Mass balance and smoothness of reciprocating engines.

Where does engine vibration come from?

One might think that the vibrations are caused by the explosive combustion of the mixture in the combustion chamber. However, this assumption is not tenable, since during the combustion of the mixture, the pressure simultaneously acts in all directions in the combustion chamber. The forces thus cancel out completely on the outside.
Instead, engine vibrations are caused directly by the rotation of the crankshaft.
If you were to hold this rotating crankshaft at the two ends in your hands, you would feel in your hands the forces that must normally absorb the crankcase. It is precisely these forces that lead to engine vibrations! (Specialist language: „free mass forces".)
With a simple balance weight you can fully compensate the free mass forces.
If you held this rotating crankshaft at their ends again in your hands, you would feel no vibration!
Unfortunately, the connecting rod and piston are added:
To simplify dividing the connecting rod by calculation into two parts. One part is beaten to the "rotating mass", the other part to the "oscillating mass" (ie to the piston).
 -  The rotating part can be easily compensated simply by making the already known balance weight even larger.
 -  The oscillating mass, on the other hand, can only be partially compensated with a rotating balance weight. Because with each further increase in the balance weight you now get a strong horizontally acting imbalance. -> The final dimensioning of the balancing weight thus represents a compromise, but in which case free mass forces remain!
For example, the balance weight of a single-cylinder engine could be dimensioned:
As I said: The mass balance made here is only a compromise, so the engine will still vibrate.
What do you do now? Increase number of cylinders.
Even with a simple in-line 2-cylinder engine (2-stroke), the so-called "first-order free mass forces" can be avoided:
Series 2-cylinder two-stroke engine:
The opposing movement makes the free mass forces wonderful. But this engine now tends to tilt its center back and forth. One speaks of „free mass moments".
The free mass moments could be easily got rid of with a series 2-cylinder four-stroke engine:
Although this no longer has free mass moments, it again has very strong free mass forces (namely exactly twice as strong as the single-cylinder engine). With the inline 4-cylinder four-stroke engine to get out of this dilemma:
He has neither free mass forces nor free mass moments (1st order *) on! That's the real reason why four-cylinder engines are so common!
*Attention: If so far of free inertia / moments was mentioned, this always referred to the so-called "1. Order". But now there is also the " 2nd order ":
An amazing fact: " The pistons moving upwards do not move at the same speed as the pistons moving downwards!".
Reader: "Can not be! Obviously, the pistons move exactly the same, just in the opposite direction! "Not at all.
Consider the cross-section of a simple two-cylinder engine:
On the left, the crankshaft is at 0 degrees, on the right, the crankshaft was rotated 45 degrees. The distance traveled by the upper piston (distance between the red lines) is clearly larger than the distance traveled by the lower piston (distance of the yellow lines). Only logical conclusion: The upper piston must have been faster!
Reader: "Something must be lazy with the drawing, that just can not be right!" Yes, yes.
Let us consider the following addition to the drawing:
We turn the crankshaft again from 0 ° to 45 °. As you know, the green and blue points move in a circular path. But let us break this movement into the partial movements 1, 2, 3 and 4 as shown in the sketch.
 -  Partial movement 1causes the upper piston to be pulled down.
 -  Partial movement 2causes the upper piston to be pulled down.
 -  Partial movement 1+2superimposed lead so much to the fact that the upper piston is pulled down.
So unspectacular, but now it comes.
 -  Partial movement 3causes the lower piston to be pushed upwards.
 -  Partial movement 4causes the lower piston ... to be pulled down!
 -  Partial movement 3+4superimposed thus lead to any "compromise". Therefore, the lower piston is slower!
Readers: "Ok, but how can one piston be slower than the other, when both are always at dead center?" Right, that would be a contradiction. Solution of the contradiction: On the second half of the way from one dead center to the other the game turns around: Then the respective other piston is faster or slower.
Long story short: There are small speed differences between the up and down pistons which lead to so-called "inertial forces and moments of second order".
What can you do about it? An inline 6-cylinder.
In the in-line 6 cylinder, the individual forces and moments of the first and second order are completely compensated. Therefore, he is in terms of smoothness essentially unbeatable.
An interesting special role takes the Boxer engine:
Overview of the Free Forces u. Moments (The larger the factor, the worse):
  Free mass forces of first order Free mass moments of first order Free mass forces of second order Free mass moments of second order
 1-cylinder 1 0 1 0
 Inline 2-cylinder 0 1 2 0
 Boxer Like 4-stroke boxers (see below)
 1-cylinder 1 0 1 0
 Inline 2-cylinder 2 0 2 0
 Inline 3-cylinder 0 1,7 0 1,7
 Inline 4-cylinder 0 0 4 0
 Inline 5-cylinder 0 0,5 0 5
 Inline 6-cylinder 0 0 0 0
 V 6 (bank angle 90°) 0 1,7 0 2,4
 V 8 (bank angle 90°) 0 0 0 0
 V12 (bank angle 60°) 0 0 0 0
 2-cylinder boxer 0 ~0 0 ~0
 4-cylinder boxer 0 0 0 ~0
 6-cylinder boxer 0 0 0 0
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