An Air-Gap Element for the Isogeometric Space-Time-Simulation of Electric Machines
For researchers in computational electromagnetics, this work provides an incremental extension of the air-gap element to isogeometric analysis and space-time methods.
This paper proposes an air-gap element for rotor-stator coupling in isogeometric space-time simulations of electric machines, enabling efficient angle-dependent coupling without requiring motion to be known in advance. The method avoids expensive quadrature for updating coupling matrices.
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.