First, some definitions: Vibration order: A vibration's order is the number of times it occurs PER CRANKSHAFT REVOLUTION. If a given vibration occurs once per 360 degrees of crankshaft travel then we refer to it as a "first-order" vibration. Vibrations which occur twice per full revolution of the crankshaft are "second-order" vibrations, etc. First order vibrations are almost always caused by static or dynamic imbalance of the crankshaft assembly (including the connecting rods and the propeller!). They can be corrected by carefully weight-matching con rods (paying attention to the weight of the con-rod big end!), crankshaft cheeks, etc. Having your prop dynamically balanced affects ONLY first-order vibrations! Torsional couple: Any two forces acting on an object will produce a torsional couple IF they do not act on the object in the same location. A torsional couple is simply a twisting force. Here are two forces acting on an object (the letter "O" without producing a torsional couple): Fig A: <--------O--------> In this example the net force is zero as there are eight force units (the dashes (-)) acting in each direction. The "O" has no desire to move at all. Here are the same two forces producing a torsional couple: [The vertical bars (|) indicate physical structures attached to the "O"] Fig B: <--------| | | O "I want to turn!" | | |--------> The "O" feels a desire to rotate counter-clockwise. Note that the forces above (< and >) may be static forces (springs for example) or DYNAMIC forces generated by centripital acceleration. Static balance: Static balance refers to an object's propensity to favor a specific orientation when suspended at its center of gravity. An object in static balance will NOT favor any specific orientation. Let us replace the dashes and force vectors in figure B above with weights at the end of arms: Fig C: @--------| | | O | | |--------@ In this figure, @ represents a given weight. The dashes and vertical bars (- and |) represent physical structure. In this example we can support the structure at O and it will have no tendency to roll one way or another. It's in static balance. The two weights cancel each other out. Dynamic balance: An object is in dynamic balance when there is no NET torsional couple which results when the the object is rotated about a specific axis. Fig C. above is NOT dynamically balanced. If we were to begin rotating the structure along the axis defined by the vertical bars (|) then it would have a strong desire to wobble. Rotation would cause both of the weights to exert a net outward force. This force would exert a torsional force on poor little "O". If we were to rotate the structure in space then the ends of each axis would describe a circle with every full rotation: Fig D. end-on view of fig C: || /\ || || || @--------(|)--------@ || || "I want to || \/ wobble!" || The object is rotating counter-clockwise as we view it. The axis of rotation - (|) - will describe a circle as it "wobbles" around. This wobble will result in a FIRST ORDER vibration. DISCUSSION In this discussion we will consider the opposed four-cylinder, four-stroke engine. The discussion is applicable to all such engines which include the Lycoming O-235, O-290, O-320, and O-360 series. The question was raised: >I was doing some research on engine torsional vibrations this >week and I can't figure out how the Lycoming/Continental uses extra >masses along the crankshaft to eliminate both primary and secondary >crankshaft forces and then feed them back into motive power. I am not sure what the poster meant by "primary and secondary crankshaft forces" but we will assume they meant one of two things: a. First and Second Order vibrations b. Primary and Secondary vibration modes of Second Order vibrations. I will TRY to explain both. Here is the layout of an O-360 crankshaft as viewed from above the aircraft. Note that all the crank throws lie in the same plane (pun intended)! Fig E: | | ---- | Cylinder #1 ------- Cylinder #2 | ---- | ---- | Cylinder #3 ------- Cylinder #4 | ---- | | The firing order of the engine is #1, #3, #2, #4. Task #1: Discuss the first-order vibration characteristics of the opposed 4-cylinder engine. Remember that we said first-order vibrations result from imbalance of the crankshaft assembly. They specifically are NOT vibrations resulting from the action of the reciprocating mass (pistons) nor from the burning of gasoline. Therefore we can remove the reciprocating parts of the engine and ignore gas effects while studying first-order vibrations. The O-360 crank is statically and dynamically balanced for first order vibrations. Remember figure C above? I said it was dynamically unbalanced. Look at figure E. It's two structures of figure C joined together but 180 degrees out of phase with one another. This produces a dynamically balanced crankshaft that has no desire to rotate about its midpoint. If spun in space it would exhibit no tendency to wobble. Why is this? Because in figure E the forces which exert a torsional couple on the midpoint are exactly balanced: Fig F (force vector diagram of fig E): |------> | <------| O "I do not want to turn, but I want to bend!" <------| | |------> There is no resultant turning force at "O" even when the object is spun. There IS however, a significant bending force on our crankshaft at "O". As it rotates, the crankshaft "feels" something like what a pencil feels if you grasp it with your thumbs and forefingers (thumbs in the middle) and try to snap it. Nevertheless, this bending force is entirely contained within the crank and produces no significant vibration (unless the crankshaft is really flexible and the bearings are really worn. But then you have a whole lot of other troubles as well). The crank also bends in the same direction (relative to the crank) all the time. Therefore this bending does not seriously contribute to fatigue failure of the crank. The magnitude of bending, not its direction, is all that changes as the engine is run. The magnitude is a function of engine RPM. Note that because of this it is the middle bearing which suffers the most distress in Lycoming 4-Cylinder engines! For the crankshaft in fig F. the first-order forces are in balance (there are as many crank throws on one side of the crank as on the other). Therefore the crankshaft is in STATIC balance. For the same crankshaft the first-order "moments" are in balance as well. Moments are just the distance from a certain point at which a force acts. Note that the crank throws on the left of the crank are equidistant from the "O." The crank throws on the right of the crank are likewise equidistant from the "O." Because the moments as well as the forces are in balance then the crank is in first-order DYNAMIC balance. Consider a crankshaft that looks like this: (And this commentary of each dynamic force and the "O"!) Fig G: | | ---- | |------> "My lever is long!" ------- "My lever is | | short!"<------| ---- | | O "I am turning clockwise!" ---- | | |------>"I my lever is short ------- "With a long | too! UNFAIR!" | enough <------| ---- lever I can | move the | Earth!" [Apologies to those with a weak stomach as well as to Atlas] The crankshaft in figure G would exhibit STRONG first-order vibrations when spun. Why? Because of the huge lever (moment) advantage of the outermost crank throws. The outermost crank throws reinforce one another - they do not cancel each other as the throws do in figure E. The innermost crank throws are imposing a force vector to counter that of the outer throws but because they are closer to the crank center they lack the mechanical advantage of the outer throws. However, the crank in figure G is just like the one in figure F in terms of mass balance. Therefore it is in STATIC balance for first-order vibrations. Figure G's crank is not in DYNAMIC balance because of the differing moments for for offsetting forces. When this crank is spun it will vibrate badly! SUMMATION: The Lycoming 4-cylinder engine is in both STATIC and DYNAMIC balance for first-order vibrations. Task #2: Discuss the second-order vibration characteristics of the Lycoming 4-cylinder engine. Remember that we said that second-order vibrations concern the reciprocating mass of an engine. Second-order vibrations are vibrations that occur twice with every revolution of the crankshaft. Why does reciprocating motion cause second-order vibration? Because for every 360 degrees of crankshaft travel the pistons accelerate twice. OR DO THEY? Refer to figure H. Pistons #1 and #2 in the Lycoming four cylinder at are top dead center when the crankshaft is at the 0 degree mark. At the same crank position the pistons in cylinders #3 and #4 are at bottom dead center. Fig H: | | ---- (|)========[#] <<== -------- <-------------------------There is a clockwise ==>> [#]========(|) twisting here ----- | <-------------There is bending here ----- (|)========[#] ==>> --------- <------------------------There is a counter- <<== [#]========(|) clockwise twisting ----- here | | [#] Piston ==== Connecting rod <<== ==>> Direction of piston travel As the crank rotates, pistons #1 and #2 start to accelerate inward. This acceleration produces an inertia force at the #1 and #2 crankpin. These forces are equal for both crankpins as well as being in opposite directions. Because they are equal in magnitude and because their direction vectors are 180 degrees opposite they are considered balanced for force. In other words, there should be no net movement and no resulting vibration. But wait a minute! There is a torsional couple because the connecting rods are displaced along the crankshaft. They do not meet the crankshaft at the same place Therefore they create a couple which tries to rotate the top half of the crankshaft clockwise. Argh! Does this mean vibration? Look at cylinders #3 and #4. They are doing the same thing but with a significant difference. They are both coming off of bottom dead center not top dead center like pistons #1 and #2. The pistons on crank pins #3 and #4 are accelerating outward. They too are balanced for force but are producing a torsional couple as well. Guess what? The couple is trying to twist the bottom half of the crankshaft counter-clockwise! The torsional couples for cylinders #1 and #2 are balanced by the couples from cylinders #3 and #4. Again, the net result is a bending at the crankshaft center but no net vibration. Are we home free? Do we have an engine free of first AND second order static AND dynamic vibration? No. Sorry! The second-order vibration balance I talked about above is only valid for the "primary" component of second-order reciprocating vibrations. Yes, Virginia, there is a secondary component of the second-order vibration and it's this guy who is going to ruin our whole day. What's going on? Unfortunately the piston travels farther from 0 degrees of crank angle to 90 degrees of crank angle than it does from 90 degrees to 180 degrees. This results in the piston accelerating faster from top dead center than it does from bottom dead center. Don't believe me? Do the trig. Note that if the connecting rods were infinitely long then we would have no secondary component and I could stop writing. Frankly, I am willing to put up with a little vibration if it means I don't have to wax an infinitely wide cowling! Because the pistons coming off of bottom dead center do not do so as fast as those coming off of top dead center we have a torsional imbalance. Inertial forces are balanced because #3 and #4 exactly counteract one another in terms of weight and speed of acceleration. Same thing for #1 and #2. Unfortunately, because #1 and #2 are moving faster, the torsional couple they create is greater than the couple created by #3 and #4. Since the couple created by #3 and #4 is supposed to counteract the couple created by #1 and #2 but can't (because of the magnitude of the couple) we have a secondary imbalance in the second-order torsional couple of our engine. We call this imbalance an imbalance of moments and it results in a rocking motion of the engine. Thank God for Lord Mounts! SUMMATION: A four cylinder Lycoming engine is balanced for both force and torque couples (moment) for first-order vibration The same engine is balanced for force of both the primary and the secondary components of second-order vibrations. It is balanced for the moment of the primary component of the second-order vibration. It is NOT balanced for the moment of the secondary component of the second-order vibration. The opposed aircraft four cylinder engine tries to rock clockwise and then counter-clockwise (when viewed from above) with each full revolution of the crankshaft. For the curious, an inline four engine has the exact same problems with secondary vibrations as our opposed four-cylinder aircraft engine. However, because the cylinders are inline vs. opposed it is unbalanced for secondary forces not moments. Instead of trying to rock back and forth the inline four-cylinder engine tries to "hop" up and down on its mounts. DYNAMIC CRANKSHAFT COUNTERWEIGHTS No attempt is made to absorb first or second-order vibrations with dynamic counterweights on the crankshaft. If present in the engine these vibrations are absorbed by the engine mounts or transmitted to the frame of the aircraft. Sometimes first or second order vibrations, where they are the result of engine configuration as opposed to mismatched parts weights, are absorbed by a counter-rotating balance shaft. More often people choose to forego the complexity of the shaft and just live with the vibration. Dynamic counterweights are used to absorb torsional vibration in the crankshaft. This is vibration which results from gas pressure on the cylinder which, in turn, causes crankshaft flexing. For a four cylinder opposed engines the orders of interest for dynamic crankshaft counterweights are usually six and eighth order vibrations. Some Lycoming four-cylinder engines incorporate dynamic counterweights to absorb these frequencies. Others just count on the relatively short and stiff crankshaft to take care of things. REFS: 1) Taylor, _The Internal Combustion Engine_ 2) Den Hartog, _Mechanical Vibrations_ 3) Schwaner, _Sky Ranch Engineering Manual_ Copyright 1994, Gregory R. Travis greg