# A Multi-Physics Modeling-Based Vibration Prediction Method for Switched Reluctance Motors
## 4 Experimental Results and Verification
### Simulation and Experimental Results
#### 4.2.3 Verification of the Vibration Prediction Model  
In order to verify the accuracy of the vibration predictive model, the SRM operates under the condition of constant torque and speed. Vibration tests were carried out both on the simulation platform and experimental setup. The drive circuit adopted asymmetric half-bridge power amplifier. The speed controller adopted a proportional integral (PI) control algorithm, and the current controller used the hysteresis control method. To begin with, the speed was set as 625 rpm and the load torque was 2.5 Nm. For the sake of simplicity, the turn-on angle and turn off angle were chosen as 40\({}^{\circ}\) and 160\({}^{\circ}\) according to [33]. In addition, the damping coefficient is determined by measuring the attenuation speed of the motor vibration amplitude after the excitation stops, and the gain of the corresponding mode is calculated according to the measured damping coefficient. The obtained parameters for the vibration prediction model are shown in Table 4.  
Since the electromagnetic force acting on the stator is directly related to the phase current, it is essential to accurately predict the current waveform. Figure 11a shows the comparison between the obtained current from the vibration prediction model and experimental results. The vibration spectrum obtained by experiment and simulation is shown in Figure 11b. It can be seen from the current curve that the experimental current value is not zero at the current turn-off point due to the zero drift of the current sensor. Although the simulation data and experimental data do not completely match because of the signal interference of the experimental platform itself, the error of current is relatively small and within an acceptable range. Simultaneously, based on Figure 11b, it can be seen from the vibration spectrum curve that the error of vibration magnitude is small, which validated the effectiveness of the proposed multi-physics modeling-based vibration prediction method.  
Then, the speed was set as 1500 rpm and the load torque was 6.0 Nm. The turn-on angle and turn off angle were also chosen as 40\({}^{\circ}\) and 160\({}^{\circ}\). Figure 12a presents the comparison between the obtained current from the vibration prediction model and experimental results for this case. The vibration spectrum obtained by experiment and simulation is illustrated in Figure 12b. It can be seen that, with the increase of speed and torque, the errors between the predicted values and the experimental results were still within the acceptable range. Consequently, the presented vibration prediction method based on multi-physical modeling can be utilized for the structural design optimization and control strategy optimization of SRMs.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode Order** & **Frequency** & **Damping Ratio** & **Gain** \\ \hline
1 & 602 & 0.0109 & 0.0000453 \\
2 & 1198 & 0.0156 & 0.0000376 \\
3 & 2966 & 0.0167 & 0.0000013 \\
4 & 3999 & 0.0172 & 0.0000292 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Transfer function parameters for Modal 1–4 orders.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mode** & **Experiment** & \multicolumn{3}{c}{**The Proposed FEA Method**} & \multicolumn{3}{c}{**FEA Considering Stator Only**} \\ \cline{3-5}
**Order** & **(Hz)** & **Predicted Frequency** & **Error (\%)** & **Predicted Frequency** & **Error (\%)** \\ \hline
**1** & 618 & 602 & 2.59 & 583 & 5.66 \\
2 & 1215 & 1198 & 1.40 & 1167 & 3.91 \\
3 & 3022 & 2966 & 1.85 & 2885 & 4.53 \\
4 & 3856 & 3999 & 3.70 & 3601 & 6.61 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Natural frequency results of FEA and the experimental method.  
Figure 11: Current and vibration spectrum under simulated and experimental platform with the speed 625 rpm and the load torque 2.5 Nm: (**a**) current and (**b**) vibration spectrum.  
Figure 12: Current and vibration spectrum under simulated and experimental platform with the speed 1500 rpm and the load torque 6.0 Nm: (**a**) current and (**b**) vibration spectrum.