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

Branimir Mrak,Hubert Mitterhofer,Bianca Wex

doi:10.3390/act11020037

Branimir Mrak, Hubert Mitterhofer + Show 1 more

Open Access

https://doi.org/10.3390/act11020037

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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.

Highlights

Magnetic springs are an alternative to mechanical springs in applications that require long lifetime with no fatigue failure
Using the extended parametric approach allows for an additional improvement in the torque characteristic fit, but a considerable root mean square (RMS) error remains
This is due to the limitations in geometry shaping feasible within the extended parametric description of the magnetic spring and is considered to be a hard limit to the performance of this method

Summary

Introduction

Magnetic springs are an alternative to mechanical springs in applications that require long lifetime with no fatigue failure. The previously demonstrated torsional magnetic springs typically have sinusoidal torque characteristics, for reasons of cost efficiency, there are many motion systems in the industrial practice that could benefit from a deviation from it. Two good examples, both highly present in reciprocating machinery are oscillating loads driven by: (i) conjugate cam-followers; and (ii) a crank-rocker mechanism. Other applications with reciprocating mechanical loads and other torque ripple phenomena can benefit from the use of magnetic springs: weaving looms and other textile machinery featuring reciprocating motion; agricultural machines, e.g., reciprocating moving parts in combine harvesters; The dwell of the cam causes a quasi-sinusoidal characteristic to only be required for a fraction of the full cam rotation, while in a crank-rocker, the non-linear kinematics can add harmonic content to the required torque, due to the deviation from ideal transmission angle of 90◦.

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