Design of a Flywheel

Introduction

A flywheel is an inertial energy-storage device. It absorbs mechanical energy and serves as a reservoir, storing energy during the period when the supply of energy is more than the requirement and releases it during the period when the requirement of energy is more than the supply.

Functions and Operation

The main function of a fly wheel is to smooth en out variations in the speed of a shaft caused by torque fluctuations. Flywheel absorbs mechanical energy by increasing its angular velocity and delivers the stored energy by decreasing its velocity

Design Approach

There are two stages to the design of a flywheel.
First, the amount of energy required for the desired degree of smoothing must be found and the (mass) moment of inertia needed to absorb that energy determined.
Then flywheel geometry must be defined that caters the required moment of inertia in a reasonably sized package and is safe against failure at the designed speeds of operation.

Design Parameters 

•  Speed Fluctuation - This gives the range of speed
• Coefficient of speed fluctuation - This gives a dimension-less ratio which is a normalized form obtained by dividing range by average

Geometry of Flywheel
The geometry of a flywheel may be as simple as a cylindrical disc of solid material, or may be of spoked construction like conventional wheels with a hub and rim connected by spokes or arms Small fly wheels are solid discs of hollow circular cross section. As the energy requirements and size of the flywheel increases the geometry changes to disc of central hub and peripheral rim connected by webs and to hollow wheels with multiple arms.

The latter arrangement is a more efficient of material especially for large flywheels, as it concentrates the bulk of its mass in the rim which is at the largest radius. Mass at largest radius contributes much more since the mass moment of inertia is proportional to mr2.

Stresses in Flywheel
Flywheel being a rotating disc, centrifugal stresses acts upon its distributed mass and attempts to pull it apart. Its effect is similar to those caused by an internally pressurized cylinder.
Analogous to a thick cylinder under internal pressure the tangential and radial stress in a solid disc flywheel as a function of its radius r is given by:

The point of most interest is the inside radius where the stress is a maximum. What causes failure in a flywheel is typically the tangential stress at that point from where fracture originated and upon fracture fragments can explode resulting extremely dangerous consequences, Since the forces causing the stresses are a function of the rotational speed also, instead of checking for stresses, the maximum speed at which the stresses reach the critical value can be determined and safe operating speed can be calculated or specified based on a safety factor.