I've noticed that there aren't really any proper tutorials in here regarding engine dynamics so, with the help of a lot of amphetamines and a free hour, I've decided to hit upon the very basics.

We can all agree that vibration in an engine is a fairly nasty thing, it causes fatigue and costs us in terms engine efficiency and therefore performance. The vibration that occurs within the workings of an engine stem from two basic sources, the least severe of which stems from the irregular torque output of reciprocating internal combustion engines. The biggest source of engine vibration can be put down to the inability to balance inertia forces due to the piston motion in certain types of engine configuration, and from here stem two sources of mechanical imbalance, rotating and reciprocating.

Rotating Balance:
It is simple to understand that any rotating object can produce nett rotating forces if not properly balanced. It's not a very big jump to go from there to understanding that the main items of concern with regard to rotating forces in our application would be the clutch assembly, alternators, flywheels and crankshaft. These out of balance forces are due to asymmetrical mass distribution about the rotating axis of the object in question. The clutch, alternators and any external flywheels can be fully balanced. However, due to the needs of reciprocating balance, certain configurations of engine rarely allow us to achieve perfect rotating balance of the crankshaft.

All particles within a spinning object produce centripetal force acting inward to force a curved path on the particles of rotating object. This force acts radially outward from each particle. If the resultant of all these forces equates to zero then the object is balanced.

There are two aspects of rotating balance, static and dynamic, which need to be considered. It is possible for an object to be statically balanced whilst being unbalanced dynamically. However the reverse of this can not be said to be true, as any object that is in static balance is also in static balance.

Static Balance:
If the object is mounted in low friction bearings with the axis of rotation horizontal then the object will remain stationary, regardless of the initial starting position.

Dynamic Balance:
This is the when a rotating mass does not produce force on the shaft on which it rotates.

Reciprocating Balance:
The piston in an engine moves along a straight line as defined by the axis of the cylinder. However, its velocity is continually changing throughout a cycle. It is stationary at both TDC and BDC (top dead centre and bottom dead centre), achieving maximum velocity somewhere around mid-stroke. Oscillating forces must be applied to the piston to cause these alternating accelerartions. If these inertia forces are not balanced internally within an engine they must pass through the conrod to the crankshaft then onto the main bearings and the crankcase.

The motion of the piston is sinusoidal and therefore so too are the acceleration forces. If the connecting rod was infinitely long, that motion would actually be truly sinusoidal, but most conrods are approximately twice the crankshaft stroke in length. This relative shortness of the rod means that, except for the TDC and BDC positions, the rod will not remain in line with the cylinder axis through a working cycle. The angularity of such a pew, pew, lazerz short conrod through a complete crankshaft revolution modifies the piston motion. With a very long conrod, we would expect that the maximum velocity would occur at 90 degrees of rotation from TDC. With a 2:1 conrod length to stroke ratio, maximum velocity occurs at just past 77 degrees.

In fact, an infinite number of highest order harmonics, which complicate the balancing of the engine, are introduced into the piston acceleration. Fortunately, as the harmonics increase in order, their magnitude decreases and so they become less important. In practice, it is usual to only consider the first and second harmonic when doing calculations. The reciprocating forces from the second harmonic, which cycle at twice engine speed, are known as secondary forces.

It is interesting if we calculate the magnitude of the reciprocating forces in typical engines. This force is proportional to the square of the rpm. Assume an engine with a 64mm strokerevving at 10,000rpm. Then for every hundred grams of reciprocating mass, a force with close to 360kgf will be generated at TDC.

For a conrod to stroke ratio of 2:1, the peak magnitude of the secondary force is one quarter that of the magnitude of the primary force.The piston is accelerated only in a straight line along the axis of the cylinder and so the reciprocating forces only act along the axis of the cylinder. However, the conrod is a bit more complicated to consider. The big end clearly rotates with the cranshaft and hence can be perfectly balanced by a counterweight to the crankshaft on the opposite side. The small end of the conrod reciprocates in exactly the same manner as the piston and so can be directly added to the total reciprocating mass of the piston and gudgeon pin but that section of the conrod which connects the big and small ends will experience a combination of linear and rotational motion.

I'll edit in an analysis of a single-cylinder engine later. I need a break from typing for awhile.

I approve of this post.

I know I don't normally mind you guys going off topic, but the guy clearly put a lot of time into that and there wasn't even an attempt to reply to it, so I moved the posts to the general automotive banter thread.

Perhaps it's just my bias because this is a technical thread. Oh well.

Just trying to teach the kiddies something mate. I guess it wasn't really worth wasting my time when all they want to do is talk about dildos huh.

Just trying to teach the kiddies something mate. I guess it wasn't really worth wasting my time when all they want to do is talk about dildos huh.

Please become a regular and join me in technical-chatter-dom :(

Seriously I haven't been posting as much as I should because there hasn't been enough stuff 'relevant to my interests'.

What do you do to have learned this stuff? Just a very interested member of the general public, or do you work in the industry?

Well, I was in the process of editing this into my last post, but firefox slutted me around so I have decided to give it a post of its very own to call home.

Single Cylinder Analysis:
Primary Forces
In order to achieve a good understanding of the principles involved in engine balance, it is first necessary to understand the concept of balance factor, as it applies to the primary forces on a single-cylinder engine. The piston applies an upward force on the conrod at TDC but when close to mid-stroke the piston is moving at maximum velocity and produces no in-line primary force. The addition of a counterweight can also be used to cancel out the force from the piston. Unfortunately, this simple idea is not the answer as when the piston achieves maximum velocity, the counterweight will produce a centripetal force that is no longer balanced by the piston. All this really achieves is replacing an inline-reciprocating force with a lateral alternating force of the same peak magnitude.

When the counterweight exactly balances the primary reciprocating forces at TDC or BDC like this, we say that we have 100% balance factor. If no attempt is made to balance the piston force, that is the crankshaft is in static balance after allowing for the mass of the rotating part of the conrod, we say that we have zero balance factor. Factors betwen 0 and 100% give rise to a combination of rotating force and reciprocating force.
-Zero Balance Factor:
We have a sinusoidal inline force but zero transverse force through the range of rotation, ie the unbalanced forces vary in magnitude but always act up or down inline with the cylinder.
-50% Balance Factor:
The peak value of the inline force reduces to half of the previous value due to the counterweight force, but we have now introduced transverse forces, also of the same magnitude, but shifted in phase by 90 degrees of crank rotation. The resultant of these two forces always sums to a constant value pointing radially outward from the crank axis, however, and interestingly enough, this constant radial force always rotates in the opposite direction to that of the crankshaft rotation.This balance factor also gives the least magnitude of the resultant of all balance factors, being 0.5 times the unbalanced peak reciprocating force.
-100% Balance Factor:
With a 100% balance factor, we see that the direction of forces has simply switched from inline to transverse with the same magnitude. At TDC and BDC, the reciprocating forces are pefectly balanced by the counterweight, which then leaves transverse forces only.

Balance factors other than these three will give rise to resultants of between 50% and 100% of the unbalanced reciprocating force and with force directions being a combination of linear and rotational, depending of the actual BF.

Balance Shafts:
In order to understand how a balance shaft works we must look back to our definition of 50% BF. A constant rotating force can easily be balanced by another constant rotating force spaced 180 degrees separate from it. However, it is not as easy as simply adding another counterweight to the crankshaft because this force rotates in the opposite direction and therefore can only be balanced by a counterweight rotating in the opposite direction. No answer is perfect though, as a balance shaft can create a rocking couple due to the distance between the lines of action of the separate forces of the crank and balance shaft. This rocking couple can be significantly lessened by the use of two balance shafts.

Optimum balance factor is determined by the characteristics of the chassis into which the engine is to go. For example, if it was easier to excite vertical rather than horizontal vibrations in a particular chassis then we would select a high balance factor in order to reduce the vertical forces and emphasise those acting horizontally, assuming an engine with a vertically-orientated cylinder.

Secondary Forces:
In a single cylinder engine, the secondary forces provide us with a harder problem to solve. The concept of balance factor as applied to the crankshaft is not relevant in this case because by definition the secondary forces vibrate at twice the rate of crankshaft rotation. We couls add a balance shaft that rotates at twice the engine speed, but that would only replace the inline forces with lateral ones as in the case of 100% BF with primary forces. However, if we used two counter-rotating balance shafts geared so they ran at twice the speed of the crankshaft then we could, in fact, eliminate the secondary forces.

That's all that I can be fucked writing for now. I'll get onto multiple cylinder engines another day. Or night. Who knows man?

What do you do to have learned this stuff? Just a very interested member of the general public, or do you work in the industry?
I'm an apprentice blacksmith, I just like knowing how things work. I'm completely self-educated in all this shit, some other shit. My formal education ended at the end of 8th grade, ahah.
:)

Does this mean that 4 balance shafts could then perfectly balance (assuming perfect tolerances) any engine? Assuming you can ignore the vibrations from cylinder banks being offset (as in V engines. Or would that just take 8 shafts?).

If so, is that the norm? Or is it too expensive to bother with...?

Well, 4 if you are talking a dual-crank engine like a stepped twin or something man. A V-engine runs off a single crank, it's in the shared crankcase. Generally.

Well, 4 if you are talking a dual-crank engine like a stepped twin or something man. A V-engine runs off a single crank, it's in the shared crankcase. Generally.

Ah, I thought you meant to use two balance shafts to balance primary, and then two to balance secondary forces.

Did you just mean two all up?

Yep. :)

Yep. :)

Cool. So my original question stands: Is this the norm or is it to costly?

Balance shafts are fitted to almost all modern engines.

I just skimmed through it, but i approve. But the kiddies just wanna talk about dildos....

And tits

First post, fifth paragraph. I believe you meant to type "dynamic" rather than "static" in one instance.

There, you've got a reply. :P

Also, layz0rz. Yay.

Good old amps