Magnetic Bearing Rotordynamic System Optimization Using Multi-Objective Genetic Algorithms

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Wan Zhong ◽  
Alan Palazzolo
Keyword(s):  
Genetic Algorithms ◽  
Magnetic Flux ◽  
System Optimization ◽  
Magnetic Bearing ◽  
Multiple Objective ◽  
Control Law ◽  
Power Losses ◽  
Geometrical Features ◽  
Spinning Shaft ◽  
Pareto Frontiers

Multiple objective genetic algorithms (MOGAs) simultaneously optimize a control law and geometrical features of a set of homopolar magnetic bearings (HOMB) supporting a generic flexible, spinning shaft. The minimization objectives include shaft dynamic response (vibration), actuator mass and total actuator power losses. Levitation of the spinning rotor and dynamic stability are constraint conditions for the control law search. Nonlinearities include magnetic flux saturation, and current and voltage limits. Pareto frontiers were applied to identify the best-compromised solution. Mass and vibration reductions improve with a two control law approach.

Rotor Power Losses in Planar Radial Magnetic Bearings — Effects of Number of Stator Poles, Air Gap Thickness, and Magnetic Flux Density

1998 ◽  
Author(s):  
P. E. Allaire ◽  
M. E. F. Kasarda ◽  
L. K. Fujita
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Eddy Current ◽  
Power Loss ◽  
Magnetic Bearing ◽  
Air Gap ◽  
Magnetic Bearings ◽  
Magnetic Flux Density ◽  
Power Losses ◽  
Loss Mechanism

Rotor power losses in magnetic bearings cannot be accurately calculated at this time because of the complexity of the magnetic field distribution and several other effects. The losses are due to eddy currents, hysteresis, and windage. This paper presents measured results in radial magnetic bearing configurations with 8 pole and 16 pole stators and two laminated rotors. Two different air gaps were tested. The rotor power losses were determined by measuring the rundown speed of the rotor after the rotor was spun up to speeds of approximately 30,000 rpm, DN = 2,670,000 mm-rpm, in atmospheric air. The kinetic energy of the rotor is converted to heat by magnetic and air drag power loss mechanisms during the run down. Given past publications and the opinions of researchers in the field, the results were quite unexpected. The measured power losses were found to be nearly independent of the number of poles in the bearing. Also, the overall measured rotor power loss increased significantly as the magnetic flux density increased and also increased significantly as the air gap thickness decreased. A method of separating the hysteresis, eddy current and windage losses is presented. Eddy current effects were found to be the most important loss mechanism in the data analysis, for large clearance bearings. Hysteresis and windage effects did not change much from one configuration to the other.

scholarly journals Radial Planar Magnetic Bearing Analysis With Finite Elements Including Rotor Motion and Power Losses

1997 ◽  
Author(s):  
R. D. Rockwell ◽  
P. E. Allaire ◽  
M. E. F. Kasarda
Keyword(s):  
Finite Element ◽  
Magnetic Flux ◽  
Flux Density ◽  
Electric Fields ◽  
Eddy Current ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Magnetic Flux Density ◽  
Magnetic Vector Potential ◽  
Power Losses

No literature is currently available which has evaluated finite element power loss models for magnetic bearings and compared the results to experimental results. In this paper a finite element model of the magnetic and electric fields in magnetic bearings, including the motion of the magnetic material in the rotor, is developed. It evaluates the two dimensional magnetic vector potential, magnetic flux density, electric field, eddy current, and power losses in an example magnetic bearing configuration. Results were obtained for both a solid rotor and a laminated rotor. For a solid rotor, both the magnetic flux density and eddy current plots at high rotational speeds are concentrated at the outer edge of the rotor. The ratio of calculated solid to laminated losses is found to be in the range of measured results by other authors. An effective axial conductivity was employed to model a laminated rotor and compared to experimental loss measurements. The correlation between measured and calculated results is quite good for a range of rotor speeds, magnetic flux density, and air gap thickness.

Rotor Power Losses in Planar Radial Magnetic Bearings—Effects of Number of Stator Poles, Air Gap Thickness, and Magnetic Flux Density

1999 ◽  
Vol 121 (4) ◽  
pp. 691-696 ◽  
Author(s):  
P. E. Allaire ◽  
M. E. F. Kasarda ◽  
L. K. Fujita
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Eddy Current ◽  
Power Loss ◽  
Magnetic Bearing ◽  
Air Gap ◽  
Magnetic Bearings ◽  
Magnetic Flux Density ◽  
Power Losses ◽  
Loss Mechanism

Rotor Power losses in magnetic bearings cannot be accurately calculated at this time because of the complexity of the magnetic field distribution and several other effects. The losses are due to eddy currents, hysteresis, and windage. This paper presents measured results in radial magnetic bearing configurations with eight pole and 16 pole stators and two laminated rotors. Two different air gaps were tested. The rotor power losses were determined by measuring the rundown speed of the rotor after the rotor was spun up to speeds of approximately 30,000 rpm, DN = 2,670,000 mm-rpm, in atmospheric air. The kinetic energy of the rotor is converted to heat by magnetic and air drag power loss mechanisms during the run down. Given past publications and the opinions of researchers in the field, the results were quite unexpected. The measured power losses were found to be nearly independent of the number of poles in the bearing. Also, the overall measured rotor power loss increased significantly as the magnetic flux density increased and also increased significantly as the air gap thickness decreased. A method of separating the hysteresis, eddy current and windage losses is presented. Eddy current effects were found to be the most important loss mechanism in the data analysis, for large clearance bearings. Hysteresis and windage effects did not change much from one configuration to the other.

Flux Density and Air Gap Effects on Rotor Power Loss Measurements in Planar Radial Magnetic Bearings

1997 ◽  
Author(s):  
P. E. Allaire ◽  
M. E. F. Kasarda ◽  
E. H. Maslen ◽  
G. T. Gillies ◽  
L. K. Fujita
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Eddy Current ◽  
Power Loss ◽  
Magnetic Bearing ◽  
Air Gap ◽  
Magnetic Bearings ◽  
Magnetic Flux Density ◽  
Power Losses ◽  
Loss Mechanism

The rotor power losses in magnetic bearings are due to eddy currents, hysteresis, and windage. The influence of air gap magnetic flux density and air gap thickness is not well understood at this time. This paper presents measured results in two magnetic bearing radial configurations with a laminated rotor. The rotor power losses were evaluated by measuring the rundown speed of the rotor, in air, after the rotor was spun up to speeds of approximately 30,000 rpm in atmospheric air. The kinetic energy of the rotor is converted to heat by magnetic and air drag power loss mechanisms during the run down. A method of separating the hysteresis, eddy current and windage losses is presented. Eddy current effects were found to be the most important loss mechanism in the data analysis. Hysteresis and windage effects did not change much from one configuration to the other. The measured rotor power loss increased significantly as the magnetic flux density increased and also increased significantly as the air gap thickness decreased.

Basic Statements of Research and Magnetic Field of Axial Excitation Inductor Generator

2011 ◽  
Vol 28 (1) ◽  
pp. 49-52
Author(s):  
Igors Stroganovs ◽  
Andrejs Zviedris
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Flux ◽  
Magnetic System ◽  
System Optimization ◽  
Magnetic Saturation ◽  
The Finite Element Method ◽  
Flux Linkage ◽  
Axial Excitation

Basic Statements of Research and Magnetic Field of Axial Excitation Inductor GeneratorIn this work the main features of axial excitation inductor generators are described. Mathematical simulation of a magnetic field is realized by using the finite element method. The objective of this work is to elucidate how single elements shape, geometric dimensions and magnetic saturation of magnetic system affect the main characteristics of the field (magnetic induction, magnetic flux linkage). The main directions of a magnetic system optimization are specified.

Comparison of Two Multiobjective Optimization Techniques With and Within Genetic Algorithms

1999 ◽  
Author(s):  
Shapour Azar ◽  
Brian J. Reynolds ◽  
Sanjay Narayanan
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Technique ◽  
Optimization Techniques ◽  
Pareto Set ◽  
Design Solution ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Continuous Variables ◽  
Optimal Set

Abstract Engineering decision making involving multiple competing objectives relies on choosing a design solution from an optimal set of solutions. This optimal set of solutions, referred to as the Pareto set, represents the tradeoffs that exist between the competing objectives for different design solutions. Generation of this Pareto set is the main focus of multiple objective optimization. There are many methods to solve this type of problem. Some of these methods generate solutions that cannot be applied to problems with a combination of discrete and continuous variables. Often such solutions are obtained by an optimization technique that can only guarantee local Pareto solutions or is applied to convex problems. The main focus of this paper is to demonstrate two methods of using genetic algorithms to overcome these problems. The first method uses a genetic algorithm with some external modifications to handle multiple objective optimization, while the second method operates within the genetic algorithm with some significant internal modifications. The fact that the first method operates with the genetic algorithm and the second method within the genetic algorithm is the main difference between these two techniques. Each method has its strengths and weaknesses, and it is the objective of this paper to compare and contrast the two methods quantitatively as well as qualitatively. Two multiobjective design optimization examples are used for the purpose of this comparison.

Parallel Single and Multiple Objectives Genetic Algorithms

2013 ◽  
pp. 73-110
Author(s):  
B. S. P. Mishra ◽  
S. Dehuri ◽  
R. Mall ◽  
A. Ghosh
Keyword(s):  
Genetic Algorithms ◽  
Processing Time ◽  
Multiple Objectives ◽  
Multiple Objective ◽  
Acceptable Solution ◽  
Multi Objective ◽  
Potential Applications

This paper critically reviews the reported research on parallel single and multi-objective genetic algorithms. Many early efforts on single and multi-objective genetic algorithms were introduced to reduce the processing time needed to reach an acceptable solution. However, some parallel single and multi-objective genetic algorithms converged to better solutions as compared to comparable sequential single and multiple objective genetic algorithms. The authors review several representative models for parallelizing single and multi-objective genetic algorithms. Further, some of the issues that have not yet been studied systematically are identified in the context of parallel single and parallel multi-objective genetic algorithms. Finally, some of the potential applications of parallel multi-objective GAs are discussed.

Ordered Incremental Multi-Objective Problem Solving Based on Genetic Algorithms

2012 ◽  
pp. 72-98
Author(s):  
Wenting Mo ◽  
Sheng-Uei Guan ◽  
Sadasivan Puthusserypady
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Problem Solving ◽  
Benchmark Problems ◽  
Multiple Objective ◽  
Nsga Ii ◽  
Incremental Approach ◽  
Strength Pareto Evolutionary Algorithm ◽  
Conflicting Objectives ◽  
Open Question

Many Multiple Objective Genetic Algorithms (MOGAs) have been designed to solve problems with multiple conflicting objectives. Incremental approach can be used to enhance the performance of various MOGAs, which was developed to evolve each objective incrementally. For example, by applying the incremental approach to normal MOGA, the obtained Incremental Multiple Objective Genetic Algorithm (IMOGA) outperforms state-of-the-art MOGAs, including Non-dominated Sorting Genetic Algorithm-II (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA) and Pareto Archived Evolution Strategy (PAES). However, there is still an open question: how to decide the order of the objectives handled by incremental algorithms? Due to their incremental nature, it is found that the ordering of objectives would influence the performance of these algorithms. In this paper, the ordering issue is investigated based on IMOGA, resulting in a novel objective ordering approach. The experimental results on benchmark problems showed that the proposed approach can help IMOGA reach its potential best performance.

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