Derivation of Hole Sensitivity Formula for Topology Optimization in Magnetostatic System Using Virtual Hole Concept and Shape Sensitivity

PurposeShape optimization using the level-set method is one of the most effective automatic design tools for electromagnetic machines. While level-set method has the advantage of being able to suppress unfeasible shape, it has a weakness of being unable to handle complex topology changes such as perforate at material region. With this method, it is only possible to define simple connected topology, and it is difficult to determine the optimal shape which has holes. Therefore, it is important to efficiently expand the searching area in the optimization process with level-set method. Design/methodology/approachIn this paper, the authors introduce the newly defined hole sensitivity which is based on concept of topological derivatives, and combine it with level-set method to effectively create holes in the search process. Furthermore, they consider a variable bandwidth of gray scale, which indicates the transition width between air and magnetic body and combine it with the hole creation method described above. With these methods, the authors aim to expand the searching area in comparison with the conventional level-set method. FindingsAs a result of applying the proposed methods to a magnetic shielding problem, the multi-layered shielding which effectively reduces the magnetic flux in the target area, is successfully produced. Originality/valueThe proposed methods enable us to effectively create a hole and to expand the searching area in the topology optimization process unlike in the case of conventional level-set method.

Section: Methods Of Creating Holementioning

confidence: 99%

Topology optimization of magnetic shielding using level-set function combined with element-based topological derivatives

Hoshino

Okamoto

Wakao

2018

“…Suppose α and β are two material to be relocated ( α has higher material property), then SE fp ( p ) is the calibrated sensitivity of the original set: where se is the original sensitivity with respect to the objective function [usually calculated by an adjoint variable method (Hong et al , 2015)], while SE α is the likelihood that the element is assigned to material α . For an element of material property α , a negative sensitivity se suggests an increase of the permeability of the element, and thus has a positive SE α and a negative SE β , and vice versa.…”

Section: Finding Optimal Direction Using Min-cut In Nonconstraint Top...mentioning

confidence: 99%

A constrained topology optimization methodology based on budget constrained min-cut

Xia

Sykulski²

2022

Purpose The purpose of this paper is to propose a novel methodology based on budget constrained Min-Cut theorem to solve constrained topology optimization (TO). Design/methodology/approach This paper establishes a weighted network with budget, which is derived from the sensitivity with respect to the constraint function. The total budget carried by the topology evaluates the extent to which the constraint is satisfied. By finding the Min-Cut under budget constraint in each step, the proposed method is able to solve constrained TO problem. Findings The results obtained from a magnetic actuator including a yoke, a coil and an armature have demonstrated that the proposed method is effective to solve constrained TO problem. Originality/value A novel methodology based on budget constrained Min-Cut is proposed to solve constrained TO problem.

“…A dot in an axi-symmetric system in Figure 1(a) is equivalent to the ring torus in Figure 1(b). In an axi-symmetric magnetostatic system, we define dot sensitivity as the variation rate per ring torus volume before and after torus generation when the minor radius of the torus is infinitesimal (Hong et al , 2015): where the volume of the torus is Δ V torus = 2π 2 Rr m 2 . The variation in the objective function because of torus generation in equation (1) is obtained by the integration of shape sensitivity for the torus dot growing from zero to r in radius as: where x is the position of the center of the dot, r m is the minor radius and F(x, r) is the objective function that depends on x and r .…”

Section: Derivation Of Dot Sensitivity Formula In An Axi-symmetric Systemmentioning

confidence: 99%

“…To solve this problem, topological sensitivity, which is called hole and dot sensitivity, was derived in a two-dimensional magnetic system. These sensitivities provide information about variation in the objective function before and after cylinder bar generation in the two-dimensional system (Hong et al , 2015; Park, 2018). With the simultaneous use of shape and topological sensitivities, the design space is expanded and includes the interface and the inside of the domain; this reduces the possibility of a local optimum convergence (Hong et al , 2015; Park, 2018; Céa et al , 2000; Novotny et al , 2003).…”

Section: Introductionmentioning

confidence: 99%

“…These sensitivities provide information about variation in the objective function before and after cylinder bar generation in the two-dimensional system (Hong et al , 2015; Park, 2018). With the simultaneous use of shape and topological sensitivities, the design space is expanded and includes the interface and the inside of the domain; this reduces the possibility of a local optimum convergence (Hong et al , 2015; Park, 2018; Céa et al , 2000; Novotny et al , 2003). This topological sensitivity mentioned above is also required for the axi-symmetric system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system

Hong

Lee

Park

2019

Self Cite

Purpose The purpose of this paper is to propose dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system. Design/methodology/approach The dot sensitivity formula for the axi-symmetric system is derived as a closed form using the continuum shape sensitivity formula. The dot sensitivity method is combined with the level set method to perform topology optimization. Findings Derived dot sensitivity analysis can generate a ferromagnetic ring torus in a vacant region. Thus, an initial design is not needed for the design material. Two design problems are tested to demonstrate the usefulness of dot sensitivity. Originality/value By simultaneously using the shape sensitivity and dot sensitivity, in axi-symmetric magnetic system, the design space is expanded and it includes the interface and the inside of the vacant region. This property can reduce the possibility of local optimum convergence.