alansimpson
Mechanical
Know where I could get information on flywheel energy storage devices?
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Flywheel Energy Storage devices
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...although it may help to be more specific when you search, since every (working) flywheel is an energy storage device.
Shigley discusses an example in his first metric edition book, Mechanical Engineering Design, 1986. I don't know if it is still in his later editions.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
On flywheels as an energy storage device, despite what common sense might tell you, the lighter the material used, the more energy you can store in rotation (square-cube law) Also, needs some fantastic bearing technology and balancing due to the high rotational speeds (energy stored varies as the square of rotational speed) Some city buses run in Europe on composite flywheels that are speeded up overnight using cheap-rate base-load electricity from nuclear power stations.
Yates said "On flywheels as an energy storage device, despite what common sense might tell you, the lighter the material used, the more energy you can store in rotation (square-cube law)"
Could you expand on that please? My common sense is shouting so loud I can't hear anything else!
Could you expand on that please? My common sense is shouting so loud I can't hear anything else!
...you want a large radius to get a high ratio of (stored energy)
flywheel mass), but I don't see where reducing mass will help.
If your flywheel was a ring with all the mass at a single radius, the ratio of stored energy to radial "burst" force is proportional to radius, but density cancels out...
flywheel mass), but I don't see where reducing mass will help.If your flywheel was a ring with all the mass at a single radius, the ratio of stored energy to radial "burst" force is proportional to radius, but density cancels out...
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alansimpson
Mechanical
ATTACHED LINK GIVES A REASONABLE EXPLINATION:
I assume you're referring to the following text from the linked page (sentence numbers are mine):
In order to optimize the energy-to-mass ratio, the flywheel needs to spin at the maximum possible speed1. This is because kinetic energy only increases linearly with Mass but goes as the square of the rotational speed2. Rapidly rotating objects are subject to centrifugal forces that can rip them apart3. Centrifugal force for a rotating object goes as M*R*w24. Thus while dense material can store more energy it is also subject to higher centrifugal force and thus fails at lower rotational speeds than low density material5. Therefore the tensile strenght is more important than the density of the material6.
1 and 2Right, rotational KE is Jw^2/2, where J is the polar mass moment of inertia about the rotational axis, and w is the rotational velocity. For a flywheel composed of a pair of opposed point masses at radius r from the axis, connected by a massless thread, J=2mr^2 (where m is the mass of each point mass). Substitution gives KE=(2m)(r^2)(w^2)/2. KE increases with the square of rotational velocity and linearly with mass. This is true even for geometries other than the ulta-simple case considered- as long as the mass distribution w/re the axis doesn't change, J increases linearly w/mass, and thus KE does.
3 yeah, yeah...
4 yes, for a point-mass rotating about an axis, the outward radial force on the point mass is m*r*w2. If you had the flywheel described above, the tension in the thread would be (m)(r)(w^2).
5 this is not demonstrated by the hand waving above. If we look at the ratio of KE to radial force for the opposed pair of point masses, we get the following:
KE/F = (m)(r^2)(w^2)/[(m)(r)(w^2)] = r. Regardless of the material density (mass of point masses), the ratio of KE to F is constant for fixed r. Thus if you wanted to use a more dense material (assuming you increase mass) with the same tensile strength as your less-dense material, you could spin the flywheel more slowly and store the same amount of energy without rupturing.
6 the author is apparently not saying "the density should be lower."
In order to optimize the energy-to-mass ratio, the flywheel needs to spin at the maximum possible speed1. This is because kinetic energy only increases linearly with Mass but goes as the square of the rotational speed2. Rapidly rotating objects are subject to centrifugal forces that can rip them apart3. Centrifugal force for a rotating object goes as M*R*w24. Thus while dense material can store more energy it is also subject to higher centrifugal force and thus fails at lower rotational speeds than low density material5. Therefore the tensile strenght is more important than the density of the material6.
1 and 2Right, rotational KE is Jw^2/2, where J is the polar mass moment of inertia about the rotational axis, and w is the rotational velocity. For a flywheel composed of a pair of opposed point masses at radius r from the axis, connected by a massless thread, J=2mr^2 (where m is the mass of each point mass). Substitution gives KE=(2m)(r^2)(w^2)/2. KE increases with the square of rotational velocity and linearly with mass. This is true even for geometries other than the ulta-simple case considered- as long as the mass distribution w/re the axis doesn't change, J increases linearly w/mass, and thus KE does.
3 yeah, yeah...
4 yes, for a point-mass rotating about an axis, the outward radial force on the point mass is m*r*w2. If you had the flywheel described above, the tension in the thread would be (m)(r)(w^2).
5 this is not demonstrated by the hand waving above. If we look at the ratio of KE to radial force for the opposed pair of point masses, we get the following:
KE/F = (m)(r^2)(w^2)/[(m)(r)(w^2)] = r. Regardless of the material density (mass of point masses), the ratio of KE to F is constant for fixed r. Thus if you wanted to use a more dense material (assuming you increase mass) with the same tensile strength as your less-dense material, you could spin the flywheel more slowly and store the same amount of energy without rupturing.
6 the author is apparently not saying "the density should be lower."
Fly wheel mass (wieght) is a critical factor - lighter materials (eg alloys) store less energy than steel or cast iron.
This can be calculated using the center of gravity of the cross section referenced to the distance away from axis of rotation & is proprtional to rotational speed (rev/min) & of course the specifc gravity of the material.
Bruce L Farrar.
Works Engineering Manager
Marshalls Mono PLC.Brookfoot Works.
Halifax W.Yorks UK
This can be calculated using the center of gravity of the cross section referenced to the distance away from axis of rotation & is proprtional to rotational speed (rev/min) & of course the specifc gravity of the material.
Bruce L Farrar.
Works Engineering Manager
Marshalls Mono PLC.Brookfoot Works.
Halifax W.Yorks UK
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