Flywheel

For other uses, see Flywheel (disambiguation).

An industrial flywheel.

A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed. Energy is transferred to a flywheel by applying torque to it, thereby increasing its rotational speed, and hence its stored energy. Conversely, a flywheel releases stored energy by applying torque to a mechanical load, thereby decreasing the flywheel's rotational speed.

Common uses of a flywheel include:

Providing continuous energy when the energy source is discontinuous. For example, flywheels are used in reciprocating engines because the energy source, torque from the engine, is intermittent.
Delivering energy at rates beyond the ability of a continuous energy source. This is achieved by collecting energy in the flywheel over time and then releasing the energy quickly, at rates that exceed the abilities of the energy source.
Controlling the orientation of a mechanical system. In such applications, the angular momentum of a flywheel is purposely transferred to a load when energy is transferred to or from the flywheel.

Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a revolution rate of a few thousand RPM.^[1] Some modern flywheels are made of carbon fiber materials and employ magnetic bearings, enabling them to revolve at speeds up to 60,000 RPM.^[2]

Carbon-composite flywheel batteries have recently been manufactured and are proving to be viable in real-world tests on mainstream cars. Additionally, their disposal is more eco-friendly.^[3]

Applications

A Landini tractor with exposed flywheel.

Flywheels are often used to provide continuous energy in systems where the energy source is not continuous. In such cases, the flywheel stores energy when torque is applied by the energy source, and it releases stored energy when the energy source is not applying torque to it. For example, a flywheel is used to maintain constant angular velocity of the crankshaft in a reciprocating engine. In this case, the flywheel—which is mounted on the crankshaft—stores energy when torque is exerted on it by a firing piston, and it releases energy to its mechanical loads when no piston is exerting torque on it. Other examples of this are friction motors, which use flywheel energy to power devices such as toy cars.

Modern automobile engine flywheel

A flywheel may also be used to supply intermittent pulses of energy at transfer rates that exceed the abilities of its energy source, or when such pulses would disrupt the energy supply (e.g., public electric network). This is achieved by accumulating stored energy in the flywheel over a period of time, at a rate that is compatible with the energy source, and then releasing that energy at a much higher rate over a relatively short time. For example, flywheels are used in riveting machines to store energy from the motor and release it during the riveting operation.

The phenomenon of precession has to be considered when using flywheels in vehicles. A rotating flywheel responds to any momentum that tends to change the direction of its axis of rotation by a resulting precession rotation. A vehicle with a vertical-axis flywheel would experience a lateral momentum when passing the top of a hill or the bottom of a valley (roll momentum in response to a pitch change). Two counter-rotating flywheels may be needed to eliminate this effect. This effect is used in reaction wheels, a type of flywheel employed in satellites in which the flywheel is used to orient the satellite's instruments without thruster rockets.

History

The principle of the flywheel is found in the Neolithic spindle and the potter's wheel.^[4]

The flywheel as a general mechanical device for equalizing the speed of rotation is, according to the American medievalist Lynn White, recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter (ca. 1070–1125) who records applying the device in several of his machines.^[4]^[5]

In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating into rotary motion.

Physics

A flywheel with variable moment of inertia, conceived by Leonardo da Vinci.

A flywheel is a spinning wheel or disc with a fixed axle so that rotation is only about one axis. Energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

$E_k=\frac{1}{2} I \omega^2$

Where:

ω is the angular velocity, and
$I$ is the moment of inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to torque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will spin when a given force is applied).

The moment of inertia for a solid cylinder is $I = \frac{1}{2} mr^2$ ,
for a thin-walled empty cylinder is $I = m r^2$ ,
and for a thick-walled empty cylinder is $I = \frac{1}{2} m({r_\mathrm{external}}^2 + {r_\mathrm{internal}}^2)$ ,^[6]

Where m denotes mass, and r denotes a radius.

When calculating with SI units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second. The resulting answer would be in joules.

The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.

$\sigma_t = \rho r^2 \omega^2 \$

Where:

$\sigma_t$ is the tensile stress on the rim of the cylinder
$\rho$ is the density of the cylinder
$r$ is the radius of the cylinder, and
$\omega$ is the angular velocity of the cylinder.

This formula can also be simplified using specific tensile strength and tangent velocity:

$\frac{\sigma_t}{\rho} = v^2$

Where:

$\frac{\sigma_t}{\rho}$ is the specific tensile strength of the material
$v$ is the tangent velocity of the rim.

Table of energy storage traits

Flywheel purpose, type	Geometric shape factor (k) (unitless – varies with shape)	Mass (kg)	Diameter (cm)	Angular velocity (rpm)	Energy stored (MJ)	Energy stored (kWh)
Small battery	0.5	100	60	20,000	9.8	2.7
Regenerative braking in trains	0.5	3000	50	8,000	33.0	9.1
Electric power backup^[7]	0.5	600	50	30,000	92.0	26.0

^[8]^[9]^[10]^[11]

High-energy materials

For a given flywheel design, the kinetic energy is proportional to the ratio of the hoop stress to the material density and to the mass:

$E_k \varpropto \frac{\sigma_t}{\rho}m$

$\frac{\sigma_t}{\rho}$ could be called the specific tensile strength. The flywheel material with the highest specific tensile strength will yield the highest energy storage per unit mass. This is one reason why carbon fiber is a material of interest.

For a given design the stored energy is proportional to the hoop stress and the volume:

$E_k \varpropto \sigma_tV$

Rimmed

A rimmed flywheel has a rim, a hub, and spokes.^[12] The structure of a rimmed flywheel is complex and, consequently, it may be difficult to compute its exact moment of inertia. A rimmed flywheel can be more easily analysed by applying various simplifications. For example:

Assume the spokes, shaft and hub have zero moments of inertia, and the flywheel's moment of inertia is from the rim alone.
The lumped moments of inertia of spokes, hub and shaft may be estimated as a percentage of the flywheel's moment of inertia, with the remainder from the rim, so that $I_\mathrm{rim}=KI_\mathrm{flywheel}$

For example, if the moments of inertia of hub, spokes and shaft are deemed negligible, and the rim's thickness is very small compared to its mean radius ( $R$ ), the radius of rotation of the rim is equal to its mean radius and thus:

$I_\mathrm{rim}=M_\mathrm{rim}R^2$

References

↑ ; "Flywheels move from steam age technology to Formula 1"; Jon Stewart | 1 July 2012, retrieved 2012-07-03
↑ , "Breakthrough in Ricardo Kinergy ‘second generation’ high-speed flywheel technology"; Press release date: 22 August 2011. retrieved 2012-07-03
↑ http://www.popularmechanics.com/technology/engineering/news/10-tech-concepts-you-need-to-know-for-2012-2
↑ 4.0 4.1 Lynn White, Jr., "Theophilus Redivivus", Technology and Culture, Vol. 5, No. 2. (Spring, 1964), Review, pp. 224–233 (233)
↑ Lynn White, Jr., "Medieval Engineering and the Sociology of Knowledge", The Pacific Historical Review, Vol. 44, No. 1. (Feb., 1975), pp. 1–21 (6)
↑ (page 10, accessed 1 Dec 2011, Moment of inertia tutorial
↑ http://www.vyconenergy.com/pq/VDCtech.htm
↑ "Flywheel Energy Calculator". Botlanta.org. 2004-01-07. Retrieved 2010-11-30.
↑ "energy buffers". Home.hccnet.nl. Retrieved 2010-11-30.
↑ "Message from the Chair | Department of Physics | University of Prince Edward Island". Upei.ca. Retrieved 2010-11-30.
↑ "Density of Steel". Hypertextbook.com. 1998-01-20. Retrieved 2010-11-30.
↑ Flywheel Rotor And Containment Technology Development, FY83. Livermore, Calif: Lawrence Livermore National Laboratory , 1983. pp. 1–2

External links

Look up flywheel in Wiktionary, the free dictionary.

Wikimedia Commons has media related to Flywheels.

Flywheel batteries on Interesting Thing of the Day.

Automotive engine

Part of the Automobile series

Basic terminology	Bore Compression ratio Crank Cylinder Dead centre Diesel engine Dry sump Engine balance Engine configuration Engine displacement Engine knocking Firing order Hydrolock Petrol engine Power band Redline Spark-ignition engine Stroke Stroke ratio Wet sump

Main components	Connecting rod Crankcase Crankpin Crankshaft Crossflow cylinder head Crossplane Cylinder bank Cylinder block Cylinder head Flywheel Head gasket Hypereutectic piston Main bearing Piston Piston ring Reverse-flow cylinder head Starter ring gear Sump

Valvetrain	Cam Cam follower Camshaft Desmodromic valve Hydraulic tappet Multi-valve Overhead camshaft Overhead valve Pneumatic valve springs Poppet valve Pushrod Rocker arm Sleeve valve Tappet Timing belt Timing mark Valve float Variable valve timing

Aspiration	Air filter Blowoff valve Boost controller Butterfly valve Centrifugal-type supercharger Cold air intake Dump valve Electronic throttle control Forced induction Inlet manifold Intake Intercooler Manifold vacuum Naturally aspirated engine Ram-air intake Scroll-type supercharger Short ram air intake Supercharger Throttle Throttle body Turbocharger Twin-turbo Variable-geometry turbocharger Variable-length intake manifold Warm air intake

Fuel system	Carburetor Common rail Direct injection Fuel filter Fuel injection Fuel pump Fuel tank Gasoline direct injection Indirect injection Injection pump Lean burn Stratified charge engine Turbo fuel stratified injection Unit injector

Ignition	Contact breaker Magneto Distributor Electrical ballast High tension leads Ignition coil Spark plug Wasted spark

Electrics and engine management	Air–fuel ratio meter Alternator Automatic Performance Control Car battery (lead–acid battery) Crankshaft position sensor Dynamo Drive by wire Electronic control unit Engine control unit Engine coolant temperature sensor Glow plug Idle air control actuator MAP sensor Mass flow sensor Oxygen sensor Starter motor Throttle position sensor

Exhaust system	Automobile emissions control Catalytic converter Diesel particulate filter Exhaust manifold Glasspack Muffler

Engine cooling	Air cooling Antifreeze (ethylene glycol) Core plug Electric fan Fan belt Radiator Thermostat Water cooling Viscous fan (fan clutch)

Other components	Balance shaft Block heater Combustion chamber Cylinder head porting Gasket Motor oil Oil filter Oil pump Oil sludge PCV valve Seal Synthetic oil Underdrive pulleys

Portal Category

Flywheel

Applications

History

Physics

Table of energy storage traits

High-energy materials

Rimmed

See also

References

External links