Research Papers: Design Automation

Free-Form Design of Electrical Machine Rotor Cores for Production Using Additive Manufacturing

[+] Author and Article Information
Michele Garibaldi

Centre for Additive Manufacturing (CfAM),
The University of Nottingham,
Nottingham NG7 2RD, UK;
Power Electronics, Machines and Control Group (PEMC),
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: michele.garibaldi@siemens.com

Christopher Gerada

Power Electronics, Machines and Control Group (PEMC),
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: chris.gerada@nottingham.ac.uk

Ian Ashcroft

Centre for Additive Manufacturing (CfAM),
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: ian.ashcroft@nottingham.ac.uk

Richard Hague

Centre for Additive Manufacturing (CfAM),
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: richard.hague@nottingham.ac.uk

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received August 3, 2018; final manuscript received December 23, 2018; published online March 13, 2019. Assoc. Editor: Samy Missoum.

J. Mech. Des 141(7), 071401 (Mar 13, 2019) (13 pages) Paper No: MD-18-1613; doi: 10.1115/1.4042621 History: Received August 03, 2018; Accepted January 01, 2019

This work presents a finite element analysis-based, topology optimization (TO) methodology for the combined magnetostatic and structural design of electrical machine cores. Our methodology uses the Bi-directional Evolutionary Structural Optimization (BESO) heuristics to remove inefficient elements from a meshed model based on elemental energies. The algorithm improves the average torque density while maintaining structural integrity. To the best of our knowledge, this work represents the first effort to address the structural-magnetostatic problem of electrical machine design using a free-form approach. Using a surface-mounted permanent magnet motor (PMM) as a case study, the methodology is first tested on linear and nonlinear two-dimensional problems whereby it is shown that the rapid convergence achieved makes the algorithm suitable for real-world applications. The proposed optimization scheme can be easily extended to three dimensions, and we propose that the resulting designs are suitable for manufacturing using selective laser melting, a 3D printing technology capable of producing fully dense high-silicon steel components with good soft magnetic properties. Three-dimensional TO results show that the weight of a PMM rotor can be slashed by 50% without affecting its rated torque profile when the actual magnetic permeability of the 3D-printed material is considered.

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Fig. 1

Cross-sectional view of the two-pole PMM used as a case study to test the proposed magnetostatic-structural TO methodology, showing the motor’s main active components and axes frame of reference

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Fig. 2

Magnetization and relative permeability curves for lamination material M250. The dashed lines show the relative permeability values used for linear analysis/optimization.

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Fig. 3

Magnetization curve of Fe-6.9%Si alloy processed using additive manufacturing/SLM

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Fig. 4

Initial performance of PMM along one pole pitch (180 deg). The plots show the rotor magnetic co-energy (a) the rated (b) and cogging torque (c).

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Fig. 5

Schematic 2D representation of the loads and boundary conditions applied to the PMM model under study

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Fig. 6

FEA meshed PMM models for the 2D (a) and 3D studies (b)

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Fig. 7

Sketch of a simple magnetostatic circuit representing the motor

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Fig. 8

Evolution histories of mean magnetic co-energy, volume fraction, and topology in the case of linear magnetostatic TO at rotor angle position θr = 30 deg

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Fig. 9

Effect of the stabilization scheme weights on convergence history in the case of nonlinear magnetic properties

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Fig. 10

Rotor TO considering a material with nonlinear magnetic properties. The final rotor topology for historical weight value 0.95 is shown in (a). In (b), the final rated torque profile is compared to that of full rotor.

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Fig. 11

Variation of the nominal torque (mean) and torque ripple (standard deviation) with the rotor angle considered during TO in case of linear and nonlinear magnetic properties. The rated torque for the full rotor is also plotted for comparison.

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Fig. 12

Pareto plot from structural-magnetostatic BESO. The numbers next to the data points are the structural weight values.

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Fig. 13

Progress of volume fraction, objective function, and maximum von Mises stress as functions of iteration number. The plots refer to the case study with σY = 100 MPa, SF = 4, and adaptive weight assignment scheme.

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Fig. 14

Rated torque profiles produced for various optimal rotor topologies obtained using different magnetostatic-structural weight combinations

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Fig. 15

Various optimized rotor topologies obtained using the structural-magnetostatic BESO method for different combinations of structural (ωs) and magnetostatic (ωm) weights. The color maps show the distributions of the flux density (left column) and von Mises equivalent stress (right column). Optimization run at rotor position θr = 45 deg.

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Fig. 16

Optimized topology using structural-magnetostatic BESO, and von Mises stress distribution under operational loading conditions. The deformed rotor is shown with (a) and without (b) permanent magnets.

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Fig. 17

Optimized three-dimensional rotor topology, before (a) and after surface smoothening (b). A rotor core produced by AM is shown in (c).



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