Trevithick's 1802 steam locomotive, which used a flywheel to evenly distribute the power of its single cylinder
Aflywheel is a mechanical device that uses the conservation ofangular momentum to storerotational energy, a form of kinetic energy proportional to the product of itsmoment of inertia and the square of itsrotational speed. In particular, assuming the flywheel's moment of inertia is constant (i.e., a flywheel with fixed mass andsecond moment of area 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 akinetic energy analogue of anelectrical capacitor. Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of anaccumulator. 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 alow-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 inreciprocating engines,flywheel energy storage, delivering energy at higher rates than the source, and controlling the orientation of a mechanical system usinggyroscope andreaction wheel. Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a maximum revolution rate of a few thousandRPM.[1] High energy density flywheels can be made of carbon fiber composites and employmagnetic bearings, enabling them to revolve at speeds up to 60,000 RPM (1 kHz).[2]
The principle of the flywheel is found in theNeolithicspindle and thepotter's wheel, as well as circular sharpening stones in antiquity.[3] In the early 11th century,Ibn Bassal pioneered the use of flywheel innoria andsaqiyah.[4] The use of the flywheel as a general mechanical device to equalize the speed of rotation is, according to the American medievalistLynn White, recorded in theDe diversibus artibus (On various arts) of the German artisanTheophilus Presbyter (ca. 1070–1125) who records applying the device in several of his machines.[3][5]
Thekinetic energy (or more specificallyrotational energy) stored by the flywheel'srotor can be calculated by. ω is theangular velocity, and is themoment of inertia of the flywheel about its axis of symmetry. The moment of inertia is a measure of resistance totorque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will accelerate when a given torque is applied). Themoment of inertia can be calculated for cylindrical shapes using mass () and radius (). For a solid cylinder it is, for a thin-walled empty cylinder it is approximately, 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 thehoop stress to the material density and to the mass. Thespecific 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 whycarbon 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 ofrotor winding, isstator 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 thehoop stress within the rotor exceeds theultimate 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 theangular velocity of the cylinder.
Arimmed flywheel has arim, a hub, andspokes.[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 tolump moments of inertia of spokes, hub and shaft into the rim. These 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]
Ashaftless 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]
Asuperflywheel 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 scientistNurbei Guilia.[14][15]
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]
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 thecrankshaft in a reciprocating engine. In this case, a crankshaft flywheel stores energy when torque is exerted on it by a firingpiston and then returns that energy to the piston to compress a fresh charge of air and fuel. Another example is thefriction motor which powers devices such astoy 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 heightensrotational 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 inpower hammers andriveting 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 asynchronous 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, the voltage of rotor and stator also must be kept in phase, which is the same as keeping the magnetic field of rotor and the total magnetic field in phase (in therotating frame reference).
^abLynn White, Jr., "Theophilus Redivivus",Technology and Culture, Vol. 5, No. 2. (Spring, 1964), Review, pp. 224–233 (233)
^Letcher, Trevor M. (2017).Wind energy engineering: a handbook for onshore and offshore wind turbines.Academic Press. pp. 127–143.ISBN978-0128094518.Ibn Bassal (AD 1038–75) of Al Andalus (Andalusia) pioneered the use of a flywheel mechanism in the noria and saqiya to smooth out the delivery of power from the driving device to the driven machine
^Lynn White, Jr., "Medieval Engineering and the Sociology of Knowledge",The Pacific Historical Review, Vol. 44, No. 1. (Feb., 1975), pp. 1–21 (6)
^Osbourne, Roger (2013).Iron, Steam & Money: The Making of the Industrial Revolution. Random House. p. 131.ISBN9781446483282.
^Li, Xiaojun; Palazzolo, Alan (2018-05-07). "Multi-Input–Multi-Output Control of a Utility-Scale, Shaftless Energy Storage Flywheel With a Five-Degrees-of-Freedom Combination Magnetic Bearing".Journal of Dynamic Systems, Measurement, and Control.140 (10): 101008.doi:10.1115/1.4039857.ISSN0022-0434.
Weissbach, R. S.; Karady, G.G.; Farmer, R. G. (April 2001). "A combined uninterruptible power supply and dynamic voltage compensator using a flywheel energy storage system".IEEE Transactions on Power Delivery.16 (2):265–270.doi:10.1109/61.915493.ISSN0885-8977.
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