An Air-Gap Element for the Isogeometric Space-Time-Simulation of Electric Machines

Abstract

Space-time methods promise more efficient time-domain simulations, in particular of electrical machines. However, most approaches require the motion to be known in advance so that it can be included in the space-time mesh. To overcome this problem, this paper proposes to use the well-known air-gap element for the rotor-stator coupling of an isogeometric machine model. First, we derive the solution in the air-gap region and then employ it to couple the rotor and stator. This coupling is angle dependent and we show how to efficiently update the coupling matrices to a different angle, avoiding expensive quadrature. Finally, the resulting time-dependent problem is solved in a space-time setting. The spatial discretization using isogeometric analysis is particularly suitable for coupling via the air-gap element, as NURBS can exactly represent the geometry of the air-gap. Furthermore, the model including the air-gap element can be seamlessly transferred to the space-time setting. However, the air-gap element is well known in the literature. The originality of this work is the application to isogeometric analysis and space-time.

Figures (4)

• Figure 1: Schematic cross-section of an electric machine. Here, the inner domain $\Omega_R$ is the rotor, $\Omega_S$ denotes the region of the stator and $\Omega_A$ denotes the region of the air-gap.
• Figure 2: Comparison of condition numbers for unscaled and scaled systems.
• Figure 3: Geometry model for the PSMS. The air-gap element connects the current-driven stator to the rotor, where the rotation is prescribed.
• Figure 4: Torque evaluation for different scenarios. The torque curves are compared for the static case, one time stepping scheme (implicit Euler) and the space-time solution.