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Hazelton, Kansas | Rick,
The amount of secondary (2 times crank speed) imbalance depends on the reciprocating mass, rpm, and L/R. Where L is rod length and R is the crank throw (or stroke/2).
Four bangers with long rods (relative to stroke) vibrate less than engines with short rods. Long rods also reduce piston side forces (and friction and wear). Everything is a compromise, and long rods obviously dictate a slightly larger, heavier engine.
I have an old Jeep (2.2L F-head) that runs remarkably smooth with no balancers. I also have a Detroit 8.5L that has balancers, but never lets you forget its a 4-banger.
Inline sixes have nearly perfect primary and secondary balance, and need no balancers.
It’s academic, but in the derivation of piston motion, there ARE a couple of “higher order” terms that are traditionally thrown out of the equation. The “2 omega” term is a close approximation. So even with well-designed balancers, the forces aren’t totally, absolutely cancelled out.
Regards.
MDS
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