Model Order Reduction of an Electromagnetic Actuator with Moving Components via Piecewise Quadratic Coupling

A large class of actuators relies on electromagnetism to generate forces or torques, which in turn cause motion. Characterizing these interactions often requires numerical methods such as the finite element method. Moving components pose a challenge for such methodologies as the topology changes, also altering the underlying equations. A well-established way to circumvent this problem is a sliding mesh approach. The components in relative motion are separated and dynamically coupled with respect to their position. This concept of coupling is fully compatible to model order reduction (MOR), which generates surrogate models of drastically smaller dimension while hardly compromising any accuracy. Previous work on MOR in this context has deployed interpolation of system matrices already coupled. In contrast, our preceding study has proposed to sample a single uncoupled system and coupling equations for a grid of positions. Models resulting from this piecewise linear computation of coupling matrices have demonstrated superior accuracy compared to established interpolation. Furthermore, this setup is compatible with MOR and even preserves the position-dependent coupling. Present study extends this coupling-focused strategy to quadratic finite elements and coupling. Hence, a piecewise quadratic function represents the changing coupling due to moving meshes. Its combination with MOR ensures minimal computational cost during operation. An electromagnetic actuator for multistable vertical displacement serves as a numerical case study.