## 4 Experiment Results and Discussion
### Model and Simulation Results with Vibration Components  
Based on the block diagram (Figure 2) presented in Section 2.2, a model was created using MATLAB Simulink (Figure 8). The electrical elements are expressed as circuit models, and mechanical elements are expressed as transfer-function models. Here, \"fcn\" is a block for expressing back EMF and is a new part that is not in the general model. To obtain a similar RPM to that of the sample motor in the model, arbitrary values were input to each parameter so that it could rotate at 6000 RPM at a rated 12 V, and the values are shown in Table 2. Back EMF measurement was only possible up to 3500 RPM owing to the limitations of the drive motor; however, in the results of Figure 7b,c, the magnitude and frequency have a constant tendency, meaning that they can be applied, even at 6000 RPM. The frequency of the back EMF function was designed to have an eighth-order component, which is a motor rotational vibration component. The back EMF of CW and CCW is expressed by Equations (7)-(9) and (10)-(12), and applied to the \"fcn\" block. \[k_{b}=\left(0.2056\times 8f+0.0932\times 10^{-3}\right)\times 10^{-3} \tag{7}\]  
\[DC=0.0207f+0.0117 \tag{8}\]\[Ea=k_{b}\sin(8\omega t)+DC \tag{9}\] \[k_{b}=\left(0.2212\times 8f-0.0315\times 10^{-3}\right)\times 10^{-3}\] (10) \[DC=0.0205f-0.0125\] (11) \[Ea=k_{b}\sin(-8\omega t)+DC \tag{12}\]  
The simulation results for the CW and CCW are shown in Figures 9 and 10. The eight-order frequency component applied to the model was confirmed in the back EMF, current, and torque. In addition, as shown in Figure 6b of Section 4.1, the vibration test results show that the frequency of the vibration component of CCW was higher than that of CW, even when the same voltage was input, whilst the magnitude was also larger. The same voltage was input in the simulation as well, and it was confirmed that the frequency of CCW was higher than that of CW, and the magnitude was also larger (Figures 9b and 10b). Table 3 summarizes the contents of this study. It can be seen that these characteristics appear the same in current (Figures 9d and 10d) and torque (Figures 9f and 10f). In addition, the harmonic of the vibration component was also confirmed in the simulation, and it can be observed that it has the same characteristics as a real motor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element Name** & **Symbol** & **Value** \\ \hline Armature resistance & R & 3.83 [\(\Omega\)] \\ Armature inductance & L & 0.274 \(\times\) 10\({}^{-3}\) [H] \\ Motor torque constant & K\({}_{\tau}\) & 0.158 [N-m/A] \\ Motor armature inertia & J & 0.557 \(\times\) 10\({}^{-3}\) [kg-m\({}^{2}\)] \\ Viscous damping, friction coefficient & B & 0.65 \(\times\) 10\({}^{-3}\) [N-m/rpm] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in MATLAB Simulink model. Figure 8: MATLAB Simulink modeling based on transfer functions and electrical circuits. On the other hand, comparing the measurement results in Figure 7a with the simulation results in Figures 9b and 10b, the simulation result waveform is drawn in a much cleaner form. This is because only the eighth-order vibration among the vibration components of the motor was considered. If vibration components other than eighth-order vibration are considered and applied to the model, simulation results more similar to actual measurements can be obtained. However, considering the eighth-order vibration, which has the greatest influence among the vibration elements of the motor, is a sufficiently significant result for predicting the vibration. Figure 9: Results of simulation with back EMF including vibration in the CW: (**a**) Back EMF time data; (**b**) back EMF FFT data; (**c**) current time data; (**d**) current FFT data; (**e**) torque time data; (**f**) torque FFT data. This model can be used in various applications.