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Abstract Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) is utilized to parameterize the level set function. With CBF, the upper and lower bounds of the design variables can be identified explicitly, compared with the trial and error approach when the radial basis function (RBF) is used. In the macroscale, the ‘color’ level set is employed to model the multiple material phases, where different materials are represented using combined level set functions like mixing colors from primary colors. At the end of this optimization, the optimal material properties for different constructing materials will be identified. By using those optimal values as targets, a second structural topology optimization is carried out to determine the exact mesoscale metamaterial structural layout. In both the macroscale and the mesoscale structural topology optimization, an energy functional is utilized to regularize the level set function to be a distance-regularized level set function, where the level set function is maintained as a signed distance function along the design boundary and kept flat elsewhere. The signed distance slopes can ensure a steady and accurate material property interpolation from the level set model to the physical model. The flat surfaces can make it easier for the level set function to penetrate its zero level to create new holes. After obtaining both the macroscale structural layouts and the mesoscale metamaterial layouts, the hierarchical multimaterial structure is finalized via a local-shape-preserving conformal mapping to preserve the designed material properties. Unlike the conventional conformal mapping using the Ricci flow method where only four control points are utilized, in this research, a multi-control-point conformal mapping is utilized to be more flexible and adaptive in handling complex geometries. The conformally mapped multi-material hierarchical structure models can be directly used for additive manufacturing, concluding the entire process of designing, mapping, and manufacturing.
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Robust Topology Optimization of Synchronous Reluctance Motors Using Cardinal Basis Function Based Level Set Method
Abstract Synchronous reluctance motors (SynRMs) have gained considerable attention in the field of electric vehicles as they reduce the need for permanent magnets in the rotor, resulting in less material and manufacturing costs. However, their lower average torque and torque ripple vibrations have been identified as key issues that require resolution. In this study, we present a SynRM design framework employing the cardinal basis functions (CBF)-based parametric level set method. The SynRms design problem is recast as a variational problem constrained by Maxwell’s equations which describe the behavior of electric and magnetic fields in the SynRM. A continuum shape sensitivity analysis is carried out using the material derivative and adjoint method. A distance regularization energy function is employed to maintain the level set function as a signed distance function during the optimization. The parametric topology optimization problem is computationally solved using the Method of Moving Asymptotes (MMA). To demonstrate the effectiveness of our approach, we present a numerical example that compares the torque characteristics of the optimal design with those of a reference design. Preliminary results show that the optimized SynRM has a 30.30% increase in average torque, along with a slight increase in torque ripple, compared to the reference model.
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- PAR ID:
- 10435135
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- ISBN:
- 978-0-7918-8731-8
- Format(s):
- Medium: X
- Location:
- Boston, Massachusetts, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DETC2023-115068
