Electromagnetic field computation for present-day demanding high-end applications such as traction drives for electric vehicles (EV) is the major building block of a complex multiphysics optimization landscape. Given feasible but limited computational resources, such as high-performance computing clusters, there is a master tradeoff between simulation accuracy and computational efficiency. By carefully combining different analysis and computational methods, the related Pareto tradeoff curve might be shifted towards higher performance. That is, rather than going for more simulation accuracy or more computational efficiency, our strategy is to go for more simulation accuracy and more computational efficiency at the same time. This requires orchestrating finite element analysis (FEA), network methods, and machine learning (ML).
With this talk, we offer a glimpse into the journey at Bosch. We set the stage with a feasibility study of a high torque density yokeless and segmented armature axial flux machine for high-speed EV drives [1]. These are proposed as replacements for traditional radial flux machines in the axle traction drive of battery EVs. The focus of the study is on torque density and the ability of such machines to operate at high speeds. Different slot-pole combinations and magnet segmentations are compared, based on several factors: their torque capability, material usage, torque density, and losses of each component (magnet, copper, and iron losses) at maximum speed.
It turns out that losses in the magnets and stator coils are both computationally demanding and a limiting factor for the considered designs. This motivates a proof-of-concept investigation in 2-D, for current diffusion in rectangular conductors, where the diffusion process is influenced by the presence of non-linear ferromagnetic material [2]. Conventional methods like FEA in time domain might turn cumbersome. High-frequency harmonics yield a small penetration depth of the currents, which needs to be resolved by the finite element discretization. In addition, the time discretization not only needs to capture the relevant harmonic contents, but also the diffusion time scale. An alternative approach orchestrates FEA with partial element equivalent circuit (PEEC) methods. The core idea is decoupling the FEA of non-linear ferromagnetic domains from the diffusion analysis of linear conducting domains, which can be treated efficiently by PEEC in the frequency domain. This novel method is applicable to complex multi-conductor configurations, even in the presence of non-linear ferromagnetic material.
Traditionally, FEA is used in the design phase of electrical machines to numerically optimize their performance, which involves computing features such as torque, losses, and flux linkages at each operating point. These intermediate features are used in turn to calculate several downstream key performance indicators (KPIs, e.g., maximum torque on limit curve). However, such computations can be quite heavy and time-consuming. Another orchestration opportunity for improving the computational efficiency and flexibility of simulations used in the design of electrical machines is hybrid modeling, which combines physics-based with data-driven models. We propose a new hybrid model [3] that combines ML with physics-based post-processing. A deep neural network (DNN) is trained on a large volume of stored FEA data in a supervised manner. The DNN maps design parameters (geometry, electrical, material) to intermediate features (torque, losses, flux linkages). During the design phase, FEA is replaced by the DNN, whose response to the design parameters is fed into a physics-based post-processing system to estimate characteristic maps and KPIs.
The talk concludes by a brief assessment of the presented orchestration methods and a birds-eye view on the simulation landscape at Bosch.

References
[1] Ma, Yiwen, et al. “Feasibility Study of High Torque Density Yokeless and Segmented Armature Axial Flux Machine for High Speed EV Drives.” IEMDC The 14th IEEE International Electric Machines and Drives Conference, 2023.
[2] Morisco, David Philipp, et al. “Extended Modelling Approach of Hairpin Winding Eddy Current Losses in High Power Density Traction Machines.” ICEM The 2020 International Conference on Electrical Machines, 2020.
[3] Parekh, Vivek, et al . “Performance Analysis of Electrical Machines Using a Hybrid Data and Physics Driven Model.” IEEE Transactions on Energy Conversion (2023).