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

 

[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

 

[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

 

[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.

 

[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

 

[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.

 

[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

 

[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.

 

[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

 

[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?

 

[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

 

[petertha]

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?

 

[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,

 

[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

 

[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

 

[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

 

[Niels Abildgaard]

5 pictures of half a revolution

 

[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.

 

[Dan Rowe]

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

 

[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