Flywheel design principles, primarily the wheel on the end of the crankshaft that gives the crankshaft momentum to carry the pistons through the compression stroke.

Normally constructed from a heavy steel or iron disc.

A flywheel has two main functions:

- Moderating speed fluctuations in an engine through its inertia. Any sudden increase due to fuelling changes or load on the system will be evened out.
- Energy storage medium, as an alternative to the chemical battery.

### Angular Acceleration

The angular acceleration of a flywheel is:

where

α = angular acceleration in [rad s^{-2}]

ω_{1,2} = angular velocity at time 1 and 2 [rad s^{-1}]

t = time between 1 and 2 [s]

### Angular Velocity

The angular velocity of a flywheel is:

where

ω = angular velocity [rad s^{-1}]

N_{rpm} = rotational speed of the flywheel [revolutions per minute]

### Coefficient of Fluctuation of Energy

This is defined as the maximum fluctuation of energy to the work done per cycle.

Six Cylinder 4-stroke gas engine | 0.031 |

Four cylinder 4-stroke gas engine | 0.066 |

Cross-compound steam engine | 0.096 |

Single cylinder double acting steam engine | 0.21 |

Single cylinder 4-stroke gas engine | 1.93 |

*Coefficient of Fluctuation of Energy*

### Coefficient of Fluctuation of Speed

The ratio of the maximum fluctuation of speed (maximum speed – minimum speed) to the mean speed.

Hammering machines | 0.2 |

Spinning machinery | 0.1 to 0.02 |

Pumping machines | 0.03 to 0.05 |

Direct drive electric machines | 0.002 |

*Coefficient of Fluctuation of Speed*

### Energy Stored

The energy stored in a flywheel is:

where

E = energy stored [J]

I = moment of inertia of the flywheel [kgm^{2}]

ω = angular velocity of the flywheel [rad s^{-1}]

If the flywheel is attached to an engine then the **energy from the engine per revolution** is given as:

where

E_{engine} = energy from engine per revolution [J]

P = engine power [W]

N_{rpm} = engine rotational speed [revolutions per minute]

### Geared Flywheel

The original gearing was done to overcome patent issues: **1781:** **Sun and planet gear** – invented by Boulton and Watt to circumvent the crank patent as they adamantly opposed cross-licensing their condenser technology. Part of the engine development timeline.

- gear noise is significant
- torque reversals as flywheel absorbs energy and then puts that energy back into moving the crank at a later point in the cycle

- gears contribute to the inertia
- gears need to be substantial
- balance between being strong enough and minimising losses – tooth to tooth shear

- flywheel runs at a higher speed
- hence more windage losses
- more structural considerations

### Maximum Fluctuation of Speed

Difference between maximum and minimum speeds during a cycle.

The fundamental flywheel design principles are around the inertia that is required to store energy, for an engine this is energy required to continue the rotation between firing strokes, and the minimal inertia that will then allow the engine to rev freely.

#### References

- “Theory and Design of Automotive Engines”, B Dinesh Prabhu, Assistant Professor, P E S College of Engineering, Mandya, KARNATAKA

Machining a flywheel is actually quite easy with a rotary table and some simple steps.

This particular flywheel is made from cast iron, but mild steel, brass, aluminium are all ok.

Proportions are also really important.

The flywheel for the Burrell traction engine took a couple of goes to get it to the right proportions. The original flywheel was too heavy looking at the rim.

I improved the flywheel with a chamfer and curved outer surface. This allowed the weight of the rim to be kept whilst giving a slimmer appearance.