First, let's define the inner radius, outer radius, and thickness of the flywheel.
Next, we'll define the mass density of the flywheel material and the Poisson's ratio. For this example, wheel assume the flywheel is made out of a steel alloy.
The final input is the angular velocity of the flywheel. To enter revolutions per minute in EngineeringPaper.xyz, [cycles/minute] is used. Note that the angular velocity needs to be multiplied by 1 [1/rad] to eliminate the radian units in the resulting energy values. For more details on representing angular velocity in EngineeringPaper.xyz, see the Torque and Shear Stress in a Power Transmission Shaft example sheet.
The energy stored in a ring shaped flywheel is provided by the following equation:
where I_m is the mass moment of inertia of the flywheel defined by:
and the mass of the flywheel is defined by:
=48.8324135525752kg
Now that everything is defined, we can query the energy value. We'll query it both in kJ and Wh so it can be more easily compared to the energy stored in a battery:
=134.358790968801kJ
=37.3218863802225Wh
Finally, it's important to check the stresses in the flywheel due to the centrifugal forces. The flywheel is of no use to us if it fractures during use. The tangential and radial components of stress can be expressed as functions of radius by the following equations [1]:
[1] Norton, R. L. "Machine design. A integrated approach, 5th Editi." (2013).
These stress values can be plotted versus radius:
Notice that the inner radius has 0[mm] added to it for the radial stress expression. This is needed since the expression for radial stress simplifies to exactly zero at the inner radius and the pressure units are lost. Adding 0[mm] prevents EngineeringPaper.xyz from simplifying the expression, thus preserving the pressure units.
It can be seen that the tangential stress dominates and is the greatest at the inner radius of the flywheel where the radial stress vanishes. Therefore, the peak stress in the flywheel can be expressed as:
=70.1954163087249MPa
This peak tangential stress value is the stress value that would need to be compared to the strength value of the flywheel material in order to determine the factor of safety for the flywheel.