Flywheel

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Trevithick's 1802 steam locomotive, which used a flywheel to evenly distribute the power of its single cylinder Thinktank Birmingham - Trevithick Locomotive(1).jpg
Trevithick's 1802 steam locomotive, which used a flywheel to evenly distribute the power of its single cylinder

A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, assuming the flywheel's moment of inertia is constant (i.e., a flywheel with fixed mass and second moment of area revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed.

Contents

Since a flywheel serves to store mechanical energy for later use, it is natural to consider it as a kinetic energy analogue of an electrical inductor. 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 smooths sufficiently small deviations in the power output of a system, thereby effectively playing the role of a low-pass filter 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 a power output in reciprocating engines, energy storage, delivering energy at higher rates than the source, controlling the orientation of a mechanical system using gyroscope and reaction wheel, etc. 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. [1] High energy density flywheels can be made of carbon fiber composites and employ magnetic bearings, enabling them to revolve at speeds up to 60,000 RPM (1  kHz). [2]

History

A flywheel with variable inertia, conceived by Leonardo da Vinci

The principle of the flywheel is found in the Neolithic spindle and the potter's wheel, as well as circular sharpening stones in antiquity. [3] In the early 11th century, Ibn Bassal pioneered the use of flywheel in noria and saqiyah. [4] The use of the flywheel as a general mechanical device to equalize 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. [3] [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 motion into rotary motion. [6]

Physics

A mass-produced flywheel Volin.jpg
A mass-produced flywheel

The kinetic energy (or more specifically rotational energy) stored by the flywheel's rotor can be calculated by . ω is the angular velocity, and is the moment of inertia of the flywheel about its axis of symmetry. The moment of inertia is a measure of resistance to torque 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 can be known by mass () and radius (). For a solid cylinder it is , for a thin-walled empty cylinder it is approximately Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\textstyle m r^2}, and for a thick-walled empty cylinder with constant density it is . [7]

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. The specific tensile strength of a flywheel can be defined as . 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.[ citation needed ]

An electric motor-powered flywheel is common in practice. The output power of the electric motor is approximately equal to the output power of the flywheel. It can be calculated by , where is the voltage of rotor winding, is stator voltage, and is the angle between two voltages. Increasing amounts of rotation energy can be stored in the flywheel until the rotor shatters. This happens when the hoop stress within the rotor exceeds the ultimate tensile strength of the rotor material. Tensile stress can be calculated by , where is the density of the cylinder, is the radius of the cylinder, and is the angular velocity of the cylinder.

Design

A rimmed flywheel has a rim, a hub, and spokes. [8] Calculation of the flywheel's moment of inertia can be more easily analysed by applying various simplifications. One method is to assume the spokes, shaft and hub have zero moments of inertia, and the flywheel's moment of inertia is from the rim alone. Another is to lump 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 . 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 (), the radius of rotation of the rim is equal to its mean radius and thus .[ citation needed ]

A shaftless flywheel eliminates the annulus holes, shaft or hub. It has higher energy density than conventional design [9] but requires a specialized magnetic bearing and control system. [10] The specific energy of a flywheel is determined by, in which is the shape factor, the material's tensile strength and the density.[ citation needed ] While a typical flywheel has a shape factor of 0.3, the shaftless flywheel has a shape factor close to 0.6, out of a theoretical limit of about 1. [11]

A superflywheel consists 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. [12] Compared to conventional flywheels, superflywheels can store more energy and are safer to operate. [13] In case of failure, a 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.[ citation needed ] The first superflywheel was patented in 1964 by the Soviet-Russian scientist Nurbei Guilia. [14] [15]

Materials

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.[ citation needed ] Cast iron flywheels are used in old steam engines. Flywheels used in car engines are made of cast or nodular iron, steel or aluminum. [16] 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. [17]

Applications

A Landini tractor with exposed flywheel Landini VL30(Italien)2.JPG
A Landini tractor with exposed flywheel

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 the fast angular velocity fluctuations of the crankshaft in a reciprocating engine. In this case, a crankshaft flywheel stores energy when torque is exerted on it by a firing piston and then returns that energy to the piston to compress a fresh charge of air and fuel. Another example is the friction motor which powers devices such as toy cars. 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 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 hammers and riveting machines.

Flywheels can be used to control direction and oppose unwanted motions. Flywheels in this context have a wide range of applications: gyroscopes for instrumentation, ship stability, satellite stabilization (reaction wheel), keeping a toy spin spinning (friction motor), stabilizing magnetically-levitated objects (Spin-stabilized magnetic levitation).

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).

See also

Related Research Articles

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In physics, angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it.

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:

<span class="mw-page-title-main">Kinetic energy</span> Energy of a moving physical body

In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.

<span class="mw-page-title-main">Precession</span> Periodic change in the direction of a rotation axis

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

In mechanics and physics, simple harmonic motion is a special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is described by a sinusoid which continues indefinitely.

<span class="mw-page-title-main">Torque</span> Turning force around an axis

In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force. It describes the rate of change of angular momentum that would be imparted to an isolated body.

<span class="mw-page-title-main">Moment of inertia</span> Scalar measure of the rotational inertia with respect to a fixed axis of rotation

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of 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 axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation by a given amount.

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In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass.

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<span class="mw-page-title-main">Rolling</span> Type of motion which combines translation and rotation with respect to a surface

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In classical mechanics, Poinsot's construction is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of the angular momentum, expressed with respect to an inertial laboratory frame. The angular velocity vector of the rigid rotor is not constant, but satisfies Euler's equations. The conservation of kinetic energy and angular momentum provide two constraints on the motion of .

<span class="mw-page-title-main">Flywheel energy storage</span> Method of storing energy

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 consequence of the principle of conservation of energy; adding energy to the system correspondingly results in an increase in the speed of the flywheel.

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A power system consists of a number of synchronous machines operating synchronously under all operating conditions. Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The angle between the two is known as the power angle, torque angle, or rotor angle. During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap magnetomotive force, creating relative motion. The equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine. The power exchange between the mechanical rotor and the electrical grid due to the rotor swing is called Inertial response.

References

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Further reading