subject to heat, hundreds of horsepower, lots of torque trying to twist it in half, and - the final straw - maybe 20,000 hammer blows every minute. Hit a length of steel pipe with a hammer and it "rings"; grab the tip between your rubbery fingers, and it stops ringing. In the same way, the repeated "hits" from the power strokes make the crankshaft "ring", it twists back and forth along its length. This twisting is severe enough to cause metal fatigue over time, breaking the crankshaft in half. The rubber in the damper does the same thing as your rubbery fingertips did to the ringing length of pipe: it reduces the amount of "ringing" in the crankshaft, and thus the risk of damage due to metal fatigue.

The only thing achieved by internally balancing your engine is that it coasts smoothly when it's turning over *without* firing. This is important, it makes for longer lived parts. But no amount of balancing, internal or external, can make the hammer blows from the power strokes go away. And it's these hammer blows that break cranks. Know how some opera singers can make a wine glass "ring" so much that it shatters? That's it, exactly. Your crank can shatter in the same way, due to "ringing" too hard for too long.

I have pretty much no experience with Z engines specifically, but I'll say this: I would NEVER run any engine I was fond of without a damper. (Go ahead, you have my permission to run any Chevy 400 small-block engines you find without a harmonic balancer; in fact, go ahead, run them without water, either!) I'll also add that the Mopar Performance Engines book, a compendium of technical advice from Chrysler engineers, specifically says that running a drag race engine without a damper will and does result in broken crankshafts. They advise against ever doing this. I'll also mention that many Mopar V8's are internally balanced. This has no effect on the advice above: cranks will break, internal balance or external balance, in an engine run hard without a crankshaft damper).

Final paragraphs for extra geekness credits: there are two common ways to dampen a vibration. One is the way shock absorbers work: immerse the moving parts in viscous goo, like shock absorber oil. This is how the very high quality FluidDampr device works, it's filled with viscous silicone goo to absorb crankshaft "ringing". Dunno if they make one for a Nissan L6, though.

The second way is to transfer the energy from the part thats vibrating to a second mass thats free to move. Sometimes called "inertial mass damping" or "tuned mass damping", the idea is to put the second mass on some kind of spring. When you do this it becomes like a tuning fork - it wants to "ring" at a specific rate. If you mount this "ringy" mass on the vibrating part you're concerned about, and tune the "ringiness" correctly, what happens is that the small "ringy" mass soaks up the vibration energy from the first part. That's how the rubber ring and outer metal ring of an OEM harmonic damper work - the outer ring is free to twist back and forth a little due to the rubberiness of the rubber ring, and the engineers who design it tune the "ring" frequency to absorb harmful crankshaft vibrations. End result: the outer ring of the harmonic balancer "rings" like crazy, the crankshaft doesn't ring much, and nothing breaks due to the give in the rubber ring.

The nice thing about the FluidDampr is that it absorbs crank vibrations over a wide rpm range, while the rubber/metal OEM dampers only work over a relatively narrow rpm range. So the FluidDampr is theoretically a better device.