Thibaut Labbe

Convexity-Oriented Mapping Method for the Topology Optimization of Electromagnetic Devices Composed of Iron and Coils

In order to perform parameter or shape optimizations, an initial topology is required which affects the final solution. This constraint is released in topology optimization methods. They are based on a splitting of the design space into cells, in which they attempt to distribute optimally predefined materials. In topology optimization, a lack of convexity has already been observed by several authors. Final results are often affected by the initial material distribution. This paper aims at improving the convexity in static electromagnetic problems where both ferromagnetic materials and coils are distributed in the design domain. The paper focuses on the mapping function used to derive the permeability of a cell from its composition. In addition to convexity issues, sensitivity concerns arise when the relative permeability of iron is large. Several methods based on a sensitivity-oriented mapping are suggested in the literature, such as the solid isotropic material with penalization (SIMP) method or the homogenization theory method (HDM). This paper shows that a geometric mapping is effective in combination with the convexity-oriented mapping to tackle both problems. This paper suggests computing the cell permeabilities by two successive mapping functions and illustrates the effectiveness of this method on the design of a switched reluctant actuator.

Torque-to-weight ratio maximization in PMSM using topology optimization

This paper focuses on the maximization of the torque-to-weight ratio of permanent magnet synchronous motors (PMSM) using a topology optimization method. It aims at finding the optimal design that either maximizes the torque for a given weight or minimizes the weight for a required torque. The analysis presented in this paper besides considers radial and tangential permanent magnets. The paper shows that the optimization always leads to the same optimal motor topology, which is scaled to achieve the required torque. In addition, a scale law is highlighted for computing the PMSM torque according to its size and is used to plot a Pareto curve that provides the achievable torque-to-weight ratio according to the motor weight.

Topology optimization method applied to the design of electromagnetic devices: Focus on convexity issues

To perform parameter and shape optimization, an initial topology is required which affects the final solution. Topology optimization methods have the advantage to release this constraint. They are based on a splitting of the design space into cells, in which they attempt to distribute optimally some given materials. In this paper, the optimization is based on a discrete formulation of the Maxwell equations obtained thanks to a finite element model. The gradient of the objective function is computed immediately from this discrete form, which is more convenient than the adjoint variable method. A line-search method (steepest descent direction) is then applied. The step size is computed by a simple and quick algorithm, to achieve good and fast convergence. Several convexity issues were already highlighted in topology optimization. We explain how we can face some of them by performing the optimization on a variable linked to the permeability by a given mapping. This mapping actually affects the value of intermediate materials and must be selected carefully to avoid the algorithm to be trapped in some local minimizers. In order to illustrate the concepts presented along the paper, the method is applied for the topology optimization of a linear reluctant actuator.

Topology Optimization Method Based on the Maxwell Stress Tensor for the Design of Ferromagnetic Parts in Electromagnetic Actuators

Topology optimization methods suffer from a lack of convexity for the design of electromagnetic devices. Local minimizers indeed prevent deterministic methods from attaining the optimal solution. The optimization result may then vary according to the initial conditions. This paper proposes a convexity-oriented method focusing on the maximization of the forces exerted on ferromagnetic parts in electromagnetic actuators. The method is based on a simultaneous optimization of two topologies by a gradient-based algorithm, the forces being computed by combining their magnetic fields within the Maxwell stress tensor. During the optimization, the two topologies converge towards a unique design using constraints whose shape is progressively modified. The method benefits from a fast convergence and produces consistent and efficient results, which is highlighted on a test problem. The method is eventually applied to a realistic problem related to the design of a switched reluctance actuator.

Original article: Two phase operation for a three phase PMSM using a control model based on a Concordia like transform associated to a classic Park transform

In aerospace applications high reliability drives are required. For electrical drives based on three phase PMSM motors, a way to improve the reliability is to allow degraded mode operation on two phases only, thanks to specifically developed power and control architectures. The aim of this paper is to present a control strategy for the two phase operation which is supported by a model based on a Concordia like transform associated to a classic Park transform. This approach maintains the advantages related to the torque control in the Park reference frame: the two active phases are still supplied with sinusoidal currents, whose amplitude is proportional to the torque. By adjusting the phase shifts, the torque ripple can be minimized or even canceled according to the emf’s shape.

Convexity-Oriented Method for the Topology Optimization of Ferromagnetic Moving Parts in Electromagnetic Actuators Using Magnetic Energy

When applied to the topology optimization of electromagnetic devices, gradient-based algorithms suffer from a lack of convexity. They usually converge to local minimizers and the obtained designs depend on the initial material distributions. This paper focuses on avoiding these local minimizers for the optimization of ferromagnetic moving parts in electromagnetic actuators. The proposed method intends to maximize the average reluctant force computed from the difference of magnetic energy between two positions of the ferromagnetic part. It relies on a problem relaxation: distinct design variables are defined to describe the ferromagnetic part in each position. Thanks to convexity-oriented constraints, the differences between the two obtained topologies are progressively reduced in order to converge towards the optimal design. The paper besides highlights sensitivity issues related to the high permeability of iron and recommends using a geometric mapping to guarantee a fast convergence. The efficiency of the method is underlined for the design of the rotor of a switched reluctant actuator. The method succeeds in avoiding local minimizers and producing efficient topologies. The method is then combined with another method dedicated to the design of parts composed of iron and coils in order to realize the global optimization of the actuator.

Modelling and torque control of a five-phase permanent-magnet synchronous motor using tooth-concentrated winding technology

This paper deals with the modelling and the control of a five-phase machine using a tooth-concentrated winding technology. It is shown that the control of the torque can be easily performed in a generalized dq reference frame, and that with this control the motor can still operate when the feeding of one phase is lost. This makes the motor under study and its control architecture a good candidate when a fault-tolerant drive is needed.

Design of magnetic thrusts using topology optimization methods

Purpose – The paper aims at optimizing magnetic thrusts in the framework of the design of high-dynamics linear actuators. The goal is to find the optimal topology of the permanent magnets in order to maximize the velocity of the actuator. Design/methodology/approach – The optimization is performed by a topology optimization method. The design space is divided in cells in which the method have to distribute permanent magnets and determine their magnetization directions. Findings – Several aspects of the optimization are discussed in the paper, such as the effect of the introduction of a weight constraint on the thrust. Some issues are highlighted regarding the length of design space for the moving part and the presence of local minimizers in the optimization problem. Research limitations/implications – Having different magnetization directions in each cell makes the manufacturing harder. The results could thus be completed either by the design of a system able to create such permanent magnets or by the introduction of a constraint limiting the number of magnetization directions. Practical implications – Finding the optimal topology of magnetic thrusts is motivated by the interest in avoiding the shocks related to mechanical thrusts. Originality/value – This paper applies the topology optimization approach for the design of magnetic thrusts in order to increase the performances of high-dynamics linear actuators.

Optimal Preliminary Design of Superconducting Bending Magnets With Active Shielding Using Topology Optimization Method

This paper presents a topology optimization-based method for optimally designing magnets. Compared to other optimization approaches for which the final solution is strongly conditioned by the initial choice of the designer, it opens the field of solutions without any a priori on the topology or the geometry of the magnet. This method is applied to the preliminary design of a 90° bending superconducting magnet with active shielding, considering the superconductor quantity as objective function and the magnetic field distribution as constraint. In order to meet manufacturability specifications, additional constraints ensure that the solutions are exclusively made of planar coils. The results highlight that the optimal distribution of superconductors on the magnet cross-section are recurrent whatever the value of design parameters like magnet radius or the current density.

Topology optimization of electromagnetic devices using oriented iron microstructures

Purpose – The purpose of this paper is to propose a mechanism avoiding the topology optimization methods, and particularly those using gradient-based algorithms, to be trapped in local minimizers when applied to the design of electromagnetic devices made of iron and permanent magnet. Design/methodology/approach – Topology optimization methods aim at finding the optimal distribution of some materials in cells subdividing a design space, regarding a specific objective function. This paper suggests to consider that each cell contains an oriented microstructure of iron whose direction and shape are optimized by the method. Findings – Coupled with convexity and sensitivity mappings quite common in the field of topology optimization, the use of the microstructure allows the optimization algorithm to converge systematically toward the same design. This achievement is illustrated on a practical case, i.e. the optimization of the rotor of a permanent magnet synchronous motor regarding its mean torque and under mass constraint. Also, this paper shows that intermediate iron materials can either be penalized or interpreted, thanks to the realistic physical relations derived from the iron microstructures. Originality/value – This paper proposes a mechanism based on an iron microstructure for avoiding the topology optimization methods and the trap of local minimizers when applied to the design of electromagnetic devices made of iron and permanent magnet.