Keep that wheel a-turnin' -- How much energy is required?

[Pinon1977]

TL;DR Summary

I need to know how much energy is required to turn a 4-foot diameter flywheel, weighing 40 lb, at a speed of 60 RPMs.

I know I'm probably overcomplicating this question, but I'm having a bit of difficulty coming up with a singular answer. I have a 4-foot diameter flywheel that I need to turn with an electric motor of an unknown horsepower. I say unknown because I I don't know what I need based upon the following criteria. 4 foot flywheel, weighing 40 lb, and I needed to turn at an RPM of RPMs. What size electric motor would I need in order to accomplish that. There will be no external force is applied upon the wheel once it starts turning, and it does not matter how long it takes to get to 60 RPMs

 

[PeroK]

It takes no energy to keep a flywheel rotating at a fixed angular frequency. The energy needed is entirely dependent on the energy losses to dissipative proceses, such as friction and air resistance.

 

[sophiecentaur]

Summary:: I need to know how much energy is required to turn a 4-foot diameter flywheel, weighing 40 lb, at a speed of 60 RPMs.

I don't know what I need based upon the following criteria. 4 foot flywheel, weighing 40 lb, and I needed to turn at an RPM of RPMs

What you do need to know is how quickly you want the wheel to get up to speed from stationary. That will indicate the sort of Power you want for your motor. The energy stored n the flywheel is not a lot - say less than 150J (that's 15W for 10seconds). You waste quite a lot of energy whilst getting the motor going but it would settle down at only a Watt or two, if the flywheel bearings are good. (Extra, of course, if the wheel is also driving something which is actually doing work.

Tell us what the actual application might be. It could be relevant.

There are other important things - like how robust the motor is, under near stalled conditions, because that's what it will need to deal with at startup. I don't know much about motor specs but I'm sure someone here can help you about the sort of stall current that motors of that power can stand. It doesn't sound expensive to me. (You would be talking in terms of a low power induction motor, I guess)

A 500W motor, such as you use in a bench grinder, would be easy to find and pretty cheap to buy (and to run - the 500W only refers to what it can supply and not what it uses when free running)

 

[russ_watters]

A 500W motor, such as you use in a bench grinder, would be easy to find and pretty cheap to buy (and to run - the 500W only refers to what it can supply and not what it uses when free running)

I'd even go way smaller than that; that's less of a flywheel than my exercise bike has. If you can start it by hand (and it has a decent bearing) you could run it with a Dremmel (which has a nice sliding speed controller...).

 

[sophiecentaur]

I'd even go way smaller than that; that's less of a flywheel than my exercise bike has. If you can start it by hand (and it has a decent bearing) you could run it with a Dremmel (which has a nice sliding speed controller...).

I wouldn't disagree with you at all. It's just that half horse motors seem to be the ones that people tend to give away. They have nice fixing feet and go one for ever.

Something I had actually forgotten is the low revs and the need for some significant down gearing from a regular mains motor to get 60rpm. As it happens, I did buy a 230 V synchronous motor with a gearbox included and it does 50rpm. On 60Hz mains, it would do the required 60RPM. It has plenty of torque for Christmas decorations and the like and it cost me about 10GBP. With a stretchy belt drive, starting would be no problem.

This looks like a job for eBay.

 

[Pinon1977]

So, by that reasoning, you are saying that a 40lbs flywheel or a 4000lbs flywheel could run at 60 rpms with the same motor and same power useage? The only difference would be the amount of time it took to get to 60 rpms? 4000lbs more time than 40lbs, obviously. That doesn't appear to be an accurate presumption to me. Please advise. Thank you

 

[Pinon1977]

Let's say that I need it to get it from 0 to 60 RPMs in 2 minutes.

 

[Pinon1977]

So, by that reasoning, you are saying that a 40lbs flywheel or a 4000lbs flywheel could run at 60 rpms with the same motor and same power useage? The only difference would be the amount of time it took to get to 60 rpms? 4000lbs more time than 40lbs, obviously.

 

[sophiecentaur]

So, by that reasoning, you are saying that a 40lbs flywheel or a 4000lbs flywheel could run at 60 rpms with the same motor and same power useage? The only difference would be the amount of time it took to get to 60 rpms? 4000lbs more time than 40lbs, obviously.

Yes, you have got the message.
The rotational energy of the flywheel is given by
E = Iω²
where I is the moment of inertia and ω is the angular velocity. If you spin it up with a motor, the power needed will depend on how soon you want it to reach the wanted velocity. Energy = Power X time
There is a practical difference between the two wheels - the heavier one would produce much higher friction forces than the lighter so that would require more running Power (but very little, compared with spinning up in a reasonable time. With equal power input, the bigger wheel would take 100 times longer (plus the extra losses, of course).
That would depend on the wheels being well balanced. If the motor is below a certain power, the bigger wheel may not even make the first revolution. There are basically two solutions to your problem. Either you can do all the calculations and all the measurements and select the smallest motor for the job. Save money that way but you need a fair bit in hand. Motors are not expensive (cheaper than a balanced flywheel with good bearings and a suitable gearing system etc etc. so a fractional hp motor that's clearly beefy enough would take care of one unknown.
The best solution to this, as I have already commented, would depend on the actual details and not the theoretical power needed to keep the wheel spinning. You should be aiming at an induction motor if it needs to spin for an extended period of time without wearing out brushes and making a noise, which is what small hand-tool motors tend to do.

Tell us what the flywheel is actually doing?

PS if the flywheel has a smooth outer edge then you may be able to edge-drive it with a rubber pulley (a bit like the old gramophone turntables). That could give you a convenient gearing down and allow some slippage at startup. A Shaded Pole motor might do the trick.

 

[Ibix]

With equal power input, the bigger wheel would take 100 times longer

That depends on the wheels' radii, doesn't it? A disk that is 100 times heavier than the lighter one has ten times the radius if it has the same thickness and density. That would make $I\propto mr^2$ 10,000 times larger - so the spinup phase would be something like 10,000 times longer.

 

[etotheipi]

The rotational energy of the flywheel is given by
E = Iω2

suspect you might have dropped a factor of ✌

 

[sophiecentaur]

That depends on the wheels' radii, doesn't it? A disk that is 100 times heavier than the lighter one has ten times the radius if it has the same thickness and density. That would make $I\propto mr^2$ 10,000 times larger - so the spinup phase would be something like 10,000 times longer.

That's a good point and it could be very relevant but details of the moment of inertia haven't been mentioned as it's an added level of calculation. You could make two wheels with the same effective radius and 100:1 ratio of masses. We sort of jumped in half way to this problem. In fact MI doesn't scale with different wheels because it could be very inconvenient to increase MI just by using a bigger radius. 100:1 is a pretty extreme example. 2:1 or even 10:1 ratio could just involve a thicker rim.
It's amazing how soon a practical problem requires serious Engineering considerations on top of any 'theory'. Engineering is all about the numbers and people try to get away with arm waving at their peril.