Optimum Design and Analysis of Axial Hybrid Magnetic Bearings Using Multi-Objective Genetic Algorithms

Abstract

Design optimization of axial hybrid magnetic thrust bearings (with bias magnets) was carried out using multi-objective evolutionary algorithms (MOEAs) and compared with the case of electromagnetic bearings (without bias magnets). Mathematical models of objective functions and associated constraints are presented and discussed. The different aspects of implemented MOEA are discussed. It is observed that the size of the bearing with bias magnets is considerably reduced as compared to the case of those without bias magnets, with the objective function as the minimization of weight for the same operating conditions. Similarly, current densities aret reduced drastically with biased magnets when the objective function is chosen as the minimization of the power loss. For illustration of various performances of the bearing, a typical design has been chosen from the final optimized population by an "a posteriori" approach. Sensitivities for both the objective functions with respect to the outer radius, the inner radius, and the height of coil are observed to be approximately in the ratio 2.5:1.6:1. Analysis of final optimized population has been carried out and is compared with the case without bias magnets and some salient points are observed in the case of using bias magnets.

A Pareto Optimal Design Analysis of Magnetic Thrust Bearings Using Multi-Objective Genetic Algorithms

“…The individual parts of the assembly have been elaborated on in a previous work [23]. Different dimensional parameters of the bearing are listed in the nomenclature.…”

“…The advantage of using Equation (24) as constraint over Equation (23) is that the coil is allowed freely to take a volume within the available space that minimizes the power loss or the weight.…”

“…In summary, Equations (18), (20), (23), (24), and (25) are inequality constraints while Equation (15) is an equality constraint. For a given h tub , by satisfying constraints mentioned in Equations (15) and (17), a minimum r oub below which there will not be a feasible solution can be determined and the specified r oub should be more than this value so that optimization of the bearing geometry can be performed.…”

“…In previous works (i.e., [22,23]), the optimal design analysis was done for a single operating load. In this work, the design analysis is carried by taking a series of operating loads, starting from 100 N to peak load, which could be feasible for given constraints.…”

“…Rao and Tiwari [21] used single-objective genetic algorithms, individually, for the optimization of power loss and weight in thrust magnetic bearings with and without bias (permanent) magnets. Subsequently, Rao and Tiwari [22,23] implemented a multiobjective evolutionary algorithm (NSGA-II) for the optimization of active magnetic thrust bearings (AMTB) purely with electro-magnets, and hybrid active magnetic thrust bearings (HAMTB) with the power loss and weight as the minimizationtype objective functions. In these works, two salient points were observed where major changes occurred in the choice of design variables.…”