First order Second order vibrations 2

[MechOEngg]

hii i am working in NVH industry from 1 year. My question is what are half order, first order, second order,third order and so on.. vibrations. I have heard these terms during technical discussion between my boss and customer.I have gone through net and find some explanations but i did not understand.
Like: First order or first harmonic balance are supposed to indicate the balancing of items that could shake an engine once in every rotation of the crankshaft i.e. having the frequency equal to one crank shaft rotation.Second order is frequency of twice in one crank rotation and so on for higher order,,,
So my query is what actually leads to these vibrations,
how does they affect engine mounts.

Please help.
This is my first question on this forum.

 

[GregLocock]

You should probably chat with your boss about this.

1/2 order -cylinder to cylinder variation in firing pressures or timing

1 order - balance of the crank

2 order- most troublesome frequency component from non sinusoidal motion of piston and conrod, worse on an inline 4 due to the crank layout

3 order - firing frequency on a 6 cylinder

1 and 2 order in particular can be very large forces, very hard to isolate in your engine mounts.

Cheers

Greg Locock


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[BrianPetersen]

1st order vibration: picture a single cylinder engine with no balance shafts. It has a vertical vibration the same frequency as crank rotation.

2nd order vibration: this one is a bit tougher. Picture a conventional inline four. The two outer pistons are 180 degree opposed to the inners. When the outers are at the top, the inners are at the bottom. Balanced, right? Not quite. Look at the angle of the connecting rods. When the pistons are at TDC/BDC, the rods are straight up and down. When the crankshaft position is mid-travel, the pistons are NOT mid-travel. The connecting rods are at an angle to the side, which means the pistons are a little below the mid-position. This happens twice per revolution, so the resulting vertical vibration is at double crank rotation frequency.

6 cylinder in-line engines have very little of either primary or secondary vibrations ... but they're awkward to package into modern automotive engine compartments.

 

[Lou Scannon]

When the crankshaft position is mid-travel, the pistons are NOT mid-travel. The connecting rods are at an angle to the side, which means the pistons are a little below the mid-position. This happens twice per revolution, so the resulting vertical vibration is at double crank rotation frequency.

That's the first time I've seen it explained that way. That's a little abstract, but not untrue. The more in-depth explanation is that, because the rod length is finite, the acceleration of the piston (+ small end of the rod) is greater at TDC than BDC, and we all know, F=ma, so the forces of the pistons at the top and bottom of the stroke do not completely cancel each other out.

6 cylinder in-line engines have very little of either primary or secondary vibrations ... but they're awkward to package into modern automotive engine compartments.

Very true, yet some of the higher spec brands (e.g. BMW & Mercedes) are still happy to accept this challenge [at least, last time I checked].


"Schiefgehen will, was schiefgehen kann" - das Murphygesetz

 

[SomptingGuy]

If you were to have a vertical totally frictionless I4 engine, you'd see that there are two crank positions where the system can sit in equilibrium (overall centre of mass at lowest point). So there must be (at least) a 2E vertical out of balance for that configuration if the crank is rotating.

The packaging compromise of the beatifully smooth I6 is that it only really works in RWD layout. So if your brand identity already involves RWD, an I6 is a sensible choice. Everything falls into place nicely.


- Steve

 

[GregLocock]

Sory i forgot, another cause of 2E is firing order of 4 cylinder engines. So if you do a full throttle run up and then a coast, the WOT run gives you the firing contribution, the coats gives you the L/R forces due to conrod length.

Cheers

Greg Locock


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[MechOEngg]

Thanks everyone for your valuable replies,
@GregLocock: Sir, I asked him & with a smile he advised me to do google.

1 and 2 order in particular can be very large forces, very hard to isolate in your engine mounts.

Could you please elaborate why are these forces very large? & what are other measures to isolate them apart from engine mounts.

 

[GregLocock]

Because they are inertial in origin, not just wimpy little explosions.

Balance shafts.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BrianPetersen]

First and second order vibrations are both helped by making the reciprocating parts as light as possible to minimize the magnitude of the vibration. But beyond that ...

To address 1st-order vibrations:

Cylinder configuration versus crank weights versus balance shafts versus engine mounts. A single needs two balance shafts, one on each side, spinning opposite direction of the crank, with both the crank and balance shaft weights correctly selected to offset the piston and con-rod. A lot of production singles make do with one balance shaft and just deal with the resulting rocking couple (my Honda motorcycle is like that). A lot of others just let 'er shake (practically every lawn mower, etc). A parallel 360-degree twin is the same as a single for purposes of vibration. A 90-degree V-twin with the correct crank counterweights has perfect primary balance. An inline triple has perfect primary up-and-down balance but they have a first-order rocking-couple imbalance that needs a counter-rotating balance shaft to offset. Triumph 3-cylinder motorcycle engines use balance shafts. Many automotive 3-cylinders have no balance shafts and they just let the engine mounts (more or less) deal with it. And so on ...

Balance your pistons and rods. Every up-and-down pair of pistons ought to have as close to the same weight as possible. Same with the con-rods, and both the small-end and big-end matter and should be balanced separately. The crank counterweights have to be correct for the pistons and rods. And so on ...

For 2nd-order vibrations:

Triples and inline-sixes have little second-order vibration. Take a look at the crankshaft in a normal (American) V8 engine. It isn't flat like an inline-four crankshaft. In each bank for each two pistons that are up-and-down there are two that are mid-travel. Reason: better second-order balance, and remember that since a 90-degree V-twin with the right crank weights has perfect primary balance on its own, stacking 4 of them end-to-end still has perfect primary balance (and you can cancel out some of the counterweights by doing this). For an inline-four ... Two counter-rotating balance shafts running twice crank speed. Or, use long rods relative to the stroke (it minimizes the origin of the second-order vibration).

The original poster would do well to study the design of the 2009-onwards Yamaha R1 1000cc inline-four - the one with the "crossplane" crankshaft - and understand why this uneven-firing engine runs smoother at high revs than its traditional even-firing competitors.

 

[SomptingGuy]

The are loads of videos like this on the WWW. All primary and secondary forces & moments internally resolved,so the engine is stationary (enough) when running. If only they weren't so expensive and complicated.

https://www.youtube.com/watch?v=Hz0tSc93yZA

- Steve

 

[EHudson]

Engine shaking forces owing to mechanical inertias result from the reciprocating motion of the piston as others have indicated.

The usual simplification is to lump the mass of the connecting rod and bearings on the crankshaft side of the rod C.G. with the crank and call that the rotating mass. The section of the connection rod from the rod C.G. to the piston is lumped with the piston, pin and rings into what is called the reciprocating mass. The rotaing bits can often be balanced with counterweights and such. Unbalanced rotating bits only generate first order (crank speed) forces.

You can find an approximation for the reciprocating force in Mark's Handbook or a book on engines. Almost all of these are based on a rapidly converging series generated by use of the binomial theorem.

The first term in the series is a cosine function of the crankshaft position. The second term contains the ratio of the crank arm radius (half the stroke) to connecting rod length (center to center) and the cosine of twice the crank angle. It is because the second term contains the double speed function that is called the second order force. The third term contains a quadruple speed term which gives a fourth order.

The forces of orders greater than one, produced by an individual cylinder are in line with the bore axis of that cylinder.

There can also be some rotary couples to deal with. Picture an opposed two cylinder engine. The crank may be in perfect static balance but because the cylinders are slightly offset from each other, the equal an opposing forces of the pistons and rods as well perhaps, as some of the rotating bits, don't line up with each other. This offset of the crank pins along the crankshaft axis leads to a couple in the twin cylinder. A three cylinder has rotating couples.

A handy chart Table 8-2 in "The Internal Combustion Engine in Theory and Practice", Charles F. Taylor Volume 2, MIT Press summarizes the characteristics of many different engine configurations. (Memory says this may be a copy of a table in a Ker Wilson book which you may well have in an NVH business).

Your mounts also need to handle the reaction torque of the engine. I always thought that Den Hartog's book on vibrations gave a pretty good summary of the engine vibration and suggest that you give it a look.