11.1.10 Flywheels in Machines

• Flywheels are used in machines to act as an energy reservoir, by storing and supplying energy when required
• They consist of a heavy metal disc or wheel that can rotate rapidly and so has a large moment of inertia
• This means it has: 
  • a high mass
  • a large radius
• This means once they start spinning, it is difficult to make them stop
• An example is a treadle (pedal) sewing machine
  • This consists of a big flywheel, connected to a small wheel by a rope which drives the sewing machine
  • A pedal is pressed which causes the flywheel to rotate, and also rotates the smaller wheel which drives the machine
  • When the pedal is not pressed, the smaller wheel will still rotate for some time due to the energy stored in the flywheel
  • This is because the flywheel has stored the rotational energy, which it can now transfer for some time after there is no input. This is used extensively in machines to control energy transfers

Application of a flywheel in a treadle sewing machine

A flywheel is used in a treadle sewing machine to create motion, even when the pedal is not pressed

• Flywheels are primarily used in engines in vehicles where they accumulate and store energy
• As it spins, its input torque is converted into rotational kinetic energy which is stored in the flywheel
  • This is a result of resisting the changes to rotation
  • The greater the moment of inertia of the flywheel, the greater the energy stored
  • This means a hoop (wheel)-shaped flywheel () is preferred over a disc-shaped one ()

Flywheel shapes: a uniform solid disc and a spoked wheel

Neglecting the mass of the spokes and axle, a disc-shaped flywheel has a smaller moment of inertia than a wheel-shaped one

• These flywheels were often fitted in large Victorian steam engines used in pumping stations and textile mills
  • They had a huge rim fitted with spokes
  • This gave a greater moment of inertia than if the same mass had been used to create a solid disc flywheel of the same diameter

• A flywheel transfers just enough power to a wheel to overcome frictional torque as it rotates
• When power is needed to the rest of the engine, the flywheel can reduce its speed and transfer some power

Uses of Flywheels

• Flywheels are used to:
  • Smooth out fluctuations in rotational speed / torque / power (such as in vehicles)
  • Store rotational kinetic energy

Smoothing Torque & Speed

• Power in an engine is not produced continuously, only in the 'power stroke' or 'combustion' part of an engine cycle, so it is released in bursts
  • This causes an engine to produce a torque that fluctuates
• The torque makes the flywheel rotate, moving a vehicle forwards
• If the torque is uneven, it will cause a jerky motion and unwanted vibrations will occur. This is a waste of energy and uncomfortable for the passengers
• The flywheel added will speed up or slow down over a period of time because of its inertia and as a result, the sharp fluctuations in torque are 'smoothed'

Uses of a flywheel in a four-cylinder engine

Flywheels smooth out the rotation of a crankshaft in a four-cylinder car

• The greater the moment of inertia of the flywheel, the smaller the fluctuation in speed

Regenerative Braking in Vehicles

• In conventional braking (say, on a bike), the kinetic energy store of the vehicle is transferred as waste through to the thermal energy store
• Instead, when regenerative brakes are applied, a flywheel is engaged and will 'charge up' by using the energy lost by braking
  • When the vehicle needs to accelerate later, the energy stored by the flywheel is used to do this
• These systems are sometimes called 'KERS' (kinetic energy recovery systems)

Diagram of a regenerative braking system

A regenerative braking system uses a flywheel which charges up from the energy lost by braking

Production Processes

• An electric motor in industrial machines can be used along with a flywheel
• The motor is used to charge up the flywheel, which can then transfer short burst of energy (such as needing to connect two materials together in a riveting machine)
• This prevents the motor from stalling, and a less powerful motor can be used

Factors Affecting the Energy Storage Capacity

• The mass of the flywheel
  • Since the moment of inertia, I is directly proportional to the mass, m, as mass increases the moment of inertia also increases
  • The rotational kinetic energy is directly proportional to the moment of inertia, so this also increases
• The angular speed of the flywheel
  • The rotational kinetic energy is proportional to the square of the angular speed
  • If the angular speed increases, the rotational kinetic energy stored also increases
• Friction
  • Although they are very efficient, flywheels can still lose some stored energy as friction and air resistance between the wheels and its bearings
  • The friction can be reduced by:
    • Lubricating bearings
    • Using bearings made of superconductors, so the flywheel can levitate and have no contact
    • Use the flywheel in a vacuum or sealed container to reduce air resistance
• The shape of the flywheel
  • For a solid disc of radius R, thickness t, mass M and density

• • The moment of inertia about the axis of rotation for a disc is

• •   The rotational kinetic energy is therefore

• • Since t and ρ are constant

• • The rotational kinetic energy stored therefore depends on the moment of inertia, determined by the shape of the flywheel