Magnetic springs are a fatigue-free alternative to mechanical springs that could enable compliant actuation concepts in highly dynamic industrial applications. The goals of this article are: (1) to develop and validate a methodology for the optimal design of a magnetic spring and (2) to benchmark the magnetic springs at the component level against conventional solutions, namely, mechanical springs and highly dynamic servo motors. We present an extensive exploration of the magnetic spring design space both with respect to topology and geometry sizing, using a 2D finite element magnetostatics software combined with a multi-objective genetic algorithm, as a part of a MagOpt design environment. The resulting Pareto-optima are used for benchmarking rotational magnetic springs back-to-back with classical industrial solutions. The design methodology has been extensively validated using a combination of one physical prototype and multiple virtual designs. The findings show that magnetic springs possess an energy density 50% higher than that of state-of-the-art reported mechanical springs for the gigacycle regime and accordingly a torque density significantly higher than that of state-of-the-practice permanently magnetic synchronous motors.

Parallel elastic actuation is a highly promising concept for assisting preplanned trajectories such as repetitive tasks in industrial machines and robots. Nevertheless, due to the persisting challenges on spring lifetime, its full potential has yet to be leveraged in the industry. We propose a novel adaptive magnetic spring as a fatigue-free spring mechanism to enable variable stiffness actuators in long lifetime applications. The spring is designed to flexibly deal with variations in operating conditions, i.e., mass customization. We propose a co-design methodology which simultaneously optimizes the sizing of the magnetic spring (for the given machine and its operating conditions), together with the controls and ideal dynamic response of the system. This mechanism and the methodology are applied to a design problem of a weaving machine drivetrain, where the benefits of the adaptive magnetic spring are highlighted with respect to a fixed stiffness magnetic spring, and the current industrial benchmark without springs. Experimentally validated findings show a consistent and considerable improvement with respect to energy consumption and peak torque reduction of up to 47% and 64%, respectively, when comparing to the current industrial benchmark.

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.