Lightweight Design of an Asymmetrical Generator Based on Topology Optimization for Helicopter

Abstract

This paper proposes a new alternating stage permanent magnet synchronous generator (ASPMSG) that is suitable for helicopter motor applications. The machine topology and the working principle of the ASPMSG are first introduced. The slot-pole matching of the motor is studied according to the application environment and requirements of the motor. In addition, the main structural parameters of the motor, such as the maximum EMF (electromotive force) and the minimum harmonic, are optimized. Finally, the topology optimization method is used to design the lightweight motor, and the optimized mass of the optimized area reaches 68.29% while the output of the ASPMSG is almost unaffected. The simulation results show that the proposed ASPMSG topology has higher power density under the conditions satisfying the application requirements of helicopter motors.

1. Introduction

The generator is the key technology to realize greater electric aircraft performance [1,2,3]. Currently, helicopter motors are developing towards high-power density and high efficiency [4]. On the premise of ensuring the output capacity and reliability of the helicopter motor, the realization of a lightweight design and the reduction of the motor volume are issues that need to be further studied.

At present, the generators used in the aviation generation system can be divided into switched reluctance motors (SRM), three-stage brushless synchronous generators (TSBSM), asynchronous generators, etc. [5]. The SRM have the advantages of a simple structure, low cost, and high reliability [6]. A circulating-current-excited switched reluctance generator system using a standard diode rectifier was proposed by Sun et al. [7], which can provide DC power with a standard diode rectifier. A novel azimuthal SRM, which could be used as a linear electric generator and had good performance in wave energy conversion, was proposed by García-Tabarés et al. [8]. However, the air gap of the SRM is larger than that of the ordinary motor, which requires additional current to establish the magnetic field. The SRM has significant torque vibration and noise and suffers high rotor loss in high-speed applications due to the effect of the pulsating magnetic field [9].

Three-stage generators are common helicopter motors due to their reliable safety. A commonly used existing generator for helicopters is a three-stage generator in which the speed is 8000 rpm, frequency is 400 Hz, rated voltage is 95 V, and total mass is 25.84 kg. The three-stage motor with a traditional structure has reliable safety, but its output power density is small, its size is large, and its structure is complex, which indicates the need for a new structure to be proposed. A new structure of a three-stage brushless synchronous generator was established by Zhao et al. [10]. One of the stator windings could be cut off after the engine was ignited to weaken the excitation current of the main motor so that the speed range could be broadened. The structure and control strategy of a new two-phase brushless exciter was proposed by Jiao et al. [11] in which the excitation winding of the exciter used two-phase symmetrical winding, and a two-phase inverter was used to provide an excitation current for the motor. However, because of the three-stage system, the structure of the motor is complex, and the weight and space occupation is larger than other generators.

A squirrel cage asynchronous motor or doubly fed asynchronous motor is also often used as an asynchronous generator (AG). The advantages of AGs are their simple structure, suitability for high-speed operation, low noise, high efficiency, and reliability. An aviation cage-type asynchronous generator, which used a parallel resonant high-frequency AC link inverter and a single-phase pulse width regulator, was investigated by Alan et al. [12]. An AG with a winding capable of switching between the double star and star delta forms was proposed by Barakin et al. [13], which used the stator winding of an autotransformer to supply power to a capacitor at a higher voltage. AGs have the disadvantage that additional magnetized reactive power is required to maintain the rotor excitation, and the digital controller is more complicated due to the nonlinearity of the control.

Compared with traditional motors, permanent magnet synchronous motors (PMSM) have the advantages of high reliability, simple structure, high-power density, and strong overload capacity. PMSM have shown great advantages for generators with strict requirements for size and weight in the aviation field. Scholars from the University of Nottingham introduced a 270 V DC high-power density PMSM generator, which used a surface-mounted permanent magnet motor. The permanent magnet adopted a samarium cobalt magnet (Sm2Co17) material, and the magnetization method was the Halbach structure to improve the air gap flux density [14,15]. A high-speed generator for aerospace applications with short-circuit protection was designed and tested. The rotor was made of solid cylindrical permanent magnets that were segmented along the axial direction and magnetized along the diameter direction in work by Ismagilov et al. [16]. Although, for the traditional PMSM generator, the power density of the surface-mounted motor is not high enough, and the built-in type will be affected by stress because the permanent magnet is located inside the rotor.

In order to further improve the power density of the motor, the lightweight method is studied. A lightweight method was proposed by Fang et al. [17] based on magnetic density to lighten the area where the magnetic density of the motor was zero, and the power density of the motor was improved to 6 kW/kg. In Terao et al. [18], a lightweight method was proposed based on the changes in the thickness of the back yoke, which needs to find the balance between magnetic flux leakage and output power density after lightweight. The tooth slot structure was optimized in work by Song et al. [19], and a separating tooth structure was proposed that could simultaneously play the role of back yoke and tooth to lighten the motor. The method based on model analysis and electromagnetic calculation is theoretical and limited by the model structure itself, and it is difficult to achieve new breakthroughs using this method.

Based on the limitations of the above motors and lightweight methods, the contribution of this paper is to propose a new alternating stage permanent magnet synchronous generator (ASPMSG) that is suitable for helicopter motor applications. This paper comprehensively analyzes the topology of the motor and the slot-pole coordination under this application environment and optimizes the parameters of the motor structure to improve the EMF (electromotive force) and reduce the harmonic content. Methods of topology optimization and a genetic algorithm are used for the lightweight design of the motor. The alternating pole method can reduce the number of permanent magnets required while maintaining a certain output capacity, with a simple structure and high reliability [20], which is combined with the lightweight method to improve the power density of the motor.

2. Machine Topology and Operation Principle

2.1. Machine Topology

Figure 1 and Figure 2 show the 3D and 2D structures of the proposed ASPMSG model, respectively. The proposed topology consists of a built-in rotor module and a stator module with 6 poles and 81 slots. A permanent magnet with alternating poles is mounted on the rotor. The magnetization direction of the permanent magnets intersects to collect the flux lines. The magnetic obstacles between the permanent magnets are in order to ensure output performance.

2.2. Operation Principle

As mentioned above, the PM is the main contributor to the generation of EMF in an ASPMSG. For the current aviation application environment, the frequency of an aeroengine is mostly 400 Hz. Therefore, when the number of pole pairs is determined to be three, the speed is also determined to be 8000 rpm. However, because of the universality of the proposed method, higher or lower speeds have no effect. This paper chose 5000 rpm as the comparison speed. The results of phase EMF and FFT (Fast Fourier Transform) analysis of the ASPMSG at 5000 rpm and 8000 rpm are shown in Figure 3 and Figure 4. It can be seen from Figure 3 and Figure 4 that the waveform of the EMF is sinusoidal and symmetrical regardless of the working state. Figure 4 shows that the fundamental harmonic of the proposed topology was dominant, while other harmonics were lower.

3. Selection of Slot-Pole Combination

This section is divided into subsections and provides a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

The operating frequency of the helicopter motor is 400 Hz, and the engine speed is 8000 rpm, according to

$$N=\frac{60f}{p}$$

(1)

where N is the speed, p is the pole pairs, and f is the frequency. The pole pairs of the motor are limited to three. The pole-slot is shown as

$$Z=2p\pm 1orZ=2p\pm 2$$

(2)

where the slot number Z must be an integer multiple of three due to the three-phase winding.

The main objective of this paper is to design a high-power density motor that considers not only the overall quality of the motor but also the loss of the motor. The fractional slot concentrated winding PMSM has the potential to improve power density, reduce cogging torque, and improve fault tolerance. In combination with the requirements of the high-power density of the motor, the winding was mainly selected from the consideration of reducing the effective mass of the motor, and the motor winding was selected as the fractional slot concentrated winding. From the perspective of lightweight and high-power density, this paper selected the design method with more slots and set up the proposed motor with 6 poles and 81 slots by using the method of pole-slot combination. Figure 5 shows the cogging torque of the proposed ASPMSG. As shown in Figure 5, the amplitude of cogging torque is less than 0.4 Nm. In this condition, the prime mover can easily tow the proposed generator and decrease working noise.

In order to achieve a better-performing and lightweight motor, the main structural parameters of the motor needed to be optimized by multiple objectives, and the motor rotors needed to be optimized by topology. An optimization flow chart is shown in Figure 6. After the optimization objective and function were determined, modeling and finite element analysis were carried out. To optimize the motor structure, a genetic algorithm was used to optimize multiple parameters, and analysis was completed to determine whether the optimization results met the design objectives. When the structure optimization was finished, the topology optimization method was used for the motor based on the Gauss finite element to achieve the purpose of a lightweight motor, which was the optimization of the power density of the motor.

4. Parameter Optimization

Each part of the motor was parameterized. When dimensions are optimized, the corresponding variables can be directly parameterized and scanned without creating new models, which facilitates the optimization of the design. The stator slot adopted the half seal pyriform trough. Figure 7 shows the parametric design of the stator slot, where x₁ is gap length, x₂ is the length of the stator yoke, x₃ is half of the slot width, x₄ is slot height, and x₅ is groove depth. In the optimization process, the outer diameter of the stator is 101 mm, and the outer diameter of the rotor is 60 mm, which is a commonly used aviation motor size.

The permanent magnet pole adopted a double-layer permanent magnet structure. Figure 8 shows the parametric design of the permanent magnet, where l₁ is the length of the outer permanent magnet, l₂ is the length of the inner permanent magnet, θ₁ is the angle of the outer permanent magnet, and θ₂ is the angle of the inner permanent magnet.

4.1. The Width and Angle of PM

PM is the main contributor of power generation in the ASPMSG, so the height and width of the PM should be optimized. Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 show the fundamental amplitude of the EMF and FFT diagrams varying with the width and angle of the PM, which are called l₁, l₂, θ₁, and θ₂ in Figure 8.

The values in Figure 9 and Figure 10 represent per unit value. The reference values of l₁ and l₂ are 27 mm and 21 mm, respectively. The larger the PMs are, the larger the electromotive force generated by the motor, which can be verified in Figure 9. It can be seen from Figure 10 that the THD of the voltage harmonic is negatively correlated with the width of the PM. When l₁ = 1 pu and l₂ = 1 pu, the fundamental amplitude of the EMF reached the maximum value, which was about 112 V, and the THD of the voltage harmonic reached the minimum value, which was about 0.247. Therefore, l₁ = 1 pu and l₂ = 1 pu were chosen to be the optimal parameters.

Figure 11 and Figure 12 show the fundamental amplitude of EMF and FFT diagrams varying with θ₁. When θ₁ = 60°, the fundamental amplitude of the EMF reached the maximum value, which was about 112 V. The fundamental amplitude of EMF at θ₁ = 55° was slightly lower than that at θ₁ = 60°. When θ₁ = 55°, the THD of the voltage harmonic reached the minimum value, which was about 0.247. Considering the compromise between the inverse potential and the THD of the voltage, θ₁ = 55° was chosen as the optimal parameter.

Figure 13 and Figure 14 show the fundamental amplitude of EMF and FFT varying with θ₂. Since the model would be distorted when the angle is less than 65°, the angle sampling point range was set from 65° to 85°. When θ₂ = 70°, the THD of the voltage harmonic reached the minimum value, which was about 0.247. The THD of the voltage harmonic at θ₂ = 65° was slightly higher than that at θ₂ = 70°. When θ₂ = 65°, the fundamental amplitude of the EMF reached the maximum value, which was about 112 V. Considering the compromise between the inverse potential and the THD of the voltage, θ₂ = 65° was chosen to be the optimal parameter.

Because the optimization parameters are coupled with each other, the influence of a single parameter on the results cannot completely determine the selection of the optimal parameters. Therefore, multi-objective optimization was employed in the design of the model. Figure 15 shows the Pareto curve of the multi-objective optimization results. The optimal parameters for selecting the angle and width according to the curve are: l₁ = 27 mm, l₂ = 21 mm, θ₁ = 55.24°, and θ₂ = 65.13°.

4.2. Parameters of the Stator Slot

The parameters of the stator slot affect the distribution of the magnetic field in the teeth and yoke of the stator and change the peak value of the flux density. Different sizes of stator slots also affect the magnitude of the EMF, armature voltage, and output torque of the motor. Therefore, the size of the stator slot should be optimized. Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21 show the fundamental amplitude of the EMF and FFT varying with the stator slot parameters, where x₁, x₂, x₃, x₄, and x₅ have been marked in Figure 7. The values in Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21 represent per unit value. The reference values of x₁, x₂, x₃, x₄ and x₅ are 1.85 mm, 6.98 mm, 0.52 mm, 0.65 mm, and 25.17 mm, respectively.

As can be seen from Figure 16 and Figure 17, the amplitude of the voltage fundamental is negatively correlated with x₁ and x₂. The harmonic distortion rate of the voltage is negatively correlated with x₁. The THD of the voltage harmonic was minimized at x₂ = 1 pu, which was about 0.247. Considering the compromise between the inverse potential and the THD of the voltage harmonic, x₁ = 1 pu and x₂ = 1 pu were chosen to be the optimal parameters. When x₁ = 1 pu and x₂ = 1 pu, the fundamental amplitude of the EMF was 0.247, and the THD of the voltage harmonic was 0.247.

It can be seen from Figure 18 and Figure 19 that the amplitude of the voltage fundamental is positively correlated with x₃ and is basically independent of x₄. When x₃ = 1.2 pu, the fundamental amplitude of EMF reached the maximum value, which was about 117 V. The harmonic distortion rate of the voltage is positively correlated with x₄ and is basically independent of x₃. The THD of the voltage harmonic was minimized at x₄ = 0.8 pu, which was about 0.244. Considering the compromise between the inverse potential and the THD of the voltage harmonic, x₃ = 1.2 pu and x₄ = 0.8 pu were chosen to be the optimal parameters.

It can be seen from Figure 20 and Figure 21 that the amplitude of the voltage fundamental is negatively correlated with x₅. The THD of the voltage harmonic was minimized at x₅ = 1 pu. Considering the compromise between the inverse potential and the THD of the voltage harmonic, x₅ = 1 pu was chosen to be the optimal parameter. Figure 22 shows the Pareto curve of the multi-objective optimization results. The optimal parameters for selecting the angle and width according to the curve are: x₁ = 1.85 mm, x₂ = 6.98 mm, x₃ = 0.52 mm, x₄ = 0.65 mm, and x₅ = 25.17 mm. The fundamental amplitude of EMF was about 112 V, and the THD of the voltage harmonic was 0.247 under this condition.

5. Lightweight Design Based on Topology Optimization

There are two definitions of motor power density, one is the power per unit volume, kW/L, and the other is the power per unit mass, kW/kg. The paper used the power per unit mass to measure the power density.

$$P_D=\frac{P}{M}$$

(3)

where P_D is the power density in kW/kg; P is the output power of the motor in kW; and M is the effective mass of the motor in kilograms.

Based on (3), this paper chose to reduce the effective mass of the motor in order to improve the power density and make it more consistent with the working requirements of the helicopter motor. In this paper, the topology optimization method was adopted as a lightweight method.

The topology optimization method uses the material properties of NGnet cells to switch between air (OFF) and specified material (ON) during evolution. A genetic algorithm (GA) is used to optimize the shape of the model, and a smooth shape can be obtained without fine-tuning the filter program. As a shape optimization method that does not require much design experience, NGnet and ON/OFF-based topology optimization represent geometric structures using the weighted sum of normalized Gaussian functions determined by NGnet elements (or called Gaussian grids). The different positions and sizes of the Gauss grid elements are comparable to the design variables. Gauss grids are evenly distributed in rectangular or cylindrical coordinates to set the same isotropic bias for all Gaussians.

The number of NGnet elements and Gauss functions affects the changes in the geometric structure that can be represented. The more Gaussian functions used the more subalgebraic quantities, algebras, and each algebraic quantity the GA needs. The total number of cases can be calculated by multiplying the sum of each algebra quantity and algebra by the sum of subalgebras. The simulation time will increase exponentially with the number of Gaussian functions used. Therefore, NGnet cells should be effectively distributed to the design area.

Figure 23 and Figure 24 show the distributions of the flux line and magnetic cloud map, respectively, which show the utilization of the magnetic field by the proposed motor. Figure 25 shows the optimized area and NGnet element distribution in the motor rotor, where the material properties of each finite element are calculated based on the values of the shape function. On and off states represent steel and air materials. It can be seen from Figure 23 and Figure 24 that three triangular regions near the permanent magnet have low magnetic density; therefore, these regions were selected as optimized areas.

Figure 26 shows the optimized topology. Figure 27 shows the mesh of the proposed machine. Small mesh size is utilized to obtain relatively accurate simulation results. Meanwhile, the slide mesh is utilized in the red region of Figure 27. In the finite element analysis, the vector potential boundary condition is utilized, as shown in Figure 28. In this paper, the rotor was composed of three units (Units I, II, and III), as shown in Figure 28. Generally, a conventional permanent generator has the same units. However, the rotor of the proposed machine has a different rotor unit. Therefore, the generator is called an “Asymmetrical Generator”. The selected optimization area was optimized, and the optimized mass of the area reached 68.29%, but the output voltage of the motor was almost unaffected, which is the advantage of the method and topology proposed in this paper.

Figure 29 and Figure 30 show the EMF and FFT of the optimized topology, respectively. Compared with the EMF before optimization, the quality of the motor was reduced, the fundamental wave amplitude of the EMF was slightly increased, and the harmonic amplitude was basically unchanged, which indicates the effectiveness of the optimization method.

6. Conclusions

This paper presents a new ASPMSG that can be used as a generator for a helicopter. The proposed topology combines the designs of an alternating pole motor and a lightweight motor. In this paper, the topology and working principle of the proposed motor were introduced, respectively. The slot pole combination of the proposed motor was studied, and the main structural parameters of the motor were optimized to maximize the EMF and minimize the harmonics. Through topology optimization, the lightweight design was carried out, and the optimized mass of the optimized area reached 68.29%, while the output of the ASPMSG was almost unaffected. In summary, compared with a conventional permanent magnet generator, the rotor of the proposed machine was composed of different units. Through different unit settings, the machine obtained a good no-load performance which is characterized by a relatively high fundamental back-EMF amplitude and low THD. Meanwhile, the design results showed that the proposed topology has reliability, high-power density, and is suitable for helicopter application environments. The experimental data will be shown in future work, and more suitable optimization algorithms will be researched and expected to be extended to more study fields, such as that of [21].