Inline 4-cylinder engines  

As commonly known, big straight-four engines require twin-balancer shafts rotating at twice the frequency as the crankshaft to reduce vibration. This is very different to 3-cylinder engines, which need a single balancer shaft running at the same frequency as crankshaft. Obviously, the vibration generated by straight-four engines is not the same as 3-cylinder engines.

The left picture shows an inline-4 engine. It fires once every 720° / 4 = 180° crank angle, hence 2 of the pistons are in exactly the same position and move in the same direction, while the remaining 2 pistons are also a pair. To avoid the end-to-end vibration as experienced in 3-cylinder engines, car makers always arrange the pistons as shown in the picture, that is, symmetrical. In other words, piston 1 and 4 are a pair, while piston 2 and 3 form another pair. Therefore movement of piston 1 will be balanced by the symmetric piston 4. The same goes for piston 2 and 3.

That’s just the end-to-end vibration with respect to the engine center. What about the resultant upward / downward vibration ? It seems that the movement of piston 1 is counter balanced by piston 2, while piston 3 counters piston 4. However, this is just skin-deep. 

More professional speaking, that just proves the balance of 1st order force. The second order force (which can be derived from equation) is normally much smaller than the 1st order force and it is rotating at twice the frequency of the 1st order force. Nevertheless, the configuration of inline-4 actually multiplies the magnitude of 2nd order force thus making it hard to ignore, especially for larger engines.

A simpler explanation is given in the below pictures, which compare a perfectly balanced boxer-4 engine with an inline-4 engine.

As seen, no matter where the crankshaft rotates to, the boxer engine has the pair of pistons always in opposite positions, directions and speeds, thus all the forces can be balanced. (if not for packaging and cost reason, boxer engines would have been the best choice) In contrast, in a straight-four engine, rotate the crankshaft a certain angle, the piston near the top end has a displacement (b), larger than that of another piston near the bottom (a). As vertical force is the product of displacement and mass of piston and divided by the time taken for such displacement, you can see the different displacements must lead to different forces, therefore complete cancellation is impossible. The resultant force is the aforementioned second order force, which rotates at twice the speed of the crankshaft.

Solution - Twin-balancer shafts

The longer the stroke, the heavier the pistons and con-rods, the more second order vibration generates. Unfortunately, car makers favour straight-four engine for its advantages of low cost and compact dimensions. Since the 80s, car engineers regard 4-pot engines larger than 2 litres in capacity to be better to be equipped with twin-balancer shafts to dampen the vibration. Although the strengthening of engine block, the use of hydraulic engine mount and lightweight pistons helped break such rules, the trend of pursuing refinement once again led many engines larger than 2 litres to use balancer shafts.

The Balancer shaft was invented by British automotive engineering master Dr. Frederick Lanchester in the early 20th century. 

Somehow Mitsubishi obtained the patent and put it into mass production in the 1976 Colt Celeste 2000, then Fiat group used it in its Lamda engine series, including the 1.6-litre Delta HF turbo and Fiat Croma / Lancia Thema's 2-litre turbo. Meanwhile, Saab 9000 and Porsche 944 also introduced it into their powerful inline fours. All these car makers obtained license from Mitsubishi.

 
To deal with second order vibration, a pair of balancer shafts is needed, driven by the engine and rotate in opposite directions to each other, at twice the speed of the crankshaft. They locate in either sides of the engine. One of them is positioned just above the crank shaft level, the other is far above. Counter weights on the balancer shafts will completely cancel the second order force, thus result in a silky-smooth rotation.

The use of 2 balancer shafts instead of a large single one is because the vibration generated by the engine is mostly in vertical direction. 2 shafts rotating in opposite direction can cancel each other’s transverse force and result in a net vertical force which is used to balance the vibration.

Without twin-balancer shafts, Porsche would have found it  impossible to make the 3-litre inline-four which powered the 944 S2 and 968. That’s the biggest four-cylinder engine in modern cars. without out it shaking the car and passengers to death.