# Power Required to Drive Large Flywheel

1. Jan 3, 2010

### Rick Rowlands

I just registered for this forum as I have a problem that needs solved. I am building an industrial museum in Youngstown, Ohio, and the centerpiece of our collection is a 230 ton stationary steam engine which we saved from a local steel mill. I am designing an electric drive for it so that we can roll it over at 15 rpm for demonstration purposes. Before I go any further here is a photo of the engine.
http://inlinethumb19.webshots.com/18130/2908668190033749120S600x600Q85.jpg

The crankshaft and flywheel weigh 230,000 lbs., and rest upon two babbitt bearings, 23" dia. x 40" long. The bearings will have a pressurized lubrication system feeding oil to the underside of the journals before startup, so the coefficient of friction may be around .015 or less. The flywheel rim is 20' dia. and has a 24" square cross section, weighing 102,000 lbs.

I want to run the engine at 15 rpm for the demonstrations.

We have some equipment here which I plan to use for the drive. We have a 20 HP series wound DC mill motor with a full load speed of 725 rpm, drawing 76 amps. The motor has a short term rating of 30 HP, 575 RPM at 116 amps. This motor will drive a planetary gear reducer with an 18.9 to 1 ratio, then from that reducer there would be a double 140 roller chain with a reduction of 2.56 to 1 before finally coupling to the engine crankshaft.

What I am concerned is if the drive has sufficient power to bring the engine up to speed, and how long would it take to accelerate to 15 rpm. Also I am looking to determine what the resistance should be for each step of a five step DC controller, as I will be using control equipment from a DC crane to operate the motor.

Thanks

2. Jan 3, 2010

### robert2734

I didn't do any math (or physics). I know of a hundred ton telescope pointed by a twelve horsepower motor. I don't know what the coefficient of friction is. I think you are in the ball park.

3. Jan 3, 2010

### dlgoff

http://www.engineersedge.com/motors/torque_electric_motor.htm
Welcome to PF

4. Jan 3, 2010

### spacester

Hi Rick,

Were you looking for guidance in doing the calcs or for someone to do all of it for you?

I'm willing to do the former but not the latter. For something like this, IMO you should know exactly how the answer was found. There is nothing really advanced here, but it isn't exactly trivial either.

5. Jan 3, 2010

### Rick Rowlands

It seems that the engineersedge formulas posted by dlgoff will answer the question regarding acceleration time, as well as torque available at full speed, which is 7000 ft. lbs. So this boils the down to torque required to get the 230,000 lb. mass up to 15 RPM from a dead stop.

From engineersedge:

"The time duration required to accelerate a application from a dead stop to operating speed is given by the following:

T = [ N x WR2 ] / [ Ta x 308 ]

Where:

T = Time ( seconds )
N = Velocity at load ( rpm )
Ta = Average Torque During start ( ft-lbs )
WR2 = Rotating Inertia (lbs-ft3)
W = Weight (lbs)
R = Radius of Gyration (ft2)
308 = Constant derived converting minutes to seconds, mass from weight, and radius to circumference"

What is rotating inertia, radius of gyration and what would be the average torque during start? How do I determine what those are?

6. Jan 3, 2010

### Staff: Mentor

Another welcome to the PF.

The correct term is Moment of Inertia:

http://en.wikipedia.org/wiki/Moment_of_inertia

That should give you what you need.

7. Jan 3, 2010

### Rick Rowlands

That gave me a lot of formulas which I don't understand and even more terms which I don't know. Anything that explains it for lets say a practical man who graduated high school with straight Ds in math?

I'm not an idiot when it comes to mechanics, how stuff works, etc., but am clueless when the hieroglyphs start appearing in equations.

8. Jan 3, 2010

### spacester

I do not like that engineersedge formula for two reasons.

First, the WR^2 term is ambiguous. They use the "X" symbol to multiply by N, but not between 'W' and 'R', and they tell you that the units for WR^2 is lbs*ft^3 which is WRONG - the units are lbs * ft^2

Second, the units of the quantity you find are the inverse of seconds: N is revolutions per minute, and you don't see minutes or seconds anywhere else, so the answer must be per unit time.

Here is my proposed corrected version:

T = Ta / (N * W * R^2)
which is valid for any units, as long as you make the conversions

To make this conversion, you have to realize that W is in lbm ("pounds mass") and T is ft*lbf (ft*pounds force)
The definition of units gives us
lbf = lbm * 32.17
So I can confirm the conversion constant of 308 with this:
2 * pi (radians/revolution) / [ (32.17 lbm / lbf) * [ 60 seconds / minute) ] = 0.003255 = (1 / 307.2)
(with this, all the units cancel except seconds - note that radians is a "dimensionless unit")

So use:
T = 307.2 * Ta / (N * W * R^2)
where
Ta = Ft-lbf
N = rev / minute
W = lbm
R = ft

You need the "Radius of Gyration", and you prolly googled it, and found, as I did, that the definitions seem to be written by mathematicians FOR mathematicians and of little help to us practical types.

But we can find this definition:
"The square root of the ratio of the moment of inertia of a plane figure about a given axis to its area."

So
R = square root of I / A
or
R = (I / A )^(1/2)

Where
R = Radius of Gyration (ft)
I = Moment of Inertia (ft^4)
A = Cross-Sectional Area (ft^2)

We know A, it is the 24 inch square you described
A = 4 ft^2

I is the tricky thing here.
The Wikipedia entry for "Moment of Inertia" is actually for the "MASS moment of Inertia" - they are trying to trick you! :-) What we need is the "AREA Moment of Inertia"
found from
I' = b * h^3 / 12 for a rectangle with the axis running thru the centroid
where
b = base (ft)
h = height (ft)
But this does not account for the distance from the axis of rotation to the centroid of our rectangle, you use the parallel axis theorem for that:
I = I' + A * d^2
where
d = distance between axes

http://www.efunda.com/math/areas/ParallelAxisTheorem.cfm

In our case, d is the radius from the center of the wheel to the center of the cross-section
I'm not seeing that number in the thread so far, but that's all we're missing to get this start-up time (which you were very well advised to look at).

I'll post this and let you turn the crank on that much before moving on - are we getting a reasonable answer? (I didn't really check the derivation of my revised version, so maybe I'm missing something.)

9. Jan 3, 2010

### Rick Rowlands

OK it will take a me a couple of rereadings of your reply to fully understand it! :)

One thing I can answer right now is that d would be 19 feet.

10. Jan 3, 2010

### spacester

Cool.

This is a neat project, good for you for taking it on.

d = 19 ft

That is a BIG SUCKER, ain't it?

For some reason the nice photo you provided is no longer showing up in my browser. I'm gonna run the numbers and wanted to check that number. I was guessing the diameter was closer to 20 feet than 40 feet . . . but remember that d here is for the radius, not the diameter.

I'll also look at my version of the equation in an effort to verify.

11. Jan 3, 2010

### Rick Rowlands

Oh sorry yes you are right. The wheel is 20' diameter, so d would be 9 feet as the rim is 24" square in cross section.

12. Jan 3, 2010

### spacester

D'oh!

Hang on, I goofed up the lbm to lbf conversion. The result is in seconds, not the inverse of seconds.

More in a few minutes . . .

13. Jan 3, 2010

### Rick Rowlands

If you would like to see more photos of the engine and our project, go here:

http://community.webshots.com/user/todengine

I moved the engine to this site over the last several years, and over the summer erected a building over it, including an 1893 EOT crane which was donated by a local company. Both the crane and the DC motor that will turn the engine will be powered by 250 VDC generated by a diesel locomotive that was donated and recently moved to the site. The project is an attempt to preserve the industrial history of the Youngstown, OH area, by saving and displaying equipment used in local industry. Everything here will operate in some manner, so I am always running into strange problems such as the one I am trying to solve in this thread.

14. Jan 3, 2010

### spacester

Corrected version:

. . . they tell you that the units for WR^2 is lbs*ft^3 which is WRONG - the units are lbs * ft^2

T = (N * W * R^2) / Ta
which is valid for any units, as long as you make the conversions

To make this conversion, you have to realize that W is in lbm ("pounds mass") and T is ft*lbf (ft*pounds force)
The definition of units gives us a conversion factor called "g-sub-c":
gc= (32.2 ft * lbm) / (lbf * s^2)

So I can confirm the conversion constant of 308 with this:
2 * pi (radians/revolution) / [ [ (32.2 ft*lbm) / (lbf * s^2) ] * [ 60 seconds / minute) ] ] = 0.003255 = (1 / 308)
(with this, all the units cancel except seconds - note that radians is a "dimensionless unit")

So use:
T = (N * W * R^2) / [ 308 * Ta ]
where
Ta = Ft-lbf
N = rev / minute
W = lbm
R = ft

OK let's plug in numbers:
R = (I / A )^(1/2)

We know A, it is the 24 inch square you described
A = 4 ft^2
I' = b * h^3 / 12 for a rectangle with the axis running thru the centroid
I' = 2 * 2^3 / 12 = 1.333 ft^4
I = I' + A * d^2
d = 9 ft

I = 1.333 ft^4 + 4 ft * 9 ft * 9 ft
I = 325.3 ft^4

R = (325.3 / 4)^(1/2)
R = 9.01 ft

Ta = 7000 ft-lbf

T = (N * W * R^2) / [ 308 * Ta ]
T = 15 rpm * 230000 * (9.01 ft)^2 / (308 * 7000 ft-lbf)
T = 129 seconds

2 minutes, 9 seconds to get this sucker going

But let's take a closer look at that 7000 ft-lbf torque. Can you show me where you got that number?

Also, we are assuming that the total mass is in the cross-section of the wheel, but a big chunk is actually in the spokes and the crankshaft, so we are being conservative here. To get a better answer, we're going to need to do a more careful calculation of the Radius of Gyration.

If the cross-section is steel at 0.283 lb/in^3 (a rule of thumb I have memorized), I calculate the wheel itself (no spokes) at 110,600 lbm which would reduce our time to 62 seconds.

edit: "more careful calculation of the Radius of Gyration" should read "more careful calculation of the Rotational Inertia"

Last edited: Jan 3, 2010
15. Jan 3, 2010

### Phrak

What is max pressure of your hydraulic system, and will the crankshafts be moving as well?

16. Jan 4, 2010

### sophiecentaur

Would this simple Measurement procedure help? There seem to be a lot of imponderables if all you are going to do is calculations.
You could try hanging a mass on the outside of the flywheel (or use a belt driven by a falling mass, somewhere else) and see what it takes to get it going. The rate at which the mass accelerates would tell you the effective mass of the system, acting at that point. That would, in effect, be measuring the MI plus Friction of the system in one go - which, I think, is what you need.
Or, if you can translate your requirement into the required peripheral speed and acceleration of the wheel, you could add masses until the acceleration is sufficient. That would tell you the actual Power needed, (Force times Speed or Torque times angular velocity etc.).

The good thing about that method is that it doesn't involve firing up any electric motors and you get a good ball-park idea of what your problem is. It would give you an idea of how long your electric motor might be expected to be 'stalled', for instance. For someone with your facilities and abilities, I am sure you could do this easily and I suspect that is how the original designers may well have worked.

17. Jan 4, 2010

### spacester

@ sophiecentaur: Excellent suggestion!

@ Rick: Let me know if you need any support doing the math for such an experiment.

@ Phrak: Good line of inquiry: It would be a shame if the lubrication was not sufficient and the babbitt bearings wear too rapidly.

18. Jan 5, 2010

### Rick Rowlands

Thanks everyone for the help. I think I have enough information now to go on. My concern was mainly if the DC motor which I have would be sufficient to get the engine turning from a dead stop, and I believe that it will be powerful enough. I've learned a little about power, acceleration, moment of inertia etc. in the process. This entire engine project has been one giant educational adventure for me!

19. Jan 5, 2010

### Bob S

Nice museum piece!

Several things:

1) Make sure the lubrication system will continue running in the event of an electrical power failure. I know of one case during a large power blackout where the journal bearings were ground up, because the generator took ~ 30 min to stop after the power failed. I have seen backup hydraulic pumps that were mechanically coupled to the flywheel.

2) Repeat the calculations in metric units to avoid ambiguities in the English system of units.

3) Brush-type electric motors do not like to "run" with a locked rotor. It will burn the commutator. How do you limit the starting (locked rotor) current? Measure the required static starting torque by tying a rope onto the flywheel and putting half a turn around the rim. How many men does it take to make it turn? Assume 1 man = 300 Newtons of force. Using R = 2.7 meters, the torque would be ~800 to 900 N-m per man.

At 15 RPM, 20 HP = 15,000 watts = torque x 2 pi RPM/60 = 1.57 x torque (in Newtons).

So the available torque (not including drivetrain losses) at 15 RPM is about 9,500 N-m. Use
http://www.unitconversion.org/unit_converter/torque-ex.html
to convert to Lb-ft (I get 7007 lb-ft).

4) Do you have any provision on how to stop the flywheel in case of an emergency?

Bob S

Last edited: Jan 5, 2010
20. Jan 5, 2010

### sophiecentaur

"2) Repeat the calculations in metric units to avoid ambiguities in the English system of units."
Oy Oy. It's decades since the 'English' used those old fashioned units! It's only the uncivilised part of the world that uses pints for anything other than Beer.

The lubrication pump has to be driven off the flywheel itself, surely. Wouldn't the original system have been like that?