Isogeometric Shape Optimization of Ferromagnetic Materials in Magnetic Actuators

We present an isogeometric shape optimization method for the design of magnetic actuators. The objective is to maximize the magnetic force of actuators, which tends to be highly dependent on the geometry around air gap. The isogeometric shape optimization is known to be robust for the actuator design, since it can preserve the exact geometry during the design optimization. Using the Maxwell stress tensor method, the magnetic force is calculated through the isogeometric analysis. The analytical design sensitivity provides geometric exactness due to the use of non-uniform rational B-splines basis functions. The optimization problem is solved using a gradient-based algorithm of modified method of feasible directions. To demonstrate the robustness of the isogeometric method, the geometric dependence of magnetic forces is investigated. In addition, the isogeometric optimization method is applied to the design problems of linear and rotating actuators, which yields the optimal shape of the ferromagnetic materials around the air gap.