# Multi-Fidelity Design Optimisation of a Solenoid-Driven Linear Compressor

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Thermo and Fluid dynamics (FLOW) Faculty of Engineering, Vrije Universiteit Brussel (VUB) Pleinlaan 2, 1050 Brussels, Belgium

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Mobility Logistic and Automotive Technology Research Group (MOBI), Department of Electrical Engineering and Energy Technology (ETEC), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

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Combustion and Robust optimisation Group (BURN), Vrije Universiteit Brussel (VUB) and Université Libre de Bruxelles (ULB), 1050 Brussels, Belgium

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Thermal Engineering and Combustion Unit, University of Mons (UMONS), Place du Parc 20, 7000 Mons, Belgium

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Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), Place du Levant, 2, 1348 Louvain-la-Neuve, Belgium

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Flanders Make, 3001 Heverlee, Belgium

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Robotics & Multibody Mechanics Research Group (R&MM), Faculty of Mechanical Engineering, Vrije Universiteit Brussel, 1050 Brussels, Belgium

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Author to whom correspondence should be addressed.

Received: 8 April 2020 / Revised: 7 May 2020 / Accepted: 8 May 2020 / Published: 11 May 2020

Improved management and impermeability of refrigerants is a leading solution to reverse global warming. Therefore, crank-driven reciprocating refrigerator compressors are gradually replaced by more efficient, oil-free and hermetic linear compressors. However, the design and operation of an electromagnetic actuator, fitted on the compression requirements of a reciprocating linear compressor, received limited attention. Current research mainly focuses on the optimisation of short stroke linear compressors, while long stroke compressors benefit from higher isentropic and volumetric efficiencies. Moreover, designing such a system focuses mainly on the trade-off between number of copper windings and the current required, due to the large computational cost of performing a full geometric design optimisation based on a Finite Element Method. Therefore, in this paper, a computationally-efficient, multi-objective design optimisation for six geometric design parameters has been applied on a solenoid driven linear compressor with a stroke of 44.2 mm. The proposed multi-fidelity optimisation approach takes advantage of established models for actuator optimisation in mechatronic applications, combined with analytical equations established for a solenoid actuator to increase the overall computational efficiency. This paper consists of the multi-fidelity optimisation algorithm, the analytic model and Finite Element Method of a solenoid and the optimised designs obtained for optimised power and copper volume, which dominates the actuator cost. The optimisation results illustrate a trade-off between minimising the peak power and minimising the volume of copper windings. Considering this trade-off, an intermediate design is highlighted, which requires 33.3% less power, at the expense of an increased copper volume by 5.3% as opposed to the design achieving the minimum copper volume. Despite that the effect of the number of windings on the input current remains a dominant design characteristic, adapting the geometric parameters reduces the actuator power requirements significantly as well. Finally, the multi-fidelity optimisation algorithm achieves a 74% reduction in computational cost as opposed to an entire Finite Element Method optimisation. Future work focuses on a similar optimisation approach for a permanent magnet linear actuator.