Sensitivity Analysis using the Virtual Work Principle For 2D Magnetostatic Problems

Abstract

The rise of shape and topology optimization techniques has opened new possibilities to find innovative designs for electromagnetic devices such as actuators or rotating machines. This paper provides an analytical sensitivity analysis for the magnetic force and torque based on the virtual work principle and suitable for those kinds of optimization.

Solid Isotropic Material with Penalization-Based Topology Optimization of Three-Dimensional Magnetic Circuits with Mechanical Constraints

“…We have seen in the previous sections that the material distribution ϱ(x) is responsible for both the magnetic µ r (x) (with Equation ( 4)) and mechanical E(x) (with Equation ( 7)) properties by defining iron (resp., air) regions where ϱ(x) = 1 (resp., ϱ(x) = 0). We can thus define a coupled optimization problem in which an optimal distribution ϱ is sought such that it simultaneously minimizes the error between B and B 0 (Equation ( 5)) while simultaneously minimizing one of the two mechanical criteria of Equation (9) or Equation (11).…”

“…Thus, the designs obtained in magnetostatic problems are not always mechanically robust. They are sometimes not manufacturable and sometimes unable to withstand the mechanical stress experienced over their lifetime [10,11]. Note that a first study was recently conducted in [12] to develop a multiphysical topology optimization code to design electrical machines using 2D simplification.…”