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Introduction

More Electric Aircraft (MEA) is a promising market in aviation that offers eco-friendly aircraft with the potential to reduce fuel consumption, emissions, and noise, thereby reducing the environmental impact of aviation [1]. Electric motors in electric aircraft are lighter than their combustion engine counterparts, directly reducing the aircraft's weight and improving its energy conversion efficiency [2]. MEA electric motors offer high power density and reliability, outperforming traditional systems. Permanent Magnet Synchronous Motors (PMSMs) with radial flux are the preferred option due to their high efficiency and power density, even at low speeds [3]. This is vital for high-power generation during take-off and landing. PMSMs don't require current in the rotor, reducing joule losses and increasing energy conversion efficiency. Their use can potentially revolutionize aviation due to lower heat production and higher energy conversion [3]. Choosing suitable materials and structural design for aerospace motors is crucial for their safe and efficient operation in extreme aerospace environments. Aluminum alloys are commonly used due to their lightweight, strength, and corrosion resistance. The design can be optimized to improve power density [4]. Several design and manufacturing factors can enhance motor power density. This analysis specifically studies how stator and rotor back yoke thickness affects power density in permanent magnet motors.

Aerospace Motor Design Challenges

Improved power density PMSMs for electric aircraft are the intended purpose. The method of lightweight structure is a means to increase power density along with satisfying the desired rated torque and lower torque ripple. Optimizing the structural design of a motor permits it to reduce its weight while maintaining its rigidity and strength. Therefore, achieving a compact structural design and finding the right balance between power density and size/weight can be challenging, which defines a major challenge for aerospace motors.

Fig. 1. Motors Design Constraints for Electric Aircraft Application

EMWorks Solutions

Computer-aided design software and advanced simulation tools allow engineers to design, optimize and analyze desired structures. In this study, improving the power density of two models of an aerospace motor is considered through the use of the EMWorks2D product. Studies consist of varying geometric parameters which are pole arc coefficient and core back yoke thickness, to give an optimal lightweight solution for the studied models. The pole arc coefficient and core back yoke thickness are important parameters that can significantly impact the motor's performance and weight. The pole arc coefficient determines the size of the motor's magnetic poles and can impact the motor's torque and efficiency, while the core back yoke thickness affects the amount of magnetic flux that can be carried by the motor's core. Performing transient studies that involve varying geometric parameters can be useful in identifying an optimal lightweight solution for a given electromagnetic system. By analyzing the behaviour of the electromagnetic fields and currents over time for different parameter values, it is possible to identify the design that provides the best balance of performance and weight.

Design Specifications

Two models of PMSM are considered to have a different combination of slots/poles are shown in the following figure [4]. Model I represents a combination of 6 slots-8poles while Model II contains 12 slots and 10 poles. The geometry and electromagnetic simulation for both models are accomplished based on specifications in the table below [4]. 

Fig. 2. Topologies of the Proposed PMSMs: (a) Model I: 6 Slots-8 Poles, (b): Model II: 12 Slots-10 Poles

Simulation Results 

1. Magnetic Flux Density and Average Torque for Initial Models

The electromagnetic simulations of the designed models permit to visualization of the magnetic flux density and calculation of the average torque. These simulations allow for a detailed analysis of the behaviour of the electromagnetic fields and currents in the system, which can help to optimize the design and ensure that it meets the desired performance criteria.
As illustrated in the following figure, the average torque is equal to 10.8 N.m and 11.78 N.m respectively for Model I and II. The average torque satisfies practically the desired rated torque for both models. The torque ripple is equal to 4.26% for Model I and 3.9% for Model II. The torque ripple for Model II is lower, its estimated power density is better than that of Model I.

Fig. 3.  Average Torque Versus Electrical Angle for PMSMs Models

Figure 4 demonstrates that the magnetic flux density in most areas of the core back yoke is between 1.58 T and 2.1 T. For HipeCo50 material, the saturation flux density is 2.35. It is a high-performance magnetic material that offers several advantages over other types of magnetic materials, including high magnetic permeability, low core loss and excellent thermal stability. These properties make it a popular choice for use in a wide range of electromagnetic applications. Thus, the iron core material is not fully used and the two models need to be optimized to give an improved power density motor. The optimization process consists of minimizing the machine mass by varying pole arc coefficient and core back yoke thickness. The main optimization objective is the achievement of an improved aerospace motor that satisfies the desired rated torque with a lower torque ripple.

Fig. 4. Magnetic Flux Density in Studied Models of PMSMs

2. Average Torque and Torque Ripple for Optimized Models

Optimization by Varying Pole Arc Coefficient 

According to the following figure, the optimal value of the pole arc coefficient is 0.945 and 0.917 respectively for Model I and II. These values ensure the desired rated output torque with the lowest torque ripple. 

Fig. 5. Output Torque and Torque Ripple Under Different Pole Arc Coefficient

Optimization by Varying Stator Back Yoke Thickness

Output torque and torque ripple under different values of rotor back yoke thickness demonstrate that the optimal value of rotor yoke thickness respecting optimization objective is 5.5 mm and 4 mm for both Model I and II. If the stator back yoke thickness exceeds the optimal value, the average output torque and the torque ripple are practically unchangeable compared to the optimal point. Whereas, the average torque is less than the optimal value if the thickness is the below the optimal thickness while the torque ripple is larger than the optimal point.

Fig. 6. Output Torque and Torque Ripple Under Different Rotor Back Yoke Thickness

Optimization by Varying Rotor Back Yoke Thickness 

Optimal values of stator back yoke thickness verifying the optimization target are 5 mm for Model I and 4 mm for Model II. If the rotor back yoke thickness is greater than the optimal value, the average output torque and the torque ripple have almost the same value compared to the optimal point. On the other hand, the average torque is less than the optimal value if the thickness is below the optimal thickness while the torque ripple is larger than the optimal point.

Fig. 7. Output Torque and Torque Ripple Under Different Stator Back Yoke Thickness

Analysis According to the Estimated Mass 

According to previous results, two optimal machines are presented with the adoption of combined three optimal parameters as mentioned in Table 2, labeled as Optimized Model I and Optimized Model II.

Table 2. Parameters of the Optimized Models

The output torque of the studied models above is presented in the following figure. The output torque for each model and its optimized structure is practically the same. The only difference between Model I and Optimized Model I is the adoption of a lightweight structure as are Model II and Optimized Model II. We can conclude that the lightweight structure design doesn’t influence the output torque.

Fig. 8. Average Output Torque for Studied Models

The calculation of the machine's mass, as shown in Table 3, proves that PMSM Model I can reduce more mass compared to Model II. For the optimized models, the Optimized PMSM Model II provides less mass than the machine corresponding to Optimized Model I.
 

Results Comparison: EMWorks2D-Reference Article [4]:

Simulation results using EMWorks2D are presented in tables below comparing to results based on the reference article. The first table represents the average output torque as a function of the pole arc coefficient and iron core back yoke thickness. The second table regroups the output average torque of the studied models before and after optimization. The results are close and the error percentage is low.