## 3 Vibration Characteristics of an Experimental IPMSM Driven under Vector Control  
In the measurement, the experimental IPMSM was driven under vector control. Figure 5 shows a typical block diagram for the vector-controlled PMSM system. In this diagram, two control loops were used; one is an inner loop to regulate the stator currents by converting to the d and q axes with the rotor position, and the other is an outer loop to control the motor speed. In this study, the d-axis current was maintained at 0. The system was composed of the motor, inverter, position sensor, two current sensors, and DSP DS1102. The switching frequency of the inverter was set to 4 kHz. The vector control diagram was carried out in the DS1102. The load condition was fixed at 0% and 70% of the rated torque by adding the load torque with a hysteresis brake. Figure 6 shows the measured vibration waveforms for the healthy motor, the motor with 7.5% demagnetized PMs in the radial direction, and the motor with 7.5% demagnetized PMs in the axial direction. The motor developed 70% of the rated torque in this measurement. It was found that the amplitude of the vibration signals emitted from the demagnetized motor was larger than that from the healthy motor.  
Figure 4: Experimental setup.  
Figure 5: Block diagram for a PMSM under a vector control strategy.  
Figure 7 shows FFT analyses of the vibration waveform emitted from the motor with radial demagnetization when the motor was running at a speed of 1200 min\({}^{-1}\). Figure 8 shows those of the motor with axial demagnetization. It was found from these figures that the vibration at 70% load  
Figure 6: Vibration waveforms at 70% load torque: (**a**) healthy motor; (**b**) R-7.5% motor; (**c**) Z-7.5% motor.  
torque was larger than that at no load torque. Since the motor was running at a speed of 1200 min\({}^{-1}\), the fundamental current frequency was 40 Hz. It can be observed from Figure 7b that the vibration had peak values at 440, 480, 520, 920, 960, and 1000 Hz, that is, at the 11 th, 12 th, 13 th, 23 rd, 24 th, and 25 th components. Since this motor has four poles, it was expected that the magnetic radial force would have a large value at 80 Hz when the motor was running at 1200 min\({}^{-1}\). However, the vibration at 80 Hz is not large. By comparing Figures 7b and 8b, we can see that the amplitude of vibration emitted from the motor with radial demagnetization was larger than that from the motor with axial demagnetization.  
Although the vibration had another peak at 820 Hz, this component did not change in correspondence with the demagnetization level. Therefore, we investigated the 11 th, 12 th, 13 th, 23 rd, 24 th, and 25 th components. Figure 9 shows the characteristics of the 12 th vibration component for load torque. The amplitude of vibration emitted from the healthy motor was almost the same for the different levels of load torque. On the contrary, the amplitude of vibration emitted from the demagnetized motor was approximately proportional to the load torque. The slope was large when the demagnetization level was large. It was also found that the amplitude of vibration emitted from the motor with radial demagnetization was about 1.5 times larger than that from the axial demagnetized motor. The 11 th, 13 th, 23 rd, 24 th, and 25 th vibration components showed similar characteristics to the 12 th component.  
Figure 8: FFT analysis of measured vibration waveforms emitted from the motor with axial demagnetization: (**a**) no load torque; (**b**) 70% load torque.  
Figure 7: FFT analysis of vibration waveforms emitted from the motor with radial demagnetization: (**a**) no load torque; (**b**) 70% load torque.