Zeger Bontinck

Optimization of a Stern–Gerlach Magnet by Magnetic Field–Circuit Coupling and Isogeometric Analysis

Stern-Gerlach magnets are used to magnetically separate a beam of atoms or atom clusters. The design is difficult, since both the magnetic field gradient and its homogeneity should be maximized. This paper proposes the numerical optimization of the devices pole-shoe shapes, starting from a reference geometry given in the literature. The main contributions of this paper are the generalization of a magnetic field-magnetic circuit coupling and the application of isogeometric analysis (IGA), which are shown to reduce the computational complexity and increase the accuracy. The field-circuit coupling significantly reduces the size of the field model part, in which the IGAs spline-based framework enables a highly accurate evaluation of local field quantities, even across elements.

Response Surface Models for the Uncertainty Quantification of Eccentric Permanent Magnet Synchronous Machines

This paper deals with the modeling and simulation of the effect of rotor eccentricity in permanent magnet synchronous machines. Static eccentricity is analyzed in a 2-D setting. The 3-D effect of an inclined rotor shaft is accounted by considering 2-D slices and interpolating on a grid constructed from finite-element simulations [response surface model (RSM)]. Common tools of uncertainty quantification, i.e., generalized polynomial chaos and Monte Carlo, are used to study the effect on the electromotive force. The novelty of this paper is the twofold use of the RSM: 1) to speed up the calculations in the 2-D setting and 2) to mimic a multislice model for inclined eccentricity.

Isogeometric analysis and harmonic stator–rotor coupling for simulating electric machines

Abstract This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator–rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example.

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator, the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by piecewise affine parametrizations of the geometry or by the design element approach, both of which avoid remeshing. Furthermore, it is shown how to robustify the optimization procedure, that is, how to deal with uncertainties on the design parameters. The overall procedure is illustrated by an academic example and by the example of a permanent-magnet synchronous machine. The examples show the advantages of deterministic optimization compared to standard and popular stochastic optimization procedures such as particle swarm optimization.

Multilevel Monte Carlo simulation of the eddy current problem with random parameters

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given example it is found that the main costs of the method are spent on the coarsest level.

Uncertainty Quantification for a Permanent Magnet Synchronous Machine with Dynamic Rotor Eccentricity

The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method. Uncertainty quantification is applied by using generalized Polynomial Chaos and Monte Carlo. It is found that the displacement of the rotor impacts the spectrum of the torque the most.