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Balance Spreadsheet

Posted by frustrated 
Balance Spreadsheet
April 25, 2012 07:25AM
The posted spreadsheet is designed to determine the unbalance characteristics of basic engine designs up through 12 cylinders. In a pinch it can perform calculations for small engines by using some of the crankpin entries to represent counterweights or other crank components such as reluctor rings. I have some more advanced and thorough sheets, but they are far less user friendly than this, and I suspect it isn't that friendly. This one should at least be useable by someone who didn't write it, even if it doesn't allow for the same degree of input.

The spreadsheet has a number of pages, each accessible via tabs at the bottom. Information regarding engine configuration is entered on one page, another page contains graphs showing primary and secondary unbalance forces for both the reference (REF) and opposing (OPP) balance planes as well as overall engine shake. A couple of other pages break the forces down into horizontal and vertical components by degree of crank rotation as well as calculating the force vectors and magnitude. The pages numbered 1 through 12 perform the basic calculations for each crankpin (or counterweight) from the data entry page.

Feel free to ask if there are any questions...



Edited 3 time(s). Last edit at 04/25/2012 03:06PM by frustrated.
open | download - BALANCE CALCULATOR.xls (5.57 MB)
Re: Balance Spreadsheet
April 25, 2012 04:12PM
That's great.
Since all the cylinders have to be the same, then how can one use a pin to simulate a rotating weight; It would add reciprocating weight as well?
Re: Balance Spreadsheet
April 25, 2012 04:24PM
Rotating weights should be cancelled by the counterweights and not contribute to the engine unbalance. Reciprocating weights shake the engine and cannot be canceled by a single crank, but the correct arrangement of cylinders and crankshaft pin angles can cause these shaking weights to cancel out.

Re: Balance Spreadsheet
April 25, 2012 09:10PM
Here are some settings for a "typical" inline 4, inline 6, V-8. Stanley and the Doble-Sentinel W-3 engine.

Note that in the left hand box, it is necessary to enter the number of cylinders (this tells the spreadsheet what to calculate and what to ignore) and note that the distance between balance planes is adjusted to keep the balance planes identically separated from the endmost crankpins.

The calculator doesn't always give exactly the right 'textbook' answer. Fer instance, it shows a bit of unbalance for a Boxer 4 layout like the old VW Beetle, though the texts say it is perfectly balanced. The texts don't generally take the offset between opposing cylinders into account, the unbalance really isn't large and they don't want to confuse the issue.

Have fun...



Edited 1 time(s). Last edit at 04/25/2012 09:11PM by frustrated.

Re: Balance Spreadsheet
April 25, 2012 09:31PM
Might as well toss in a few more examples, then let anyone so inclined experiment on their own.

To see the effect of pin orientation, try running the I-6, then change the pin angles to 0-60-120-180-240-300 and then to 0-180-120-300-240-60 and if you are REALLY bored, even try 0-120-240-0-120-240....

Bonus "ATTABOY" to anyone who can figure out what is strange about 3 cylinder radials!

Edited 3 time(s). Last edit at 04/26/2012 09:13AM by frustrated.

Re: Balance Spreadsheet
April 26, 2012 12:52PM
You said in a pinch the extra pins could be used as counterweights. How would you do that, in the spreadsheet, to get more balance to an unbalanced engine? For example a single pin radial needs weight on the crankshaft to balance, right?

The rotating weight input doesn't seem to do anything. I can't find reference to it elsewhere in the sheet.

EDIT:What pops out in the radial 3 simulation, is the crankshaft total load, which looks sinusoidal at 3x frequency. If I knew why, maybe it wouldn't seem odd. Can I get a cookie for that?

Edited 6 time(s). Last edit at 04/26/2012 02:40PM by sidrug.
Re: Balance Spreadsheet
April 26, 2012 11:14PM
Lemme see...

First off, this program is really designed to analyze the reciprocating forces in an engine. The rotating mass input doesn't do anything, years ago I meant to do more with the program but the value of adding that kind of information just wasn't worth my effort.

Yes, the counterweight is supposed to counterbalance the crankpin and the crankpin arms....and the crankpin bearings and the portion of the connecting rod weight that is considered to be rotating.....and usually it should also counterbalance 1/2 the reciprocating weight of the connecting rod, piston, wrist pin, rings and wrist pin bushings.

You really don't need a program to calculate how to balance the crank itself, the balancing formula for the pins and counterweights is almost always that one must balance for all the rotating weights plus half the reciprocating weights attached to that crankpin. This holds true if you add a single balance shaft to cancel primary shaking forces, it will be weighted to be equal to the other half of the reciprocating forces and because it rotates in the opposite direction of the crank the pair of them alternately cancel and reinforce each other to create a sinusoidal output along the axis of the cylinder. If you plan on using two balance shafts to cancel primary unbalance, then balance the crank only for the rotating forces because the two shafts will cancel the reciprocating.

What the spreadsheet really does well is analyze different engine geometries so that you can make decisions regarding how to set up an engine. For example, there are two really good solutions for the straight 8. An ideal inline 4 cylinder steam car crank would look different than one for a 4 stroke gas engine due to the extra power pulses. Questions like this come up in situations like whether you want to go with a single plane crank or two plane crank in an engine....production V-8s are almost always 2 plane because it is smoother, but the smoothness is achieved by cancelling the rotating unbalance force with heavier counterweights. Racing V-8s more often use 1 plane cranks even though the are less well balanced because they are lighter, accelerate quicker and also because the firing order allows for much less complicated exhaust plumbing. I balanced a two plane crank a few years back that won at Sebring, so I can't say there are any hard and fast rules.

If you wanted to simulate a rotating force, such as a counterweight, you would enter the position along the crank in the cylinder offset column then enter the angle of the rotating force as the pin angle, set the cylinder angle as 0. The separate pages accessed through tabs 1-12 do the calculations for each crankpin, you would have to go to the page corresponding to that data entry and enter the unbalance force in all the rows in column C (taking care to check that the angle in the first row is the angle the force should be found at n the crank). Since rotating forces have no secondary unbalances, you would also have to go to column H and enter 0 in each row.

Here's a few hints on reading the outputs. If your graph has two sine waves of equal height, the sum is a rotating force with the angle relative to the crank being dependant on the horiztontal locations of both waves. Checking the Sums or Output pages, if the primary forces are constant and change 1 degree for each angle of crank rotation, the primary force is rotating and can be canceled with a counterweight. For secondary unbalance, the force should also be constant but the angle should change exactly 2 degrees for each degree of crank rotation.

If either the horizontal force is a sine wave and the vertical is a straight line, the force is a side to side shake; if these are reversed, it is a vertical shake.

Vertical and horizontal forces that are unequal sine waves indicate an elliptical force distribution

Just for the fun of it, go back to the 3 cylinder radial and note at what angle the secondary unbalance is found for each degree of crank rotation....... I never found any references to this one, just popped out at me one day when someone asked me about the engine.


Re: Balance Spreadsheet
April 27, 2012 10:05AM

If you wanted to simulate a rotating force, such as a counterweight, you would enter the position along the crank in the cylinder offset column then enter the angle of the rotating force as the pin angle, set the cylinder angle as 0. The separate pages accessed through tabs 1-12 do the calculations for each crankpin, you would have to go to the page corresponding to that data entry and enter the unbalance force in all the rows in column C (taking care to check that the angle in the first row is the angle the force should be found at n the crank). Since rotating forces have no secondary unbalances, you would also have to go to column H and enter 0 in each row.

That doesn't work. If it did, it would show a sine horizontal force and a sine vertical force, 90' out of phase. It shows only straight lines.
Re: Balance Spreadsheet
April 27, 2012 11:17AM
A rotating force IS a straight line. A reciprocating force is a sine wave. A sine wave in both the horizontal and vetical planes of equal magnitude resolves out into a rotating force....if you look at a perpendicular trammel or one of those toys (nothing grinder, nothing machine, etc) you can see how that works out.

The graph shows degrees on one axis, magnitude on the other. A rotating force will have the same magitude at 0, 1, 2, 3...357,358 and 359 degrees and will thus assumes as straight line when graphed as a function of magnitude and angle. The critical factor is what angle the force should be at for any given crank angle, and you need to examine the tables to see that.

A reciprocating force has zero magnitude at top and bottom centers and hits peak magnitude at about 90-degrees for the primary force and 45 degrees for the secondary. Hence, it assumes a sine wave when graphed as a function of magnitude and angle..
Re: Balance Spreadsheet
April 27, 2012 01:19PM
There clearly is something I'm not getting. If I had a balanced crankshaft only (no pistons), and put a weight on it, spun it, and let the graphs tell me the forces, what should they show?

I thought this should be the same force as a 90' v2 single pin with infinite fork and blade rods - and that does seem to show correctly in the graph.

Re: Balance Spreadsheet
April 27, 2012 03:57PM
Yes, a balanced shaft with an unbalance force added to it will show a straight line for the total unbalance force and two identical sine waves for the vertical and horizontal components, just as you show.

The spreadsheet is primarily designed to show the engine shake created by the reciprocating forces. Crank balance does not automatically mean the engine is balanced. Symmetrical cranks, those that are exactly identical to the left and right of center, should be balanced when no weight is on them. Non-symmetrical cranks are often NOT balanced with no attached weight. For example:

An inline 4 has crankpins at 0-180-180-0 degrees; the two outer pistons are always going one direction and the two inner pistons are always going the opposite direction. The outer pistons create a shake in one direction, the inner pistons create a shake in the opposite direction, and because the shakes are of equal force and opposite direction, they cancel out.

A V-8 has pins at 0-90-270-180. There are two pistons in a 90 degree vee on each pin, thier shakes resolve out as rotating forces. The forces are in opposite directions on each end because the pins are 180 degrees apart and the two inner pins are 90 degrees away and create another rotating force which affects each end based on the distance from that end, so they tend to cancel each other somewhat. Whatever rotating forces are left from the two inner pins interact with the outboard rotating forces and cause a larger force to appear at an angle somewhere between the inner and outboard proportionate to the relative strengths of the force components. Because these pistons are creating a rotating force on each end of the crank, the counterweights have to create an opposing force. Unlike the inline 4, the V-8 crank for a balanced engine is not balanced itself....it has to create a rotating couple to cancel the couple created by all the pistons.

The trick in designing an engine is to lay out the cylinders and crankpins so that the reciprocating forces cancel one another out as much as possible. Because the connecting rod creates a secondary shaking force, not all solutions will cancel the primary and secondary forces. In a V-8 the shaking forces are horiztontal and they reverse every 90 degrees, the two outboard pairs of cylinders create a shake in one direction that is perfectly opposed by the two inboard pairs of cylinders, so the V-8 engine is perfectly balanced. The inline 4 is perfectly balanced for primary force, but since the forces reverse every 90 degrees and because the pins are 180 degrees apart, the secondary shakes all line up and cause the engine to jump. So, the V-8 crank is unbalanced while the V-8 engine is balanced, the I-4 crank is balanced while the I-4 engine isn't.....

A while back I posted a paper I wrote for a SACA meet, which was later a Bulletin article, you can read it here:


It should explain better, with pictures.


Re: Balance Spreadsheet
April 27, 2012 06:28PM
We still don't understand each other it seems. I wanted to simulate a counterweight, so that I could see which forces could be cancelled. I thought that is what you answered to, and I did what you said, and it only produced a constant vertical or horizontal force, which is assumed to not be possible anyway (levitation).

So what I have done now is written a V2, for which I can set the reciprocating weight separately from the rest. Its secondary force is set to zero. That should be exactly like a counterweight on the crank. Here is a Y (rad3) with the V2 for balance.

This is probably intuitive to you so you don't need that function.

What is the fat black line on the graphs?

Edited 2 time(s). Last edit at 04/27/2012 06:39PM by sidrug.

Re: Balance Spreadsheet
May 02, 2012 06:35AM

Sorry for the delay in responding, had to go out of town and only been able to look in for a few moments at a time.

I have no idea what the black line is, it doesn't show up on my spreadsheets. Microsoft does some weird stuff, seems like every time I copy files from one computer to another, or from one version of Office to another, some kind of formatting issue arises. I asume Bill Gates is doing some kind of pyschological experiment to determine how exasperated users will become without committing suicide.

You're right, going back and looking at the results, the sheet isn't working as I remember. It's been a lot of years since I programmed in a counterweight and I obviously remembered it wrong. I know there is a relatively simple way to do it, but damned if I can remember how anymore. For the most part, I haven't worried about programming counterweights into the spreadsheet for years, rotary forces are easily interpreted in the columnar pages...if a primary force is identical and advances a degree for every degree of revolution, it is rotary and an identical counterbalance force in the opposite direction is needed. The best solution is to add the counterbalance force to the counterweight on the balance plane, then the force doesn't affect the opposite end. If that isn't possible, a set of ratio problems provide the quick answer as to what weights can do the job on any specified plane.

I probably should go back and add a counterbalance function to this spreadsheet, just to make it simple, will put that into the "To do" box. At the moment I'm trying to finish up a proposal for a company interested in building steam gen sets, figuring out how to design the components to be cheap, easy to manufacture, rugged and efficient is kind of a challenge....so I'm cribbing as much as I can from old patent files and automotive engineering.


Re: Balance Spreadsheet
May 04, 2012 11:23AM
Steam genny sounds great fun. How much power? Fixed speed AC?

I modded your sheet to get some counterbalance. A bit clumsy but it's a start, maybe. Just added 4 cylinders and modified them a bit. Maybe you want to check it out, so I'm attaching it. Just set the counterweight mass to zero and it works the same as before.
Here is what is changed:
input: a few extra inputs
cw sheets: C5, D5, F5, G5, B12, C12->, H-L 12->
sums: b7 ->, AI-AL
2 new graphs
lower resolution and ods format to fit the forum and my slow pc

Edited 2 time(s). Last edit at 05/04/2012 11:29AM by sidrug.
open | download - BALANCE CALCULATOR-lowres.ods (786.3 KB)
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