3600 RPM Flywheel - 400 Lb*ft^2!!

[Slagathor]

I have a customer that would like a flywheel added to pump system so as to prevent downsurge in a pipeline during power failure. Much cost and time has gone into developing this "solution". The problem, as I see it, is that no one bothered to see how challenging the development of a flywheel this large, at this speed, would be.

I designed a flywheel for a mixed load (combination of inertial and brake loading) dynamometer some years back...and it scared the heck out of me. That wheel peaked at 1500 RPM...and was about 20" in diameter. It was a plain disc (not ideal for RPM limit vs diameter, but most effective from a mfg cost perspective). At 3600 RPM...the stresses multiply nearly 6 fold from 1500...

I have a spreadsheet I created, which takes the general solution of a spinning disc problem from Timoshenko Part II (Advanced Theory and Problems) and makes a usable quick ideal world stress calculator. The question I have...is safety factor. Because the potential for catastrophic failure and loss of life is non-trivial with a flywheel...I have heard of huge safety margins being applied...ie max stresses of 10% of yield. This is to allow for the uncertainty of micro defects creating stress concentrations in the material. Is it really necessary to be this conservative if you are mfg from quality alloy plate...like 4140?

Example 1:
4142 High Carb...Heat Treated has a yield of 90,000 psi and a UTS of 140,000 psi. This is big bucks....probably $3000 for a 24"x24"x7" round raw material drop out. So...if we could manage to make a 6.75" thick x 23.5" OD Flywheel..the peak stress will be 11,950 psi at the ID (assuming a 3.5" rotor bore ID which is used to align a pair of heavy hubs, which actually bolt the flywheel). The radial stresses at the inner surface are of course zero. About 30-40 off center...I will have through holes for bolting up of hubs...so...to determine stresses there...I will have to look at the combined tensile (6200 psi) and radial (4300 psi) stresses...calculate from there...and THEN apply a stress concentration factor for the through hole. But the time I am done with this...I can see a real world stress potential in the range of 20,000 psig.... 200,000 yield on the material...?? Not going to happen

So this means go smaller on the diameter...which will drive up the thickness and weight.

Example 2:
Same material. Limit OD to 15.5". This will result in a peak stress...when conbined stresses..and concentration...is taken into account of about 9000 psig....or 10% of yield. The problem is this 15.5" OD wheel will need to be 35" thick..and it will weigh 2000#. Now..I have a shaft...not a wheel...and I start to get into rotor dynamics issues...mfg costs notwithstanding.

So...back to my question....how much safety factor for a wheel machined from high quality wrought alloy plate?

By the way...any PEs out there want to stamp this thing?

 

[Slagathor]

FYI...I did not clearly state it...except in the header...but the required inertia is 400 Lb*Ft^2 for each pump/motor....

 

[GregLocock]

If you'd asked me to guess, a 3600 rpm 2 foot diameter flywheel would be made of cast steel.

Cheers

Greg Locock


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[Slagathor]

Greg,

Due to mfg issues...I am pretty much limited to wrought material. Patterns to do a casting will be prohibitively expensive. To get around the stress issues (tangential stress peaks at ID...and radial stress peaks at about 35% from inner to outer diameter)...classic flywheel designs use an outer ring with spokes....hence the cast design. No can do for this small small run.

So...being limited to a plain disc drives up my stresses from the ID...to about 50% of the way to the OD. At 3600 RPM....24" OD will result in stress concentrations around the hub bolt holes exceeding 20ksi... That was not my question. My question was...how much safety margin is needed? I have heard of MUCH more conservative safety factors (yield being as much as 10-20 times calculated max stress) being used for flywheel stresses than other components due to the consequences.... With 20,000 psi stresses around bolt holes...and 90,000 psi yield (414x HT Plate)...that is not much safety factor to allow for micro defects, etc.... That is only 4.5 times stress to yield...

 

[prex]

No reason to be that conservative.
I have here 12 flywheels 21" dia. 4" thick that have occasionally turned at 3000 rpm (normally at 1500-2000 rpm) without problems, and they have holes in their body.
My mechanics book says a reasonable limit for common steels would be 0.25 to 0.4 Y, but this is an old book (1950), I guess the upper limit is quite acceptable.
But for the above flywheels at 3600 rpm with a small axial hole the tangential stress at the hole is much smaller than what you quote, you should revise your spreadsheet...

prex
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[rb1957]

i don't design flywheels but ...

why are you limited to a plain disc ? machining is too expensive ? ... sorry, but you have to pay the piper somewhere along the line.

how about heat treating 4140 to 160/180 ksi (ftu) ?

would interference fit bushes help the stress at the bolt holes ?

putting on a big SF and working the material to (only) fty is pretty conservative design.

do you have to account for the bolt loads from torque being applied to the flywheel ? or does this only happen as the flywheel is being spooled up ? spooling down ??

 

[MintJulep]

For perspective, you're looking at roughly two train wheels.

Granted, your RPM is higher. But flywheels don't get pounded by rail joints, abused by sliding when the brakes lock, or go through big thermal cycles during braking.

Maybe just pressing some train wheels on a shaft is a cheap and ready-made solution.

 

[Artisi]

As a bit of a side issue at this stage, but have you looked at / considered the starting torque / motor capability / control panel etc in getting the pump and flywheel away from zero and upto speed?

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[1gibson]

Maintenance may hate you (they probably will anyway with this huge flywheel) but you might consider redesigning the pump-motor coupling to add as much mass as possible.

Where on the shaft do you have room to fit this flywheel? What type of pump is it (vertical, horizontal?)

 

[MintJulep]

If my math is right - and very possibly it isn't - your max energy storage is in the realm of 0.7 kW-hours.

Well within the capability of the current generation of energy storage batteries such as

http://www.khi.co.jp/english/gigacell/intro/spec.html

Consider an electrical solution.

As Artisi points out, it's unlikely that you'll be able to start this beast across the line, so you're going to need some electronics to soft start it anyway.

 

[Slagathor]

prex,

Thank you for speaking directly to my question.

My spread sheet is correct. I hand checked the calc. The high numbers I came up with were a result of guessing at a combined stress....then adding a stress concentration factory on top of that...

So...if we were to design to have a peak stress of 15% of yield...that would be justifiable? I think we can make that work....

 

[MiketheEngineer]

You might consider a VERY heavy shield around it??

 

[prex]

What kind of stress concentration did you take?
My handbook says that the maximum stresses at a hole through the disk are
max[σ]_t=3[σ]_t-[σ]_r
max[σ]_r=3[σ]_r-[σ]_t
Also these peak stresses influence fatigue only: you should check fatigue with a range (variation) of those stresses over anticipated functional cycles.


prex
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[rb1957]

normally i would think combining stress concentration with a design loadcase would be very conservative (like prex mentions above, combining stress concentration with working loadcases as part of fatigue design). normally for design cases (in my case once in a lifetime loads) i'd say that stress concentrations give you local plasticity which the structure should be able to absorb, rather than designing to stress*Kt*SF < fty.

but in this case the load (3600 rpm) will be seen frequently so i think consideration of stress concentrations is reasonable.

i think stress*Kt*SF < fty is very conservative.

i think i suggested installing interference fit bushes at the bolt holes as a means to reduce the stress concentration effect (maybe i did, maybe i just thought i did !?). but if you don't want to machine the plate (too expensive ?), then i guess you don't want to install bushes either.

by your calc you're getting a local stress of 8 ksi *3 = 24 ksi at the edge of the hole, doesn't sound like much on 90 ksi fty steel. but this has no fastener load (bearing); i'd worry about the effects of bolt loading, mostly in unloading the flywheel, particularly in the event of a failure (so it's more of an impact load).

just my 2c ...

 

[GregLocock]

Sorry I wasn't suggesting cast steel as an ideal flywheel material, I was just pointing out that a fairly crude material would probably work OK, therefore either your calc is wrong, or you are being overly conservative which is forcing you to go to a higher spec material. You are insistent your calc is OK, therefore, follow Sherlock Holmes.





Cheers

Greg Locock


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[Slagathor]

Thank you everyone. I have been digging a little more, and most of the references I saw with regards to using large safety factors on flywheels related to smoothing of torque for reciprocating loads (ie engines). In this case, the load and speed will be very uniform as we have an induction motor driving a pump with high vane counts on the impeller. Very smooth rotor system. So, while the flywheel does spin pretty fast (3600 RPM / 60HZ)...the stresses that would be impacted by say..a vibration at that frequency...are NOT my high stresses due to internal inertial stresses. The internal stresses are essentially steady state. I feel a safety factor between max calculated stress and yield of 4x top 5x is prudent.

NOW I can start getting into detail with regards to calculation of combined stresses..and looking at concentrations due to my bolt holes.

I am not opposed to installing press fit bushings at the holes. I like that idea...

 

[JStephen]

"For perspective, you're looking at roughly two train wheels...Granted, your RPM is higher..."

My first thought was "Wonder if a truck wheel with tire would work..." but a quick calculation showed that 3600 rpm works out to around 400 mph, and finding truck wheels and tires made for that speed might be a bit of a challenge as well!

 

[rb1957]

no more of a challenge than finding 400 mph train wheels !?

 

[MintJulep]

no more of a challenge than finding 400 mph train wheels !?

Current steel wheel train speed record is 357 mph, so not that far away.

As noted earlier, the flywheel application is relatively benign compared to the train wheel application.