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https://en.wikipedia.org/wiki/Engine_balance --- Causes of secondary imbalance ---
A piston travels further during the top half of its motion than during the bottom half of its motion, which results in non-sinusoidal vibrations called secondary vibration.
The difference in distance travelled is due to the rotation of the connecting rod. At 90 degrees after top dead centre (TDC) the crankshaft end of the conrod is exactly at the halfway point of its stroke, however the angle of the conrod (ie the left-right movement, when looking down the crankshaft) means that the piston end of the conrod must be lower than the halfway point, in order for the conrod to maintain a fixed length. The same also applies at 270 degrees after TDC, therefore the piston end travels a greater distance from 270 degrees to 90 after TDC than it does in the 'bottom half' of the crankshaft rotation cycle (90 degrees to 270 degrees after TDC). In order to travel this greater distance in the same amount of time, the piston end of the connecting rod must experience higher rates of acceleration during the top half of its movement than in the bottom half.
This unequal acceleration results in higher inertia force created by the mass of a piston (in its acceleration and deceleration) during the top half of crankshaft rotation than during the bottom half. <<<
Engine output is ultimately a result of combustion pressure above the piston. No pressure, no push. This pressure is not fixed, and changes throughout the combustion cycle. Chemistry, combustion chamber geometry and thermodynamics are three of many variables determining the magnitude and timing of the trapped burning charge pressure. Another complicating variable is ignition timing, which for a given mixture & compression ratio can deliver different pressure curve outputs depending on the initiation period chosen. Operating RPM is yet another.
The Wiki article addresses mechanical components. As it points out, the piston travel isn't linear throughout the stroke, so depending upon where the piston is in the stroke cycle the available gas pressure at that time determines torque transmitted to the crankshaft. This pressure varies continuously with any change in throttle opening, ignition advance, air temperature, cylinder wall & piston temperature, fuel grade, ad nauseum. So given that the motive pressure driving the entire system fluctuates continuously as it interacts with a non-linear mechanical vibrating system, it has to affect the resultant mechanical vibration output.
The only "clean" way to check vibration of the mechanical component would be to run it at various speeds in vacuum. This is precisely what the steam turbine-generator operators do when balancing their units, run under vacuum. Then they run it again under load to see how much the pressure & flow of steam impinging on the blades actually changes things. If it shakes under load but not vacuum, there's probably a blade/nozzle/diaphragm issue. This is roughly analogous to the boat racers spin-balancing their props, then bolting them on and making a speed run. Faster times for a given motor probably means you guessed right. If it tears off the driveshaft, well there's no substitute for cubic dollars, eh?
Successful competitors are as a group pretty keen observers. In my career as an electrical troubleshooter, I learned to rely on my co-workers observations. When the powerplant operators told me device "X" was doing such and such, it was my task to determine how & why. In more than one instance the wiring and elementary diagrams said one thing, 40 years of undocumented field changes quite another. I am totally with you in that physics doesn't lie, but I also know that there are very few pure scenarios involving machinery. The task is to ferret out the useful stuff, like Burt Munro did 80 years ago at Bonneville. Really, a 200 MPH flathead Indian Scout? Now THAT's unbelievable....
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https://en.wikipedia.org/wiki/Burt_Munro)