## 5 Conclusions  
To model the motor considering noise and vibration, the motor was modeled by adding the back EMF, including the vibration component, to the equations and block diagrams of the classic motor model. To model the vibration component of the back EMF, the back EMF of the test motor was measured with an oscilloscope. Based on these results, a back EMF function was generated using the eighth-order component and DC components. A simulation was performed based on the model to which the vibration component was added, and it was found that the result was the same as that of the measured component. The conclusions of this study are as follows:  
1. To create a model expressing noise and vibration from the traditional motor equation, it was confirmed that the back EMF is composed of the sum of harmonic and DC components rather than constants and is expressed as a block diagram based on the equation.
2. The back EMF value was measured using an actual motor, and experiment results confirmed that the vibration components of the motor and back EMF tended to be identical. However, it was confirmed that CW and CCW, which should theoretically be the same, are different in actual motors. This was attributed to the difference between the DC component and the eighth-order component of the back EMF. However, further research on the harmonic components observed in the noise component of the CCW should be conducted.
3. The entire model was constructed based on the block diagram, and it was modeled using MATLAB Simulink based on the electric circuit and transfer function. To verify the reliability of the model, the measured back EMF value was applied to the model, and it was confirmed that the predicted vibration component was consistent with the actual vibration component. This will be of great help in predicting the main vibration component in a brushed DC motor. Given that it does not include all vibration components, it can be expressed in a simpler form than the actual measurement result; however, it is still successful as it predicts the largest vibration component.
4. The brushed DC motor model created in this study to predict the vibration component of the motor can be applied in various fields. For example, if R, L, and C are attached to the tip of the motor resistor and inductor and used as a filter, they can be applied to reduce noise and vibration. Alternatively, the vibration component generated by the motor can be predicted when a specific load is applied.  
Methodology, D.W.; Project administration, H.K.; Software, J.K. and K.H.; Writing--review & editing, H.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Hyundai Motor's industry-academic research project. This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the Grand Information Technology Research Center support program (IITP-202-2020-0-01791) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2021R1F1A1062389).  
The authors declare no conflict of interest.