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Abstract
A Pareto optimal design analysis is carried out on the design of magnetic thrust bearings using multi-objective genetic algorithms. Two configurations of bearings have been considered with the minimization of power loss and weight of the bearing as objectives for performance comparisons. A multi-objective evolutionary algorithm is utilized to generate Pareto frontiers at different operating loads. As the load increases, the Pareto frontier reduces to a single point at a peak load for both configurations. Pareto optimal design analysis is used to study characteristics of design variables and other parameters. Three distinct operating load zones have been observed.
NOMENCLATURE
| Symbol | = | Parameter |
| Ac | = | Cross-sectional area of the coil |
| Ag | = | area of the air gap at poles |
| Bg | = | magnetic flux density |
| Br | = | remnant magnetic flux of the permanent magnet |
| Fmax | = | maximum force on the bearing |
| Fmin | = | minimum force on the bearing |
| H | = | magnetic field intensity |
| J | = | coil current density |
| Jmax | = | maximum current density |
| Jmin | = | minimum current density |
| Jsat | = | saturation current density |
| Ka | = | actuator loss factor |
| Kf | = | flux leakage factor |
| Ki | = | coil mmf loss factor |
| P | = | power loss in the coil |
| Pmax | = | maximum power loss allowed in insulation |
| Tcr | = | critical operating temperature of the bearing |
| T∞ | = | temperature of the cooling medium |
| Vc | = | volume of the coil |
| W | = | overall weight of the bearing |
| Wc | = | weight of the coil |
| Wm | = | weight of the bias magnets |
| Ws | = | weight of the stator iron |
| hc | = | height of the coil |
| htub | = | maximum allowed height of the bearing |
| lg | = | air gap |
| lg0 | = | operating gap |
| lgmax | = | maximum gap allowed |
| lgmin | = | minimum gap allowed |
| lm | = | thickness of bias magnets |
| ld | = | length of path of magnetic flux in disc |
| ni | = | magneto motence due to electro magnet |
| rci | = | inner radius of the coil |
| rco | = | outer radius of the coil |
| ri | = | inner radius of bearing |
| ro | = | outer radius of the bearing |
| roub | = | maximum allowed outer radius of the bearing |
| tb | = | back wall thickness of the bearing |
| tc | = | thickness of the coil |
| ti | = | inner wall thickness of the bearing |
| to | = | outer wall thickness of the bearing |
| xmax | = | maximum allowed displacement of the rotor from the operating position |
| Λ | = | coefficient of thermal conduction |
| φg | = | magnetic flux |
| γ | = | weight density of the material |
| η | = | coil packing factor |
| μ0 | = | permeability of the vacuum |
| ϑa | = | magneto motence due to electro magnet |
| ϑm | = | magneto motence due to permanent magnet |
| ρ | = | electrical resistivity of the coil material |