An effective combinatorial scheme for magnets shape optimization (original) (raw)
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Topology and shape optimization are still rarely applied to problems in electromagnetic design due to the computational complexity and limited commercial tooling, even though components such as electrical motors, magnetic springs or magnetic bearings could benefit from it, either to improve performance (reducing torque ripple and losses through shaping harmonic content in back electromotive force) or reduce the use of rare-earth materials. Magnetic springs are a fatigue free alternative to mechanical springs, where shape optimization can be exploited to a great degree—allowing for advanced non-linear stiffness characteristic shaping. We present the optimization methodology relying on a combination of several approaches for characteristic shaping of magnetic springs through either a modular design approach based on: (i) Fourier order decomposition; (ii) breaking conventional design symmetry; or (iii) free shaping of magnets through deviation from a nominal design using problem formul...
Shape and Topological Optimization for Electromagnetism Problems
2010
This paper presents a topological shape optimization problem technique for electromagnetic problems using the topological sensitivity analysis and topological derivative. The objective function that represents the design objective is expressed in terms of magnetic field. The adjoint method is used to optimize the distribution of magnetics fields. Some numerical results that demonstrated the validity of the proposed approach are presented.
Shape Optimization for the ESRF II Magnets
2014
Magnets are a keystone of the ESRF upgrade programme. The specifications of the magnets of the ESRF II lattice are stringent: high gradients, extended Good Field Region (GFR) and vertical gaps large enough for the X-ray beam ports. The magnet design approach is presented here. Shape optimization of the magnet poles is systematically used. The magnet design is treated as an ill-posed, non linear, constrained problem. Iterative algorithms have been developed; the algorithms converge in less than 10 iterations, leading to very short computation time. This design method has been applied to high gradient quadrupole magnets. The shape optimization leads to original pole profiles.
Innovative computational methods for shape optimization
2002
The objective of this paper is to investigate the efficiency of combinatorial optimization methods and in particular algorithms based on evolution strategies, when incorporated into structural optimization problems. Evolution strategies algorithms are used either on a stand-alone basis, or combined with a conventional mathematical programming technique. Advanced domain decomposition techniques are also proposed particularly tailored for parallel solution of large-scale sensitivity analysis problems.
Optimization of Permanent Magnet Assemblies Using Genetic Algorithms
IEEE Transactions on Magnetics, 2000
This paper describes the utilization of genetic algorithms to optimize the topology of assemblies of permanent magnets. Conventional genetic algorithms are modified to employ pixel refinement to improve the computational efficiency of the optimization process. An example case is demonstrated for optimizing the figure of merit of a permanent magnet dipole. By using only four magnetization directions, a figure of merit value of 0.11 is achieved using the proposed optimization method.
IEEE Transactions on Magnetics, 1993
A new shape design sensitivity formula for magnetostatic problems is derived analytically employing the material derivative concept in continuum mechanics. In order to express the design sensitivity as a function of shape variation only, the adjoint variable is defined. Since the formula is expressed as boundary integration of state and adjoint variables over deformed boundary, the boundary element method is employed to evaluate the variables accurately on the boundary. The proposed algorithm is applied to the pole-shape optimization of a quadrupole magnet through which the validity is proved.
Optimization of Magnetization Directions in a 3-D Magnetic Structure
IEEE Transactions on Magnetics, 2010
This study introduces a design method for determining the optimized magnetization directions in 3-D magnetic systems. Based on a modified topology optimization method, discrete magnetizations are investigated in six directions (). The finite-element method is used for the 3-D magnetostatic field analysis. The proposed method is applied to the design of a magnet pattern having "onesided flux" and the design results show that the optimized magnet pattern appears as one or two Halbach arrays according to the shape of the design domain. The optimization process is accomplished by using sequential linear programming and the adjoint variable method.
Optimal design method by using the boundary element analysis for plural permanent magnets
IEEE Transactions on Magnetics, 1992
This paper describes an optimal design method for plural permanent magnets. When the size of the magnets are unknown variables, the equation that optimizes the size in desired flux distribution becomes non-linear. From this point of view, a new domain element called a "size modification element" is conceived. The presented technique is based on the specific element and the least square method to determine the optimum size or position of the plural permanent magnets.
A fast finite-difference algorithm for topology optimization of permanent magnets
Journal of Applied Physics
We present a finite-difference method for the topology optimization of permanent magnets that is based on the FFT accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparsion to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.