# Balancing Engines



## JorgensenSteam

I have seen a number of posts on balancing single-cylinder steam engines, and have pondered how to do that correctly for many years.

Some have stated that engine balance is beyond the capabilities of the home modeler, but I think an engine can be balanced if you understand what you are trying to accomplish.

The first thing to understand is that there is static balance (objects not in motion), and this is commonly seen when the engine crank, rod, piston, etc. is placed on knife edges and balanced such that the weight of the piston, connecting rod, crank throw, etc. equals the weight of the counterbalance weights.

Then there is dynamic balance, and this is the balance you try to achieve while the engine is running, and the parts are either rotating (like the crankshaft) or reciprocating back and forth (like the piston, piston rod, crosshead, etc.).

An engine that is statically balanced only without any attention to dynamic balance can generate great deal of vibration when it runs.

It is also important to remember that the formula for dynamically balancing a vertical engine differs from the formula used to dynamically balance a horizontal engine, since gravity plays a larger role in the vertical engine.

If you are balancing your engine using knife edges, you are not balancing your engine when it runs.

Pat J


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## JorgensenSteam

I found a formula in an old public domain book, as follows for calculating the counterbalance weight(s) for steam engines, as follows:

Equation for minimizing engine vibration:

W1 = [K*(W2+W3)*r] / X

where:

W1 = weight of the counterweight (lbs.)
W2 = weight of the crank webs outside of the main shaft and crank pin (lbs.)
W3 = weight of reciprocating parts (piston, piston rod, crosshead, one half the weight of the connecting rod) (lbs.)

X = distance of center of mass of counterweight from center of the crankshaft (inches)

K = constant (use 0.67 for minimum vibration at right angles to the engine centerline, use 0.75 for minimum vibration at crank dead center)

r = distance from center of crankshaft to center of crank pin (inches)

Generally, vertical engines should tend toward using the 0.67 value for "k", and horizontal engines should tend towards using the 0.75 value for "k".

I am gussing that the weight calculated is the total for both counterweights if the engine does not have a single crank disk.

I punched these forumulas into an spreadsheet, using a 0.5 multiplier for the crankshaft and associated bearings and cap (half the weight of the connecting rod), and then drew up a counterweight which fits the end of the crankshaft web, and clipped it off in Solidworks until it was approximately the right weight.

Luckily, Solidworks (and Alibre ?) gives you the mass of each part, and also the center of mass location on the counterbalance, which is needed in the formula, and can be tedious to determine manually.

I have not tested these formulas yet, but they seem to be on the right track for dynamically balancing a steam engine.

Pat J


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## JorgensenSteam

Here is the file for the above spreadsheet.

Please verify the accuracy of the foumulas in this spreadsheet, as this is my first attempt at this, and the forumulas have not been verified.

Pat J

Edit:

Drats, the internet Gods will not let me upload a spreadsheet file, so here is the spreadsheet, renamed with a .JPG extension. You can download it and rename the extension to .XLS
Just right click on the file name, pick "save target as", and when saving, type over the .JPG and change it to .XLS 

View attachment Counterweight-Calculations-01.jpg


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## Entropy455

The apparent mass-loading of the piston on the crankshaft changes significantly between top-dead-center, and 120 degrees from TDC. For this reason, it is impossible to perfectly balance a single cylinder engine. You can however achieve a reasonable average balance that will provide as smooth as possible operation.

Generally, the counterweight must balance half of all reciprocating mass, plus all of the rotating mass.

The equation to calculate the mass that must be balanced out is as follows: piston weight + linear shaft weight + pin weight + ring(s) weight + small end con rod weight, all divided by two, plus the large end con rod weight. Units are mass (kg, gram, pound, ounce, etc  your choice). Being an Ohio born American, I choose to do engineering calculations in English units  which are certainly more difficult to work with than metric units  but I digress.

The hard part about balancing an engine is properly differentiating between balancing mass and rotating inertia. They are not the same. For example, the units of balancing mass are lbm*ft (mass times the centroid-distance from the axis of rotation). The units of rotating inertia are lbm*ft^2 (mass times the centroid-distance from the axis of rotation squared).

The calculated mass value (calculated above) is assumed to be acting on the center-axis of the connecting rod journal (i.e. at the stroke of the engine).

For example, if you calculate a 90-ounce mass, and the engine has a 4 inch stroke, the out-of-balance condition is 360 inch-ounces. Thus you must ensure that the crankshaft has a 360 inch-ounce counterbalance, thats 180-degrees out from the connecting rod journal. This can be accomplished by placing a 180 ounce mass, with a centroid of two inches from the crankshaft centerline, or 72 ounces at five inches, etc.

The important thing to remember is that the 360 inch-ounce out-of-balance is the net balance of the bare crank (rod disconnected, and flywheel disconnected  unless the flywheel is neutrally balanced). The connecting rod journal will subtract from the counterweights contribution, so you must analyze the entire crankshaft. Note: you can also counterbalance the crank at the flywheel. This increases stress in the rotating assembly, and increases torsional harmonics, but works. Placing the counterweights directly opposite of the rod-journal really is the best engineering practice.

If you have computer software for modeling, it will quickly calculate the center mass of the crank, and also the centroid of rotation location. When this value equates to 360 inch-ounces, youre there!

Or you can do it the engineering way, and use a cylindrical coordinate system to calculate the mass distribution with integral calculus (which is my preference, because I refuse to pay 7-grand for Autodesk Inventor. . . . . .)

This balancing method works on all simple crank-slider type single cylinder engines.

If you require additional information on balancing locomotive linkage, or linkage design, the analysis is more complex. An excellent source of information is Design of Machinery by Robert L. Norton. This a calculus based engineering text that contains a wealth of knowledge. It also has an excellent chapter on camshaft design.


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## JorgensenSteam

I have formulas for both a vertical and horizontal engine balance.
I will post and try and use a more clear example.

Pat J


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## Entropy455

There "should" be trivial differences between balancing a vertical engine, verses a horizontal engine.

Generally speaking, the rotating mass distribution is the dominant design factor, not the orientation of the rotating assembly.

I suppose that for exceptionally large engines turning in the tens-of-rpm, with pistons weighing hundreds of pounds, and linkage weighing in the tons  a correction factor for vertical orientation verses horizontal orientation might be warranted.

Consider that an unbalanced single cylinder engine (typical modern gasoline engine design), with a 3 bore and a 3.5 stroke, will see about 10,000 pounds of force at 3400 rpm. At 6000 rpm, the acceleration force approaches 30,000 pounds!

Thus the difference in out-of-balance acceleration forces will be 10,002 pounds in the vertical, and 10,000 pounds in the horizontal position (basically +/- the weight of the piston) at 3400 rpm. Or said another way, the weight of the piston applies 1-G of acceleration force onto the crankshaft. However the crankshaft will subject the pistons mass to well over 1000-G force of acceleration. 

Also the friction drag-forces will be much greater than the weight of the piston. . . So will the dynamic forces on the compression stroke. . .

I am interested in seeing the difference between the two equations nonetheless.


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## JorgensenSteam

I reviewed the formula, and the difference between the vertical and horizontal engine is in the "k" factor.

I edited the text in the post above, and added the following paragarph:

Generally, vertical engines should tend toward using the 0.67 value for "k", and horizontal engines should tend towards using the 0.75 value for "k".

I think you are correct about the gravity not coming into play until the mass of the piston and rod become large, but for historical reasons, I like to keep the old forumulas intact.

So this is my best guess at applying the forumla to an actual steam engine.
Anybody want to try and verify if this is accurate or not?

Pat J


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## Niels Abildgaard

Balancing can be done on the drawing board.
Model Your engine in 3D Cad and eliminate the stationary parts.
Put the moving parts in let us say 8 positions around the working circle.The puter can easily find the common center of gravity and you can then plot the trace during one revolution.
Ad mass (or remove) on counterweigth until center of gravity movement is minimum in the direction where vibrations will harm most.
I have tried to model real connecting rods,and compared maschine calculated mass with measured mass.
Differense was usually within 5 parts in thousand.


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## JorgensenSteam

Niels-

Sounds interesting, I think I understand what you are saying.
I will have to try that with 3D.

I have not plotted in 3D yet, but will look at that.
I know 3D will produce the data for movement, etc.

Pat J


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## Entropy455

I am trying to make sense of the equation you posted: W1 = [K*(W2+W3)*r] / X

The value of W2 has me confused. The crank webs will certainly add mass that must be balanced out by W1. However the crankshafts rod journal mass appears to be neglected within the equation. Neglecting the rod journal's mass will introduce significant error.

The constant K does not appear to be correcting for this.

The equation takes all of the reciprocating mass, and some of rotating mass (it neglects the rod journal, and big-end weight of the con-rod), then it applies it to the moment arm (r), then scales it down by a factor of K. Dividing by X gives W1 in the correct units of mass.

Connecting rod geometry can vary drastically. To accurately balance an engine, you need to weigh the small end as reciprocating mass, and the large end as rotating mass. Simply taking half of the con-rods mass can introduce significant error, as some rods can be quite heavy-ended on the crank side.

The equation as written will likely overbalance the engine. The vertical orientation value of K will further overbalance the engine.

The designers back in the day likely drafted this equation because it worked. However what they were really doing was over-sizing the counterweight, and it appeared to make the engine run smoother. This was becasue the extra inertia stored more kinetic energy, causing the engine to overcome friction at lower rpm.

The extra inertia will smooth out engine operation. However an overbalanced engine is still an out-of-balanced engine. At higher rpm, there will be noticeable acceleration forces shaking the machines foundation.

Are there more assumptions to the variables, that are not listed?


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## Maryak

Way back in my formative years, with nothing much else to do  It was a challenge to get the 2 HP cylinders to be in sync with each other during your watch. When this was achieved, (by a series of judicious taps of the throttles with a wheel spanner), lo and behold a most wondrous thing occurred......................1000 tons of ship would start to bounce through the water in time with the engines.

NOW THAT'S BALANCE. ;D

Next on this little adventure was to lay bets to see how long it would be before the OOW rang down from the bridge requesting we cease and desist. 

Sorry to hijack your thread but it has remained a source of amusement, (and a little pride), over many years.

Best Regards
Bob


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## petertha

Niels Abildgaard  said:
			
		

> Put the moving parts in let us say 8 positions around the working circle.The puter can easily find the common center of gravity and you can then plot the trace during one revolution. Ad mass (or remove) on counterweigth until center of gravity movement is minimum in the direction where vibrations will harm most.



I would be particularly interested to see some screen captures of this process, even applied to a simple engine configuration.

How would you know the 'direction will vibrations will harm most' to begin with?

Would the proposed method apply to a typical radial with master rod & link rods etc?


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## Niels Abildgaard

Hello Peter

It will be a pleasure to make a small comic strip illustrating the process.
It takes a little time like an old hunting dog hearing shoots;I was an Engineering lecturer once and loved it.

It is not an easy question to answer concerning most harmfull direction of residual unbalance;Maryak describes it quite well.
I assume that there was a residual unbalance up and down on the two main engines and when in phase it exited the whole ship hull as a bar in a Marimba musical instrument.
It is not easy to change the frequency of a whole ship so if it had been a re curing problem counterweight mass should be added so that the up and down part was zero and then accepting more and always a certain vibration in horizontal plane.
For an aircraft engine next to perfect balance is a must and luckily radials come very close.
I think a lot of people had a good job calculating balance mass on radials before computers and their result is poorer than the one to be schemed using 3D cad.
The geometry of master ,slave rods is NOT trivial,


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## steamer

Things get more complicated with compounds and triples as the reciprocating mass is different for each leg, and they are usually at 90 degrees ( on a cross compound) or 120 degrees as on a 3 legged triple...Some compomise is usually required

And beware the natural frequency!  Though it sounds like Bob had fun finding one :big:

Dave


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## JorgensenSteam

It does not surprise me that the old forumla may be off.

I have seen other items from old books that are incorrect, but were general practice 130 years ago, such as neglecting the angularity of the valve rod. If you look at the excact geometry of neglecting the angularity of the valve rod on a computer, you can see it introduces significant error.

I think the 3D approach mentioned that Neils mentions above would be a simple and accurate way to balance an engine, and there would be no error in how you consider the mass of each part.

Charles Porter of the Porter-Allen engine fame mentions in his book that a higher mass for the reciprocating parts causes the engine to run without knocking, even when the connecting rod bearings are lose, but he really does not explain very well why this is. Charles Porter designed the first "high speed" steam engine in the mid 1800's (150 rpm).

Pat J


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## steamer

Another way of dealing with the balance issue on large stuff was to split the LP up into two cylinders.  Then they put those cylinders , usually, at the either end of the engine. The result was a 4 legged triple. In doing so the mass of each of the pistons, HP, IP, LP LP though not identical, was pretty close.  Large Navel recips were put together that way as they were very fast turners for their size in terms of piston speed. 120 rpm with a 4 foot stroke is fast when the cross head is the size of a Volkswagen bettle....I would want my life insurance paid up if I was to be on the deck plates in that engine room!....but I'd do it! :big:
 :big:

Dave


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## Niels Abildgaard

5 pictures of half a revolution


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## Niels Abildgaard

OK we are only allowed 4 picture per post so here comes no 5

It shows moving parts from a Volvo outboard (Two stroke of course.Fourstrokes are misconceptions)

For each situation center of gravity was asked (One click)

Top  0 mm and 22.77
 45  -1,18     21.42
 90  -1,68     18.65
135 -1.18     16.61
180 -0       15.97

For a complete revolution the center of gravity of these moving parts will oscillate from -1.68 to 1.68 or 3.36 mm horizontally and from 22.77 to 15.97 vertically or 6.8 mm up and down.

This do not sound much but if You try to move 1.9 kg (total mass of moving parts ) 6.8 mm up and down 100 times a second You need some illegal hormones.


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## Dan Rowe

steamer  said:
			
		

> Large Navel recips were put together that way as they were very fast turners for their size in terms of piston speed. 120 rpm with a 4 foot stroke is fast when the cross head is the size of a Volkswagen bettle....I would want my life insurance paid up if I was to be on the deck plates in that engine room!....but I'd do it! :big:
> :big:



Dave,
I worked the Sulzer low speed diesel ships because in the crankcase you could forget it was a diesel the lower running gear is the same as the steam engine days.

Notice I changed my avatar to an old snap shot of me in a Sulzer RLB 90. The piston is 900mm diameter and has a rod that goes to a crosshead guide just like a steam engine. The gland was used to keep the crankcase and the lower piston space seperate.

In the photo I was ridding the piston down so I would be at the right height to use a 4" angle grinder to grind the ridge to pull the piston which weighs 4.5 tons with the rod.

The top speed of the low speed Sulzers is 100-120 rpm depending on the model.

Dan


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## Niels Abildgaard

Hello again
If we remove 70 gram from counterweight as shown on picture center will not move sidewards but up and down 11.13 mm compared to 6.8 before.Perfect transverse and horrible vertical.



Regards
Niels


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## petertha

Niels Abildgaard  said:
			
		

> For each situation center of gravity was asked (One click)
> Top  0 mm and 22.77
> 45  -1,18     21.42
> 90  -1,68     18.65
> 135 -1.18     16.61
> 180 -0       15.97



Thanks Neils. So to continue on... 

I made a graphical plot of your CG points, (X=0, Y=22.7) then (X=-1.18, Y=21.42) ... etc. which correspond to the 180 deg rotation segment at 45 deg stops. I'm not sure what the curve itself would look like intercepting these points, I just drew a spline for demonstration. Presumably the remaining 180-360 deg rotation portion would be the same curve mirrored on the vertical datum line? Now what? By adding more or less counter weight to the assembly & re-calculating CG's & a new resultant curve, what are we tryin to achieve? A minimum area curve? A curve shaped in a certain orientation? An area 'lowered' to the 0,0 datum?

I've always thought the Cad power of 1-click CG determination of assemblies could be put to some powerful use for engine design, but I'm just not clear how!


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## steamer

Dan Rowe  said:
			
		

> Dave,
> I worked the Sulzer low speed diesel ships because in the crankcase you could forget it was a diesel the lower running gear is the same as the steam engine days.
> 
> Notice I changed my avatar to an old snap shot of me in a Sulzer RLB 90. The piston is 900mm diameter and has a rod that goes to a crosshead guide just like a steam engine. The gland was used to keep the crankcase and the lower piston space seperate.
> 
> In the photo I was ridding the piston down so I would be at the right height to use a 4" angle grinder to grind the ridge to pull the piston which weighs 4.5 tons with the rod.
> 
> The top speed of the low speed Sulzers is 100-120 rpm depending on the model.
> 
> Dan




Hey Dan! Cool! Can you imagine an open crank pit with forced lubrication!...You have to go about yout duties with slickers on....YIKES!

Dave


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## Niels Abildgaard

Hello Peter

Computers cannot make experience and commonsense superfluous.If I was making a Lawnmover engine I would ad so much mass that travel in the two directions were equal.Worlds best motorbike MZ250 was balanced no traverse and a lot up and down .
Due to a rather clever motor mount rubber spring system it was as pleasant vibrationwise as a BMW.I have had both and prefer ed 
MZ


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## petertha

Niels Abildgaard  said:
			
		

> ...cannot make experience and commonsense superfluous.



...neither of which I have in significant quantity! ;D

I guess I'm saying... I'm drawing an engine in Cad anyway. So I have the ability to easily determine the CG's of individual engine components and their their relative movement paths. Does this ability help me in any way towards the general balancing guideline that is often referenced to -> "counterweight must balance half of all reciprocating mass, plus all of the rotating mass".


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## Niels Abildgaard

Hello Peter

Exactly
If you have identical travel sidevise and upwards You have balanced all rotating and half the oscillating.


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## JorgensenSteam

Niels Abildgaard  said:
			
		

> Balancing can be done on the drawing board.
> Model Your engine in 3D Cad and eliminate the stationary parts.
> Put the moving parts in let us say 8 positions around the working circle.
> The puter can easily find the common center of gravity and you can then plot the trace during one revolution.
> Ad mass (or remove) on counterweigth until center of gravity movement is minimum in the direction where vibrations will harm most.
> I have tried to model real connecting rods,and compared machine calculated mass with measured mass.
> Difference was usually within 5 parts per thousand.



I will try and clarify what Niels is saying above.
Niels will have to correct me if I don't understand it correctly.

Balancing an engine can be done using a 3D modeling program that calculated the center of gravity for assemblies. (And maybe in a 2D drafting program if that program calculates the center of mass of multiple objects).

Model only the piston, ring, connecting rod and nut, crosshead, crosshead pin and nut, connecting rod and brasses, crankshaft, and the proposed counterweights, and put these in an assembly.

With some 3D programs, depending on which options you have, you can output data for a revolving assembly, just as Charlie Docksteader does with his valve gear program. If you know how (I don't yet), you can find the X, Y and Z positions of each moving part, and also other data such as velocity, acceleration, and apparently center of gravity not only of each part, but of the assembly as a whole.

Have the 3D program rotate the parts for one revolution (360 degrees), and record the X and Y location of the center of mass at eight different points (or record continuously if your program will do that). I guess we could consider the Z axis, but lets keep it restricted to changes in the center of mass in the X and Y direction only.

As the parts rotate, the center of mass will probably shift around in an elliptical shape, if the location of the center of mass of the entire assembly is plotted in a polar plot.

Now adjust the mass of the counterweight(s) (some crankshafts have a single crank disk and a single counterbalance weight, and some have two crank disks and two counterbalance weights) so that the change in the location of the center of mass of the assembly is minimized in either the vertical or horizontal direction.

All balancing of engines is a compromise between vertical and horizontal balance, so pick which axis (X or Y) in which you want to minimize the vibration from the engine, or make the X and Y axis vibration equal if so desired.



			
				Niels Abildgaard  said:
			
		

> If we remove 70 gram from counterweight as shown on picture center will not move sidewards but up and down 11.13 mm compared to 6.8 before.Perfect transverse and horrible vertical.



So if I understand the above correctly, if you remove 70 grams of mass from the counterweight in the example, then you get a flattened ellipse, which becomes a vertical line.



			
				Niels Abildgaard  said:
			
		

> Computers cannot make experience and commonsense superfluous.


This is my favorite line. My slant on it is "The data that your computer produces is only as good as the data that the person who input the data, and who programmed the computer, or in other words, garbage in, garbage out. Neils solution for balancing engines is a simple and elegant solution, and yet not one I would ever have thought of. Yes, experience and common sense can easily trump everything else.


			
				Niels Abildgaard  said:
			
		

> If you have identical travel sidevise and upwards You have balanced all rotating and half the oscillating.


If you look at the individual center of mass of each separate component, and the movement of the same, then I would think you would have to do a vector sum of the movement of the center of mass for all of the rotating parts. I think this is what the computer program is doing for you though (calculating the movement of the center of mass for the assembly as one entity).

Pat J


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## petertha

Niels Abildgaard  said:
			
		

> Exactly...If you have identical travel sidevise and upwards You have balanced all rotating and half the oscillating.



So for graphical representation using the same sketch.... Example Engine A has the resultant curve using your example x,y data. The red arrow is the vertical extent, green arrow is the horizontal extent (what you call travel). Example Engine B we have made some internal changes, like counterweight size, different material density, dimensional layout or whatever. Now it's resultant curve shape is defined by the orange line for example. It's vertical extent is now reduced to a value closer to the horizontal value. So this means we have acheived a net improvement in terms of balance? And the area within the curve or shape is of no real consequence value for these purposes?


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## JorgensenSteam

I am guessing here, but it seems like you have to do a polar plot, and use the entire 360 degrees, and the shape has to be like an ellipse?

The ellipse does not necessarily have to center on the 0,0 point, but if you take the center point around which the combination of moving part masses are moving, and put that at 0,0, then you should seen X and Y numbers that alternate between positive and negative?

Am I correct on this?

I think the area under the curve always has some meaning, but I can't remember in this case what it means.
The slope of the line of velocity is acceleration (rate of change of velocity).


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## petertha

BigOnSteam  said:
			
		

> I am guessing here, but it seems like you have to do a polar plot, and use the entire 360 degrees, and the shape has to be like an ellipse?



I'm not sure myself, thats why I was asking for clarification! 

To me, a polar plot would allow a series of 2 dimensions: an 'amount' & some corresponding angle, like '7.5' at 135 deg. I *think* he is saying at a particular crank angle position, say 45 deg, the combined CG the entire assembly occurs at X=-1.18 & Y=21.42. So I'm not clear how a polar could display 3 parameters simultaneously? (degrees, X and Y). But I'm certainly no math whiz & rarely use plots like this.

I'm now thinking maybe the 'half plots' I was volunteering earlier as a graphical representation of his example data (representing 0-180 deg rotation) might be misleading & incorrect though in terms of balance. Presumably the other half of data would be symetrical though (the 180-360 deg crank rotation portion). So maybe the correct extent of the horizontal (green arrow) spans the symetrical shape curve & right away looks closer in amount to the vertical. But maybe the goal is still to get the horizontal & vertical as close to equal?

In terms of your comment that the "shape has to be like an ellipse"... I really can't say. Hopefully more input will reveal the light!


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## JorgensenSteam

I read about the data that Alibre will produce from a motion study, and you can get position (X,Y), velocity, and acceleration, in a printout like a spreadsheet, and also get a graph of any of these valvues.

I am sure you could import the data into a spreadsheet, and calculate a number of values.

I remember F = m A, (force = mass * acceleration) from years ago, and I guess you could calculate the total forces in the X and Y direction as the engine rotates, but I am not sure exactly how.

I would think the plot would have to be symmetrical, since the same thing happens at TDC and BDC?

I also know that the piston velocity drops to zero at TDC and BDC, and maximum acceleration of the piston will be where the graph of the velocity is steepest.

I will read up on Solidworks, and see what it can calculate.

Pat J


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## Niels Abildgaard

Hello Peter and Pat

Pat is rigth.The plot must be a polar plot to be of any use.
Pat is wrong as it will not be symmetrical top and bottom.
If the conrod was very long it would be symmetrical ,but a short conrod makes the motion more violent in top dead centre than the low one.
Again for a new engine I would try to makecenter of gravity travel equal.


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## JorgensenSteam

Ok, I think I understand what Neils is doing.

In Solidworks, if you open an assembly, such as Niels has shown, with the piston, connecting rod, and crankshaft, and go to Tools, Mass Properties, the center of mass of the entire assembly is shown in X, Y and Z coordinates.

If you have your constraints set correctly for your mates for the parts, then you can manually rotate the crankshaft, and the rod and piston will follow the movement.

For each new location that you rotate the crank to, you can hit the "Recalcuate" button in the Mass Properies window, and the X, Y and Z center of mass coordinates for the entire assembly will generally (but not always) change to different values.

I will look and see if Alibre will do the same.

Pat J


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## JorgensenSteam

Looks like if you open an assembly of the moving parts in Alibre, and select Tools, Measurement Properties, and then pick the Calculate button in the pop-up dialog box, you can also get the X, Y and Z coordinates for the center of mass.

Again, you have to have the constraints (mates) set correctly on the parts of the assembly, so that when you rotate the crankshaft, the connecting rod and piston move correctly.

I will try and post an Alibre file for an example here.

Pat J


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## steamer

Another plus for longer conrods is that the maximum piston velocity should be lower with a long rod vs a short one, to say nothing of side forces on the cross head guide which will be lower with a longer rod. With an infinitly long connecting rod the piston velocity profile would be sinusoidal.  A real rod will have angularity affects
These affects can have a adverse effects on a crankshaft with a large rotating mass, like a propeller, which could be attributed to balance but in actuallity, are torsional in nature. All the operator will hear is all the bearings hammering.
A length of 4-5 times the crank throw (2 -2.5 times the stroke) is fairly long


Dave


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## petertha

BigOnSteam  said:
			
		

> ...
> ...open an assembly...with the piston, connecting rod, and crankshaft, and go to Tools, Mass Properties, the center of mass of the entire assembly is shown in X, Y and Z coordinates....For each new location that you rotate the crank to, you can hit the "Recalcuate" button in the Mass Properies window, and the X, Y and Z center of mass coordinates....



Pat, thats exactly what I assumed Neils was showing in his example. Using his data, at a specific crank angle (45 deg), the assembly centroid was determine to be (X= -1.18mm) & (Y=21.42mm). And by assembly, I am assuming it encompasses the individual contributions from all the parts you reference. So the curve I have volunteered as a graphical representation simply connects the X,Y dots in a cartesian manner, but corresponds to the respective 0 to 180 deg crank angle 'stops'. That yields what I loosely called the half-curve. Then if we assume it's symmetrical (left to right, not up & down) it yields the curve I show in post #28 which encompasses the whole 0-360 deg rotation. Point 0,0 reference is far below the screen & doesn't seem to matter I assume.

So if this is correct up to this point, I guess I'm asking for confirmation: is the objective for ideal balance to make the horizontal & vertical 'amounts' EQUAL (as I've shown in colored arrows)?

If these plots or the procedure is incorrect somehow, please elaborate & correct me.


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## petertha

Niels Abildgaard  said:
			
		

> Hello Peter and Pat
> Pat is rigth.The plot must be a polar plot to be of any use.



Okay... maybe you could elaborate a bit. What IS a polar plot? How does one construct one? I'm assuming this graphical representation of your example assembly [Angle,X,Y] centroid data is therefore NOT a polar plot?

I feel like the apprentice baker who wants to make nice bread... so far we have 100% agreement on 'flour, water, eggs & salt'. ;D
Just kidding, this has been enlightening & interest to me. I just don't quite have a complete understanding.


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## mklotz

> What IS a polar plot?



In an x-y plot we plot a point by going out to the x value on the x-axis and then up/down to the y value on the y-axis.

In a polar plot we have a distance r and an angle theta. We plot a point by finding the angle on the angular scale and then going out along that angle line a distance equivalent to r.

The relations between x,y and r,theta are:

r = sqrt (x^2 + y^2)
theta = arctan (y/x)


x = r*cos(theta)
y = r*sin(theta)

Some functions are simpler to plot in one system; some in another. For instance, one would need to specify a large number of x,y pairs to plot a circle on an x-y (Cartesian) plot. On a polar plot, a circle is simply r=constant for all values of theta.

Similarly, plotting a rectangle in polar coordinates would be nightmarish. In Cartesian coordinates it would be dead simple.


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## Niels Abildgaard

Hello Peter

The ideal balance for a single cylinder engine must be the one where broken screws,carburetors etc are minimum.
This varies from case to case.It does not make any sense to go outside the envelope of no balance for oscillating parts (pure up and down forces) and full reciprocating(meaning only transverse forces.
All this is not completely true due to the finite length of connecting rod but this starts to get out of hand.
I still think Your onion shape curve is wrong but I do not know how it should look.Could we make it free for all?


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## Niels Abildgaard

Hello again

The ideal comic strip would be a small animation showing a slowly revolving crank,rod piston assembly with an arrow superimposed showing force magnitude and direction.We shall have three cases .No reciproc balance ,half and total.
Then the role of the socalled second order forces can be shown as well.
My wife is ill so please feel free to enter Your thougths.My soul is sometime a way.


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## JorgensenSteam

I guess my interest in balancing steam engines came from this engine that was built by my Dad, and with no counterbalances.

Nice little engine, but it literally hops up and down on the table when it runs, and so that started my thinking about how I could find some sort of semi-accurate method of dynamically balancing a steam model.

I considered adding counterbalances to this engine, but I don't really want to do that without some sort of scientific approach, and I want to balance other engines also in a predictable fashion.

Pat J

Edit:
Peter Quote: I feel like the apprentice baker who wants to make nice bread... so far we have 100% agreement on 'flour, water, eggs & salt'.  

Peter, I could not agree with you more. Pat J


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## petertha

mklotz  said:
			
		

> In a polar plot we have a distance r and an angle theta. We plot a point by finding the angle on the angular scale and then going out along that angle line a distance equivalent to r. The relations between x,y and r,theta are: r = sqrt (x^2 + y^2)



Yes, thats how kind of how I interpreted polar plots. In this case we have a table of data where each angular 'step' of crankshaft position has an associated X and Y centroid position. So a series of [Angle, X, Y] relationships.

Now I will volunteer my guess of a polar plot. Maybe this will be the lucky one! I find myself in a strange position of trying to 'guess the answer' here ;D I've attached Neils data & calculated R based on the square root equation. Then I plotted the [Angle,R] coordinates for 0-180 deg rotation & mirrored on the other side assuming it matches 180-360 deg rotation. (...in a high priced Cad program because apparently Excel does not offer polar plots). Does THIS help our balancing effort in any way?


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## JorgensenSteam

I am going to have to try and simplify this problem, and maybe start with just a counterweight, and revolve it, then add an equal counterweight 180 degrees from it, then perhaps shift the angle between them.

Somehow, the plot would have to change to a vertical or horizontal line if I understand Niels correctly, when the balance is all either horizontal or vertical.

Pat J


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## JorgensenSteam

Ok, here is my start of trying to figure out engine balance using Niels method.

I started with a plain crank with no counterbalances, and looked at the X, Y and Z coordinates for the center of mass (shown on the right) as I tried various positions and configurations.

I will add a counterbalance tomorrow and see what happens.

Pat J


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## JorgensenSteam

More configurations:


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## Ken I

It is more or less impossible to completely ballance any engine (although radials can get damn close).

In a single cylinder, if your crank ballance web matches the rotary imballance forces, then it does nothing for the forces generated by accellerating the non-rotating mass (piston and part of the conrod mass)

Maximum accelleration occurs at minimum velocity (ie TDC & BDC) and at approximately mid-stroke there is no accelleration (its about to change from acelleration to decelleration).

Adding ballancing mass reduces the vertical out of ballance at the expense of introducing a lateral out of ballance (but it does help).

The obvious way of dealing with non-rotating inertial masses is by opposing cylinders but even here they are not equal and opposite because of the finite conrod length. Additionaly this intoduces a torque couple because of the cylinder offsets which introduces a rocking vibration into the engine.

A conventional 4 cylinder in line IC engine suffers from this and in some cars this is countered by a rotating "countershaft" of eccentric masses running at engine speed to counter the remaining or introduced forces from the primary ballancing.






Above - my ballancing set up :-

A pair of stanley knife blades are near frictionless and the conrod is supported at the big end by a thin thread - obviously this method is only as good as the friction at the big end will permit so it is loose (not fully tightened) and lubricated.

Mount the whole affair on a zeroed scale - if the big end is heavy you can attatch a thin line and pull up - if its light push down. 
The value on the scale gives some idea of the mass of material needed to be removed from the parralell portion of the webs (if heavy) or from the offset (if light).

By working up and down you can also see the hysteresis in value induced by the big end friction and you can average the result. 

This setup moves to an imballance of about 2.5g mostly due to big end friction.

Sure this is a static ballance only but if its not statically ballanced its not dynamically ballenced either.

As per the above this method is ignoring the imballance created by accelleration forces.

I calculated the webs as per vector diagams suggested in the earlier posts.

Ken


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## metalmad

Hi Ken
your pic does not seem to be working Mate
Pete


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## JorgensenSteam

I can see Ken's photo.

That is interesting Ken, I will have to study that a bit more to see if statically balancing an engine produces a larger counterweight than dynamically balancing an engine.

Looking at the formula from the old book again:

W1 = [K*(W2+W3)*r] / X

We could rewrite it as:

X*W1 = K*r*(W2+W3)

or distance times mass equals K times distance times the sum of two masses.

I will think on it some more.

Pat J


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## Ken I

The attachment shows a straightforward

m1*r1 = m2*r2 calculation

The mass on the left is the rotating mass of the conrod - weighed at the big end centreline whilst supporting (suspending) the small end, plus the big end pin (and any other varables such as the difference in mass of the steel pin vs the bronze webs etc.)

The mass on the right is calculated from the material density etc and the CoG - via a process of guesstimating and adjusting the width (marked "adjust") until it "ballances"

Ken


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## Captain Jerry

A balanced engine is one where every reciprocating mass and every orbiting mass is offset by an equal mass moving in the opposite direction at the same velocity. I don't think that I ever posted this video, but here is a balanced engine. It is suspended only by the air line. The only unbalanced vibrations are torsional.





At slow speed, just before shutoff, some torsional vibration shows, which probably indicates one or more cylinders are lazy.

Jerry


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## petertha

BigOnSteam  said:
			
		

> Ok, here is my start of trying to figure out engine balance using Niels method. ...I will add a counterbalance tomorrow and see what happens.
> Pat J



Pat, I think what you have shown is that the program is calculating the centroid properly.
    Angle  X    Y     Z   pic
TDC 0     0   +0.1574  0   02
BDC 180    0   -0.1584  0   03
    270  -0.1584 0     0   05

But recognize at this stage you have a situation of 100% rotating parts. The path of the centroid through 360 deg crank rotation would be a perfect circle. Balancing is relatively easy, put an appropriate counterweight on the opposing side until you get a new centroid of X=0, Y=0. You can choose a small mass at a long radius or a large mass at short radius, but the objective would be to make the circle path converge to a dot (I think).

But this is not quite an engine yet. There are no 100% reciprocating components (like a piston or wristpin) or partial recip/rotate components (like a connecting rod) which will make an irregular path. Thats where the fun begins. What I interpreted what Niels offered was a similar X,Y,Z centroid, but from ALL components. The question is then...what now?.


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## petertha

Ken I  said:
			
		

> ... my ballancing set up .....Sure this is a static ballance only but if its not statically ballanced its not dynamically ballenced either. Ken



Im glad you provided this picture because it is indicative of what I have seen displayed in other model engine balancing articles. I notice that the piston & related 'reciprocating only' parts (ring, wristpin etc) have been removed from the assembly.

So does this satisfy the usual quoted balancing goal: "the counterweight must balance half of all reciprocating mass, plus all of the rotating mass"?


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## Entropy455

You can take a snapshot of an engine assembly with auto-cad type software, and determining center mass an engine assembly. But the information is not helpful for balancing  as only the crankshaft is in pure rotation.

To balancing an engine, you must determine the magnitude of acceleration forces, and also the direction in which those acceleration forces are applied to the crankshafts rod journal.

More specifically - the instantaneous piston acceleration can accurately be calculated as a function of crankshaft angular displacement, at a given rpm, using some rather involved linkage analysis calculations. This acceleration when applied to the mass of the piston, will give you the instantaneous linear force that is applied to the connecting rod. The connecting rod will then transfer this force to the crankshaft. It is this force that needs to be balanced out. The problem is that the direction in which the force is applied to the crankshaft changes significantly with respect to crankshaft rotation  as does the size of the force itself. Further compounding the problem is that the connecting rod will introduce its own acceleration forces into the system. Which like the piston, will significantly change in both direction and magnitude as the crankshaft is rotating. And if that wasnt enough  the dynamic force effects of the combustion event will change the apparent mass-loading of the reciprocating components  thus if the engine is ideally balanced over the intake and exhaust stroke, it will be slightly out-of-balance during the compression and power stroke.

Thus there is no such thing a precisely balanced single cylinder engine. Even with the best achievable balance, there will always be a range of crankshaft rotation where the engine is a little underbalanced, and a range where the engine is a little overbalanced. However if done correctly, the out-of-balance acceleration forces will be minimized, and the engine will run rather smoothly.

Achieving maximum dynamic balance requires extensive engineering analysis. It is very time consuming, and is unnecessary for all but the highest of rpm engines. There is such thing as close counts. You can achieve a reasonable and acceptable dynamic balance using the following guidelines: the counterweight must balance half of all reciprocating mass, plus all of the rotating mass. Calculating the counterbalance mass is the easy part. The hard part for most folks is incorporating the mass correctly into the crankshafts counterweight design.

The auto-cad type software is an excellent tool for doing this. You can verify that your crankshaft (and only the crankshaft) has the proper counterbalance that youve calculated.

However unless the software contains dynamic linkage analysis algorithms, which it probably does not, youll gain nothing in finding the center-mass of the entire rotating assembly.

If you have the machinery to accomplish the task, you can physically attach the equivalent rotating-mass to the connecting rods journal, spin it up, and tweak the counterweights mass as needed to minimize the measured accelerations (aka, the fine tuning aspects of dynamic balancing). You still need a starting point for this process  in that the counterweights will be properly sized on paper, long before the crankshaft is even fabricated.

FWIW, single cylinder engines crankshafts are not typically dynamically balanced on a machine, because they cannot be "truely balanced". Multi cylinder engines can however be truly balanced via dynamic balancing  as is commonly done in the V-8 automotive and marine racing community.


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## Ken I

petertha  said:
			
		

> So does this satisfy the usual quoted balancing goal: "the counterweight must balance half of all reciprocating mass, plus all of the rotating mass"?



Sort of - yes - but clearly that is a rule of thumb.

If you consider my photo with the smallend suspended the "Mass" of the conrod bearing down would be half if the conrod was symetrical (ie the small end was the same as the big end) but its not so more that half its mass is bearing down (in the photo) but that is the mass that is effectively being rotated out of ballance by the crank (this statement is not true for all angular positions due to conrod length) and along with any other rotating component - such as the big end journal must be accomodated.

If you consider all the moving masses to have two components, one rotating and one oscillating (again this is not stricly true either) then only the rotating forces can be ballanced - at mid stroke (or thereabouts) when the oscillating components are being neither accelerated or decellerated there is nothing in that component to ballance out - so additional counter weight (which might null out or reduce the accelleration forces at TDC or BDC) will be generating a force sideways - hence an out of ballance condition - hence my comment that any additional ballancing mass over static ballance (in a single cylinder engine) will diminish vibration in the vertical plane by increacing the vibration in the horizontal plane.

Having said that some overballance from static is beneficial - about half the reciprocating mass - imagine you have a vertical vector force of 1 but by reducing it to 0.5 you introduce a horizontal vector of 0.5 the new compound vector is (0.5^2)+(0.5^2)]^0.5 = 0.707 which is an improvement - so there again the rule of thumb of half the reciprocating mass.

With a single cylinder engine its always going to be a mess.

Ken


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## Admiral_dk

It will still not solve the problem of the single cylinder engine completely (impossible), but a balanceshaft can help quite a bit on a bigger engine. I have a 350 cc single as my winter motorcycle and vibrations are not a factor.

Here's a link to a simple explanation http://www.dansmc.com/counterbalancers.htm

In the original problem - if you just balance the rotational forces away, by calculating the weight of the big-end and part of the conrod - I'm sure that most of your hopping is gone.


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## JorgensenSteam

Thanks very much to input from all, it is very enlightening.

I will have to drink some more coffee and re-read all the posts several times to make sure I can absorb what it being said, but I think I am getting the ideas down.

The next step for me, after verifying how the center of mass moves for a symmetrical crankshaft, and an asymmetrical crankshaft, is to add in the remaining components into an assembly, set the proper constraints, add a fixed bearing so that I can rotate the crankshaft and have the piston and crosshead move back and forth, and then again note the X, Y and Z movement of the center of mass of the entire assembly, using an approximately sized counterweight from the old formula.

I can then modify the counterweigh size slightly and look at what is happening to the center of mass of the entire assemby.

I will try and set this up in the next day or so.

Pat J


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## JorgensenSteam

BigOnSteam  said:
			
		

> Equation for minimizing engine vibration:
> 
> Formula No.3:
> W1 = [K*(W2+W3)*r] / X
> 
> where:
> 
> W1 = weight of the counterweight (lbs.)
> W2 = weight of the crank webs outside of the main shaft and crank pin (lbs.)
> W3 = weight of reciprocating parts (piston, piston rod, crosshead, one half the weight of the connecting rod) (lbs.)
> 
> X = distance of center of mass of counterweight from center of the crankshaft (inches)
> 
> K = constant (use 0.67 for minimum vibration at right angles to the engine centerline, use 0.75 for minimum vibration at crank dead center)
> 
> r = distance from center of crankshaft to center of crank pin (inches)
> 
> Generally, vertical engines should tend toward using the 0.67 value for "k", and horizontal engines should tend towards using the 0.75 value for "k".



Ok, my tiny mind is slowly working this problem out (I hope), and I think this is what the others have already said (correct me guys if I mis-state something below, I am still trying to understand all this).

From the above equation, if we use a static balance situation, and just place the crankshaft on knife edges, with the counterweights on one side and the connecting rod, crosshead and pin, piston rod, piston, and ring hanging straight down on the other side, then we would have the counterweight mass (W1) times the distance of the center of mass of the counterweight from the center of the crankshaft (X) equaling the total mass of the crank pin plus the mass of the connecting rod, crosshead and pin, piston rod, piston and ring times the distance from the center of the crankshaft to the center of the crank pin (r), or:

Formula No.1:
W1*X = (W2+W3)*r

The assembly if statically balanced would stay in a horizontal position, like a balance used to measure weights, and in rotation, it should be perfectly balanced at TDC and BDC, but overbalanced at the crank quarters, and so would have a lot of horizontal forces (assuming a vertical engine), but not much in the way of vertical forces.

Formula No.3 (the original old formula) modifes the static balance situation by making the counterweight mass times distance "x" less than the mass of the parts on the other side times the distance "r", and the reduction in counterweight mass is half of the connecting rod weight, plus a reduction of between 25% and 33% due to the "k" constant multiplier.

So if you use the old formula, you are reducing the value for the mass on the side opposite the counterbalances by around 1/3.
If the crankshaft is on the quarter, then the formula for a static situation would be (?):

Formula No.2:
W1*X = (W2+half the connecting rod weight)*r

although the connecting rod would not be symmetrical in shape, so the above forumula would be approximate.
This formula should reduce or eliminate most of the side-to-side forces, but would result in higher vertical forces.

The counterweight required for Formula No. 2 would be much smaller than the counterweight required for Formula No.1, since Formula No.2 leaves out the crosshead, piston rod, piston, etc. masses.

So Formula No.1 (static balance) creates a counterweight that is too large, and Forumla No.2 (horizontal balance) creates a counterweight that is too small, so Formula No.3 (the original formula) strikes a balance between these two values.

Also, as others have mentioned, the crosshead, crosshead pin, piston piston rod, etc. are not revolving, so to multiply their weights by a distance "r" is treating them like the spinning ice skater who varies their speed when spinning by moving their arms closer or further away from their body, but these weights are not spinning, so there is apparently some fudging there in the formula.

The thing to remember is that balancing a single engine is at best a compromise between vertical and horizontal forces, but certainly using formula No.3 should restult in a significant reduction in out of balance forces, although not a perfect situation, perhaps an improved situation, since with no counterbalance at all, the engine will have no vertical or horizontal balance.

Pat J


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## petertha

Entropy455  said:
			
		

> There is such thing as close counts. You can achieve a reasonable and acceptable dynamic balance using the following guidelines: the counterweight must balance half of all reciprocating mass, plus all of the rotating mass. Calculating the counterbalance mass is the easy part. The hard part for most folks is incorporating the mass correctly into the crankshafts counterweight design.



Thanks for a great reply. So specific to my immediate application, a 5 cyl radial 4-stroke, I will have a configuration like this picture. There is some latitude to making the counterweight 'wedge' shape larger or smaller (or replaceable/tweakable for that matter). Also by choosing specific materials in 3DCad, I will have a good handle on the expected finished weights of all components in real life. So along the lines of what you are saying, striving to achieve a "reasonable and acceptable dynamic balance" off the drawing board, how do I handle parts like the master rod & link rods - ie the parts that are some 'mixture' of rotating & reciprocating motion?

I'll throw out this (completely unfounded, non-engineering) thought out to see if it makes any sense or can be applied. (It's like a bad mental itch I have that won't go away ;D ...tell me if I'm barking up the wrong tree.)

- if I look at say the counterweight or the crankpin as a single element, it has a centroid, easy to spit out in Cad. If I trace that centroid through a 360 deg of crank rotation, it makes a perfect circle. So its weight gets a 'score' of 100%, meaning purely rotational. 

-if I look at the piston as a single element, it has a centroid. If I trace that centroid through a 360 deg of crank rotation, it makes a line. So its weight gets a 'score' of 50%, meaning purely reciprocating. 

- a connecting rod's centroid would have a path maybe like an elipse or a cam shape. Is there anything I can do with this resultant dimensional path shape that says it gets a relative weight score of say 72% & assists in how to treat it in the simple balance method? Also, if the rod was shaped real fat at the bottom, its centroid would be lower & the path would be more concentrated to the bottom end. One would think this would be useful in some way?


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## Entropy455

Here is machine-shop way to balance a single cylinder engine:

Weigh the small end of the connecting rod, and record this value as reciprocating mass.

Weigh the large end of the connecting rod, and record this value as rotating mass.

Note: the small-end rod weight, plus the big-end rod weight, should equal the total weight of the rod. If it doesnt, retake the measurements, as you did something wrong.

Add up the weights of all pure reciprocating components (i.e. the small-end of connecting rod, the piston, rings, wrist-pin, etc). Divide this number by two.

Take the above number (which is equal to half of all reciprocating mass), and add it to the weight of the large-end of the connecting rod (the rotating mass). This number is the final equivalent mass that must be balanced out by the crankshaft.

Machine a cylinder on the lathe that weighs the same as your equivalent mass, as calculated above. Be sure to include a small eye bolt for attaching string, or dental floss.

Manufacture your crankshaft with oversized counterweights (because its easier to remove metal than it is to add it). Suspend the crankshaft on a set of machined parallels. Ensure the parallels are perfectly level and free of debris  as the crank must be able to roll freely with the smallest of effort.

Attach the equivalent mass to the crankshafts connecting rod journal with some small string, or dental floss. The rod journals line of action must be parallel to the supports, and perpendicular to the string (as shown). The string must be perfectly in-line with the center-axis of the rod journal. If the string is off-center, is will introduce significant error.

If the crankshaft rotates clockwise, machine away material from the red area of the crank, until there is no rotation.

If the crankshaft rotates counterclockwise, you need to add material to the red area of the crank, until there is no rotation.

Remember that a very small rotation is still a rotation.

The engine is balanced when there is no crankshaft rotation. When you get close, you can drill holes in the counterweights to sneak up on the final mass, in lieu of lathe operations where you can overshoot.

This method will provide more than adequate results, and permit you to run a neutrally balanced flywheel - - - in a single cylinder engine. . . .


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## metalmad

OK now this i can use !!
nice one Entropy455
Pete


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## dy

just happened onto this discussion, between vise-cleaning and fetching screws for tooling:

This occurs to me:

first: separate all the various forces, such that the crankshaft (by itself), the big end of the connecting rod as it rotates, the small end as it reciprocates - all of these, handle separately.

second: put each of these separate elements onto a polar vector diagram, with the angular displacement corresponding to the position of the crankpin as it rotates through a complete circle of 360 degrees, and the length of the vector the corresponding force;

thirdly: sum the effects of all the separate elements. This will give total force applied to the crankpin expressed through the center of rotation.

four: add or subtract weight opposite the crankpin to give the 'nearest to even' level of force through a complete cycle. Note that this will be 'best' at a range of power settings and RPM.

I hope this is clear enough to help. (If I weren't so rusty regarding programming, I'd possibly try to write a program to print the values.)

Dennis


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## Ken I

dy  said:
			
		

> sum the effects of all the separate elements. This will give total force applied to the crankpin expressed through the center of rotation.



Done that - you will still come to the same results expressed above.

Entropy45's method is going to produce the best overall ballance for a single cylinder engine.

Best is not fully ballanced - which is simply impossible on a single cylinder. Yeah I know nothing is ever fully ballanced but a single cylinder is the worst case.

A friend of mine who raced bikes - once got the bright idea to reassemble a two stroke twin so that both cylinders were up at the same time (this crank assembly permitted this error) - he called it a "twingle" - he was hoping to reproduce the torque of a single thumper - it didn't work and the vibrations gave you double vision.

Ken


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## GreenTwin

I stumbled across a reference to this post somewhere while reading threads on this forum.
Now I can't find the post I was reading.
LOL, I am certainly losing my mind.
I had totally forgotten about this thread.

This was started many years ago in a former life.
It was not so interesting what I posted here, but what others added into the mix, which really gave me some good ideas on how to balance an engine using Solidworks, and not using calcuations.

Time is erasing my memory slowly but surely..
This one is rather hazy in my memory.

I will have to re-read this thread, since I am still building engines, and still need to balance them (more so as I get into IC work).

Edit:
I recall finding a Yamaha 650 twin in a lake one time, and I recovered it and rebuilt it.
I was rather surprised to see that both cylinders moved up and down together (if my memory is correct).
Makes sense if you think about it, since you can fire cylinder the cylinders 180 degrees from each other using this configuration.
It did vibrate a lot when it ran.
Great bike but I much prefer the Yamaha 500 single, such as the TT offroad engine, or the street version of that, which I forget the name.
The Yamaha single had a perfectly flat torque curve (I have a printout), and it runs like a hairy gorilla, ie: you better be hanging on very tightly when you open the throttle, regardless of what gear you are in.
Someone interviewed the engineer in Japan that designed the TT500 engine, and he said it was a very difficult design, but he finally got it optimized in the end.  He said there was no good way to balance it, and so they mounted the footpegs and other items in rubber.
You could literally plow fields with a TT engine.  It is a beast.
.


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