Topology Optimization of Functionally Graded Structure for Electromechanical Device

Abstract

The functionally graded structure has a spatially different distribution of microstructure or materials. This characteristic of a functionally graded structure has relatively better performance in the same weight. However, it is very hard work to design and manufacture a functionally graded structure for target performance by considering both macrostructure and microstructure. There has been some research on developing methods of designing a functionally graded structure. Multi-scale topology optimization is a design optimization method that can design simultaneously both macrostructure and microstructure. While previous research of multi-scale topology optimization has been conducted in the structural design problem, it has been hardly carried out structural design in the magnetic problem. In this research, the multi-scale topology optimization is applied to structural design in the magnetic problem and the mapping scheme is proposed for manufacturing. The analysis has to be conducted prior to the designing process. Because the functionally graded structure is a heterogeneous structure that has spatially diverse microstructures, a very high computation cost is required for performance analysis. The homogenization analysis calculates homogenized material properties based on a heterogeneous unit cell and it can reduce the computation cost. Homogenized magnetic permeability used in this research is calculated by the homogenization analysis depending on each design variable of the heterogeneous unit cell. The homogenized magnetic permeability is used for topology optimization as a material interpolation function. The design variable for penalization is added to obtain a clear layout of the structure. As a result, the functionally graded structure for an electromechanical device with a clear layout is designed.

The post-processing is conducted to manufacture the design optimization result. In this study, the lattice mapping scheme is proposed for the manufacturability of design results. In the mapping process, the design result is divided by mapping size, and the design variable is converted to the mapped geometry in CAD software through being averaged on the mapping domain.

In this research, the topology optimization based on homogenization analysis, and lattice mapping scheme for manufacturing are applied to an optimization problem for magnetic force maximization. The design optimized functionally graded structure has a higher magnetic force than a non-functionally graded structure at a low volume constraint range. The design optimization result is converted to manufacturable results by mapping process and the mockup model is manufactured by 3D printing to confirm the manufacturability.