On torque computation in electric machine simulation by harmonic mortar methods

Abstract

The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the torque computation are derived by energetic considerations, and their realization by harmonic mortar finite element and isogeometric analysis discretizations is discussed. Numerical tests are presented to illustrate the theoretical results and demonstrate the potential of harmonic mortar methods for the evaluation of torque ripples.

Robust Design Optimization of Electric Machines with Isogeometric Analysis

“…where H = νB denotes the magnetic field strength, with B as the magnetic flux density, and both A z and H θ are evaluated in their respective rotor or stator local coordinate systems in dependence on the rotation angle α. This ensures the continuity of the magnetic vector potential A z and the azimuthal magnetic field strength H θ across Γ ag [24]. A visualization of the the boundary conditions can be found in Figure 1.…”

“…This matrix contains block diagonal entries of sine and cosine functions, thereby eliminating the need for the reassembly of the coupling matrix for each α. This improves the computational efficiency when evaluating multiple rotation angles [24]. For more details about the discretization procedure, see [9].…”

How to build the optimal magnet assembly for magnetocaloric cooling: Structural optimization with isogeometric analysis

“…In the context of IGA, harmonic mortaring has been proposed to efficiently simulate rotating electric machines, see, e.g., Merkel et al (2021), Bontinck et al (2018) and Egger et al (2022). This method is also suitable for the case of a magnetocaloric cooling device.…”

“…Here, the stiffness matrix 𝐊, the discrete solution vector for the magnetic vector potential 𝐮, and the contribution of the permanent magnets 𝐛 are separated on the domains 𝛺 rt and 𝛺 st . Further details on the coupling matrices 𝐆 rt , 𝐆 st and the coupling coefficients 𝝀 can be found in Egger et al (2022) and Bontinck et al (2018).…”

“…Using this formulation, the torque can be directly computed using the Lagrange multipliers 𝝀, as explained in Egger et al (2022).…”