Internal Combustion Engines and vibration

Today I've done some reading about the conversion of mechanical effort, from a translation setting - linear applied force, and linear movement - to a rotational one : torque and spinning motion.

What I had in mind is a piston, with a connecting rod and a crank that drives a wheel around an axis. The typical mechanism you see in a steam engine.

Then, while exploring the subject, I've realised that car engines are built mainly on the same principle, although they have -nowadays - not one, but 4, 6 or 8 pistons. As I had suspected, a single piston does a very imperfect conversion of mechanical power. Some of the translational effort is lost in the process, through friction or - even worse - vibration. I found out that the supression of the vibration movements that come from piston motion in an automobile engine is quite an engineering topic. It is called engine balancing or - as refering to what it is meant to achieve instead of the process itself - engine smoothness.
Better balancing of the engine means energetic efficiency - thus lower fuel consumption, - less mechanical stress on the crankshaft and pistons - therefore a car engine that lives longer - and, last but not least, less noise and vibration for the driver to endure. The gains become all the more important when the engine is designed to run at high rev.

The balancing of an engine is mainly an issue for the engine designer - who decides how many pistons, and their relative configuration - V, W, straight or boxer - as well as complementary balancing mechanisms, such as flywheels and balance shafts. But it is also a puzzle for the mechanic who tunes the engine: the balance is initially calculated for an engine with all its original parts. If some parts are replaced or simply become loosened through use, then a retuning becomes crucial.

Your usual car cruises between 2 000 and 6 000 rpm, but Formula 1 racing monsters can handle up to 20 000 rpm. When the rev doubles the centrifugal / centripetal efforts on the rotating parts quadruple ! Needless to say that F1 cars use the most accurate balancing techniques. And in spite of that end up in a museum (at best) after only a few races - well, engine wear-off is not the only one responsible for their demise. It would be actually interesting to know what can still be used from a racing car when it is deemed to be no longer fit for competition.

Back to engine smoothing ! The subject is vast; I'll come back to it later, perhaps with some math in support, to give a feeling of the challenges involved.