Investigating the Potential of Two Large Diameter Magnetic Bearings
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- Institutt for elkraftteknikk 
MAGNETIC bearings for large diameters and low rotational speeds are rarely developed and utilized due to poor competitive ability. They require little maintenance and offer high reliability, but until now mechanical bearings have outperformed them for slow rotating applications, only high speed applications have been able to justify the cost. With NdFeB magnets the quality of magnets has gone up and the cost down, making a new niche possible; large diameter ring bearings which can reduce the price and weight of the hub and bearing construction /: I (see chapter I). A literature study has been conducted to identify promising bearing technologies. One permanent magnet bearing, the PASF bearing, and one heteropolar self regulating electrodynamic bearing, the null flux bearing, were selected for further investigation /:II. PASF bearings are passive permanent magnet (PM) bearings employing change of magnetic reluctance to create force :/III. A. SLC is defined by Khoo et al. as the ratio between the maximum achievable force and the total self-weight of a magnetic bearing . They claim PASF bearings can achieve a SLC up to 450:1, ten times higher than conventional repulsive bearings. With this in mind, we have tried to make a simple PASF bearing with better performance than the RPMB described in . The bearings have been modelled in COMSOL and further evaluated in MATLAB /:VI. Results from the PASF computations showed an axial force shape of the PASF bearing very different from that of the RPMB. The axial force curve is steep in axial direction close to the center position:/ III. C. Axial force increases with radial displacement, as opposed to the RPMB. Stabilizing the PASF bearing might be difficult due to high radial stiffness /:VII. B. Axial PASF bearings work in both axial directions without tradeoffs between force and stiffness or concern of touching. It can be constructed to utilize the magnets in a range of the magnetization curve where they work at the maximum energy product  and where the risk of permanent demagnetization is minimal :/ III. C. Null flux coils are used in Maglev trains , and have also been utilized in flywheel bearings . When they are situated in a desired centre position the sum of magnetic flux through the closed coil loop will be zero, and the coil will neither exert force nor consume power. When displaced from this position there will be a net flux passing through the coil. Moving the coil gives an alternating flux which will induce currents, giving a restoring force /:IV. A. Hence, null flux bearings require speed to function. Forces were calculated based on equations for induced currents and forces on currents in magnetic fields, as is also done in  and /:IV. B. Two different drag force equations were found using two different methods. Identifying the right equation will later be done by measurements. Axial forces are proportional to axial displacement, while drag forces are proportional to the square of axial displacement. As a result of a trade off between induced current amplitude and coinciding current and magnetic flux density, maximum force occurs when the impedance angle is 45 degrees. The bearing initially suggested, which is to be built, will only produce 5% of its own weight when displaced 2 mm/:IV. D. Connecting a given inductance in series with the existing ones increases the force to 77% of the rotor weight. Speed also influences the performance of the bearing. The term unloader has been introduced by Lembke . In theory this bearing gives a constant force and no stiffness, hence it does not contribute to bearing stability /:VII. A. It would be very practical in applications exposed to constant forces such as gravity. Calculations performed indicate that theory does not correspond to reality in our case :/V. Further investigation is of interest, but has not been carried out in this project.Earnshaws theorem  constitutes the basis for magnetic bearing stability theory. The consequence of the physics described in the theorem is that there is no method of stabilizing a fully levitated bearing with only permanent magnets /:VII. However, there are ways of stabilizing permanent magnet bearings. Combinations of a mechanical bearing, electromagnetic bearing, diamagnetic bearing or electrodynamic bearing and a permanent magnet bearing is not covered by the theorem. Stiffness is the change in force with respect to position. The sum of the bearing stiffnesses in all dimensions must be positive for a bearing to be stable/:VII. A. Earnshaw claims this is not possible for magnetic dipoles, and that the sum will always be zero. Our calculations neither confirmed, nor invalidated this allegation/:VII. B. A null flux bearing can contribute with a positive stiffness, making the sum positive. For measurement and verification purposes, two test jigs were planned and nearly completed /:VIII. The test jigs were constructed to allow axial force measurements with radial and axial displacement for both bearing types /:IX. AError! Reference source not found.. Rotor and stator for both the PASF and null flux bearing were to be made of reinforced epoxy cast from the same moulds. This way the construction would be very strong, and changes in bearing design would be easy to implement in new casts:/0. Several aspects of the building process were expected to involve difficulties. Magnet mounting turned out to be easier than suspected. Two of the main challenges when moulding epoxy is air bubbles and releasing the cast from the mould. Air bubbles were practically avoided, but releasing the cast resulted in a broken mould, terminating the building process and postponing the measurements for the time being. A lot of work is still to be done. Finishing the moulding and assembling and performing the planned measurements are first in line. Further calculations on PASF bearings may include increasing the number of fingers and including back iron in the middle PASF finger. For the null flux bearing, varying the impedance of the coils by serial connecting inductances could improve the performance significantly. Investigating the dynamics of the null flux bearing is essential for further work on the bearing. Finally, combining a weak repulsive bearing with a null flux bearing to realise complete levitation might be feasible.