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 |