A flywheel is
a mechanical device specifically designed to efficiently store rotational energy. Flywheels resist changes in rotational speed by
their moment of inertia. The amount of energy stored in a
flywheel is proportional to the square of its rotational speed. The way to change a flywheel's stored energy is by
increasing or decreasing its rotational speed applying a torque aligned with its axis of symmetry,
Common uses of a flywheel include:
·
Smoothing
the power output of an energy source. For example, flywheels are used in reciprocating
engines because
the active torque from the individual pistons is intermittent.
·
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.
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. 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).
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 than traditional lithium ion batteries.
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 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)
PHYSICS
A
flywheel with variable moment of inertia, conceived by Leonardo da vinci.
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 :
where:
·
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
·
for
a thin-walled empty cylinder is
,
,
·
and
for a thick-walled empty cylinder is
where m denotes mass, and 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.
where:
·
is
the tensile stress on the rim of the cylinder
·
is
the density of the cylinder
·
is
the radius of the cylinder, and
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, and GFRP
stands for glass-fiber reinforced polymer.
|
Material
|
Specific tensile strength
|
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
|
The
table below shows calculated values for mass, radius, and angular velocity for
storing 500 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.
|
Material
|
Energy storage (J)
|
Mass (kg)
|
Radius (m)
|
Angular velocity (rpm)
|
Efficiency (J/kg)
|
Energy density (kWh/kg)
|
|
Cast Iron
|
500
|
0.0166
|
1.039
|
1465
|
30121
|
0.0084
|
|
Aluminum Alloy
|
500
|
0.0033
|
1.528
|
2406
|
151515
|
0.0421
|
|
Maraging steel
|
500
|
0.0044
|
1.444
|
2218
|
113636
|
0.0316
|
|
Composite: CFRP (40% epoxy)
|
500
|
0.001
|
1.964
|
3382
|
500000
|
0.1389
|
|
Composite: GFRP (40% epoxy
|
500
|
0.0038
|
1.491
|
2323
|
0.0365
|
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) |
Energy density (kWh/kg)
|
|
Small battery
|
0.5
|
100
|
60
|
20,000
|
9.8
|
2.7
|
0.027
|
|
Regenerative braking in trains
|
0.5
|
3000
|
50
|
8,000
|
33.0
|
9.1
|
0.003
|
|
0.5
|
600
|
50
|
30,000
|
92.0
|
26.0
|
0.043
|
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 to the material density and to the mass.
·
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
WORKING