Thinking About Engine Vibration

[Hugh Janus]

A counterbalancer is used to lessen a single’s primary shaking force that moves along the cylinder centerline. (KTM/)

We can analyze a lot of engine vibration situations by a simple method: adding up the forces that act at four positions of the crankshaft: top dead center (TDC), 90 degrees after top dead center (ATDC), bottom dead center (BDC), and 270 degrees ATDC.

A single-cylinder piston internal-combustion engine vibrates because the startings and stoppings of its piston generate inertial shaking forces. As the crankshaft yanks the rising piston to a stop at TDC, the whole engine is, to a degree, pulled upward along with it. Ninety degrees later, with the piston mainly coasting in mid-stroke, there is very little piston-generated inertia force. Then, as the crank decelerates the piston to BDC 90 degrees after that, the force required to stop and reverse the piston’s motion drags the whole engine downward. And halfway up its stroke, 90 degrees later, the piston is again mostly coasting and generating little up or down force.

This shows us that a simple single-cylinder engine’s piston generates a primary shaking force, meaning one in step with crank rotation, acting along the cylinder center line. There is essentially no forward-and-back force at 90 degrees to the cylinder axis because when the piston is in these positions it is mostly coasting.

Engineers thought they could do better by attaching counterweights to the crankshaft at 180 degrees to the location of the crankpin. Sure enough, when they added enough counterweight to cancel 25 percent of the engine’s reciprocating weight—namely the piston, rings, wrist pin, and the small end of the connecting rod—the engine felt a bit smoother. Now, as the piston stopped and reversed at TDC, the upward yank on the engine was reduced by 25 percent. Better yet, peak loading on the crankshaft’s main bearings was also reduced by 25 percent.

This wasn’t all gravy though. When the crank turned 90 degrees more, as before the piston, mostly coasting now, generated close to zero up-or-down force. But as the piston moved from TDC to 90 degrees ATDC, that 25 percent counterweight we added was now pulling the engine to the rear, one-quarter as hard as did the unbalanced piston at TDC or BDC. This is something new.

Continuing around the circle, the piston decelerates and reverses direction at BDC. There, because of the 25 percent balance weight, which is now trying to lift the engine, the downward force on the engine is only 75 percent as great as with no counterweight at all. Less vertical shaking force is good, and so is less peak force on main bearings.

Now as the crank turns another 90 degrees, putting the piston into coasting mode in mid-stroke, there is close to zero piston shaking force. But there is that 25 percent counterweight, directly opposite the crankpin, trying to yank the engine forward.

OK, to review: We’ve reduced the up-and-down shaking force by 25 percent, and we’ve reduced peak forces on crank main bearings by 25 percent. Those are good gains, worth pursuing further.

We don’t have to consider the rotating parts, such as the big end of the connecting rod, its bearing, and the crankpin. Because these parts only rotate, we can balance them with counterweights placed opposite to them on the crank. In this discussion we’ll assume this has been done, so we don’t have to consider rotating imbalance.

If a little bit of counterweight is good, how about increasing our crank counterweight to 50 percent of the reciprocating mass? Let’s check the four stations: TDC, 90 degrees ATDC, BDC, and 270 degrees ATDC (and return to TDC). Now we find similar but larger effects. The vertical yankings of the piston as it starts and stops at TDC and BDC are reduced by 50 percent and so is peak crank main bearing load. Excellent. But now, because we’ve doubled our counterweight mass, we’ve caused our engine to be yanked forward and back by that heavier counterweight twice as hard as before at the 90- and 270-degree positions. And if we think through the four crank positions, we find that now the counterweight is yanking the engine forward and back just as hard as the piston is yanking the engine up and down. If we draw a diagram of these forces, we find that as the crankshaft rotates one way, the arrow representing the shaking force is half as long as it was before we added any counterweight, and that this arrow is rotating opposite to the crankshaft.

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Here’s why. At TDC, the piston’s upward yank is being reduced 50 percent by the downward yank of the counterweight. At 90 ATDC, the piston is in mid-stroke, mostly coasting, and so it produces near-zero shaking force. But the 50 percent counterweight, being located at 180 degrees from the crankpin, is now yanking the engine to the rear with its 50 percent. The imbalance force has not changed; it’s still 50 percent of the original unbalanced force, but it has now rotated to the rear, where it’s yanking the engine rearward. We continue to BDC, where the piston’s inertia is driving the engine downward at 100 percent, but half of that force is now canceled by the counterweight, which is now yanking upward one-half as hard. As a result, the net downward force on the engine remains 50 percent of the original unbalanced piston inertia force.

Now we come to 270 degrees ATDC, which places the piston again at mid-stroke, coasting and generating no shaking force to speak of. But the pesky 50 percent counterweight is trying to pull the engine forward. Therefore the unbalanced force remains unchanged, at 50 percent of the unbalanced piston’s inertia force. In other words, by counterweighting at 50 percent of the engine’s reciprocating parts weight, we have changed the original up-and-down shaking force, that peaked at 100 percent at TDC and BDC, into a constant force one-half as large—which is rotating opposite to the crankshaft.

At this point it doesn’t take a very clever engineer to say, “Hey, let’s gear another shaft to the crank so they rotate in opposite directions at identical speeds, and let’s put a counterweight on it which cancels this constant rotating imbalance force that we’ve created by counterweighting the crank at 50 percent.” This is exactly how counter-rotating primary balancers work.

But what if we continue to add counterweight, beyond 50 percent? Again, we can map it all out, crank position by crank position. At TDC, the piston is trying to yank upward with 100 percent of its reciprocating weight, but at the same time, a 75 percent counterweight is yanking down, leaving a net 25 percent. The same will be true at BDC, but reversed in direction. This is good; vertical shaking force has now been reduced to 25 percent of what it was in the original non-counterweighted engine. But at 90 degrees and 270 degrees, we’ve created a monster. The piston is coasting in those two positions, generating little shaking force, but those bigger 75 percent counterweights are yanking the engine forward or back quite hard now. And peak force on crank main bearings is rising again; instead of the 50 percent we saw with 50 percent counterweighting, now we are back at 75 percent.

The news is no better with a 100 percent counterweight; all it accomplishes is to move the shaking force from the up-and-down direction of the original unbalanced engine to a back-and-forth direction. And our peak main bearing force is back up at 100 percent, just as bad as in the unbalanced engine.

This explains why so many engines are balanced at 50 percent of their reciprocating mass: because doing so cuts the main bearing peak inertia force in half and offers an opportunity to add a contrarotating balance shaft that can cancel essentially 100 percent of shaking force.

I use words like “essentially” and “mostly” because there is a second source of inertial shaking force: the angling of the connecting rod, as its big end swings around in a circle on the crankpin. This angling generates a twice-per-revolution variation in piston height of roughly one-quarter the amplitude of the primary piston inertial shaking force. The name for this beast is secondary shaking force (called “secondary” because it occurs at twice crankshaft speed). Many of today’s inline four-cylinder engines with 180-degree (flat) crankshafts have secondary balance shafts which rotate at twice crankshaft speed to cancel this force.

Using this same method of adding up forces from piston inertia and rotating counterweight, we can also see how a 90-degree V-twin (both con-rods sharing a common crankpin) can be given near-perfect primary balance by adding a counterweight that cancels 100 percent of one piston’s inertia force.

Top dead center: The piston in the vertical cylinder is at TDC and the 100 percent counterweight is directly opposite it, yanking in the opposite direction, so the two forces add to zero. In the horizontal cylinder the piston is near mid-stroke, coasting, so it contributes little inertia force. There is no net primary shaking force.

Ninety degrees ATDC: Now the piston in the vertical cylinder is at half-stroke, coasting, and generates little or no inertia force. The piston in the horizontal cylinder is at TDC, yanking forward, but the 100 percent counterweight, being at 180 degrees to the crankpin, is pulling in the opposite direction with the very same force and so cancels it. No net primary shaking force.

Bottom dead center: The piston in the vertical cylinder is at BDC, pulling the engine downward as it slows and reverse direction, but the 100 percent counterweight is at 180 degrees to it, canceling its force. The piston in the horizontal cylinder is at mid-stroke, neither accelerating nor decelerating, and so generating near-zero inertia force. Result? No net primary shaking force.

And at 270 degrees ATDC: This situation is the reverse of that at 90 degrees ATDC; the piston in the horizontal cylinder is now at BDC, and the 100 percent counterweight, being at 180 degrees to its force, cancels it. The piston in the vertical cylinder is at mid-stroke, where it generates little net force. Again, no net primary shaking force.

This is why 90-degree V-twin engines, such as those made by Ducati and Moto Guzzi, are balanced in this way.

Those of you who have experience with classic British parallel twins, such as Triumph, BSA, and Norton, know that such engines were typically balanced, not at 50 percent of reciprocating weight, but in a range of 65 to 85 percent. How does this fit into the above discussion?

The answer is it doesn’t. What happens with such engines is that up-and-down shaking force is felt more acutely by rider and passenger than forward-and-back shaking. As the balance factor is raised, vertical shaking grows smaller and fore-and-aft shaking grows larger. It was typical in developing such engines to balance a set of several cranks at different balance factors (in percentage) and to then road test to find out which was least unpleasant to ride.

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