# A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis

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## Abstract

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## 1. Introduction

## 2. Basic Method

#### 2.1. EMD

_{n}(t) is residual error function, and represents average trend of signals. IMF components ${c}_{1}$,${c}_{2}$,${c}_{3}$,$\mathrm{...}$,${c}_{n}$ contain different elements respectively from low to high frequency of signals.

#### 2.2. EEMD

- Step 1:
- Gaussian white noise sequences are added to the target data.
- Step 2:
- The new target data is decomposed into a series of IMFs according to the EMD algorithm.
- Step 3:
- Different Gaussian white noise sequences with the same amplitude are added to the data for each time; repeat Step 1 and Step 2.
- Step 4:
- The mean value of the various IMF is taken as the final result, that is:

_{j}(t) represents the ${j}^{th}$ IMF component of the original signal by the EEMD method, $N$ is the time of added white noise.

#### 2.3. Hilbert Transform

## 3. Experimental Environment and Theoretical Calculation

#### 3.1. Experimental Environment

#### 3.2. Theoretical Calculation of the Fault Characteristic Frequency of the Roller Bearing

_{d}is the roller element diameter, P

_{d}is pitch diameter, and $\phi $ is angle (°) of the roller element.

## 4. Fault Feature Extraction and Analysis

#### 4.1. Fault Vibration Signal Decomposition

#### 4.2. Selection of the Optimal Mode

#### 4.3. Fault Feature Analysis Based on the Hilbert Transform

## 5. Transmission Analysis of the Vibration Signal

#### 5.1. Transmission Analysis of the Fault Vibration Signal for the Inner Ring

#### 5.2. Transmission Analysis of the Fault Vibration Signal for the Outer Ring

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 10.**The optimal mode envelope spectrum of the drive end of the outer ring at the 6 o’clock position.

**Figure 11.**The optimal mode envelope spectrum of the fan end of the outer ring at the 6 o’clock position.

**Figure 12.**The optimal mode envelope spectrum of the drive end of the outer ring at the 3 o’clock position.

**Figure 13.**The optimal mode envelope spectrum of the fan end of the outer ring at the 3 o’clock position.

**Figure 14.**The optimal mode envelope spectrum of the drive end of the outer ring at the 12 o’clock position.

**Figure 15.**The optimal mode envelope spectrum of the fan end of outer ring at the 12 o’clock position.

Types | Inside Diameter | Outside Diameter | Thickness | Rolling Diameter | Pitch Diameter |
---|---|---|---|---|---|

SKF6205-2RS | 0.9843 | 2.0472 | 0.5906 | 0.3126 | 1.537 |

Inner Ring (Hz) | Outer Ring (Hz) | Rolling Element (Hz) |
---|---|---|

162.19 | 107.29 | 141.08 |

Index | Inner Ring (Hz) | Outer Ring (Hz) |
---|---|---|

Theoretical value | 162.19 | 107.29 |

Calculated value | 164.06 | 105.47 |

Error | 1.87 | 1.82 |

Accuracy rate | 98.85% | 98.30% |

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**MDPI and ACS Style**

Deng, W.; Zhao, H.; Yang, X.; Dong, C.
A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis. *Symmetry* **2017**, *9*, 60.
https://doi.org/10.3390/sym9050060

**AMA Style**

Deng W, Zhao H, Yang X, Dong C.
A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis. *Symmetry*. 2017; 9(5):60.
https://doi.org/10.3390/sym9050060

**Chicago/Turabian Style**

Deng, Wu, Huimin Zhao, Xinhua Yang, and Chang Dong.
2017. "A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis" *Symmetry* 9, no. 5: 60.
https://doi.org/10.3390/sym9050060