Flywheels in Machines (AQA A Level Physics): Revision Note

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

• 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 ($I=m{r}^2$) is preferred over a disc-shaped one ($I=\frac{1}{2}m{r}^2$)

Flywheel shapes: a uniform solid disc and a spoked wheel

• 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

Flywheels for production processes

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 and 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'

• 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)

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

    • using 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 $\rho$
    $M=\rho V=\pi R^{2}t\rho$
    

  • The moment of inertia about the axis of rotation for a disc is$I=\frac{1}{2}M{R}^2=\frac{1}{2}\left(\pi R^{2}t\rho \right)R^2=\frac{1}{2}\left(\pi t\rho \right)R^4$
    

  • The rotational kinetic energy is therefore
    $E_k=\frac{1}{2}I{\omega }^2$
    $E_k=\frac{1}{2}\left(\frac{1}{2}\left(\pi t\rho \right)R^4\right){\omega }^2$
    

  • Since $t$ and $\rho$ are constant
    $E_k\propto R^4{\omega }^2$

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