Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

Abstract

Permanent magnet-assisted synchronous reluctance motors (PMSynRM) have a significantly higher average torque than synchronous reluctance motors. Thus, determining an optimal design results in a multi-material topology optimization problem, where one seeks to distribute ferromagnetic material, air and permanent magnets within the rotor in an optimal manner.This study proposed a novel density-based distribution scheme, which allows for continuous magnetization direction instead of a finite set of angles. Thus, an interpolation scheme is established between properties pertaining to magnets and non-linear materials. This allows for new designs to emerge without introducing complex geometric parameterization or relying on the user's biases and intuitions. Toward reducing computation time, Nitsche-type mortaring is applied, allowing for free rotation of the rotor mesh relative to the stator mesh. The average torque is approximated using only four-point static positions. This study investigates several interpolation schemes and presents a new one inspired by the topological derivative. We propose to filter the final design for the magnetization angle using K-mean clustering accounting for technical feasibility constraints of magnets. Finally, the design of the electrical motor is proposed to maximize torque value.

Topology Optimization for Electromagnetics: A Survey

“…In [61], a different interpolation method is proposed by D. Lukàš through the scheme In Lukàš approach the transition threshold between two material properties is ρ = 0.5 in the limit of high p. where the "gray scales" depend only on the parameter p, which cannot be too large, in order to avoid convergence problems [33]. Lastly, the so-called reluctivity based mapping proposed for electromagnetic TO is defined [62] g…”

Topology optimization for magnetic circuits with continuous adjoint method in 3D

“…During the optimization process, the intermediate points have to be penalized to enforce local optimization solvers to converge to binary solutions representing, for example, air or material. Bendsoe et al have introduced the well-known solid isotropic material with penalization (SIMP) approach and various penalization schemes can be found in Sigmund (2003, 1999), Sanogo and Messine (2018) and Gauthey et al (2021). It is worth noting that SIMP-based methods are widely used in professional solvers, for example, OptiStruct of Altair company.…”

“…From approaches in mechanics, some studies were done to solve topology optimization design problems in electromagnetism dealing with Maxwell equations. Specially in magnetostatics, to solve these kinds of problems, the adjoint method has also been developed (Sanogo et al, 2014;Youness and Messine, 2019b;Gauthey et al, 2021Gauthey et al, , 2023. In Sanogo (2016), magnetic circuits were designed in such a way.…”

“…In Sanogo (2016), magnetic circuits were designed in such a way. More recently, the nonlinearity of ferromagnetic material has been taken into account in Youness and Messine (2019a) and Gauthey et al (2021). Moreover, some new material schemes also called penalization schemes were introduced for this SIMP method dedicated to problems in magnetostatics (Sanogo and Messine, 2018;Gauthey et al, 2021).…”

Multi-material topology optimization using Wachspress interpolations for designing a 3-phase electrical machine stator

“…Concerning MMTO applied to electrical machines, many works use heuristic approaches as in Sato, Watanabe, and Igarashi [27] and Jung, Ro, and Jung [28], mainly to optimize only the rotor of electrical machines. Density-based methodologies are also used to optimize rotors of different kinds of actuators, such as wound field synchronous machines [29], permanent magnet synchronous reluctance motors [30,31], or permanent magnet synchronous machines [32], and can be hybridized with shape optimization [33]. By contrast, very few works tackle the stator optimization.…”