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Secondary engine balance 3
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GregLocock
Automotive
However, it is not just at second order, the fourier series for that waveform has components 1,2,4,6,8, etc
A scotch yoke has a pure sinusoidal displacement graph, hence has only a first order component.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
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BrianPetersen
Mechanical
When the crank throw is 90 degrees from the top/bottom, the connecting rod bottom end is off to the side, which means the piston is not at halfway, it is sitting a little lower than the halfway position.
Do that on an inline four, and when the crank throws are at 90 degrees, the pistons are all below the halfway point. When the crank throws are straight up and down, two pistons are at top, two are at bottom. Figure out where the center-of-gravity is in both cases. There's your answer for the traditional inline-four secondary-imbalance buzzy vertical-shake vibration at higher revs.
And that's not the only thing going on in an inline-four. When the pistons are all TDC/BDC, their kinetic energy is zero. When things are at 90 degrees, their total kinetic energy is at a maximum, and neglecting combustion/compression forces, that kinetic energy came from the crankshaft. Result ... instantaneous crank rotation speed is lower at the 90-degree point than at TDC/BDC, neglecting combustion forces. That happens twice per revolution ... and if you again look at conservation of momentum, the irregular rotation speed of the crankshaft also translates to an irregular rotation speed of the cylinder block. The average rotation speed of the cylinder block is obviously zero, but the instantaneous might not be. More buzzing.
And speaking of that combustion force ... that also happens twice per revolution on an inline-four, and it's phased differently from the inertial effect and the magnitude depends on where your foot is on the accelerator pedal.
There's a lot going on at twice crank rotation speed in an inline-four.
Do that on an inline four, and when the crank throws are at 90 degrees, the pistons are all below the halfway point. When the crank throws are straight up and down, two pistons are at top, two are at bottom. Figure out where the center-of-gravity is in both cases. There's your answer for the traditional inline-four secondary-imbalance buzzy vertical-shake vibration at higher revs.
And that's not the only thing going on in an inline-four. When the pistons are all TDC/BDC, their kinetic energy is zero. When things are at 90 degrees, their total kinetic energy is at a maximum, and neglecting combustion/compression forces, that kinetic energy came from the crankshaft. Result ... instantaneous crank rotation speed is lower at the 90-degree point than at TDC/BDC, neglecting combustion forces. That happens twice per revolution ... and if you again look at conservation of momentum, the irregular rotation speed of the crankshaft also translates to an irregular rotation speed of the cylinder block. The average rotation speed of the cylinder block is obviously zero, but the instantaneous might not be. More buzzing.
And speaking of that combustion force ... that also happens twice per revolution on an inline-four, and it's phased differently from the inertial effect and the magnitude depends on where your foot is on the accelerator pedal.
There's a lot going on at twice crank rotation speed in an inline-four.
SomptingGuy
Automotive
BrianPeterson said:
And all the beatiful mathematics that comes with it will be lost if/when we move away from reciprocating engines as prime movers. 100-ish years of steam, then 100-ish years of internal combustion.
- Steve
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BrianPetersen
Mechanical
A single has exactly the same secondary imbalance for exactly the same reason, it's just superimposed on top of a (normally much more massive) first-order imbalance.
A single with balance shafts that counteract the first-order imbalance will still have the secondary imbalance for exactly the same reason that an inline-four does.
Remember that these balance factors are a sum of ALL of the higher-order frequencies; see the link in Greg's post above. Just because you have a big first-order imbalance that dominates the situation doesn't mean the rest of them don't exist as well!
A single with balance shafts that counteract the first-order imbalance will still have the secondary imbalance for exactly the same reason that an inline-four does.
Remember that these balance factors are a sum of ALL of the higher-order frequencies; see the link in Greg's post above. Just because you have a big first-order imbalance that dominates the situation doesn't mean the rest of them don't exist as well!
An inlne 4 arranges all the secondaries so they add, not cancel.
The crank must tug on The pair at TDC tomake them "hurry" away from TDC due to the stroke/rod length relationship. The crank doesn't have to tug very hard on the pair at BDC because they tend to "dwell" at BDC. At each pair's TDC the crank is being yanked upwards. It is almose like there is extra piston assembly spinning uncounterweighted at 2x crank speed
The crank must tug on The pair at TDC tomake them "hurry" away from TDC due to the stroke/rod length relationship. The crank doesn't have to tug very hard on the pair at BDC because they tend to "dwell" at BDC. At each pair's TDC the crank is being yanked upwards. It is almose like there is extra piston assembly spinning uncounterweighted at 2x crank speed
SomptingGuy
Automotive
The waveform of piston motion (displacement, velocity, acceleration) can be created by summation of the fundamental and all its harmonics. Each is a sine wave, but when you add them up, you get the familiar form that looks like a squashed/stretched single wave. The relative amplitudes of the harmonics (compared with the fundamental) depends on the ratio of rod length to crank throw. You need an infinite ratio to eliminate all harmonics. Or a different mechanism.
Combining and phasing sets of pistons to cancel these harmonics is part of engine balancing.
- Steve
Combining and phasing sets of pistons to cancel these harmonics is part of engine balancing.
- Steve
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I understand, that in, for example, inline 4 engine, when pair of piston (1 and 4) goes down from TDC, other pair goes up from BDC (2 and 3), that pair, which goes down, moves faster and create secondary imbalance, at 90deg secondary balance force curve changes direction, because, that pair which goes up from BDC (2 and 3), now is going faster nor 1 and 4 pistons, because from 270deg to 90deg is more way which piston must travel. And I understand, that when pistons is at 90deg, center of gravity is lower, and when pistons is at TDC and BDC, center of gravity is higher. But when is only one cylinder in engine, and when crankshaft turns 90deg from TDC, secondary balance curve also changes direction, like in inline 4 engine, but there is no other pistons, which goes upward faster, when that cylinder goes downward slower, it's only one cylinder, and I don't understand, why, when is only one cylinder, secondary balance curve change direction at 90deg and at 270deg? In single cylinder engine, when piston goes down, from TDC to BDC, all vertical forces moves down, yes? And when piston goes up, from BDC to TDC, all vertical forces goes up? If yes, then why secondary forces change direction at 90deg and 270deg in single cylinder engine? Thank You for Your answers, it's really interesting to me 
BrianPetersen
Mechanical
Because at 90/270, that's where the connecting rod's angle is at its outer extremity and changes direction.
Think of it this way. The primary "sine wave" is the main up-and-down motion. The secondary (twice-frequency) "sine wave" is the component introduced by the connecting rod going side-to-side. If you look ONLY at that connecting rod side-to-side motion and neglect the primary up-and-down for the moment, the piston will be highest at 0/180 and lowest at 90/270.
It's not quite that simple, because that secondary motion is not purely sinusoidal which means there are higher-order frequencies as well.
Think of it this way. The primary "sine wave" is the main up-and-down motion. The secondary (twice-frequency) "sine wave" is the component introduced by the connecting rod going side-to-side. If you look ONLY at that connecting rod side-to-side motion and neglect the primary up-and-down for the moment, the piston will be highest at 0/180 and lowest at 90/270.
It's not quite that simple, because that secondary motion is not purely sinusoidal which means there are higher-order frequencies as well.
SomptingGuy
Automotive
Don't think of the piston as "going up" or "going down". All those diagrams of the 4 strokes of an IC engine can create this mental picture of the piston as some kind of elevator. It's not an elevator, it's always smoothly moving.
- Steve
- Steve
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Link
You need to understand Fourier series. If you have an engineering degree and they didn't teach Fourier series, you should find another University and start again.
Any signal (but especially repeating ones) can be broken down into a series of simple sine waves which "add up" to form an exact copy of that signal. Each sine wave is twice the frequency of the previous.
The secondary force is not an "extra" force being applied. The piston motion (and therefore the force) is not a pure sinewave due to crank/rod/slider geometry. It is "close" to a sinewave at crank frequency so that sinewave is the starting point (fundamental) of the Fourier series. Most of the deviation from this pure sine wave is corrected by adding the first harmonic (double frequency) component (for the reasons given by other posters), but additional frequencies (at much lower amplitudes) are also present. The first harmonic is the "secondary balance" we are discussing.
Engineering is the art of creating things you need, from things you can get.
You need to understand Fourier series. If you have an engineering degree and they didn't teach Fourier series, you should find another University and start again.
Any signal (but especially repeating ones) can be broken down into a series of simple sine waves which "add up" to form an exact copy of that signal. Each sine wave is twice the frequency of the previous.
The secondary force is not an "extra" force being applied. The piston motion (and therefore the force) is not a pure sinewave due to crank/rod/slider geometry. It is "close" to a sinewave at crank frequency so that sinewave is the starting point (fundamental) of the Fourier series. Most of the deviation from this pure sine wave is corrected by adding the first harmonic (double frequency) component (for the reasons given by other posters), but additional frequencies (at much lower amplitudes) are also present. The first harmonic is the "secondary balance" we are discussing.
Engineering is the art of creating things you need, from things you can get.
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SomptingGuy
Automotive
I did like the animation on that wiki page, worht a direct link here:
This is the way I like to think of the terms of a Fourier series. Dynamically, as rotating complex vectors. The artist here has switched the normal convention of X-real, Y-imag (or rotated them), but the basic concept of independence and superposition (addition) of is shown very well. Real signal in the time domain is the projection of the summation on the real axis.
- Steve
This is the way I like to think of the terms of a Fourier series. Dynamically, as rotating complex vectors. The artist here has switched the normal convention of X-real, Y-imag (or rotated them), but the basic concept of independence and superposition (addition) of is shown very well. Real signal in the time domain is the projection of the summation on the real axis.
- Steve
" But why these secondary forces going up, when piston is or going at BDC? "
The crank is saying, " come here, piston ", speaking by proxy thru the connecting rod.
Force is related to acceleration. Velocity can be +, minus, or zero and acceleration can still exist. I'm accelerating at 1 g and I'm just sitting in my chair.
The crank is saying, " come here, piston ", speaking by proxy thru the connecting rod.
Force is related to acceleration. Velocity can be +, minus, or zero and acceleration can still exist. I'm accelerating at 1 g and I'm just sitting in my chair.
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