Calculating Deflection of a Rotating Flywheel with Load Applied at Known Radius

[cstoos]

I am trying to calculate the theoretical deflection of a flywheel on a large diesel engine in an attempt to use it in measuring generator efficiency. I need to theoretical values in order to better understand instrumentation needs. I want to run the test in place and space is very very limited.

It is a steel crank shaft on large marine diesel engine. The crank is bolted to a 38.5 in diameter x 1.5 in thick fly wheel. A 35.5 inch by .75 inch thick 'flex plate' is bolted to the fly wheel with bolts on 34 inch centers. It is bolted through a spacer ring that separates the two plates. The 'flex plate' is then bolted to the generator drive shaft.

So engine turns crank which turns flywheel. Fly wheel turns flex plate. Flex plate drives generator shaft.

Does anybody know how I can calculate deflection of a rotating disc which will allow for a load to be applied at a known radius?

I have attatched a pdf with a rough sketch of the system. I do not need it solved, just a hint as to how to approach the problem. Thanks.

 

[tvavanasd]

I would suggest that you include a diagram for clarity.
Is it necessary to consider that the elements are rotating in your initial deflection calculation?

 

[brewnog]

I'm intrigued. How will flywheel deflection help indicate efficiency?

 

[cstoos]

It is fairly inaccessable, so the shafts cannot be instrumented. I am trying to find the deflection in order to calculate torque since I will know the rpm's. If I can calculate torque I can find horsepower into the generator. The generator output is easily measurable and I can determine the efficiency using the relation.

The whole problem is that I want to test multiple generators on multiple engines without removing them from their mounts.

 

[brewnog]

I don't understand, in what plane do you want to measure shaft deflection? How does this indicate torque?

 

[cstoos]

......frustration has got the better of me. Thanks for the interest, but I am shelving this problem until next week since it is not an urgent need. My brain hurts.

If anyone wants to help...

Goal: measure deflection in rotating disc with hole in center using strain gauges at 45 degree angles from radius normal to central hole. Then, somehow, use that deflection to calculate torque. Torque then gives me horsepower (or watts). The strain gauges will have to be on the flat surface of the flex plate, meaning the mounted side of the strain gauge will be facing perpindicular to the axis of rotation.

Sorry I can't be more clear. This issue has consumed me for a week now. I seems like it should be simple. I need to step back and take a new look at it.

Anyways, here is as far as I got with my original reply if anyone wants to stare at some equations.

"Let's see. I can only instrument the flex plate as seen in the attatched drawing. It is essentially a rotating disc with a central hole in it.

So, my stress equations are:

$$\sigma$$_r =((3+$$\mu$$)/8)*$$\rho$$²$$\omega$$²*(R²+r_hole²+R²r_hole²/r²-r²)


$$\sigma$$_theta=((3+$$\mu$$)/8)*$$\rho$$²$$\omega$$²*(R²+r_hole²+R²r_hole²/r²-(1-$$\mu$$)r_hole²/(3+$$\mu$$))"

 

[brewnog]

I think I understand, you're looking to measure the twist between the centre of the shaft (from engine crankshaft) and the periphery from where the drive is taken. Flywheels are really chunky components and I'd be surprised if you get a meaningful measurement from this, but let me know how you get on!

 

[cstoos]

Yeah, pretty much...except it will be measured on a plate bolted to the flywheel through a spacer ring. I put flywheel in the title so people would know more or less what I was talking about. The flywheel is 1.5in thick. The plate is only .75 in thick and 34 in in diameter (that is, 34 inches center to center distance on the bolts that transfer the engine force) with a hollow drive shaft that goes to the generator bolted to it. I did a theoretical strain calculation and it is a measurable quantity, I just don't know how to get from strain to torque without knowing the deflection.

Anyways, like I said...it seems simple, but has proven to be much more difficult than I was hoping.

 

[Jobrag]

I don't think that you are going to have a lot of luck with this, the only system that I know of that will accurately measure torque of a drive shaft is a device made by a company called torquemeters (http://www.torquemeters.com/) they involve highly acurately machined torque tubes with a phonic wheel at each end, by looking at the phase shift of the output of pickups at each end of the shaft the twist of the tube is calculated and hence power. To give an adea of the problems involved with this the length of the cables between the pickups and detectors if not the same will effect the results.
If you want to calculate generator efficiency you might be better looking at the other end and measuring the heat rejection from the cooler, lube oil and body.

 

[cstoos]

It is done now by measuring heat. I am looking for a more precise way to accomplish the task.

 

[Jobrag]

If you are using a diesel engine is have you thought about taking indicator cards and calculating engine power from those? It's a long time since I did that kind of stuff and I don't know how accurate it would be.

 

[cstoos]

Indicator cards will be too expensive to do on 16 cylinders and it also doesn't account for power used by other engine accessories.

 

[brewnog]

What's your issue with strain gauging the alternator mounts or drive shaft?

 

[cstoos]

It is too hard to get to in the space available. It is also not an easily interchangeable part that can be switched from engine to engine like the plate. The whole point is to have an easily (or easier) method to measure multiple engine/generator combos without removing either from their mounted position.

 

[brewnog]

Fair enough. It's certainly a challenge. I test power generation engines for a living, we normally have to rely on alternator efficiencies to calculate shaft power. Let me know how you get on.

 

[Jobrag]

Tell your salesmen to sell the rated power at the generator terminals, then you don't have to muck around with generator efficiancy just the overall package figures.

 

[brewnog]

No good for a loose engine supplier who tests as a genset though!

 

[Jobrag]

Scrap the genset and buy a dynamometer.

 

[brewnog]

I guess if measuring torque in a non-intrusive manner is an issue for the OP, that might not address his solution either...

 

[cstoos]

Yeah, the fact that these engine generator combos are inside locomotives makes the dyno an impossibility.

Another issue I haven't brought up is the fact that in place testing allows for ignoring power loss due to other accessories (water pumps, oil pumps, etc...).

This as well as the fact that locomotive engines/generators are not easily removeable is what makes it difficult. Regardless, I think the original point of my post has been lost. I was looking for equations and instead got an interesting conversation about the purpose.
Not that I mind, but it hasn't really gotten me anywhere.

So, on a rotating disc with a hole in the middle that has the drive force on the outside and the load force on the inside, how do I calculate deflection from measured strain?

 

[Jobrag]

If you are measuring the strain directly do you need to calculate the deflection? Normally you measure the deflection and calculate the strain. I'm not sure whether you can calculate the torque through the flywheel by one strain gauge measurement, and unless you calibrate each flywheel, I really don't think that you are going to get any better results then your present method.

 

[cstoos]

It won't be one strain gauge. It will most likely be a four gauge rosette setup of some sort that way it is temperature compensated.

The reason I was looking at deflection is I cannot find any equations for a disc to go straight from strain to torque.

For example, if instrumenting the shaft it would be:

T=$$\frac{EI\epsilon}{1+\nu}$$

Then

HP = $$\frac{TV}{5252}$$ where V is engine speed.

and 1 HP = 745.7 Watts.


Now, how do I do that on a disc? How can it be accomplished by instrumenting the flat face?

 

[brewnog]

Have you looked in Roark?

 

[Jobrag]

How do I get a readable image of the black box things?

 

[cstoos]

No, brewnog, I have not. I have Mark's Standard Handbook for MEs by Avallone here and an old copy of Shigley. I looked up the Roark book just now and it looks like it may have what I need. Guess it is time to order it.

 

[cstoos]

Black box things?

So, after looking through quite a few books, exhausting google, and reading a bunch of published papers I have come to the conclusion that the problem I am trying to solve has not ever been solved completely before. Rotating disks seem to be an impossible task.

In fact, I read the words "rotating disks with more than one moment force acting upon it
has never been completely solved, therefore an approximation..."

I am thinking of other ways to accomplish my task now, but I figured you guys may want an update.

Brewnog, Jobrag...thanks for the interest. Oh, and I uploaded an actual picture to show the space limitations I was referring to.

 

[brewnog]

Indulge me, what's the engine?

I'm surprised this hasn't been solved before to be honest. Is there any chance you could get one of the discs onto (something like) a brake and apply different static torques, and correlate these against your strain gauge rosette measurements?

 

[cstoos]

I believe that one is an EMD 645E3C.

I thought about doing that actually. That is a last resort though, since the only way to do it that we have available is with a bar and a crane.

As far as the problem goes, apparently there is too much flex in a disk and that is why it hasn't been solved completely. I guess they never considered a disk that is bolted to an even stiffer disk. Ha.