Optimization of Electromagnetic Layout for E-machine in Electric Vehicles: Achieving High Performance,Efficiency and NVH

Abstract

The development of electric vehicles (EVs) presents the challenge of optimising electric machines to enhance efficiency, compactness, noise, vibration, harshness (NVH), and affordability, while reducing the dependence on heavy rare-earth materials to reduce the CO₂ footprint of electric powertrains. This paper introduces a comprehensive optimization approach for the electromagnetic design of permanent magnet synchronous machines (PMSMs), employing a combination of Design of Experiment (DoE) and Robust Neural Networks (RNN). The optimization framework is utilised to comprehensively address the multiple objectives of an electric machine, including efficiency, noise, vibration, harshness (NVH), and cost. The integration of Artificial Intelligence (AI)-driven modelling has resulted in significant performance improvements, achieving up to 96% total efficiency over the entire load cycle with substantial NVH reductions of up to 20 dB, while reducing the magnet rare earth materials by 35% compared to the baseline. Furthermore, this methodology reduces the simulation time by up to 90%, demonstrating the potential of combining neural network optimization with conventional finite element simulation techniques. The validation of the AI-driven optimization approach with the measurement of the baseline and optimised electric machines for efficiency and vibration is demonstrated for correlation.

Keywords

Electric machines electromagnetic optimization and modelling design of experiment optimization neural network-modelling multi-objective and multi-physics optimization topology optimization robustness and sensitivity analysis electric drive E-machine efficiency noise vibration and harshness (NVH)electromagnetic finite element modelling

1 Introduction

In the development of electric vehicles (EV), optimising electric machines (e-machines) is crucial for enhancing sustainability, efficiency, and performance. A crucial focus of innovation lies in the optimization of electromagnetic layouts, which involves harmonising diverse demands such as performance, efficiency, compactness, noise, vibration, and harshness (NVH) requirements, while minimising the use of heavy rare earth materials and CO₂ footprints [1–3]. Despite advancements in simulation technologies and optimization algorithms, achieving equilibrium continues to be a complex task.

In this paper, a comprehensive use case introducing an all-in-one optimization approach for electromagnetic layouts of permanent magnet synchronous machines (PMSM) is presented. This approach employs a multi-objective optimization method that combines the design of experiment (DoE) and Robust Neural Networks (RNN) to enhance the efficiency and performance of e-machines while considering the complexities of design compactness, cost-effectiveness, noise, vibration, and harshness (NVH).

This paper is organised as follows: Section 2 covers the study’s framework for the optimization of electromagnetic layouts of PMSM, highlighting the use of Design of Experiment (DoE) and Robust neural network (RNN) methodologies. Section 3 highlights the optimization results in a comparative manner between different PMSMs topologies in terms of their driving cycle efficiencies, electromagnetic and mechanical order separation, and the reduction in the use of rare earth materials as magnets to minimise cost. In Section 4, the validation of the optimization methodology is correlated between the simulated and measured efficiency and the measured improvement in noise and vibration between the baseline and optimised electric drive.

2 Topology Optimization with Design of Experiment (DoE) Approach

The electric machine design process starts with various possible electromagnetic layouts with many slots and poles combinations of permanent magnet synchronous machine (PMSM); in this study PMSM was selected due to its high torque, power densities and high efficiency, while the cost of the magnetic materials was balanced through the optimization. For each electric machine topology, the selected geometries of the electric machine parts such as the stator, rotor, magnets, and copper dimensions were parameterized with a predefined range, as shown in the example in Fig. 1.

The selected parameters and their ranges were used to create a design space/matrix using the D-optimal approach, which is a computer-aided optimization design that involves selecting the most optimal subset of electric machine variants from all possible geometric combinations. The goal of the D-optimal approach is to maximize the information gained from the combination of electric machine variants while minimizing the overall size of the design space compared to the full factorial approach [8].

Fig. 1.

Parameterization of permanent magnet synchronous machine topologies.

2.1 Design Matrix

The design matrix denoted as X in Eq. (1) is an n × β matrix.

y = X β + ϵ .

(1)

“y” and “ϵ” are both vectors with as many elements as there are runs in the experiment. The number of runs, also known as the sample size, is denoted by the variable “n”. The vector “y” contains the n responses, while the vector “ϵ” contains the “n” deviations between the responses and “β” represents the unknown parameters of the model [4].

2.2 Criteria for D-optimality

Once the design matrix “X” is defined, the criterion for selecting the best design space/matrix is to maximize the determinant of the information matrix |X^′X|. This implies that the optimal design matrix X^∗ consists of “n” experiments that maximize the determinant of (X^′X), as shown in Eq. (2). The connection between the design matrix and the determinant explains the use of the “D” in the term “D-optimal” [8].

| X^{*^{'}} X^{*} | = max (| X^{'} X |) .

(2)

The design space/matrix was implemented using AVL software CAMEO^{^TM}, an example of a parameterized PMSM geometries is shown in Fig. 2, where each blue dot represents a unique e-machine geometric variant. Minimizing the optimization design matrix is a crucial step because the generated design space is used in finite element simulations, which are limited in terms of resources, as well as to reduce the development time of the electric machine and cope with the many changes that occur during the development. For instance, the D-optimal approach generates a design matrix for the 14 geometry parameters demonstrated in Fig. 1 with approximately 800 electric machine variations that can be simulated in 8 hours, while a full factorial method generates more than 10000 electric machines that would take more than 110 hours for the same modelling prediction accuracy.

Fig. 2.

Design space/matrix of parameterized geometries of permanent magnet synchronous machine topology.

The obtained geometries were then analysed using electromagnetic finite element in JMAG^{^TM} as shown in Fig. 3 to obtain any quantitative responses that are of interest for optimization such as torque, power, losses, electromagnetic critical forces, and active weights for cost optimization.

Fig. 3.

Electromagnetic finite element analysis in JMAG^{^TM} of e-machine topologies (left: 48 slots, 8 poles, 6 hairpins per slot with 1V rotor and right: 72 slots, 6 poles, 8 hairpins per slot with 2V rotor).

Artificial Intelligence (AI) is then used through a Robust Neural Network (RNN) to model and predict the electric machine responses. Through RNN modelling, not only can the nonlinearity of the electromagnetic responses be built, but also the interactions between the geometry parameters and responses were optimized. The quality of the modelling between the actual response and RNN models can be assessed using metrics such as R-squared (R2), as shown in Fig. 4.

Fig. 4.

Robust Neural Network (RNN) modelling of electric machine responses.

With the previously mentioned modelling sequence, many PMSM topologies can be optimized simultaneously for multiple objectives, such as torque and power requirements, critical electromagnetic forces for noise, vibration, and harshness (NVH), driving cycle efficiency, and the active cost of the e-machines to find the optimal e-machine topology with its optimized geometries.

Figure 5 illustrates the multi-objective optimization targets for various electric machine responses, such as maximizing peak torque while minimizing cost and weight. Through this approach, Pareto fronts of optimal e-machine topologies and geometries can be obtained, where each dot in the Pareto front represents an optimal set of electric machine geometries, resulting in a design that can be further analysed through finite element simulation.

Each e-machine configuration comprises a combination of numbers of slots, poles, and hairpin layers per slot, which are marked by different colours in Fig. 6. There are numerous geometric possibilities for each configuration variant, and each geometric variation has distinct responses to the same objective such as torque and losses. Considering these circumstances, it is impractical to manually determine the optimal electric machine solution. Instead, artificial intelligence (AI) through a Robust Neural Network (RNN) was utilized to produce billions of new variants (as depicted by the red cloud in Figs 5 and 6) and to identify the optimal electric machine topology with its optimal set of geometric parameters, a genetic algorithm was used to generate Pareto fronts. It is worth noting that the generated electric machine variants by the neural network can be affected by the outliers simulated variants fed to the neural network model especially at the borders of the shown red cloud in Figs 5 and 6, the prediction of those variants performance by neural network modelling could have uncertainties, proposed methodologies in [14] using techniques related to AI (in particular, soft computing and fuzzy similarities) could improve the prediction in such area.

Fig. 5.

Simultaneous multi-objectives optimization of PMSM topology: (a) maximize peak torque with minimum cost, (b) maximize peak torque with minimum weight.

Fig. 6.

Simultaneous multi-objectives optimization of different PMSM topologies (left) with AI generated variants and pareto front optimal solutions (right).

The variants within the Pareto front shown in Figs 5 and 6 representing the optimal set of geometries of the optimized topologies are then extracted and compared relative to each other for several aspects such as efficiency, power density, cost and noise, vibration, and harshness (NVH) (initially in terms of electromagnetic order collisions with gears’ mechanical orders). Figure 7 shows a relative comparison of optimized PMSM topologies based on their power density and cost.

Fig. 7.

Relative comparison between different optimized PMSM topologies for power density versus cost.

3 Optimization Results

The Worldwide Harmonized Light Vehicles Test Cycle (WLTC) was employed to evaluate the efficiency of the optimized e-machine variants in a standardized manner. This standard cycle is utilized to determine the levels of pollutants, CO₂ emissions, and fuel consumption of traditional and hybrid vehicles as well as the range of fully electric vehicles [12]. The required torque-speed profile, which is dependent on the electric vehicle’s requirements, mass, and class, is shown in Fig. 8. The energy consumption was calculated collectively for the entire WLTC load cycle for every electric machine variant during the optimization process.

Fig. 8.

Worldwide Harmonised Light Vehicles Test (WLTC) torque and speed profiles.

A closer comparison between the optimized topologies in terms of their efficiency in the WLTC driving cycle and their geometric features, such as total length, outer stator diameter, and shaft diameter, is shown in Fig. 9. Additionally, the electromagnetic force orders that depend on the number of poles and slots are compared to the transmission gear orders to avoid order collisions that can impose noise, vibration, and harshness (NVH) issues. It can be seen that each topology has its advantages and disadvantages. A higher number of poles, such as 14 and 12 poles (V1 to V4), would allow for smaller weights and packages, as the end windings are shorter because of the shorter pole pitch. They also have an advantage for NVH because their lowest nonzero space order has a higher eigenmode shape that is more difficult to excite, and their electromagnetic orders (multiples of rotor poles and slots) are far from the initial gear orders of (23, 25, 46, 50) used in this application. On the other hand, their efficiencies are at the lower end in the comparison, as higher poles mean higher synchronous frequency and therefore higher iron losses, such as eddy and hysteresis losses, additionaly higher poles require higher switching frequency which has impact on inverter losses.

In contrast, topologies with lower number of poles (V5 to V13) get better efficiency due to lower synchronous frequencies, while their weight and package would increase due to longer end-windings. Moreover, these topologies require greater attention to NVH, as their lowest non-zero space orders are lower, easier to excite and can overlap with gears orders. In this study, the highest priority was placed on achieving the highest efficiency, and thus, variant 12 was chosen for its topology of 8 poles, 48 slots with double-V magnets rotor configuration and 8 hairpins per slot. This optimized electric machine variant achieved the highest efficiency of 96% of the entire driving cycle with compromised total length and electromagnetic orders in comparison to the other optimized topologies.

Fig. 9.

Comparison between optimal generated PMSM DoE topologies.

Figure 10 shows the efficiency map of variant 12, illustrating the torque and speed characteristics of this variant, and the load points of the WLTC driving cycle are also illustrated on the efficiency map. It can be seen that the optimization enabled the e-machine to cover most of the WLTC load points within its highest efficiency regions, which is the goal of such optimization in which the e-machine is utilized in its most efficient regions to improve the overall energy consumption of the vehicle powertrain.

The efficiency map presented in Fig. 10 demonstrates the electric machine efficiency over the torque and speed range of variant 12, as well as the load points of the Worldwide Harmonized Light Vehicles Test Procedure (WLTC) driving cycle. It is evident from the map that the optimization process enabled the electric machine to cover the majority of the WLTC load points within its highest-efficiency regions, especially the highest energy demanding loads. This is the primary objective of such an optimization, as the electric machine is utilized in its most efficient regions to enhance the overall energy consumption of the vehicle powertrain.

Fig. 10.

Optimized 8P48S PMSM topology (Variant 12) with 96% efficiency in driving cycle (WLTC).

Simultaneously, an initial examination of Noise, Vibration, and Harshness (NVH) was conducted by analyzing the analytical Campbell diagram, which displays the collision of noise orders between mechanical gear orders and electromagnetic orders stimulated by the chosen e-machine topology. As illustrated in Fig. 11, the initial two-stage gear orders of (23, 25, 46, 50) intersect the electromagnetic orders of the selected e-machine topology with a ratio of less than 5%, particularly at mechanical orders of 25 and 50 with electromagnetic orders of 24 and 48, respectively. Consequently, such issues can be prevented by adjusting the number of teeth in the first gear stage to 26 and the second gear stage to 23, thereby updating the gear mechanical orders to (23, 26, 46, 52) to avoid order collisions in the early development stage.

In order to minimize the electromagnetic excitation caused by electromagnetic stator forces, which is included in the optimization, to a level below the noise sound power target of the e-machine, a noise, vibration, and harshness (NVH) simulation is conducted to verify that the noise and vibration of the optimized e-machine, including its electromagnetic excitation, are below the noise sound power target level. Figure 12 demonstrates that the optimized e-machine has a reduced noise level compared with the baseline e-machine and has achieved its target.

Fig. 11.

Campbell Plot showing the relative order separation between V12 PMSM (8 poles, 48 slots) with the mechanical gear orders.

Fig. 12.

Per-unit sound power level between baseline e-machine and optimized e-machine geometry.

The utilization of such optimization methodology allows for the examination of specific factors, such as the weights of the active materials that have the most influence on the cost of the electric drive, including permanent magnets, copper, and lamination steel. The objective of this analysis was to identify an optimized material weight distribution that provides a cost-effective e-machine solution. Permanent magnets, in particular, have the greatest impact on cost because of the use of heavy rare earth materials such as neodymium (Nd), which is essential for magnetic field density and torque production. In addition, dysprosium (Dy) and terbium (Tb) are used to increase the magnet coercivity required to operate at higher temperatures, which can reach up to 180–200 °C at high speeds, and to prevent demagnetization caused by higher temperatures and/or external electromagnetic fields from the stator windings. As illustrated in Fig. 13, there is an inverse relationship between e-machine losses at low speeds and torque areas where the driving cycle loads are concentrated. It can be observed at 1552 rpm and a load of 55 Nm that decreasing losses will result in an increase in magnet weights, and consequently, an increase in cost. However, reducing the magnet weight for cost increases the losses. Nevertheless, with such an optimization approach, an optimal electric machine solution could be obtained with a reduction of over 35% in the magnet weight and a decrease of approximately 20% in the e-machine losses, as illustrated by the green box in Fig. 13.

Fig. 13.

Design of experiment optimization results: relation between total losses to magnets weight at 1552 rpm, 55 Nm.

4 Validation

To verify the efficacy of the analysis and optimization techniques employed, an evaluation of the World Harmonized Light Vehicle Test Procedure (WLTC) efficiency of the front and rear electric axles in the vehicle was conducted, and the results were compared with simulations. As illustrated in Fig. 14, a strong correlation was observed. The impact of the optimization of electric machine electromagnetic forces on noise, vibration, and harshness (NVH) was demonstrated through structural vibration measurements and comparisons between the A and B samples. As indicated in Fig. 15, the NVH improvement was evident in the structure-borne measurement in the B-sample. Specifically, the vibration noise was reduced by 15 dB with the new optimized electric machine and by 20 dB on the inverter housing, which is also affected by the vibration and noise excitation from the electric machine.

Fig. 14.

Correlation between measured and simulated WLTC of front and rear electric axles including e-machine, inverter and transmission.

Fig. 15.

Structure borne NVH measurement of A-sample and optimized B-sample of electric drive.

5 Conclusions

In this paper, artificial intelligence (AI) methods were utilised comprehensively to optimise electric machines through multi-objective genetic algorithms and robust neural networks (RNN), in order to reduce the optimization design spaces, resulting in decreased simulation time by 90% and resources needed to find the optimal electric machine topology. Such optimization algorithms were utilised to analyse vast amounts of data collected from electromagnetic finite element simulations. Neural networks were used to identify patterns, correlations, and co-dependencies between various input parameters, such as electric machine topologies and geometries, and their impact on performance, cost, and noise, vibration, and harshness (NVH). This led to a global optimization of all attributes of electric drives.

The paper presented optimization case studies in electric machine design, where Design of Experiment (DoE) optimization is utilised for multiple objectives, including torque density, cost, and NVH, to find the optimal PMSM topology in terms of the number of poles, slots, and number of hairpin layers in the slot with its optimal geometry to maximize the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) efficiency of the electric machine to 96% while reducing the use of rare earth materials by more than 35% to provide a cost-effective electric drive solution. The optimization methodology was also verified through measurements to reduce noise and vibration levels by more than 20 dB between development samples to meet the noise, vibration, and harshness (NVH) requirement.

Footnotes

Acknowledgements

The authors would like to thank AVL CAMEO team for the support and for providing powerful neural network and artificial intelligence methodologies that are used in such electric drive applications.

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