Methodology for Shape Optimization of Magnetic Designs: Magnetic Spring Characteristic Tailored to Application Needs

Abstract

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 formulations such as spline and polynomials for material boundary definitions. Each of the parametrizations is formulated into a multi-objective optimization problem with both performance and material cost, and solved using gradient free optimization techniques (direct search, genetic algorithm). The methodology is employed on several benchmark problems—both academic and application inspired magnetic spring torque characteristic requirements. The resulting designs fit well with the requirements, with a relatively low computational cost. As such, the methodology presented is a promising candidate for other design problems in 2D shape optimization in electrical motor research and development.

Novel Adaptive Magnetic Springs for Reliable Industrial Variable Stiffness Actuation

“…Additionally, the design flexibility demonstrated in a recent publication [32] allows for shaping of the magnetic spring torque. The shaping is achieved through two different approaches: (i) Fourier decomposition of the desired characteristic, combining several springs with sinusoidal characteristics into a single assembly; (ii) re-shaping of the magnetic domains, resulting in a free-shape limited only by magnet and back iron manufacturability (e.g., minimum thickness, air gap size, feasible magnetizations, etc.).…”

“…In this section, the magnetic spring geometry is optimized, given a physical parameterization. Herein, the most pertinent details of the magnetic optimization are covered, while for a more general overview of the methodology the reader is directed to [32].…”

“…In specific cases where magnet segmentation is desired, leading to more than one magnets per magnetic pole, the user still needs to override this allocation. This approach builds on previous publications [6,32], and integrates it into the system design approach.…”

“…This is a significant weakness, as assemblies with back irons are necessary to guide the flux, i.e., limit the stray flux that causes inefficient designs and magnetic disturbance in the surroundings of the actuator, possibly attracting unwanted metallic particles or even generating external forces. In [32], we exploited the available computational power and a finite elements model (FEM) combined with the notions of topology optimization, giving a more general approach to spring tailoring. As its main weakness, this approach only included limited notions of manufacturability, e.g., operates at the tens of centimetres scale where the design freedom is expected to be larger, and would require either limited shaping capabilities or advanced manufacturing technology (e.g., additive manufacturing or metal injection moulding).…”