Flywheel Storage System
Figure 1 : The basic layout of the simulation.
A company with extensive experience in wind farms approached SteornLab to provide simulation services in order to evaluate the use of flywheel storage systems as an energy storage solution for wind farms.
The background to the study was based on the issue that wind energy availability frequently does not coincide with the requirements of the electricity grid in terms of power needs. Therefore many possible solutions have been examined by the industry that would facilitate harnessing peak wind power and storing this energy until it is required by the grid.
The computer simulation carried out by SteornLab was centred around the possible design and weight of flywheels that could be supported by permanent magnets as an alternative to expensive active magnetic bearings or traditional bearings that would be subjected to high friction and therefore impose losses in the system.
The study compared various sizes of flywheel with a concentric ring bearing design to provide radial support within the flywheel system. By varying the size and weight of the flywheel in the simulation (and therefore the required performance for the magnetic bearings) various parameters could be established for its overall performance and suitability as a solution for wind energy storage.
The client company reviewed the SteornLab report and concluded that while further detailed analysis was required and a prototype system would need to be constructed, the performance of the system utilising permanent magnets with low friction traditional deep groove ball bearings was comparable to complicated and energy hungry active magnetic bearings.
The use of ring magnets to support a flywheel
A model of a ring magnet bearing was created in FLUX3D. The bearing consists of two sets of ring magnets vertically separated so that they do not affect each other. The inner magnets are rigidly attached to a rotating cylinder, while the outer magnets are fixed in position. The magnetisation of all magnets is in the axial direction. The parameters of the magnets are given in Table 1 below. When the magnets are aligned there are no forces involved. However the system is in an unstable equilibrium. If the inner magnets are displaced radially there will be a restoring force upon them. If they are displaced axially there will an increase in the axial force which will push the magnets further away from the aligned position. The magnet material was assigned to be NdFeB-grade N50M. This has a remanence of 1.43 T, and a relative permeability of 1.091043. The magnetic configuration is shown in figure 1.
| Description | Parameter | Value [mm] |
| Height of magnets | H1 | 20 |
| Inner radius of inner magnet | R11 | 40 |
| Outer radius of inner magnet | R12 | 60 |
| Inner radius of outer magnet | R21 | 64 |
| Outer radius of outer magnet | R22 | 84 |
| Magnetic gap | g | 4 |
| Vertical separation of bearings | Len | 200 |
Figure 1 : Dimensions of the magnets
Axial Displacement
The first simulation involved raising the inner magnets with respect to the outer magnets and calculating the axial force upon the inner magnets. The result is shown in figure 2. The force is in the same direction as the displacement. This data can be used to calculate the weight that the bearing could support at any given displacement.
Figure 2 : The axial force on the inner magnets versus the axial displacement of the magnet. Click to expand.
It is envisaged that the weight of the model flywheel would be 200kg, hence the required force needed to support the flywheel is 1,962N. A displacement of greater than 5mm would supply this force. Due to the positive slope of the force at this point it also meets the requirement to keep the system stable in the radial direction.
The plot of supportable weight versus the displacement is shown in figure 3. Because the resultant force on the flywheel in the vertical direction is unstable it would be necessary to use a mechanical pivot above the magnetic bearings. The vertical force on this pivot point would then be the difference between the upward axial magnetic force and the gravitational pull on the flywheel. For example from figure 2 if the vertical displacement of the magnets is set at 6mm, the upward force is 2165N, which means that the force on the pivot point is 203N, which is equivalent to a weight of 21kg. By setting the vertical height of the inner magnets closer to the 5mm limit, the resultant force on the pivot can be reduced to as low a level as required, provided that it remains positive.
Figure 3 : Supportable weight versus axial displacement
Radial Displacement
The second simulation involved moving the inner magnets radially with respect to the outer magnets and calculating the force upon the inner magnets. At the operating point of 5mm the restoring force as a function of the radial displacement is shown in figure 4. It is a linear function of the displacement, which means that the flywheel would execute Simple Harmonic Motion in the radial direction if it was displaced radially from its aligned position. The spring constant of the force is 1.14x105 Nm-1, hence with a mass of 200 kg the frequency of oscillation would be 3.8 Hz.
Figure 4 : The radial restoring force versus the radial displacement.
The radial displacement of the inner magnets also has the effect of changing the axial force. This effect is shown in figure 5.
Figure 5 : The axial force versus the radial displacement.
As the flywheel is oscillating in the radial direction the change in the axial force would mean a variation in the friction at the pivot point. The flywheel would not oscillate in the axial direction as its motion is constrained by the pivot.
Because the top of the flywheel shaft is in permanent contact with the pivot point, any lateral displacement of the magnets means that the flywheel is no longer aligned to the vertical axis. Figure 6 shows the radial restoring force caused by a radial displacement at the mid point of the magnets when the fixed pivot point is assigned to be 400mm above the magnet centre. The period of oscillation for the radial motion is reduced to 3.5 Hz compared to the lateral displacement case.
Figure 6 : The radial force versus the radial displacement with fixed pivot point.
Because the magnetic arrangement is symmetrical in the angular direction there is no torque on the flywheel due to the bearings. Even when the magnets are misaligned from their nominal radial position the torque is negligible.