# B How large of a flywheel can my motor spin?

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1. Mar 1, 2017

### nick_g

Hi All,

I'm hoping you all can help me with what I think should be some relatively simple calculations. I'm looking to determine how large (diameter / weight) of a flywheel a particular AC motor can spin from a stop to full RPM given the torque / HP of the motor.

For instance, if I have a 1/3 HP 115v AC motor, which operates at 1725 RPM, I know the torque is ~1.02 lbs/ft. How large of a flywheel can this motor spin safely without risk of over-taxing the motor? Is there a formula to figure this out?

Nick

Edit: This is basically just so I know in advance that I won't cause a motor to overheat / burn out if i try to spin the flywheel on it.

2. Mar 1, 2017

### Staff: Mentor

Your question needs to specify how much time is allowed to accelerate. If we ignore friction, and the torque/speed characteristics of the motor, then any tiny motor can accelerate the flywheel giving infinite time.

You also need to specify the type of motor. Many motors have very poor torque starting from a dead stop. Traction motors have very good starting torque.

Can you photograph the nameplate of the motor and upload it here?

3. Mar 1, 2017

### CWatters

+1

Once up to speed the power required is determined by bearing friction and air resistance not the mass of the flywheel.

4. Mar 1, 2017

5. Mar 1, 2017

### Staff: Mentor

I looked at the Dayton web page. I can't find the torque-speed curve.

Wait a few hours, we have some good motor experts on this site.that may be able to help. @jim hardy tag.

As @CWatters said, you also need to know the friction in the motor, flywheel and bearings. In other words, how much power does it need to keep running after reaching full speed?

6. Mar 1, 2017

### jim hardy

This purports to be the curves for your motor.

https://www.grainger.com/ec/pdf/6K778_16.pdf

purple line M is torque. I extended it on down to zero speed with Paint.

Observe torque starts out low at standstill , builds to a peak 20X greater, then drops off quickly as RPM moves into operating range.. That's how induction motors work.

Would another old-timer kindly check my physics? Been having senior moments of late.

Just like F = MA,
Torque = M(oment of Inertia) X A(cceleration in radians per second2)

Your desired final speed is almost 1800 RPM which is 1800 X 2π radians per second
to reach that in 10 seconds requires average acceleration of 180π rad/sec/sec.
Acceleration can start out somewhat slower and finish somewhat faster

but you need to pick a flywheel with a moment of inertia that your motor can accelerate into its higher torque range within just a few seconds . Else you'll waste all your 10 second start time with motor laboring at low speed.

Let us just pick a MOI to give half the requisite average acceleration at zero RPM.

Torque at zero speed = 1.5 ft⋅lbs
1.5 ft⋅lbs = MOI X ½ 180π rad/sec2
MOI = 1.5/90π = 5.305 X10-3 ft⋅lbs/sec2 , radians having no units
NOTE lbs is pounds force not mass
now to calculate MOI
i'll guess your flywheel will be a thin disc like a grinding wheel
http://hyperphysics.phy-astr.gsu.edu/hbase/tdisc.html

I = ½MR2
Hmm you get to trade off diameter for mass.
Let's just pick a six inch diameter, half a foot, radius ¼ foot

0.005305 = ½MR2
0.005305 = ½M X ¼2
M = 0.005305 / (½ X ¼2) = 0.1698
NOTE : Since we expressed force in pounds , mass is in slugs
0.1698slugs X 32.174 lbf/slug (at 1g) = 5.46 pounds

so a small diameter flywheel can be pretty heavy. A bigger diameter will have to be lighter.
Look at the MOI formula -
I = ½MR2
If you keep same mass by doubling the diameter and reducing the thickness , you quardruple the MOI.
(Geometry pop quiz- by how much would you have to reduce thickness? hint- not half)

I really suggest that you repeat my arithmetic using Newton-Meters and kilograms to make sure i haven't inverted something.

When you try this thing out, listen carefully to the motor.
You'll hear its rate of acceleration increase with speed as it walks up its speed-torque curve. It almost snaps over the peak.
Once you recognize that sound and relate it in your mind's eye to that curve, it helps you "feel" induction motor behavior.

Torque falls off as square of applied voltage. That's why long extension cords that drop voltage are so deadly to induction motors - they never make it to torque peak so current stays high , see the blue "I" curve up above. They'll burn up.

Okay that's induction motors in a nutshell.
I hope you get interested enough to do some predictive iterative calculations.
Calculate acceleration from standstill, new speed after one second,
insert new torque from curve for that speed, calculate new acceleration, new speed at end of that additional second,
insert that greater torque,
etc
If you curve fit that torque curve you could simulate startup with say 1/10 second intervals in a spreadsheet and play with flywheel weights and diameters. I loved to do that sort of thing in BASIC before Miscroshaft forced everybody from QBASIC into spreadsheets. I never went along.

Of course all this neglects air friction on flywheel, another reason to keep it small diameter so edge velocity is slow.

last but not least - SAFETY
DO NOT MAKE SOMETHING THAT'S FLIMSY AND CAN FLY APART !
It WILL embed pieces of itself in the floor, walls and spectators. I've done that with a brass fan blade.
EDIT that motor is set up for belt drive. I'd suggest you not mount a heavy flywheel on that shaft, it's only intended for a light pulley..
Go to the hardware store , buy a quality grinding wheel rated for 3600 RPM because you'll run it at half that speed. Get a proper mounting attachment too.
(oops)
Beware junkshop wheels because you never know if they got dropped and have a crack.

______________________________________

end digression.

Last edited: Mar 1, 2017
7. Mar 1, 2017

### sophiecentaur

I may have missed it but I can't find the application for this flywheel and the required spec. If it's for temporary energy storage, it will need to be pretty massive, even for a modest number of Watt Hours of stored energy. The energy supplied from your motor if it gives around 250W (1/3hp) for 10s, will be a mere 2.5kJ. Is that the amount of energy that you need?
I wouldn't reckon that would be an optimal solution when there are many other sources of wheels. Grinding wheels have been known to shatter and they don't have much of an MOI, compared with a steel wheel. I would suggest a washing machine drum and bearing (they are rated at 1600rpm with an uneven load of wet clothes). Moreover, if you run it inside the tub, you have a built in safety cage for it.
But the choice of solution really depends on the details of what you want it for and how much energy you want from it.

8. Mar 1, 2017

### jim hardy

I tried to answer this question,
but i'm notorious for "answering the wrong question" .

Also i noticed that motor is set up for belt drive, shaft is designed for a pulley see https://www.grainger.com/ec/pdf/6K778_12.pdf
i'd not recommend mounting a heavy overhung flywheel on that half inch flatted shaft

so i think i'll go back and strike that grinding wheel suggestion

old jim

9. Mar 2, 2017

### sophiecentaur

Our problem here is that "large weight / diameter' could mean absolutely anything. It needs to be pointed out (I tried) that the actual size of the wheel makes a difference. The purpose of a flywheel can be Energy Storage, filtering out speed variations due to changing load or drive power and gyroscopic effect. On the other hand, the unintended existence of a 'flywheel', in the form of a large and heavy piece of machinery, can introduce an unwanted lag in spin up / spin down time. nick_g needs to let us know which of those the OP applies to before we can get any further - except, of course, it's fun to chew the fat about flywheels in general.

10. Mar 2, 2017

### nick_g

Hi all,

this is very helpful, thanks. The "flywheel" is being used to generate a gyroscopic stabilizing effect. I'm an artist and am using this in a sculpture, so nothing really needs to be set in stone or incredibly precise, i just want to make my flywheel / motor system safe and not create a fire hazard.

Best,

nick

11. Mar 2, 2017

### sophiecentaur

Ahh. At least I spotted the possibility. If a gyroscope is your aim then you should not really be thinking of a quick run up time. Again, we need to know the mass and size of the structure to be able to help you but it sounds to me that this part of the project really requires the help of a qualified mechanical engineer in the design. I can see a strong need for health and safety to be factored in from the very start. A rogue gyroscope, let loose from its mounting could really spoil your day.
I would strongly disagree with the idea that "nothing really needs to be set in stone or incredibly precise". We're in the same neck of the woods as explosives, toxic chemicals and high voltage electricity so the specification would need to be pretty precise. PF is very risk averse about these things and my safety advice should be taken seriously. (Public liability insurance will require things to be pukka.)
Having put that great damper on things, I should still like to be able to discuss ball park figures, if you could start us of with some ball park figures about the size of this thing. I would imagine you would spin up the gyro and then let it run down as it does its stuff on your sculpture.

12. Mar 2, 2017

### jim hardy

Ahhhhh, an objet d'art !

Being a longtime fan of "shabby chic" and "steampunk" i'd look for something along this line

http://www.ebay.com/itm/Heavy-Duty-...-Polishing-Wheel-Wire-Brush-Ect-/232254340852

it's made to safely hold something heavy on right end
and left end can be belted to most any sort of motor.

Pay careful attention to pulley sizes for they'll determine speed
and PF has old threads on how to rescue washing machine motors.

As with any rotating machine, keep it safe for tiny fingers - belt guard and shield around spinning parts.
You'll want the flywheel well balanced so get something that's intended to be spun. Perhaps a grinding wheel ,
or the flywheel from a junked small engine re-drilled by a machinist to fit your shaft .

old jim

13. Mar 2, 2017

### jim hardy

NIck -
So will something that gets torn apart by centrifugal force.
See my remark above about the brass fan blade. I pulled chunks out of the floor that had embedded themselves a half inch into solid white oak. A spruce drawer front looked like somebody hit it with an axe, chopped through two inches of it..
Miraculously none of us kids had any body parts in the plane of rotation else we'd have lost them.

Energy in a rotating assembly is to be respected. Learn that lesson from my mistake not yours.

Thanks Sophie.

old jim