As the performance of permanent-magnet synchronous generators improves, research on device noise is also becoming important. This study analyzes the causes of electromagnetic noise, such as the back electromotive force, cogging torque, torque ripple, unbalanced magnetic force, and harmonics that occur during operation for each DC and AC load. In particular, it shows that the influence of the waterfall diagram changes depending on the harmonic order of the torque ripple. By combining 2D finite element analysis and 3D mechanical analysis, electromagnetic analysis can be used to analyze the noise-generating relationship. Based on the analysis results, the electromagnetic noise generation results depending on the load are presented. The electromagnetic performance and mechanical reliability of the designed model were verified by comparing the finite element method and experimental results.

Permanent-magnet synchronous generators (PMSGs) are used worldwide because of their many advantages, such as high efficiency, high power density, simple mechanical structure, no excitation loss, and easy maintenance.1,2 Owing to these advantages, they are used in various fields, such as aerospace, marine, home appliances, and vehicles.3,4 They are essential to our lives, and as the electromagnetic performance of the generator increases, vibration and noise also increase.5 Therefore, an analysis to reduce the mechanical or electromagnetic noise during generator operation while securing the required electromagnetic performance is essential.5,6

This study analyzes the causes of noise and vibration caused by the electromagnetic characteristics that occur during the operation of DC and AC loads using finite element analysis (FEA). Electromagnetic analysis was performed for different load conditions and various electromagnetic vibration causes, such as torque ripple, back electromotive force (EMF), and unbalanced magnetic force (UMF) at the same output and power.7,8 The harmonic components of the electromagnetic vibration source under AC and DC load conditions were obtained using a fast Fourier transform, and mechanical analyses, such as noise and vibration were performed according to the analyzed vibration source. By combining 3D FEA with DC and AC load circuits, the waveforms and harmonic components of current and voltage were derived. The validity of the derived finite element method was verified through experimental results.

Figures 1(a) and 1(b) show the experimental setup and equipment for measuring the vibration/noise, respectively. (c) and (d) Show the 2D and 3D analysis models of the PMSG, respectively. To compare the characteristics based on the driving method, analyses and experiments were conducted using the same motor, and the load resistance value for each driving method was set to that with the same performance. The DC load resistance was set to 6 ohms and the AC load resistance was set to 4.5 ohms. All other design variables remained the same. Tables I and II represents Design of analysis model and Output characteristics of direct drive PMSG under DC and AC load conditions, respectively.

FIG. 1.

Analysis model and experimental setup: (a) experimental setup, (b) experimental equipment, (c) 2D analysis model, (d) 3D analysis model.

FIG. 1.

Analysis model and experimental setup: (a) experimental setup, (b) experimental equipment, (c) 2D analysis model, (d) 3D analysis model.

Close modal
TABLE I.

Design specifications of analysis model.

ParameterValue (mm)ParameterValue
Outer radius of stator 100 Width slot opening 1 (mm) 
Outer radius of rotor 56 Width of tooth width 2 (mm) 
Magnet thickness Pole/slot combination 4/24 
Air gap Pole arc ratio 0.8 
Axial length 45   
ParameterValue (mm)ParameterValue
Outer radius of stator 100 Width slot opening 1 (mm) 
Outer radius of rotor 56 Width of tooth width 2 (mm) 
Magnet thickness Pole/slot combination 4/24 
Air gap Pole arc ratio 0.8 
Axial length 45   
TABLE II.

Output characteristics of direct drive PMSG under DC and AC load conditions.

ParametersDC loadAC loadUnit
Output voltage 40.5 51.8 Vrms 
Output current 5.8 6.3 Arms 
Output power 405 413 
Core loss 7.5 10.9 
PM loss 0.05 0.1 
Copper loss 49.45 57.3 
Efficiency 87.6 86 
ParametersDC loadAC loadUnit
Output voltage 40.5 51.8 Vrms 
Output current 5.8 6.3 Arms 
Output power 405 413 
Core loss 7.5 10.9 
PM loss 0.05 0.1 
Copper loss 49.45 57.3 
Efficiency 87.6 86 
The electromagnetic torque is calculated as a product of the back EMF and current, which is expressed as
T=32K1I1+12I1n=1,oddKn1+2cos(n1)2π3×cos(n1)pωrt+12I1n=1,oddKn1+2cos(n+1)2π3×cos(n+1)pωrt
(1)
where ωr denotes the rotational speed, t denotes the time, Kn denotes the back-EMF coefficient, I1 denotes the peak of the current, and n and p indicate the nth-order harmonic and number of pole pairs, respectively.9,10 Here, the first term represents the average electromagnetic torque, and the second and third terms represent the torque ripples produced by the total harmonic distortion (THD) of the back EMF and current, respectively.9,10 Therefore, the amplitudes of the harmonics of the back EMF and current affect the magnitude of the torque ripple.9,10

Therefore, it is essential to analyze the harmonic characteristics of the back EMF, current, and torque ripple. Figures 2(a) and 2(b) show the back EMF and its fast Fourier transform (FFT), respectively, which affect the torque ripple. The back EMF waveform in the DC load state was not linear compared to the back EMF of the AC load, and the FFT of back EMF also confirmed that the fifth and ninth frequencies occurred significantly. Figures 2(c) and 2(d) show the branch current and FFT of branch current that affect the torque ripple. Likewise, it can be confirmed that the current waveform of the DC load is not linear, and when checking the FFT of branch current, it was confirmed that the fifth and seventh harmonic orders occur. Therefore, owing to the characteristics of the back EMF and current, the torque ripple is large, and many harmonics are generated. Figures 3(a) and 3(b) show the torque ripple and FFT of torque ripple, respectively. The torque ripple in the DC load was large, and the FFT of torque ripple confirmed that the sixth harmonic occurred. These electromagnetic properties cause vibration and noise.

FIG. 2.

Characteristic analysis results: (a) back-EMF, (b) FFT of back-EMF, (c) branch current, and (d) FFT of branch current.

FIG. 2.

Characteristic analysis results: (a) back-EMF, (b) FFT of back-EMF, (c) branch current, and (d) FFT of branch current.

Close modal
FIG. 3.

Characteristic analysis results: (a) torque ripple, (b) FFT of torque ripple, (c) UMF, and (d) FFT of UMF.

FIG. 3.

Characteristic analysis results: (a) torque ripple, (b) FFT of torque ripple, (c) UMF, and (d) FFT of UMF.

Close modal
The electromagnetic force generated in the gap between the stator and rotor is derived using the Maxwell stress tensor and is expressed as:11,
F=1μ0Br212B2ir+1μ0BrBθiθ
(2)
where Br and Bθ denote the radial flux density and tangential air-gap magnetic flux density, respectively.11 The radial and tangential electromagnetic force densities in the air-gap are expressed as follows:
fr=12μ0(Brg2Bθg2)
(3)
fθ=12μ0BrBθ
(4)
where Brg and Bθg denote the radial and tangential air-gap magnetic flux densities, respectively. The radial and tangential force densities cause UMF to occur depending on the force applied to the structure of the motor or stator surface.12,13 The generated UMF is affected by the symmetry of the force density distribution and can be derived through a coordinate transformation after converting it into X and Y components.12,13 Here, the forces acting along the x-axis and y-axis can be expressed as
Fx=rlstk2μ002π[(Bθg2Brg2)cosθ2BrgBθgsinθ]dθ
(5)
Fy=rlstk2μ002π[(Bθg2Brg2)sinθ+2BrgBθgcosθ]dθ
(6)
where lstk and r represent the axial and air-gap lengths, respectively. Figures 3(c) and 3(d) show the UMF and FFT of UMF characteristics for the DC and AC loads, respectively. This was confirmed through the fast Fourier transform analysis results. The fifth and ninth harmonic orders occurred in the DC load, which increased to the 6n order.

Figures 4(a) and 4(b) show 3D waterfall diagrams for each DC and AC load, respectively. The 3D waterfall diagram results allowed us to check the frequency of noise generated according to the rpm for each DC or AC load. In particular, we focused on verifying the fifth, seventh, and ninth harmonics identified in the electromagnetic FFT of UMF characteristics. By checking the bands of harmonic orders occurring in the electromagnetic characteristics of the DC load, it was confirmed that a 5–20 dB difference occurred at the corresponding frequency. Figures 4(c) and 4(d) show the experimental results for the DC and AC loads, respectively. To verify the 3D FEA results, we conducted experimental measurements of the generator operation for each load. Experimental measurements were performed using gap sensors and microphones. This was verified by comparing the simulation and experimental results. Considering that a frequency domain with the rotation period of a four-pole generator was generated and that noise with the same tendency was generated in the same frequency and speed range as the simulation, sufficiently reliable experimental results were obtained. This proved the validity of the simulation results. Additionally, by checking the resonance frequency of the generator assembly, it was confirmed that the frequencies generated on the DC and AC load conditions were far from the resonance frequency.

FIG. 4.

Noise/Vibration analysis results: (a) FEM analysis result of DC load condition, (b) FEM analysis of AC load condition, (c) experiment result of DC load condition and (d) experiment result of AC load condition.

FIG. 4.

Noise/Vibration analysis results: (a) FEM analysis result of DC load condition, (b) FEM analysis of AC load condition, (c) experiment result of DC load condition and (d) experiment result of AC load condition.

Close modal

Generally, DC loads are characterized by square wave currents, while AC currents are known to be sinusoidal as well. DC loads with sinusoidal currents typically have larger harmonic distortions compared to AC loads, which are known to be the primary cause of noise and vibration generation. Therefore, in this study, electromagnetic analyses were conducted for AC and DC loads to compare the frequency effects on noise generated during generator operation under DC and AC loads. Utilizing the 2D FEM and conducting FFT analysis on electromagnetic data concerning DC and AC loads, it was determined that the electromagnetic characteristics of DC loads exhibit nonlinearity, accompanied by the generation of harmonics. In addition, a waterfall diagram of PMSG was derived by mapping the electromagnetic force of the inner stator using 3D FEM. The analysis results reveal that harmonic distortions generated by DC loads are more pronounced at the fifth, seventh, and ninth harmonics compared to AC loads. To verify the proposed analysis results, the experiment measured NVH characteristics under DC and AC load conditions and showed similar trends to the analysis results. Therefore, based on the proposed analysis method, the design of PMSG can be performed to improve NVH characteristics through analysis of electromagnetic excitation sources and harmonic orders according to load conditions. In addition, NVH characteristics can be improved by avoiding the natural frequency of the PMSG system and the frequency of harmonics generated from the PMSG.

This research was supported by Korea Institute of Marine Science and Technology Promotion (KIMST) funded by the Ministry of Oceans and Fisheries, Korea (RS-2023-00254688, Advancement of Wave Energy Converters Applicable to Breakwater for Commercialization).

The authors have no conflicts to disclose.

Woo-sung Jung: Writing – original draft (equal). Hoon-Ki Lee: Formal analysis (equal). Jun-Won Yang: Formal analysis (equal). Kyong-Hwan Kim: Resources (supporting). Ji-Yong Park: Resources (supporting). Kyung-Hun Shin: Writing – review & editing (equal). Jang-Young Choi: Writing – review & editing (equal).

The data that support the findings of this study are available on request from the corresponding authors. The data are not publicly available due [STATE RESTRICTIONS SUCH AS PRIVACY OR ETHICAL RESTRICTIONS].

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