# Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Introduction

#### 2.1. Turn Domain Resampling Technique

#### 2.2. Structural Elements and Morphological Algorithms

#### 2.2.1. Structural Elements

_{i}according to the peak and trough value of each impact of the original signal in actual operation, so as to make the filtering result more accurate. The following table shows the structural elements of each scale.

#### 2.2.2. Mathematical Morphology

#### 2.3. Variable Multi-Scale Morphological Filtering (VMSMF)

- ①
- Ni − Nm = 1, to analyze from the first impact to the end of the last impact;
- ②
- Ni − Nm = −1, discard the head and tail impact and analyze the middle part;
- ③
- Ni = Nm& the minimum occurs first, discard the last shock signal and analyze the rest;
- ④
- Ni = Nm& the maximum occurs first, discard the first shock signal and analyze the rest.

## 3. Simulation Signal Analysis

## 4. Experimental Signal Verification

## 5. Conclusions

## 6. Discussion

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of sampling order selection. (

**a**) Sampling order is too low, (

**b**) sampling order is too high.

**Figure 2.**Schematic diagram of resampling signal selection. (

**a**) The resampling position coincides with the original signal position; (

**b**) The resampling position is between two adjacent points.

**Figure 3.**Time-frequency waveforms of each window function. (

**a**) Time domain waveforms, (

**b**) frequency domain waveform.

**Figure 5.**Distribution of extreme points of time-domain signals: (

**a**) represents one more minimum point than maximum point, (

**b**) means that the minimum point is one less than the maximum point, (

**c**) means that the minimum point first appears when the minimum point and the maximum point are the same, (

**d**) indicates that the minimum point and the maximum point are the same, with the maximum point appearing first.

**Figure 7.**Original time domain signal and FFT transformation. (

**a**) Original time domain signal. (

**b**) FFT transformation of the original signal.

**Figure 8.**Resampling signal and FFT transform. (

**a**) Resampling signal. (

**b**) FFT transform of resampling signal.

**Figure 11.**Spectrum envelope used different ways. (

**a**) Used Hanning windows as structural elements. (

**b**) Used Hamming windows as structural elements. (

**c**) Used MSMF as structural elements. (

**d**) Used VMSMF as structural elements.

**Figure 12.**Comprehensive test bench for power drive fault diagnosis. 1 peed control device, 2 drive motor, 3 bearing seat, 4 secondary planetary gearbox, 5 fixed shaft gearbox, 6 load device.

**Figure 15.**The original signal of the planetary gearbox. (

**a**) is the time domain signal of the original health components; (

**b**) is the time-domain signal of the original solar wheel wear state; (

**c**) is the FFT transform spectrum diagram of the original health components; (

**d**) is the FFT transform spectrum diagram of the original solar wheel wear state.

**Figure 16.**Resampling angular domain signal and its envelope spectrum waveform. (

**a**) the waveform of resampling signal in healthy state; (

**b**) the waveform of the resampling signal for sun wheel failure.

**Figure 17.**VMSMF signal and its envelope spectrum waveform. (

**a**) the waveform of filtering signal in healthy state; (

**b**) the waveform of the filtering signal for sun wheel failure; (

**c**) the FFT envelope spectra of health filtering signals; (

**d**) the FFT envelope spectra of filtering signal for sun wheel fault.

Window Function | 40,000 Groups | 20,000 Groups | 10,000 Groups | 5000 Groups | 2000 Groups | 1000 Groups |
---|---|---|---|---|---|---|

Hamming | 0.5259 | 0.5310 | 0.5460 | 0.5943 | 0.2828 | 0.2235 |

Rectangle | 0.1551 | 0.2198 | 0.3117 | 0.4382 | 0.4002 | 0.0022 |

Hanning | 0.5297 | 0.5334 | 0.5458 | 0.5953 | 0.2807 | 0.1499 |

Chebyshev | 0.5658 | 0.6020 | 0.6658 | 0.7514 | 0.5732 | 0.7872 |

Scales | Length | Height |
---|---|---|

1 | 3 | a_{1}{$\omega $_{1}(0), $\omega $_{1}(1), $\omega $_{1}(2),} |

2 | 4 | a_{2}{$\omega $_{2}(0), $\omega $_{2}(1), $\omega $_{2}(2), $\omega $_{2}(3)} |

3 | 5 | a_{3}{$\omega $_{3}(0), $\omega $_{3}(1), _{3}(2), $\omega $_{3}(3), $\omega $_{3}(4)} |

… | … | … |

n | n + 2 | a_{n}{$\omega $_{n}(0), $\omega $_{n}(1), $\omega $_{n}(2), $\omega $_{n}(3), …, $\omega $_{n}(n + 1)} |

Serial Number | Key Parts of Planetary Gearbox | Number |
---|---|---|

1 | number of sun gear teeth | 20 |

2 | number of planetary gear teeth | 40 |

3 | number of ring gear teeth | 100 |

4 | number of planetary rings | 3 |

Points | 2 × 10^{5} | 1 × 10^{5} | 5 × 10^{4} | 2 × 10^{4} | 1 × 10^{4} | |
---|---|---|---|---|---|---|

Types | ||||||

MSMF | 23,925.4 s | 6231.4 s | 1851.5 s | 402.7 s | 140.3 s | |

VMSMF | 825.02 s | 201.37 s | 52.9 s | 10.7 s | 4.77 s |

Types | Sample Frequency/Fs | Maximum Speed of Input Shaft/ns | Maximum Mesh Frequency/fm | Solar Wheel Equivalent Fault Characteristic Frequency/fs | Sampling Time/t | |
---|---|---|---|---|---|---|

Data | ||||||

5120 Hz | 1800 r/min | 600 Hz | 2.4 Hz | 10 s |

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**MDPI and ACS Style**

Liu, T.; Cui, L.; Zhang, C.
Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering. *Symmetry* **2021**, *13*, 52.
https://doi.org/10.3390/sym13010052

**AMA Style**

Liu T, Cui L, Zhang C.
Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering. *Symmetry*. 2021; 13(1):52.
https://doi.org/10.3390/sym13010052

**Chicago/Turabian Style**

Liu, Tongtong, Lingli Cui, and Chao Zhang.
2021. "Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering" *Symmetry* 13, no. 1: 52.
https://doi.org/10.3390/sym13010052