## 2 Experimental PMSM with Demagnetization  
Figure 1 shows the rotor of an experimental four-pole IPMSM with parameters 1.5 kW, 3000 min\({}^{-1}\), 4.8 Nm, and 5.6 A. A part of the PM material of one of four poles was altered to a non-magnetic material so as to mimic the effect of demagnetization. The PM material was Neodymium N39 UH, which has residual magnetic flux density 1.25 T and density 7.65 kg/m\({}^{3}\). The non-magnetic material was stainless steel, which has density 7.8 kg/m\({}^{3}\); thus, the weight of the non-magnetic material was almost the same as that of the PM.  
Figure 1: Rotor of the experimental interior permanent magnet synchronous motor (IPMSM): (**a**) rotor configuration; (**b**) photograph of rotor.  
This paper reports experiments on the same stator and the same rotor using different PMs because slight differences between motors can affect the vibration characteristics, especially if the amount of demagnetization is very slight. We took into account two types of demagnetization. One is demagnetization in the radial direction, shown in Figure 2. One pole is composed of four PMs, and the thickness of the four PMs which composed one pole was reduced by 10%, 20%, or 30%; that is, the total volume of PM material used was decreased by about 2.5%, 5.0%, or 7.5%, respectively, in separate experiments, in order to imitate demagnetization or imperfect magnetization. The other is demagnetization in the axial direction, shown in Figure 3. The axial length of two of the four PMs per pole was reduced by 20%, 40%, or 60%; that is, the total volume of PM material used was decreased by about 2.5%, 5.0%, or 7.5%, respectively. Therefore, the PM volume of one pole for axial demagnetization was approximately the same as that for radial demagnetization. In order to remove eccentricity, non-magnetic materials were inserted into the region where the PM volume was decreased. Table 1 shows the volume of PMs for each demagnetization. Here, \"Healthy\" denotes the motor with fully magnetized PMs, R-2.5% denotes the motor with PMs demagnetized in the radial direction by about 2.5%, Z-2.5% denotes the motor with PMs demagnetized in the axial direction by about 2.5%, and so on. As PMs were manufactured in 0.1 mm steps, the reduction of PM volume denoted by 2.5% is not an exact value.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PM** & **L (mm)** & **W (mm)** & **H (mm)** & **V (mm\({}^{3}\))** & **V/V\({}_{\textbf{Healthy}}\)** \\ \hline Healthy & 22.6 & 20.2 & 2.2 & 16070 & - \\ R-2.5\% & 22.6 & 20.2 & 2.0 & 15704 & 0.977 \\ R-5.0\% & 22.6 & 20.2 & 1.8 & 15339 & 0.955 \\ R-7.5\% & 22.6 & 20.2 & 1.6 & 14974 & 0.932 \\ Z-2.5\% & 18.0 & 20.2 & 2.2 & 15661 & 0.975 \\ Z-5.0\% & 13.4 & 20.2 & 2.2 & 15252 & 0.950 \\ Z-7.5\% & 8.8 & 20.2 & 2.2 & 14843 & 0.924 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions of PMs.  
Figure 3: PMs for axial demagnetization: (**a**) magnet configuration; (**b**) photograph of magnet.  
Figure 2: PMs for radial demagnetization: (**a**) magnet configuration; (**b**) photograph of magnet.  
Figure 4 shows the experimental setup used to measure the vibration. An experimental IPMSM was driven by an inverter controlled by a Digital Signal Processor (DSP) DS1102 (dSPACE Japan K.K., Shinagawa, Japan). A PV08A (Rion Co. Ltd., Japan) piezoelectric acceleration pickup was attached to the top of the stator and was connected to a UV-06 charge amplifier. The vibration and torque signals were measured using a LABVIEW (2009, National Instruments, Japan) system.