Flywheel

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 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 returns it 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.

Modern automobile engine flywheel

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, see gyroscope. Flywheels in this context have a wide range of applications from gyroscopes for instrumentation to ship stability and satellite stabilization (reaction wheel), to keep a toy spin spinning (friction motor), to stabilize 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).

The principle of the flywheel is found in the Neolithic spindle and the potter's wheel, as well as circular sharpening stones in antiquity.[4]

The mechanical flywheel, used to smooth out the delivery of power from a driving device to a driven machine and, essentially, to allow lifting water from far greater depths (up to 200 metres (660 ft)), was first employed by Ibn Bassal (fl. 1038–1075), of Al-Andalus.[5][6][7][8]

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.[4][9]

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.

A flywheel is a spinning wheel, or disc, or rotor, rotating around its symmetry axis. Energy is stored as kinetic energy, more specifically rotational energy, of the rotor:

• ${\displaystyle E_{k}={\frac {1}{2}}I\omega ^{2}}$

where:

• ${\displaystyle E_{k}}$ is the stored kinetic energy,
• ω is the angular velocity, and
• ${\displaystyle I}$ 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 for a solid cylinder is ${\displaystyle I={\frac {1}{2}}mr^{2}}$,
• for a thin-walled empty cylinder is ${\displaystyle I=mr^{2}}$,
• and for a thick-walled empty cylinder is ${\displaystyle I={\frac {1}{2}}m({r_{\mathrm {external} }}^{2}+{r_{\mathrm {internal} }}^{2})}$,[10]

where ${\displaystyle m}$ denotes mass, and ${\displaystyle r}$ denotes a radius.

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

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.

• ${\displaystyle \sigma _{t}=\rho r^{2}\omega ^{2}\ }$

where:

• ${\displaystyle \sigma _{t}}$ is the tensile stress on the rim of the cylinder
• ${\displaystyle \rho }$ is the density of the cylinder
• ${\displaystyle r}$ is the radius of the cylinder, and
• ${\displaystyle \omega }$ is the angular velocity 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:

${\displaystyle P=(V_{i})(V_{t})\left({\frac {\sin(\delta )}{X_{S}}}\right)}$

where:

• ${\displaystyle V_{i}}$is the voltage of rotor winding, which is produced by field interacting with the stator winding
• ${\displaystyle V_{t}}$is stator voltage
• ${\displaystyle \delta }$is the torque angle (angle between two voltages)

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.[11] 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.[12]

The table below contains calculated values for materials and comments on their viability for flywheel applications. CFRP stands for carbon-fiber-reinforced polymer, and GFRP stands for glass-fiber reinforced polymer.

Material	Specific tensile strength ${\displaystyle \left(\mathrm {\frac {kJ}{kg}} \right)}$	Comments
Ceramics	200–2000 (compression only)	Brittle and weak in tension, therefore eliminate
Composites: CFRP	200–500	The best performance—a good choice
Composites: GFRP	100–400	Almost as good as CFRP and cheaper
Beryllium	300	The best metal, but expensive, difficult to work with, and toxic to machine
High strength steel	100–200	Cheaper than Mg and Ti alloys
High strength Al alloys	100–200	Cheaper than Mg and Ti alloys
High strength Mg alloys	100–200	About equal performance to steel and Al-alloys
Ti alloys	100–200	About equal performance to steel and Al-alloys
Lead alloys	3	Very low
Cast Iron	8–10	Very low[13]

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.

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

• Dual-mass flywheel
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• Diesel rotary uninterruptible power supply
• List of moments of inertia
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• kBox
• Fidget Spinner

Look up flywheel in Wiktionary, the free dictionary.

• Media related to Flywheels at Wikimedia Commons
• Flywheel batteries on Interesting Thing of the Day.
• Flywheel-based microgrid stabilisation technology., ABB
• PowerStore