TheInfoList

A flywheel is a mechanical device which uses the conservation of
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a close ...
to store
rotational energyRotational energy or angular kinetic energy is kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body o ...
; a form of kinetic energy proportional to the product of its
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational ax ...

and the square of its
rotational speed Rotational speed (also known as speed of revolution or rate of rotation), of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute Revolutions per minute (abbreviated rpm ...
. In particular, if we assume the flywheel's moment of inertia to be constant (i.e., a flywheel with fixed mass and
second moment of area The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area Area is the quantity that expresses the extent of a two-dimensional region, ...
revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed.. Since a flywheel serves to store mechanical energy for later use, it is natural to consider it as a
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body of a given mass from rest to its stated velocity. Having gaine ...
analogue of an . Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of an accumulator. As with other types of accumulators, a flywheel inherently smoothes sufficiently small deviations in the power output of a system, thereby effectively playing the role of a
low-pass filter A low-pass filter (LPF) is a filter that passes signals with a frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial freq ...

with respect to the mechanical velocity (angular, or otherwise) of the system. More precisely, a flywheel's stored energy will donate a surge in power output upon a drop in power input and will conversely absorb any excess power input (system-generated power) in the form of rotational energy. Common uses of a flywheel include: * Smoothing the power output of an energy source. For example, flywheels are used in
reciprocating engine , internal combustion, gasoline engine, gasoline piston engine. A reciprocating engine, also often known as a piston engine, is typically a heat engine (although there are also pneumatic motor, pneumatic and hydraulic motor, hydraulic reciprocatin ...
s because the active torque from the individual pistons is intermittent. * Energy storage systems * Delivering energy at rates beyond the ability of an energy source. This is achieved by collecting energy in a flywheel over time and then releasing it quickly, at rates that exceed the abilities of the energy source. * Controlling the orientation of a mechanical system,
gyroscope A gyroscope (from Ancient Greek γῦρος ''gûros'', "circle" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining Orientation (geometry), orientation and angular velocity. It is a spinning wheel or disc in ...

and
reaction wheel A reaction wheel (RW) is a type of flywheel used primarily by spacecraft for three-axis attitude control, which does not require Rocket engine, rockets or external applicators of torque. They provide a high pointing accuracy, and are particularly u ...
Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a maximum revolution rate of a few thousand RPM.; "Flywheels move from steam age technology to Formula 1"; Jon Stewart , 1 July 2012, retrieved 2012-07-03 High energy density flywheels can be made of carbon fiber composites and employ
magnetic bearing A magnetic bearing is a type of bearing that supports a load using magnetic levitation. Magnetic bearings support moving parts without physical contact. For instance, they are able to levitate a rotating shaft and permit relative motion with ver ...

s, enabling them to revolve at speeds up to 60,000 RPM (1 kHz)., "Breakthrough in Ricardo Kinergy ‘second generation’ high-speed flywheel technology"; Press release date: 22 August 2011. retrieved 2012-07-03

# Applications

Flywheels are often used to provide continuous power output in systems where the energy source is not continuous. For example, a flywheel is used to smooth fast angular velocity fluctuations of the
crankshaft A crankshaft is a shaft Shaft may refer to: Rotating machine elements * Shaft (mechanical engineering), a rotating machine element used to transmit power * Line shaft, a power transmission system * Drive shaft, a shaft for transferring torque ...

in a reciprocating engine. In this case, a crankshaft flywheel stores energy when torque is exerted on it by a firing
piston A piston is a component of reciprocating engine , internal combustion piston engine. A reciprocating engine, also often known as a piston engine, is typically a heat engine (although there are also pneumatic Pneumatics (from Greek ‘wind, ...

, and returns it to the piston to compress a fresh charge of air and fuel. Another example is the
friction motor A friction motor is a simple mechanism to propel toy cars, trucks, trains, action figures and similar toys. The motor consists of a large flywheel which is connected to the drive wheels of the toy via a very low gear ratio, so that the flywheel revo ...

which powers devices such as
toy car A model vehicle or toy vehicle is a Physical model, miniature representation of an automobile. Other miniature motor vehicles, such as trucks, buses, or even ATVs, etc. are often included in this general category. Because many miniature vehicles ...

s. In unstressed and inexpensive cases, to save on cost, the bulk of the mass of the flywheel is toward the rim of the wheel. Pushing the mass away from the axis of rotation heightens
rotational inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), kn ...
for a given total mass. A flywheel may also be used to supply intermittent pulses of energy at power levels that exceed the abilities of its energy source. This is achieved by accumulating energy in the flywheel over a period of time, at a rate that is compatible with the energy source, and then releasing energy at a much higher rate over a relatively short time when it is needed. For example, flywheels are used in
power hammer Power hammers are mechanical forging hammers that use a non-muscular power source to raise the hammer preparatory to striking, and accelerate it onto the work being hammered. Also called "Open Die Power Forging Hammers." They have been used by ...
s and
riveting machines A rivet is a permanent mechanical fastener. Before being installed, a rivet consists of a smooth cylinder (geometry), cylindrical shaft with a head on one end. The end opposite to the head is called the ''tail''. On installation, the rivet is ...
. Flywheels can be used to control direction and oppose unwanted motions. Flywheels in this context have a wide range of applications from
gyroscope A gyroscope (from Ancient Greek γῦρος ''gûros'', "circle" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining Orientation (geometry), orientation and angular velocity. It is a spinning wheel or disc in ...

s for instrumentation to
ship stability ''Ship stability'' is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on centers of gravity, centers of buoyancy, t ...

and satellite stabilization (
reaction wheel A reaction wheel (RW) is a type of flywheel used primarily by spacecraft for three-axis attitude control, which does not require Rocket engine, rockets or external applicators of torque. They provide a high pointing accuracy, and are particularly u ...
), to keep a toy spin spinning (
friction motor A friction motor is a simple mechanism to propel toy cars, trucks, trains, action figures and similar toys. The motor consists of a large flywheel which is connected to the drive wheels of the toy via a very low gear ratio, so that the flywheel revo ...

), to stabilize magnetically levitated objects (
Spin-stabilized magnetic levitationImage:Levitron-levitating-top-demonstrating-Roy-M-Harrigans-spin-stabilized-magnetic-levitation.ogg, 300px, A brief demonstration and small explanation about the ''Levitron'' branded levitating top device which demonstrates the spin-stabilized magnet ...
) Flywheels may also be used as an electric compensator, like a synchronous compensator, that can either produce or sink reactive power but would not affect the real power. The purposes for that application are to improve the power factor of the system or adjust the grid voltage. Typically, the flywheels used in this field are similar in structure and installation as the synchronous motor (but it is called synchronous compensator or synchronous condenser in this context). There are also some other kinds of compensator using flywheels, like the single phase induction machine. But the basic ideas here are the same, the flywheels are controlled to spin exactly at the frequency which you want to compensate. For a synchronous compensator, you also need to keep the voltage of rotor and stator in phase, which is the same as keeping the magnetic field of rotor and the total magnetic field in phase (in the rotating frame reference).

# History

The principle of the flywheel is found in the
Neolithic The Neolithic period is the final division of the Stone Age, with a wide-ranging set of developments that appear to have arisen independently in several parts of the world. It is first seen about 12,000 years ago when the first developments of ...
spindle and the
potter's wheel , Germany ) , image_map = , map_caption = , map_width = 250px , capital = Berlin , coordinates = , largest_city = capital , languages_type = Official language , languages = German language, German , demonym = Germans, German , ...

, as well as circular sharpening stones in antiquity.Lynn White, Jr., "Theophilus Redivivus", ''Technology and Culture'', Vol. 5, No. 2. (Spring, 1964), Review, pp. 224–233 (233) In early 11th century
Ibn Bassal Ibn Bassal ( ar, ابن بصال) was an 11th-century Andalusian Arab The Arabs (singular Arab ; singular ar, عَرَبِيٌّ, ISO 233 The international standard are technical standards developed by international organizations (intergover ...
pioneered the used on flywheel in noria and saqiya. The use of the flywheel as a general mechanical device to equalize the speed of rotation is, according to the American medievalist
Lynn White Lynn Townsend White Jr. (April 29, 1907 – March 30, 1987) was an American historian. He was a professor of medieval In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organiza ...
, recorded in the ''De diversibus artibus'' (On various arts) of the German artisan
Theophilus Presbyter Theophilus Presbyter (Floruit, fl. c. 1070–1125) is the pseudonymous author or compiler of a Latin text containing detailed descriptions of various Middle Ages, medieval arts, a text commonly known as the ''Schedula diversarum artium'' ("List of v ...
(ca. 1070–1125) who records applying the device in several of his machines. In the
Industrial Revolution The Industrial Revolution was the transition to new manufacturing processes in Great Britain, continental Europe Mainland or continental Europe is the contiguous continent of Europe, excluding its surrounding islands. It can also be ...
,
James Watt James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) was a Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-European langu ...

contributed to the development of the flywheel in the
steam engine from Stott Park Bobbin Mill, Cumbria, England A steam engine is a heat engine In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energ ...

, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating motion into rotary motion.

# Physics

A flywheel is a spinning wheel, or disc, or rotor, rotating around its symmetry axis. Energy is stored as
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body of a given mass from rest to its stated velocity. Having gaine ...
, more specifically
rotational energyRotational energy or angular kinetic energy is kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body o ...
, of the
rotor ROTOR was an elaborate air defence radar Radar is a detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft An aircraft is a vehicle that is able to flight, fly ...
: * $E_k = \frac I \omega^2$ where: * $E_k$ is the stored
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body of a given mass from rest to its stated velocity. Having gaine ...
, * ω is the
angular velocity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. " ...

, and * $I$ is the
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational ax ...

of the flywheel about its axis of symmetry. The moment of inertia is a measure of resistance to
torque In physics and mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Dis ...

applied on a spinning object (i.e. the higher the moment of inertia, the slower it will accelerate when a given torque is applied). * The moment of inertia for a solid cylinder is $I = \frac mr^2$, * for a thin-walled empty cylinder is $I = m r^2$, * and for a thick-walled empty cylinder is $I = \frac m\left(^2 + ^2\right)$, where $m$ denotes mass, and $r$ denotes a radius. When calculating with units, the units would be for mass,
kilograms The kilogram (also kilogramme) is the SI base unit, base unit of mass in the International System of Units (SI), the metric system, having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is oft ...
; for radius, metres; and for angular velocity,
radian The radian, denoted by the symbol \text, is the SI unit for measuring angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''sides'' of the angle, sharing a common endpoint, called the ''verte ...

s per
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession ...
and the resulting energy would be in
joule The joule ( ; symbol: J) is a derived unit of energy In physics, energy is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to a physical body, body or physical system to perform W ...

s. Increasing amounts of rotation energy can be stored in the flywheel until the rotor shatters. This happens when the
hoop stress In mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Displacement (vecto ...
within the rotor exceeds the
ultimate tensile strength Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or F_\text within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle tensil ...
of the rotor material. * $\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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. " ...

of the cylinder. A flywheel powered by electric machine is common. The output power of the electric machine is approximately equal to the output power of the flywheel. The output power of a synchronous machine is: $P=\left(V_i\right)\left(V_t\right)\left \left( \frac\right \right)$ where: * $V_i$ is the voltage of rotor winding, which is produced by field interacting with the stator winding * $V_t$ is stator voltage * $\delta$ is the torque angle (angle between two voltages)

# Material selection

Flywheels are made from many different materials; the application determines the choice of material. Small flywheels made of lead are found in children's toys. Cast iron flywheels are used in old steam engines. Flywheels used in car engines are made of cast or nodular iron, steel or aluminum. Flywheels made from high-strength steel or composites have been proposed for use in vehicle energy storage and braking systems. The efficiency of a flywheel is determined by the maximum amount of energy it can store per unit weight. As the flywheel's rotational speed or angular velocity is increased, the stored energy increases; however, the stresses also increase. If the hoop stress surpass the tensile strength of the material, the flywheel will break apart. Thus, the tensile strength limits the amount of energy that a flywheel can store. In this context, using lead for a flywheel in a child's toy is not efficient; however, the flywheel velocity never approaches its burst velocity because the limit in this case is the pulling-power of the child. In other applications, such as an automobile, the flywheel operates at a specified angular velocity and is constrained by the space it must fit in, so the goal is to maximize the stored energy per unit volume. The material selection therefore depends on the application. The table below contains calculated values for materials and comments on their viability for flywheel applications. CFRP stands for
carbon-fiber-reinforced polymer Carbon fiber reinforced polymer (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Curr ...
, and GFRP stands for glass-fiber reinforced polymer. The table below shows calculated values for mass, radius, and angular velocity for storing 250 J. The carbon-fiber flywheel is by far the most efficient; however, it also has the largest radius. In applications (like in an automobile) where the volume is constrained, a carbon-fiber flywheel might not be the best option.

# Table of energy storage traits

For comparison, the energy density of petrol (gasoline) is 44.4 MJ/kg or 12.3 kWh/kg.

## High-energy materials

For a given flywheel design, the kinetic energy is proportional to the ratio of the
hoop stress In mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Displacement (vecto ...
to the material density and to the mass: * $E_k \varpropto \fracm$ $\frac$ 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 Carbon fiber reinforced polymer (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Curr ...

is a material of interest. For a given design the stored energy is proportional to the hoop stress and the volume: it is true. * $E_k \varpropto \sigma_tV$

# Design

## Rimmed

A rimmed flywheel has a rim, a hub, and spokes. Calculation of the flywheel's moment of inertia 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 majority from the rim, so that $I_\mathrm=KI_\mathrm$ 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: * $I_\mathrm=M_\mathrmR^2$

## Shaftless

A shaftless flywheel eliminates the annulus holes, shaft or hub. It has higher energy density than conventional design but requires a specialized magnetic bearing and control system. The specific energy of a flywheel is determined by * $\frac = K \frac$ In which $K$ is the shape factor, $\sigma$ the material's tensile strength and $\rho$ the density. A typical flywheel has a shape factor of 0.3. Better designs, such as the shaftless flywheel, have a shape factor close to 0.6, the theoretical limit is about 1.

## Superflywheel

The first superflywheel was patented in 1964 by the Soviet-Russian scientist Nurbei Guilia. A superflywheel consist of a solid core (hub) and multiple thin layers of high-strength flexible materials, such as special steels, carbon fiber composites, glass fiber, or graphene, wound around it. Compared to conventional flywheels, superflywheels can store more energy and are safer to operate In case of failure, superflywheel does not explode or burst into large shards, like a regular flywheel, but instead splits into layers. The separated layers then slow a superflywheel down by sliding against the inner walls of the enclosure, thus preventing any further destruction. Although the exact value of energy density of a superflywheel would depend on the material used, it could theoretically be as high as 1200 Wh (4.4 MJ) per kg of mass for graphene superflywheels.

*
Dual-mass flywheel A dual-mass flywheel (DMF or DMFW) is a rotating mechanical device that is used to provide continuous energy (rotational energyRotational energy or angular kinetic energy is kinetic energy In physics, the kinetic energy of an object is the ene ...
*
Flywheel energy storage Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel's rotational speed is reduced as a co ...
*
Accumulator (energy)An accumulator is an energy storage Energy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an Accumulat ...
*
Diesel rotary uninterruptible power supply Most forms of uninterruptible power supply (UPS) can be either powered by battery (electricity), battery or flywheel energy. These are ready for immediate use at the instant that the mains electricity fails, but the relatively small and finite amou ...
*
List of moments of inertia Moment of inertia, denoted by , measures the extent to which an object resists rotational acceleration about a Rotation around a fixed axis, particular axis, and is the rotational analogue to mass (which determines an object's resistance to Linear a ...
*
Clutch Single dry-clutch friction disc. The splined hub is attached to the disc with springs to damp chatter. A clutch is a mechanical device that engages and disengages power transmission Transmission may refer to: Science and technology * Power ...

*
Fidget Spinner A fidget spinner is a skill toy, toy that consists of a bearing (mechanical), ball bearing in the center of a multi-lobed (typically two or three) flat structure made from metal or plastic designed to spin along its axis with very little effort. F ...

# References

* * * https://pserc.wisc.edu/documents/general_information/presentations/presentations_by_pserc_university_members/heydt_synchronous_mach_sep03.pdf