Balancing Act

Just in case John L's having a dull day at work...

....why do inline-4's with 180-degree crank phasing need a balance shaft?

The way I can picture it to myself, primary balance is taken care of thanks
to one pair of pistons rising when the other two are falling, and secondary
thanks to one pair of rods swinging backwards when the other pair are
swinging forwards.

Does the imbalance arise from the fact that the pistons falling from TDC are
moving faster than the pistons rising from BDC, or is there more to it?

This question should also be used by Manning as an indication of how that
engine CGI I'd offered to do for him is progressing...

 

Wouldn't have a clue!

Sounds reasonable.

Eh? Wouldn't you need a really flexible crankshaft to achieve that?

Moike

 

Nope. It's a direct consequence of the piston-conrod-crank arrangement,
which causes the piston motion not to be sinusoidal.

It takes about 5 minutes to show that piston speed as a function of crank
position is given by

v(theta)=(s/2)sin(theta)(1+(s/2)cos(theta)/sqrt(l^2-((s/2)sin(theta))^2)

where s=stroke, l=conrod length, and theta=0@TDC.

For theta=[0, Pi/2] (piston leaving TDC) and [3Pi/2, 2Pi] (piston
approaching TDC), the cos(theta) term is positive, which means that the
correction to the simple sinusoidal is greater than 1, and for theta=[Pi/2,
3Pi/2] (piston approaching and departing BDC), cos(theta) is negative,
making the correction less than 1, so at a given angle in the second and
third quarter of a crank revolution, the piston travels slower than at the
corresponding angle in the first and fourth quarter.

Weird, huh?

Thinking further, the imbalance cycles twice per crank revolution, first
when one pair of pistons is approaching TDC, then when they're leaving TDC,
then when the other pair takes its turn to do the same... problem redressed
by having a balance weight spin at twice crank speed (weight swings upwards
when there are pistons leaving TDC, downwards when there are pistons
approaching TDC).

Answered my own bloody question there...

 

Never a dull day ...

Cheers
Goaty

 

Awwww, you just wanted to show off. Did pretty good too
****, now I'm confused.

Red ZZR11

 

Gotta love a scientist, didn't even have to answer him

The above sounds right - it's a secondary imbalance which can be bearable
if left unbalanced - hence the traditional inline 4 "buzz". That italian
website I posted ages ago had a heap of stuff on it.

If you send me a valid email address I'll send you a PDF you'll love (the
iprimus address is valid - the deja one isn't )

JL

 

'cause God hates UJMs too!
Clem

 

Ooh ooh; 'cause UJMs are jus' UNNATURAL; that's why!!
Clem

 

Intact Kneeslider said....

IK> Does the imbalance arise from the fact that the pistons falling from TDC
IK> are moving faster than the pistons rising from BDC, or is there more to
IK> it?

Elastic conrods, perhaps?

 

Intact Kneeslider said....

IK> It takes about 5 minutes to show that piston speed as a function of crank
IK> position is given by

IK> v(theta)=(s/2)sin(theta)(1+(s/2)cos(theta)/sqrt(l^2-((s/2)sin(theta))^2)

Er, shouldn't there be an apostrophe just here...^?

IK> Weird, huh?

Not the word that I would've used....